Module: Numo::Linalg::Blas

Defined in:
ext/numo/linalg/blas/blas.c,
ext/numo/linalg/blas/blas_c.c,
ext/numo/linalg/blas/blas_d.c,
ext/numo/linalg/blas/blas_s.c,
ext/numo/linalg/blas/blas_z.c,
lib/numo/linalg/function.rb

Constant Summary

FIXNAME =
{
 cnrm2: :csnrm2,
 znrm2: :dznrm2,
}

Class Method Summary collapse

Class Method Details

.call(func, *args) ⇒ Object

Call BLAS function prefixed with BLAS char ([sdcz]) defined from data-types of arguments.

Examples:

c = Numo::Linalg::Blas.call(:gemm, a, b)

Parameters:

  • func (Symbol)

    function name without BLAS char.

  • args

    arguments passed to Blas function.



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# File 'lib/numo/linalg/function.rb', line 17

def self.call(func,*args)
  fn = (Linalg.blas_char(*args) + func.to_s).to_sym
  fn = FIXNAME[fn] || fn
  send(fn,*args)
end

.caxpy(x, y, [alpha: 1]) ⇒ Numo::SComplex

CAXPY constant times a vector plus a vector.

Parameters:

  • x (Numo::SComplex)

    vector (>=1-dimentional NArray).

  • y (Numo::SComplex)

    vector (>=1-dimentional NArray, inplace allowed).

  • alpha (Float)

    (default=1.0)

Returns:

  • (Numo::SComplex)

    y = alpha * x + y



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# File 'ext/numo/linalg/blas/blas_c.c', line 481

static VALUE
blas_s_caxpy(int argc, VALUE const argv[], VALUE UNUSED(mod))
{
    VALUE x, y, alpha;
    narray_t *na1, *na2;
    ndfunc_arg_in_t ain[2] = {{cT,0},{OVERWRITE,0}};
    ndfunc_t ndf = {iter_blas_s_caxpy, STRIDE_LOOP, 2, 0, ain, 0};

    dtype g;
    VALUE kw_hash = Qnil;
    ID kw_table[1] = {id_alpha};
    VALUE opts[1] = {Qundef};

    CHECK_FUNC(func_p,"caxpy");

    rb_scan_args(argc, argv, "2:", &x, &y, &kw_hash);
    rb_get_kwargs(kw_hash, kw_table, 0, 1, opts);
    alpha = option_value(opts[0],Qnil);
    g     = RTEST(alpha) ? m_num_to_data(alpha) : m_one;

    COPY_OR_CAST_TO(y,cT);
    GetNArray(x,na1);
    GetNArray(y,na2);
    CHECK_DIM_GE(na1,1);
    CHECK_DIM_GE(na2,1);
    CHECK_NON_EMPTY(na1);
    CHECK_NON_EMPTY(na2);
    CHECK_SAME_SHAPE(na1,na2);

    na_ndloop3(&ndf, &g, 2, x, y);
    return y;
}

.ccopy(x, y) ⇒ nil

CCOPY copies a vector x to a vector y.

Parameters:

  • x (Numo::SComplex)

    vector (>=1-dimentional NArray).

  • y (Numo::SComplex)

    vector (>=1-dimentional NArray).

Returns:

  • (nil)


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# File 'ext/numo/linalg/blas/blas_c.c', line 417

static VALUE
blas_s_ccopy(VALUE UNUSED(mod), VALUE x, VALUE y)
{
    narray_t *na1, *na2;
    ndfunc_arg_in_t ain[2] = {{cT,0},{OVERWRITE,0}};
    ndfunc_t ndf = {iter_blas_s_ccopy, STRIDE_LOOP, 2,0, ain,0};

    CHECK_FUNC(func_p,"ccopy");

    CHECK_NARRAY_TYPE(x,cT);
    CHECK_NARRAY_TYPE(y,cT);
    GetNArray(x,na1);
    GetNArray(y,na2);
    CHECK_DIM_GE(na1,1);
    CHECK_DIM_GE(na2,1);
    CHECK_NON_EMPTY(na1);
    CHECK_NON_EMPTY(na2);
    CHECK_SAME_SHAPE(na1,na2);

    na_ndloop(&ndf, 2, x, y);

    return Qnil;
}

.cdotc(x, y) ⇒ Numo::SComplex

CDOTC forms the dot product of two complex vectors

  CDOTC = X^H * Y

Parameters:

  • x (Numo::SComplex)

    vector (>=1-dimentional NArray).

  • y (Numo::SComplex)

    vector (>=1-dimentional NArray).

Returns:

  • (Numo::SComplex)

    op(x) dot y



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# File 'ext/numo/linalg/blas/blas_c.c', line 98

static VALUE
blas_s_cdotc(VALUE mod, VALUE x, VALUE y)
{
    VALUE     ans;
    narray_t *na1, *na2;
    size_t    nx, ny, shape[1]={1};
    ndfunc_arg_in_t ain[2] = {{cT,1},{cT,1}};
    ndfunc_arg_out_t aout[1] = {{numo_cSComplex,0,shape}};
    ndfunc_t ndf = {iter_blas_s_cdotc, NDF_EXTRACT, 2,1, ain,aout};

    CHECK_FUNC(func_p,"cdotc_sub");

    GetNArray(x,na1);
    GetNArray(y,na2);
    CHECK_DIM_GE(na1,1);
    CHECK_DIM_GE(na2,1);
    CHECK_NON_EMPTY(na1);
    CHECK_NON_EMPTY(na2);
    nx = COL_SIZE(na1);
    ny = COL_SIZE(na2);
    CHECK_SIZE_EQ(nx,ny);

    ans = na_ndloop(&ndf, 2, x, y);

    return ans;
}

.cdotu(x, y) ⇒ Numo::SComplex

CDOTU forms the dot product of two complex vectors

  CDOTU = X^T * Y

Parameters:

  • x (Numo::SComplex)

    vector (>=1-dimentional NArray).

  • y (Numo::SComplex)

    vector (>=1-dimentional NArray).

Returns:

  • (Numo::SComplex)

    op(x) dot y



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# File 'ext/numo/linalg/blas/blas_c.c', line 165

static VALUE
blas_s_cdotu(VALUE mod, VALUE x, VALUE y)
{
    VALUE     ans;
    narray_t *na1, *na2;
    size_t    nx, ny, shape[1]={1};
    ndfunc_arg_in_t ain[2] = {{cT,1},{cT,1}};
    ndfunc_arg_out_t aout[1] = {{numo_cSComplex,0,shape}};
    ndfunc_t ndf = {iter_blas_s_cdotu, NDF_EXTRACT, 2,1, ain,aout};

    CHECK_FUNC(func_p,"cdotu_sub");

    GetNArray(x,na1);
    GetNArray(y,na2);
    CHECK_DIM_GE(na1,1);
    CHECK_DIM_GE(na2,1);
    CHECK_NON_EMPTY(na1);
    CHECK_NON_EMPTY(na2);
    nx = COL_SIZE(na1);
    ny = COL_SIZE(na2);
    CHECK_SIZE_EQ(nx,ny);

    ans = na_ndloop(&ndf, 2, x, y);

    return ans;
}

.cgemm(a, b, [c, alpha: 1, beta:0, transa:'N', transb:'N', order:'R']) ⇒ Numo::SComplex

CGEMM performs one of the matrix-matrix operations

  C := alpha*op( A )*op( B ) + beta*C,

where op( X ) is one of

  op( X ) = X   or   op( X ) = X**T   or   op( X ) = X**H,

alpha and beta are scalars, and A, B and C are matrices, with op( A ) an m by k matrix, op( B ) a k by n matrix and C an m by n matrix.

Parameters:

  • a (Numo::SComplex)

    matrix (>=2-dimentional NArray).

  • b (Numo::SComplex)

    matrix (>=2-dimentional NArray).

  • c (Numo::SComplex)

    matrix (>=2-dimentional NArray, optional, inplace allowed).

  • alpha (Float)

    (default=1.0)

  • beta (Float)

    (default=0.0)

  • transa (String or Symbol)

    if ‘N’: Not transpose a, if ‘T’: Transpose a. (default=’N’)

  • transb (String or Symbol)

    if ‘N’: Not transpose b, if ‘T’: Transpose b. (default=’N’)

  • order (String or Symbol)

    if ‘R’: Row-major, if ‘C’: Column-major. (default=’R’)

Returns:

  • (Numo::SComplex)

    returns c = alpha*op( A )*op( B ) + beta*C.



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# File 'ext/numo/linalg/blas/blas_c.c', line 1881

static VALUE
blas_s_cgemm(int argc, VALUE const argv[], VALUE UNUSED(mod))
{
    VALUE     a, b, c=Qnil, alpha, beta;
    narray_t *na1, *na2;
    blasint   ma, ka, kb, nb, tmp;
    size_t    shape[2];
    ndfunc_arg_in_t ain[3] = {{cT,2},{cT,2},{OVERWRITE,2}};
    ndfunc_arg_out_t aout[1] = {{cT,2,shape}};
    ndfunc_t ndf = {iter_blas_s_cgemm, NO_LOOP, 3, 0, ain, aout};

    args_t g;
    VALUE kw_hash = Qnil;
#if GE
    ID kw_table[5] = {id_alpha,id_beta,id_order,id_transa,id_transb};
#elif TR
    ID kw_table[7] = {id_alpha,id_beta,id_order,id_side,id_uplo,id_transa,id_diag};
#else
    ID kw_table[5] = {id_alpha,id_beta,id_order,id_side,id_uplo};
#endif
    VALUE opts[7] = {Qundef,Qundef,Qundef,Qundef,Qundef,Qundef,Qundef};

    CHECK_FUNC(func_p,"cgemm");

    rb_scan_args(argc, argv, "21:", &a, &b, &c, &kw_hash);
    rb_get_kwargs(kw_hash, kw_table, 0, 5+TR*2, opts);
    alpha    = option_value(opts[0],Qnil);
    g.alpha  = RTEST(alpha) ? m_num_to_data(alpha) : m_one;
    beta     = option_value(opts[1],Qnil);
    g.beta   = RTEST(beta)  ? m_num_to_data(beta)  : m_zero;
    g.order  = option_order(opts[2]);
#if GE
    g.transa = option_trans(opts[3]);
    g.transb = option_trans(opts[4]);
#else
    g.side   = option_side(opts[3]);
    g.uplo   = option_uplo(opts[4]);
#endif
#if TR
    g.transa = option_trans(opts[5]);
    g.diag   = option_diag(opts[6]);
#endif

    GetNArray(a,na1);
    GetNArray(b,na2);
    CHECK_DIM_GE(na1,2);
    CHECK_DIM_GE(na2,2);
    ma = ROW_SIZE(na1); // m
    ka = COL_SIZE(na1); // k (lda)
    kb = ROW_SIZE(na2); // k
    nb = COL_SIZE(na2); // n (ldb)

#if GE
    SWAP_IFCOLTR(g.order,g.transa, ma,ka, tmp);
    SWAP_IFCOLTR(g.order,g.transb, kb,nb, tmp);
    CHECK_INT_EQ("ka",ka,"kb",kb);
    g.m = ma;
    g.n = nb;
    g.k = ka;
#else
    CHECK_SQUARE("a",na1); // ma == ka
    SWAP_IFCOL(g.order, kb,nb, tmp);
    // row major             L    R
    //ma = ROW_SIZE(na1); // m or n
    //ka = COL_SIZE(na1); // m or n (lda)
    g.m = kb; // m
    g.n = nb; // n (ldb)
    if (g.side == CblasLeft) {
        CHECK_SIZE_EQ(ka, g.m);
    } else {
        CHECK_SIZE_EQ(ka, g.n);
    }
#endif

    SWAP_IFROW(g.order, ma,nb, tmp);

#if TR
    if (c != Qnil) {
        rb_raise(rb_eArgError,"wrong number of arguments (3 for 2)");
    }
    COPY_OR_CAST_TO(b,cT);
    ndf.nin = 2;

    na_ndloop3(&ndf, &g, 2, a, b);
    return b;
#else

    if (c == Qnil) { // c is not given.
        ndfunc_arg_in_t ain_init = {sym_init,0};
        ain[2] = ain_init;
        ndf.nout = 1;
        c = INT2FIX(0);
        shape[0] = nb;
        shape[1] = ma;
    } else {
        narray_t *na3;
        int nc;
        COPY_OR_CAST_TO(c,cT);
        GetNArray(c,na3);
        CHECK_DIM_GE(na3,2);
        nc = ROW_SIZE(na3);
        if (nc < nb) {
            rb_raise(nary_eShapeError,"nc=%d must be >= nb=%d",nc,nb);
        }
        //CHECK_LEADING_GE("ldc",g.ldc,"m",ma);
    }
    {
        VALUE ans = na_ndloop3(&ndf, &g, 3, a, b, c);

        if (ndf.nout == 1) { // c is not given.
            return ans;
        } else {
            return c;
        }
    }
#endif
}

.cgemv(a, x, [y, alpha: 1, beta:0, trans:'N', order:'R']) ⇒ Numo::SComplex

CGEMV performs one of the matrix-vector operations

  y := alpha*A*x + beta*y,   or   y := alpha*A**T*x + beta*y,   or
  y := alpha*A**H*x + beta*y,

where alpha and beta are scalars, x and y are vectors and A is an m by n matrix.

Parameters:

  • a (Numo::SComplex)

    matrix (>=2-dimentional NArray).

  • x (Numo::SComplex)

    vector (>=1-dimentional NArray).

  • y (Numo::SComplex)

    vector (>=1-dimentional NArray, optional, inplace allowed).

  • alpha (Float)

    (default=1.0)

  • beta (Float)

    (default=0.0)

  • trans (String or Symbol)

    if ‘N’: Not transpose , if ‘T’: Transpose . (default=’N’)

  • order (String or Symbol)

    if ‘R’: Row-major, if ‘C’: Column-major. (default=’R’)

Returns:

  • (Numo::SComplex)

    returns y = alpha*op(A)*x + beta*y.



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# File 'ext/numo/linalg/blas/blas_c.c', line 728

static VALUE
blas_s_cgemv(int argc, VALUE const argv[], VALUE UNUSED(mod))
{
    VALUE     a, x, y=Qnil, alpha, beta;
    narray_t *na1, *na2;
    blasint   ma, na, nx;
#if GE
    blasint   tmp;
#endif
    size_t    shape[1];
    ndfunc_arg_in_t ain[4] = {{cT,2},{cT,1},{OVERWRITE,1},{sym_init,0}};
    ndfunc_arg_out_t aout[1] = {{cT,1,shape}};
    ndfunc_t ndf = {iter_blas_s_cgemv, NO_LOOP, 3, 0, ain, aout};

    args_t g;
    VALUE kw_hash = Qnil;
#if GE
    ID kw_table[4] = {id_alpha,id_beta,id_order,id_trans};
#elif TR
    ID kw_table[6] = {id_alpha,id_beta,id_order,id_uplo,id_trans,id_diag};
#else
    ID kw_table[4] = {id_alpha,id_beta,id_order,id_uplo};
#endif
    VALUE opts[6] = {Qundef,Qundef,Qundef,Qundef,Qundef,Qundef};

    CHECK_FUNC(func_p,"cgemv");

    rb_scan_args(argc, argv, "21:", &a, &x, &y, &kw_hash);
    rb_get_kwargs(kw_hash, kw_table, 0, 4+2*TR, opts);
    alpha   = option_value(opts[0],Qnil);
    g.alpha = RTEST(alpha) ? m_num_to_data(alpha) : m_one;
    beta    = option_value(opts[1],Qnil);
    g.beta  = RTEST(beta)  ? m_num_to_data(beta)  : m_zero;
    g.order = option_order(opts[2]);
#if GE
    g.trans = option_trans(opts[3]);
#else
    g.uplo  = option_uplo(opts[3]);
#endif
#if TR
    g.trans = option_trans(opts[4]);
    g.diag  = option_diag(opts[5]);
#endif

    GetNArray(a,na1);
    CHECK_DIM_GE(na1,2);
    ma = ROW_SIZE(na1);
    na = COL_SIZE(na1);

    GetNArray(x,na2);
    CHECK_DIM_GE(na2,1);
    nx = COL_SIZE(na2);
#if GE
    SWAP_IFCOL(g.order, ma, na, tmp);
    g.m = ma;
    g.n = na;
    SWAP_IFTRANS(g.trans, ma, na, tmp);
#else
    CHECK_SQUARE("a",na1);
#endif
    CHECK_INT_EQ("na",na,"nx",nx);
    shape[0] = ma;

#if TR
    if (y != Qnil) {
        rb_raise(rb_eArgError,"wrong number of arguments (3 for 2)");
    }
    COPY_OR_CAST_TO(x,cT);
    ndf.nin = 2;
    na_ndloop3(&ndf, &g, 2, a, x);
    return x;

#else // GE,SY,HE

    if (y == Qnil) { // c is not given.
        ndf.nout = 1;
        ain[2] = ain[3];
        y = INT2FIX(0);
        shape[0] = ma;
    } else {
        narray_t *na3;
        COPY_OR_CAST_TO(y,cT);
        GetNArray(y,na3);
        CHECK_DIM_GE(na3,1);
        CHECK_SIZE_GE(na3,nx);
    }
    {
        VALUE ans;
        ans = na_ndloop3(&ndf, &g, 3, a, x, y);

        if (ndf.nout == 1) { // c is not given.
            return ans;
        } else {
            return y;
        }
    }
#endif
}

.cgerc(x, y, [a, alpha: 1, order:'R']) ⇒ Numo::SComplex

CGERC performs the rank 1 operation

  A := alpha*x*y**H + A,

where alpha is a scalar, x is an m element vector, y is an n element vector and A is an m by n matrix.

Parameters:

  • x (Numo::SComplex)

    vector (>=1-dimentional NArray).

  • y (Numo::SComplex)

    vector (>=1-dimentional NArray).

  • a (Numo::SComplex)

    matrix (>=2-dimentional NArray, m-by-n symmetric matrix, optional, inplace allowed).

  • alpha (Float)

    (default=1.0)

  • order (String or Symbol)

    if ‘R’: Row-major, if ‘C’: Column-major. (default=’R’)

Returns:

  • (Numo::SComplex)

    returns a.



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# File 'ext/numo/linalg/blas/blas_c.c', line 1259

static VALUE
blas_s_cgerc(int argc, VALUE const argv[], VALUE UNUSED(mod))
{
    VALUE     ans;
    VALUE     x, y, a=Qnil, alpha;
    narray_t *na1, *na2;
    blasint   mx, ny, tmp;
    size_t    shape[2];
    ndfunc_arg_in_t ain[4] = {{cT,1},{cT,1},{OVERWRITE,2},{sym_init,0}};
    ndfunc_arg_out_t aout[1] = {{cT,2,shape}};
    ndfunc_t ndf = {iter_blas_s_cgerc, NO_LOOP, 3, 0, ain, aout};

    args_t g;
    VALUE kw_hash = Qnil;
    ID kw_table[2] = {id_alpha,id_order};
    VALUE opts[2] = {Qundef};

    CHECK_FUNC(func_p,"cgerc");

    rb_scan_args(argc, argv, "21:", &x, &y, &a, &kw_hash);
    rb_get_kwargs(kw_hash, kw_table, 0, 2, opts);
    alpha   = option_value(opts[0],Qnil);
    g.alpha = RTEST(alpha) ? m_num_to_data(alpha) : m_one;
    g.order = option_order(opts[1]);

    GetNArray(x,na1);
    GetNArray(y,na2);
    CHECK_DIM_GE(na1,1);
    CHECK_DIM_GE(na2,1);
    mx = COL_SIZE(na1); // m
    ny = COL_SIZE(na2); // n
    g.m = mx;
    g.n = ny;

    SWAP_IFCOL(g.order, mx,ny, tmp);

    if (a == Qnil) { // c is not given.
        ndf.nout = 1;
        ain[2] = ain[3];
        a = INT2FIX(0);
        shape[0] = mx;
        shape[1] = ny;
    } else {
        narray_t  *na3;
        blasint    ma, na;
        COPY_OR_CAST_TO(a,cT);
        GetNArray(a,na3);
        CHECK_DIM_GE(na3,2);
        ma = ROW_SIZE(na3); // m
        na = COL_SIZE(na3); // n (lda)
        CHECK_SIZE_EQ(ma,mx);
        CHECK_SIZE_EQ(na,ny);
    }

    ans = na_ndloop3(&ndf, &g, 3, x, y, a);

    if (ndf.nout = 1) { // a is not given.
        return ans;
    } else {
        return a;
    }
}

.cgeru(x, y, [a, alpha: 1, order:'R']) ⇒ Numo::SComplex

CGERU performs the rank 1 operation

  A := alpha*x*y**T + A,

where alpha is a scalar, x is an m element vector, y is an n element vector and A is an m by n matrix.

Parameters:

  • x (Numo::SComplex)

    vector (>=1-dimentional NArray).

  • y (Numo::SComplex)

    vector (>=1-dimentional NArray).

  • a (Numo::SComplex)

    matrix (>=2-dimentional NArray, m-by-n symmetric matrix, optional, inplace allowed).

  • alpha (Float)

    (default=1.0)

  • order (String or Symbol)

    if ‘R’: Row-major, if ‘C’: Column-major. (default=’R’)

Returns:

  • (Numo::SComplex)

    returns a.



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# File 'ext/numo/linalg/blas/blas_c.c', line 1378

static VALUE
blas_s_cgeru(int argc, VALUE const argv[], VALUE UNUSED(mod))
{
    VALUE     ans;
    VALUE     x, y, a=Qnil, alpha;
    narray_t *na1, *na2;
    blasint   mx, ny, tmp;
    size_t    shape[2];
    ndfunc_arg_in_t ain[4] = {{cT,1},{cT,1},{OVERWRITE,2},{sym_init,0}};
    ndfunc_arg_out_t aout[1] = {{cT,2,shape}};
    ndfunc_t ndf = {iter_blas_s_cgeru, NO_LOOP, 3, 0, ain, aout};

    args_t g;
    VALUE kw_hash = Qnil;
    ID kw_table[2] = {id_alpha,id_order};
    VALUE opts[2] = {Qundef};

    CHECK_FUNC(func_p,"cgeru");

    rb_scan_args(argc, argv, "21:", &x, &y, &a, &kw_hash);
    rb_get_kwargs(kw_hash, kw_table, 0, 2, opts);
    alpha   = option_value(opts[0],Qnil);
    g.alpha = RTEST(alpha) ? m_num_to_data(alpha) : m_one;
    g.order = option_order(opts[1]);

    GetNArray(x,na1);
    GetNArray(y,na2);
    CHECK_DIM_GE(na1,1);
    CHECK_DIM_GE(na2,1);
    mx = COL_SIZE(na1); // m
    ny = COL_SIZE(na2); // n
    g.m = mx;
    g.n = ny;

    SWAP_IFCOL(g.order, mx,ny, tmp);

    if (a == Qnil) { // c is not given.
        ndf.nout = 1;
        ain[2] = ain[3];
        a = INT2FIX(0);
        shape[0] = mx;
        shape[1] = ny;
    } else {
        narray_t  *na3;
        blasint    ma, na;
        COPY_OR_CAST_TO(a,cT);
        GetNArray(a,na3);
        CHECK_DIM_GE(na3,2);
        ma = ROW_SIZE(na3); // m
        na = COL_SIZE(na3); // n (lda)
        CHECK_SIZE_EQ(ma,mx);
        CHECK_SIZE_EQ(na,ny);
    }

    ans = na_ndloop3(&ndf, &g, 3, x, y, a);

    if (ndf.nout = 1) { // a is not given.
        return ans;
    } else {
        return a;
    }
}

.chemm(a, b, [c, alpha: 1, beta:0, side:'L', uplo:'U', order:'R']) ⇒ Numo::SComplex

CHEMM performs one of the matrix-matrix operations

  C := alpha*A*B + beta*C,

or

  C := alpha*B*A + beta*C,

where alpha and beta are scalars, A is an hermitian matrix and B and C are m by n matrices.

Parameters:

  • a (Numo::SComplex)

    matrix (>=2-dimentional NArray).

  • b (Numo::SComplex)

    matrix (>=2-dimentional NArray).

  • c (Numo::SComplex)

    matrix (>=2-dimentional NArray, optional, inplace allowed).

  • alpha (Float)

    (default=1.0)

  • beta (Float)

    (default=0.0)

  • side (String or Symbol)

    if ‘L’: op(A)*B (left-side op), if ‘R’: B*op(A) (right-side op). (default=’L’)

  • uplo (String or Symbol)

    if ‘U’: Upper triangle, if ‘L’: Lower triangle. (default=’U’)

  • order (String or Symbol)

    if ‘R’: Row-major, if ‘C’: Column-major. (default=’R’)

Returns:

  • (Numo::SComplex)

    returns c = alpha*op( A )*op( B ) + beta*C.



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# File 'ext/numo/linalg/blas/blas_c.c', line 2500

static VALUE
blas_s_chemm(int argc, VALUE const argv[], VALUE UNUSED(mod))
{
    VALUE     a, b, c=Qnil, alpha, beta;
    narray_t *na1, *na2;
    blasint   ma, ka, kb, nb, tmp;
    size_t    shape[2];
    ndfunc_arg_in_t ain[3] = {{cT,2},{cT,2},{OVERWRITE,2}};
    ndfunc_arg_out_t aout[1] = {{cT,2,shape}};
    ndfunc_t ndf = {iter_blas_s_chemm, NO_LOOP, 3, 0, ain, aout};

    args_t g;
    VALUE kw_hash = Qnil;
#if GE
    ID kw_table[5] = {id_alpha,id_beta,id_order,id_transa,id_transb};
#elif TR
    ID kw_table[7] = {id_alpha,id_beta,id_order,id_side,id_uplo,id_transa,id_diag};
#else
    ID kw_table[5] = {id_alpha,id_beta,id_order,id_side,id_uplo};
#endif
    VALUE opts[7] = {Qundef,Qundef,Qundef,Qundef,Qundef,Qundef,Qundef};

    CHECK_FUNC(func_p,"chemm");

    rb_scan_args(argc, argv, "21:", &a, &b, &c, &kw_hash);
    rb_get_kwargs(kw_hash, kw_table, 0, 5+TR*2, opts);
    alpha    = option_value(opts[0],Qnil);
    g.alpha  = RTEST(alpha) ? m_num_to_data(alpha) : m_one;
    beta     = option_value(opts[1],Qnil);
    g.beta   = RTEST(beta)  ? m_num_to_data(beta)  : m_zero;
    g.order  = option_order(opts[2]);
#if GE
    g.transa = option_trans(opts[3]);
    g.transb = option_trans(opts[4]);
#else
    g.side   = option_side(opts[3]);
    g.uplo   = option_uplo(opts[4]);
#endif
#if TR
    g.transa = option_trans(opts[5]);
    g.diag   = option_diag(opts[6]);
#endif

    GetNArray(a,na1);
    GetNArray(b,na2);
    CHECK_DIM_GE(na1,2);
    CHECK_DIM_GE(na2,2);
    ma = ROW_SIZE(na1); // m
    ka = COL_SIZE(na1); // k (lda)
    kb = ROW_SIZE(na2); // k
    nb = COL_SIZE(na2); // n (ldb)

#if GE
    SWAP_IFCOLTR(g.order,g.transa, ma,ka, tmp);
    SWAP_IFCOLTR(g.order,g.transb, kb,nb, tmp);
    CHECK_INT_EQ("ka",ka,"kb",kb);
    g.m = ma;
    g.n = nb;
    g.k = ka;
#else
    CHECK_SQUARE("a",na1); // ma == ka
    SWAP_IFCOL(g.order, kb,nb, tmp);
    // row major             L    R
    //ma = ROW_SIZE(na1); // m or n
    //ka = COL_SIZE(na1); // m or n (lda)
    g.m = kb; // m
    g.n = nb; // n (ldb)
    if (g.side == CblasLeft) {
        CHECK_SIZE_EQ(ka, g.m);
    } else {
        CHECK_SIZE_EQ(ka, g.n);
    }
#endif

    SWAP_IFROW(g.order, ma,nb, tmp);

#if TR
    if (c != Qnil) {
        rb_raise(rb_eArgError,"wrong number of arguments (3 for 2)");
    }
    COPY_OR_CAST_TO(b,cT);
    ndf.nin = 2;

    na_ndloop3(&ndf, &g, 2, a, b);
    return b;
#else

    if (c == Qnil) { // c is not given.
        ndfunc_arg_in_t ain_init = {sym_init,0};
        ain[2] = ain_init;
        ndf.nout = 1;
        c = INT2FIX(0);
        shape[0] = nb;
        shape[1] = ma;
    } else {
        narray_t *na3;
        int nc;
        COPY_OR_CAST_TO(c,cT);
        GetNArray(c,na3);
        CHECK_DIM_GE(na3,2);
        nc = ROW_SIZE(na3);
        if (nc < nb) {
            rb_raise(nary_eShapeError,"nc=%d must be >= nb=%d",nc,nb);
        }
        //CHECK_LEADING_GE("ldc",g.ldc,"m",ma);
    }
    {
        VALUE ans = na_ndloop3(&ndf, &g, 3, a, b, c);

        if (ndf.nout == 1) { // c is not given.
            return ans;
        } else {
            return c;
        }
    }
#endif
}

.chemv(a, x, [y, alpha: 1, beta:0, uplo:'U', order:'R']) ⇒ Numo::SComplex

CHEMV performs the matrix-vector operation

  y := alpha*A*x + beta*y,

where alpha and beta are scalars, x and y are n element vectors and A is an n by n hermitian matrix.

Parameters:

  • a (Numo::SComplex)

    matrix (>=2-dimentional NArray).

  • x (Numo::SComplex)

    vector (>=1-dimentional NArray).

  • y (Numo::SComplex)

    vector (>=1-dimentional NArray, optional, inplace allowed).

  • alpha (Float)

    (default=1.0)

  • beta (Float)

    (default=0.0)

  • side (String or Symbol)

    if ‘L’: op(A)*B (left-side op), if ‘R’: B*op(A) (right-side op). (default=’L’)

  • uplo (String or Symbol)

    if ‘U’: Upper triangle, if ‘L’: Lower triangle. (default=’U’)

  • order (String or Symbol)

    if ‘R’: Row-major, if ‘C’: Column-major. (default=’R’)

Returns:

  • (Numo::SComplex)

    returns y = alpha*op(A)*x + beta*y.



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# File 'ext/numo/linalg/blas/blas_c.c', line 1102

static VALUE
blas_s_chemv(int argc, VALUE const argv[], VALUE UNUSED(mod))
{
    VALUE     a, x, y=Qnil, alpha, beta;
    narray_t *na1, *na2;
    blasint   ma, na, nx;
#if GE
    blasint   tmp;
#endif
    size_t    shape[1];
    ndfunc_arg_in_t ain[4] = {{cT,2},{cT,1},{OVERWRITE,1},{sym_init,0}};
    ndfunc_arg_out_t aout[1] = {{cT,1,shape}};
    ndfunc_t ndf = {iter_blas_s_chemv, NO_LOOP, 3, 0, ain, aout};

    args_t g;
    VALUE kw_hash = Qnil;
#if GE
    ID kw_table[4] = {id_alpha,id_beta,id_order,id_trans};
#elif TR
    ID kw_table[6] = {id_alpha,id_beta,id_order,id_uplo,id_trans,id_diag};
#else
    ID kw_table[4] = {id_alpha,id_beta,id_order,id_uplo};
#endif
    VALUE opts[6] = {Qundef,Qundef,Qundef,Qundef,Qundef,Qundef};

    CHECK_FUNC(func_p,"chemv");

    rb_scan_args(argc, argv, "21:", &a, &x, &y, &kw_hash);
    rb_get_kwargs(kw_hash, kw_table, 0, 4+2*TR, opts);
    alpha   = option_value(opts[0],Qnil);
    g.alpha = RTEST(alpha) ? m_num_to_data(alpha) : m_one;
    beta    = option_value(opts[1],Qnil);
    g.beta  = RTEST(beta)  ? m_num_to_data(beta)  : m_zero;
    g.order = option_order(opts[2]);
#if GE
    g.trans = option_trans(opts[3]);
#else
    g.uplo  = option_uplo(opts[3]);
#endif
#if TR
    g.trans = option_trans(opts[4]);
    g.diag  = option_diag(opts[5]);
#endif

    GetNArray(a,na1);
    CHECK_DIM_GE(na1,2);
    ma = ROW_SIZE(na1);
    na = COL_SIZE(na1);

    GetNArray(x,na2);
    CHECK_DIM_GE(na2,1);
    nx = COL_SIZE(na2);
#if GE
    SWAP_IFCOL(g.order, ma, na, tmp);
    g.m = ma;
    g.n = na;
    SWAP_IFTRANS(g.trans, ma, na, tmp);
#else
    CHECK_SQUARE("a",na1);
#endif
    CHECK_INT_EQ("na",na,"nx",nx);
    shape[0] = ma;

#if TR
    if (y != Qnil) {
        rb_raise(rb_eArgError,"wrong number of arguments (3 for 2)");
    }
    COPY_OR_CAST_TO(x,cT);
    ndf.nin = 2;
    na_ndloop3(&ndf, &g, 2, a, x);
    return x;

#else // GE,SY,HE

    if (y == Qnil) { // c is not given.
        ndf.nout = 1;
        ain[2] = ain[3];
        y = INT2FIX(0);
        shape[0] = ma;
    } else {
        narray_t *na3;
        COPY_OR_CAST_TO(y,cT);
        GetNArray(y,na3);
        CHECK_DIM_GE(na3,1);
        CHECK_SIZE_GE(na3,nx);
    }
    {
        VALUE ans;
        ans = na_ndloop3(&ndf, &g, 3, a, x, y);

        if (ndf.nout == 1) { // c is not given.
            return ans;
        } else {
            return y;
        }
    }
#endif
}

.cher(x, [a, alpha: 1, uplo:'U', order:'R']) ⇒ Numo::SComplex

CHER performs the hermitian rank 1 operation

  A := alpha*x*x**H + A,

where alpha is a real scalar, x is an n element vector and A is an n by n hermitian matrix.

Parameters:

  • x (Numo::SComplex)

    vector (>=1-dimentional NArray).

  • a (Numo::SComplex)

    matrix (>=2-dimentional NArray, inplace allowed).

  • alpha (Float)

    (default=1.0)

  • uplo (String or Symbol)

    if ‘U’: Upper triangle, if ‘L’: Lower triangle. (default=’U’)

  • order (String or Symbol)

    if ‘R’: Row-major, if ‘C’: Column-major. (default=’R’)

Returns:

  • (Numo::SComplex)

    return a



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# File 'ext/numo/linalg/blas/blas_c.c', line 1494

static VALUE
blas_s_cher(int argc, VALUE const argv[], VALUE UNUSED(mod))
{
    VALUE     ans;
    VALUE     x, a, alpha;
    narray_t *na1, *na3;
    blasint   nx, na;
    size_t    shape[2];
    ndfunc_arg_in_t ain[3] = {{cT,1},{OVERWRITE,2},{sym_init,0}};
    ndfunc_arg_out_t aout[1] = {{cT,2,shape}};
    ndfunc_t ndf = {iter_blas_s_cher, NO_LOOP, 2, 0, ain, aout};

    args_t g;
    VALUE kw_hash = Qnil;
    ID kw_table[3] = {id_alpha,id_order,id_uplo};
    VALUE opts[3] = {Qundef,Qundef,Qundef};

    CHECK_FUNC(func_p,"cher");

    rb_scan_args(argc, argv, "11:", &x, &a, &kw_hash);
    rb_get_kwargs(kw_hash, kw_table, 0, 3, opts);
    alpha   = option_value(opts[0],Qnil);
    g.alpha = RTEST(alpha) ? NUM2DBL(alpha) : 1;
    g.order = option_order(opts[1]);
    g.uplo  = option_uplo(opts[2]);

    GetNArray(x,na1);
    CHECK_DIM_GE(na1,1);
    nx = COL_SIZE(na1); // n

    if (a == Qnil) { // c is not given.
        ndf.nout = 1;
        ain[1] = ain[2];
        a = INT2FIX(0);
        shape[0] = shape[1] = nx;
    } else {
        COPY_OR_CAST_TO(a,cT);
        GetNArray(a,na3);
        CHECK_DIM_GE(na3,2);
        CHECK_SQUARE("a",na3);
        na = COL_SIZE(na3); // n (lda)
        CHECK_SIZE_EQ(na,nx);
    }

    ans = na_ndloop3(&ndf, &g, 2, x, a);

    if (ndf.nout == 1) { // a is not given.
        return ans;
    } else {
        return a;
    }
}

.cher2(x, y, [a, alpha: 1, uplo:'U', order:'R']) ⇒ Numo::SComplex

CHER2 performs the hermitian rank 2 operation

  A := alpha*x*y**H + conjg( alpha )*y*x**H + A,

where alpha is a scalar, x and y are n element vectors and A is an n by n hermitian matrix.

Parameters:

  • x (Numo::SComplex)

    vector (>=1-dimentional NArray).

  • y (Numo::SComplex)

    vector (>=1-dimentional NArray).

  • a (Numo::SComplex)

    matrix (>=2-dimentional NArray, inplace allowed).

  • alpha (Float)

    (default=1.0)

  • uplo (String or Symbol)

    if ‘U’: Upper triangle, if ‘L’: Lower triangle. (default=’U’)

  • order (String or Symbol)

    if ‘R’: Row-major, if ‘C’: Column-major. (default=’R’)

Returns:

  • (Numo::SComplex)

    returns a.



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# File 'ext/numo/linalg/blas/blas_c.c', line 1604

static VALUE
blas_s_cher2(int argc, VALUE const argv[], VALUE UNUSED(mod))
{
    VALUE     ans;
    VALUE     x, y, a, alpha;
    narray_t *na1, *na2, *na3;
    blasint   nx, ny, na;
    size_t    shape[2];
    ndfunc_arg_in_t ain[4] = {{cT,1},{cT,1},{OVERWRITE,2},{sym_init,0}};
    ndfunc_arg_out_t aout[1] = {{cT,2,shape}};
    ndfunc_t ndf = {iter_blas_s_cher2, NO_LOOP, 3, 0, ain, aout};

    args_t g;
    VALUE kw_hash = Qnil;
    ID kw_table[3] = {id_alpha,id_order,id_uplo};
    VALUE opts[3] = {Qundef,Qundef,Qundef};

    CHECK_FUNC(func_p,"cher2");

    rb_scan_args(argc, argv, "21:", &x, &y, &a, &kw_hash);
    rb_get_kwargs(kw_hash, kw_table, 0, 3, opts);
    alpha   = option_value(opts[0],Qnil);
    g.alpha = RTEST(alpha) ? m_num_to_data(alpha) : m_one;
    g.order = option_order(opts[1]);
    g.uplo  = option_uplo(opts[2]);

    GetNArray(x,na1);
    GetNArray(y,na2);
    CHECK_DIM_GE(na1,1);
    CHECK_DIM_GE(na2,1);
    nx = COL_SIZE(na1); // n
    ny = COL_SIZE(na2); // n
    CHECK_INT_EQ("nx",nx,"ny",ny);

    if (a == Qnil) { // c is not given.
        ndf.nout = 1;
        ain[2] = ain[3];
        a = INT2FIX(0);
        shape[0] = shape[1] = nx;
    } else {
        COPY_OR_CAST_TO(a,cT);
        GetNArray(a,na3);
        CHECK_DIM_GE(na3,2);
        CHECK_SQUARE("a",na3);
        na = COL_SIZE(na3); // n (lda)
        CHECK_SIZE_EQ(na,nx);
    }

    ans = na_ndloop3(&ndf, &g, 3, x, y, a);

    if (ndf.nout == 1) { // a is not given.
        return ans;
    } else {
        return a;
    }
}

.cherk(a, [c, alpha: 1, beta:0, uplo:'U', trans:'N', order:'R']) ⇒ Numo::SComplex

CHERK performs one of the hermitian rank k operations

  C := alpha*A*A**H + beta*C,

or

  C := alpha*A**H*A + beta*C,

where alpha and beta are real scalars, C is an n by n hermitian matrix and A is an n by k matrix in the first case and a k by n matrix in the second case.

Parameters:

  • a (Numo::SComplex)

    matrix (>=2-dimentional NArray, n-by-k, inpace).

  • c (Numo::SComplex)

    matrix (>=2-dimentional NArray, n-by-n, optional, inpace).

  • alpha (Float)

    (default=1.0)

  • beta (Float)

    (default=0.0)

  • uplo (String or Symbol)

    if ‘U’: Upper triangle, if ‘L’: Lower triangle. (default=’U’)

  • trans (String or Symbol)

    if ‘N’: Not transpose , if ‘T’: Transpose . (default=’N’)

  • order (String or Symbol)

    if ‘R’: Row-major, if ‘C’: Column-major. (default=’R’)

Returns:

  • (Numo::SComplex)

    returns c.



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# File 'ext/numo/linalg/blas/blas_c.c', line 1727

static VALUE
blas_s_cherk(int argc, VALUE const argv[], VALUE UNUSED(mod))
{
    VALUE     ans;
    VALUE     a, c, alpha, beta;
    narray_t *na1, *na3;
    blasint   na, ka, nc, tmp;
    size_t    shape[2];
    ndfunc_arg_in_t ain[3] = {{cT,2},{OVERWRITE,2},{sym_init,0}};
    ndfunc_arg_out_t aout[1] = {{cT,2,shape}};
    ndfunc_t ndf = {iter_blas_s_cherk, NO_LOOP, 2, 0, ain, aout};

    args_t g;
    VALUE kw_hash = Qnil;
    ID kw_table[5] = {id_alpha,id_beta,id_order,id_uplo,id_trans};
    VALUE opts[5] = {Qundef,Qundef,Qundef,Qundef,Qundef};

    CHECK_FUNC(func_p,"cherk");

    rb_scan_args(argc, argv, "11:", &a, &c, &kw_hash);
    rb_get_kwargs(kw_hash, kw_table, 0, 5, opts);
    alpha   = option_value(opts[0],Qnil);
    beta    = option_value(opts[1],Qnil);
#line 85 "gen/../tmpl/syrk.c"
    g.alpha = RTEST(alpha) ? DBL2NUM(alpha) : 1;
    g.beta  = RTEST(beta)  ? DBL2NUM(beta)  : 0;
#line 91 "gen/../tmpl/syrk.c"
    g.order = option_order(opts[2]);
    g.uplo  = option_uplo(opts[3]);
    g.trans = option_trans(opts[4]);

    GetNArray(a,na1);
    CHECK_DIM_GE(na1,2);

    na = ROW_SIZE(na1); // n
    ka = COL_SIZE(na1); // k (lda)
    SWAP_IFCOLTR(g.order,g.trans, na,ka, tmp);
    g.n = na;
    g.k = ka;

    if (c == Qnil) { // c is not given.
        ndf.nout = 1;
        ain[1] = ain[2];
        c = INT2FIX(0);
        shape[0] = na;
        shape[1] = na;
    } else {
        COPY_OR_CAST_TO(c,cT);
        GetNArray(c,na3);
        CHECK_DIM_GE(na3,2);
        nc = ROW_SIZE(na3);
        if (nc < na) {
            rb_raise(nary_eShapeError,"nc=%d must be >= na=%d",nc,na);
        }
        //CHECK_LEADING_GE("ldc",g.ldc,"n",na);
    }

    ans = na_ndloop3(&ndf, &g, 2, a, c);

    if (ndf.nout == 1) { // c is not given.
        return ans;
    } else {
        return c;
    }
}

.cscal(a, x) ⇒ Numo::SComplex

CSCAL scales a vector by a constant.

Parameters:

  • a (Float)

    scale factor

  • x (Numo::SComplex)

    vector (>=1-dimentional NArray).

Returns:

  • (Numo::SComplex)

    returns a*x.



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# File 'ext/numo/linalg/blas/blas_c.c', line 554

static VALUE
blas_s_cscal(VALUE mod, VALUE a, VALUE x)
{
    scal_t g[1];
    narray_t *na1;
    ndfunc_arg_in_t ain[1] = {{OVERWRITE,0}};
    ndfunc_t ndf = {iter_blas_s_cscal, STRIDE_LOOP, 1,0, ain,0};

    CHECK_FUNC(func_p,"cscal");

  
#line 56 "gen/../tmpl/scal.c"
    if (RTEST(a)) {g[0] = m_num_to_data(a);} else {g[0]=m_one;}
  
    COPY_OR_CAST_TO(x,cT);
    GetNArray(x,na1);
    CHECK_DIM_GE(na1,1);
    CHECK_NON_EMPTY(na1);

    na_ndloop3(&ndf, g, 1, x);

    return x;
}

.csscal(a, x) ⇒ Numo::SComplex

CSSCAL scales a complex vector by a real constant.

Parameters:

  • a (Float)

    scale factor

  • x (Numo::SComplex)

    vector (>=1-dimentional NArray).

Returns:

  • (Numo::SComplex)

    returns a*x.



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# File 'ext/numo/linalg/blas/blas_c.c', line 618

static VALUE
blas_s_csscal(VALUE mod, VALUE a, VALUE x)
{
    scal_t g[1];
    narray_t *na1;
    ndfunc_arg_in_t ain[1] = {{OVERWRITE,0}};
    ndfunc_t ndf = {iter_blas_s_csscal, STRIDE_LOOP, 1,0, ain,0};

    CHECK_FUNC(func_p,"csscal");

  
    if (RTEST(a)) {g[0] = NUM2DBL(a);} else {g[0]=1;}
  
#line 58 "gen/../tmpl/scal.c"
    COPY_OR_CAST_TO(x,cT);
    GetNArray(x,na1);
    CHECK_DIM_GE(na1,1);
    CHECK_NON_EMPTY(na1);

    na_ndloop3(&ndf, g, 1, x);

    return x;
}

.cswap(x, y) ⇒ nil

CSWAP interchanges two vectors.

Parameters:

  • x (Numo::SComplex)

    vector (>=1-dimentional NArray).

  • y (Numo::SComplex)

    vector (>=1-dimentional NArray).

Returns:

  • (nil)


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# File 'ext/numo/linalg/blas/blas_c.c', line 361

static VALUE
blas_s_cswap(VALUE UNUSED(mod), VALUE x, VALUE y)
{
    narray_t *na1, *na2;
    ndfunc_arg_in_t ain[2] = {{OVERWRITE,0},{OVERWRITE,0}};
    ndfunc_t ndf = {iter_blas_s_cswap, STRIDE_LOOP, 2,0, ain,0};

    CHECK_FUNC(func_p,"cswap");

    CHECK_NARRAY_TYPE(x,cT);
    CHECK_NARRAY_TYPE(y,cT);
    GetNArray(x,na1);
    GetNArray(y,na2);
    CHECK_DIM_GE(na1,1);
    CHECK_DIM_GE(na2,1);
    CHECK_NON_EMPTY(na1);
    CHECK_NON_EMPTY(na2);
    CHECK_SAME_SHAPE(na1,na2);

    na_ndloop(&ndf, 2, x, y);

    return Qnil;
}

.csymm(a, b, [c, alpha: 1, beta:0, side:'L', uplo:'U', order:'R']) ⇒ Numo::SComplex

CSYMM performs one of the matrix-matrix operations

  C := alpha*A*B + beta*C,

or

  C := alpha*B*A + beta*C,

where alpha and beta are scalars, A is a symmetric matrix and B and C are m by n matrices.

Parameters:

  • a (Numo::SComplex)

    matrix (>=2-dimentional NArray).

  • b (Numo::SComplex)

    matrix (>=2-dimentional NArray).

  • c (Numo::SComplex)

    matrix (>=2-dimentional NArray, optional, inplace allowed).

  • alpha (Float)

    (default=1.0)

  • beta (Float)

    (default=0.0)

  • side (String or Symbol)

    if ‘L’: op(A)*B (left-side op), if ‘R’: B*op(A) (right-side op). (default=’L’)

  • uplo (String or Symbol)

    if ‘U’: Upper triangle, if ‘L’: Lower triangle. (default=’U’)

  • order (String or Symbol)

    if ‘R’: Row-major, if ‘C’: Column-major. (default=’R’)

Returns:

  • (Numo::SComplex)

    returns c = alpha*op( A )*op( B ) + beta*C.



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# File 'ext/numo/linalg/blas/blas_c.c', line 2088

static VALUE
blas_s_csymm(int argc, VALUE const argv[], VALUE UNUSED(mod))
{
    VALUE     a, b, c=Qnil, alpha, beta;
    narray_t *na1, *na2;
    blasint   ma, ka, kb, nb, tmp;
    size_t    shape[2];
    ndfunc_arg_in_t ain[3] = {{cT,2},{cT,2},{OVERWRITE,2}};
    ndfunc_arg_out_t aout[1] = {{cT,2,shape}};
    ndfunc_t ndf = {iter_blas_s_csymm, NO_LOOP, 3, 0, ain, aout};

    args_t g;
    VALUE kw_hash = Qnil;
#if GE
    ID kw_table[5] = {id_alpha,id_beta,id_order,id_transa,id_transb};
#elif TR
    ID kw_table[7] = {id_alpha,id_beta,id_order,id_side,id_uplo,id_transa,id_diag};
#else
    ID kw_table[5] = {id_alpha,id_beta,id_order,id_side,id_uplo};
#endif
    VALUE opts[7] = {Qundef,Qundef,Qundef,Qundef,Qundef,Qundef,Qundef};

    CHECK_FUNC(func_p,"csymm");

    rb_scan_args(argc, argv, "21:", &a, &b, &c, &kw_hash);
    rb_get_kwargs(kw_hash, kw_table, 0, 5+TR*2, opts);
    alpha    = option_value(opts[0],Qnil);
    g.alpha  = RTEST(alpha) ? m_num_to_data(alpha) : m_one;
    beta     = option_value(opts[1],Qnil);
    g.beta   = RTEST(beta)  ? m_num_to_data(beta)  : m_zero;
    g.order  = option_order(opts[2]);
#if GE
    g.transa = option_trans(opts[3]);
    g.transb = option_trans(opts[4]);
#else
    g.side   = option_side(opts[3]);
    g.uplo   = option_uplo(opts[4]);
#endif
#if TR
    g.transa = option_trans(opts[5]);
    g.diag   = option_diag(opts[6]);
#endif

    GetNArray(a,na1);
    GetNArray(b,na2);
    CHECK_DIM_GE(na1,2);
    CHECK_DIM_GE(na2,2);
    ma = ROW_SIZE(na1); // m
    ka = COL_SIZE(na1); // k (lda)
    kb = ROW_SIZE(na2); // k
    nb = COL_SIZE(na2); // n (ldb)

#if GE
    SWAP_IFCOLTR(g.order,g.transa, ma,ka, tmp);
    SWAP_IFCOLTR(g.order,g.transb, kb,nb, tmp);
    CHECK_INT_EQ("ka",ka,"kb",kb);
    g.m = ma;
    g.n = nb;
    g.k = ka;
#else
    CHECK_SQUARE("a",na1); // ma == ka
    SWAP_IFCOL(g.order, kb,nb, tmp);
    // row major             L    R
    //ma = ROW_SIZE(na1); // m or n
    //ka = COL_SIZE(na1); // m or n (lda)
    g.m = kb; // m
    g.n = nb; // n (ldb)
    if (g.side == CblasLeft) {
        CHECK_SIZE_EQ(ka, g.m);
    } else {
        CHECK_SIZE_EQ(ka, g.n);
    }
#endif

    SWAP_IFROW(g.order, ma,nb, tmp);

#if TR
    if (c != Qnil) {
        rb_raise(rb_eArgError,"wrong number of arguments (3 for 2)");
    }
    COPY_OR_CAST_TO(b,cT);
    ndf.nin = 2;

    na_ndloop3(&ndf, &g, 2, a, b);
    return b;
#else

    if (c == Qnil) { // c is not given.
        ndfunc_arg_in_t ain_init = {sym_init,0};
        ain[2] = ain_init;
        ndf.nout = 1;
        c = INT2FIX(0);
        shape[0] = nb;
        shape[1] = ma;
    } else {
        narray_t *na3;
        int nc;
        COPY_OR_CAST_TO(c,cT);
        GetNArray(c,na3);
        CHECK_DIM_GE(na3,2);
        nc = ROW_SIZE(na3);
        if (nc < nb) {
            rb_raise(nary_eShapeError,"nc=%d must be >= nb=%d",nc,nb);
        }
        //CHECK_LEADING_GE("ldc",g.ldc,"m",ma);
    }
    {
        VALUE ans = na_ndloop3(&ndf, &g, 3, a, b, c);

        if (ndf.nout == 1) { // c is not given.
            return ans;
        } else {
            return c;
        }
    }
#endif
}

.csyr2k(a, b, [c, alpha: 1, beta:0, uplo:'U', trans:'N', order:'R']) ⇒ Numo::SComplex

CSYR2K performs one of the symmetric rank 2k operations

  C := alpha*A*B**T + alpha*B*A**T + beta*C,

or

  C := alpha*A**T*B + alpha*B**T*A + beta*C,

where alpha and beta are scalars, C is an n by n symmetric matrix and A and B are n by k matrices in the first case and k by n matrices in the second case.

Parameters:

  • a (Numo::SComplex)

    matrix (>=2-dimentional NArray, n-by-k).

  • b (Numo::SComplex)

    matrix (>=2-dimentional NArray, n-by-k).

  • c (Numo::SComplex)

    matrix (>=2-dimentional NArray, n-by-n, optional, inpace).

  • alpha (Float)

    (default=1.0)

  • beta (Float)

    (default=0.0)

  • uplo (String or Symbol)

    if ‘U’: Upper triangle, if ‘L’: Lower triangle. (default=’U’)

  • trans (String or Symbol)

    if ‘N’: Not transpose , if ‘T’: Transpose . (default=’N’)

  • order (String or Symbol)

    if ‘R’: Row-major, if ‘C’: Column-major. (default=’R’)

Returns:

  • (Numo::SComplex)

    returns c.



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# File 'ext/numo/linalg/blas/blas_c.c', line 2817

static VALUE
blas_s_csyr2k(int argc, VALUE const argv[], VALUE UNUSED(mod))
{
    VALUE     ans;
    VALUE     a, b, c=Qnil, alpha, beta;
    narray_t *na1, *na2, *na3;
    blasint   na, ka, kb, nb, nc, tmp;
    size_t    shape[2];
    ndfunc_arg_in_t ain[4] = {{cT,2},{cT,2},{OVERWRITE,2},{sym_init,0}};
    ndfunc_arg_out_t aout[1] = {{cT,2,shape}};
    ndfunc_t ndf = {iter_blas_s_csyr2k, NO_LOOP, 3, 0, ain, aout};

    args_t g;
    VALUE kw_hash = Qnil;
    ID kw_table[5] = {id_alpha,id_beta,id_order,id_uplo,id_trans};
    VALUE opts[5] = {Qundef,Qundef,Qundef,Qundef,Qundef};

    CHECK_FUNC(func_p,"csyr2k");

    rb_scan_args(argc, argv, "21:", &a, &b, &c, &kw_hash);
    rb_get_kwargs(kw_hash, kw_table, 0, 5, opts);
    alpha    = option_value(opts[0],Qnil);
    g.alpha  = RTEST(alpha) ? m_num_to_data(alpha) : m_one;
    beta     = option_value(opts[1],Qnil);
    g.beta   = RTEST(beta)  ? m_num_to_data(beta)  : m_zero;
    g.order  = option_order(opts[2]);
    g.uplo   = option_uplo(opts[3]);
    g.trans  = option_trans(opts[4]);

    GetNArray(a,na1);
    GetNArray(b,na2);
    CHECK_DIM_GE(na1,2);
    CHECK_DIM_GE(na2,2);

    na = ROW_SIZE(na1); // n
    ka = COL_SIZE(na1); // k (lda)
    SWAP_IFCOLTR(g.order, g.trans, na, ka, tmp);

    nb = ROW_SIZE(na2); // n
    kb = COL_SIZE(na2); // k (ldb)
    SWAP_IFCOLTR(g.order, g.trans, kb, nb, tmp);
    CHECK_INT_EQ("na",na,"nb",nb);
    CHECK_INT_EQ("ka",ka,"kb",kb);
    g.n = nb;
    g.k = kb;

    SWAP_IFROW(g.order, na, nb, tmp);

    if (c == Qnil) { // c is not given.
        ndf.nout = 1;
        ain[2] = ain[3];
        c = INT2FIX(0);
        shape[0] = nb;
        shape[1] = na;
    } else {
        COPY_OR_CAST_TO(c,cT);
        GetNArray(c,na3);
        CHECK_DIM_GE(na3,2);
        nc = ROW_SIZE(na3); // n
        if (nc < nb) {
            rb_raise(nary_eShapeError,"nc=%d must be >= nb=%d",nc,nb);
        }
        //CHECK_LEADING_GE("ldc",g.ldc,"n",na);
    }

    ans = na_ndloop3(&ndf, &g, 3, a, b, c);

    if (ndf.nout = 1) { // c is not given.
        return ans;
    } else {
        return c;
    }
}

.csyrk(a, [c, alpha: 1, beta:0, uplo:'U', trans:'N', order:'R']) ⇒ Numo::SComplex

CSYRK performs one of the symmetric rank k operations

  C := alpha*A*A**T + beta*C,

or

  C := alpha*A**T*A + beta*C,

where alpha and beta are scalars, C is an n by n symmetric matrix and A is an n by k matrix in the first case and a k by n matrix in the second case.

Parameters:

  • a (Numo::SComplex)

    matrix (>=2-dimentional NArray, n-by-k, inpace).

  • c (Numo::SComplex)

    matrix (>=2-dimentional NArray, n-by-n, optional, inpace).

  • alpha (Float)

    (default=1.0)

  • beta (Float)

    (default=0.0)

  • uplo (String or Symbol)

    if ‘U’: Upper triangle, if ‘L’: Lower triangle. (default=’U’)

  • trans (String or Symbol)

    if ‘N’: Not transpose , if ‘T’: Transpose . (default=’N’)

  • order (String or Symbol)

    if ‘R’: Row-major, if ‘C’: Column-major. (default=’R’)

Returns:

  • (Numo::SComplex)

    returns c.



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# File 'ext/numo/linalg/blas/blas_c.c', line 2686

static VALUE
blas_s_csyrk(int argc, VALUE const argv[], VALUE UNUSED(mod))
{
    VALUE     ans;
    VALUE     a, c, alpha, beta;
    narray_t *na1, *na3;
    blasint   na, ka, nc, tmp;
    size_t    shape[2];
    ndfunc_arg_in_t ain[3] = {{cT,2},{OVERWRITE,2},{sym_init,0}};
    ndfunc_arg_out_t aout[1] = {{cT,2,shape}};
    ndfunc_t ndf = {iter_blas_s_csyrk, NO_LOOP, 2, 0, ain, aout};

    args_t g;
    VALUE kw_hash = Qnil;
    ID kw_table[5] = {id_alpha,id_beta,id_order,id_uplo,id_trans};
    VALUE opts[5] = {Qundef,Qundef,Qundef,Qundef,Qundef};

    CHECK_FUNC(func_p,"csyrk");

    rb_scan_args(argc, argv, "11:", &a, &c, &kw_hash);
    rb_get_kwargs(kw_hash, kw_table, 0, 5, opts);
    alpha   = option_value(opts[0],Qnil);
    beta    = option_value(opts[1],Qnil);
#line 88 "gen/../tmpl/syrk.c"
    g.alpha = RTEST(alpha) ? m_num_to_data(alpha) : m_one;
    g.beta  = RTEST(beta)  ? m_num_to_data(beta)  : m_zero;
#line 91 "gen/../tmpl/syrk.c"
    g.order = option_order(opts[2]);
    g.uplo  = option_uplo(opts[3]);
    g.trans = option_trans(opts[4]);

    GetNArray(a,na1);
    CHECK_DIM_GE(na1,2);

    na = ROW_SIZE(na1); // n
    ka = COL_SIZE(na1); // k (lda)
    SWAP_IFCOLTR(g.order,g.trans, na,ka, tmp);
    g.n = na;
    g.k = ka;

    if (c == Qnil) { // c is not given.
        ndf.nout = 1;
        ain[1] = ain[2];
        c = INT2FIX(0);
        shape[0] = na;
        shape[1] = na;
    } else {
        COPY_OR_CAST_TO(c,cT);
        GetNArray(c,na3);
        CHECK_DIM_GE(na3,2);
        nc = ROW_SIZE(na3);
        if (nc < na) {
            rb_raise(nary_eShapeError,"nc=%d must be >= na=%d",nc,na);
        }
        //CHECK_LEADING_GE("ldc",g.ldc,"n",na);
    }

    ans = na_ndloop3(&ndf, &g, 2, a, c);

    if (ndf.nout == 1) { // c is not given.
        return ans;
    } else {
        return c;
    }
}

.ctrmm(a, b, [alpha: 1, side:'L', uplo:'U', transa:'N', diag:'U', order:'R']) ⇒ Numo::SComplex

CTRMM performs one of the matrix-matrix operations

  B := alpha*op( A )*B,   or   B := alpha*B*op( A )

where alpha is a scalar, B is an m by n matrix, A is a unit, or non-unit, upper or lower triangular matrix and op( A ) is one of

  op( A ) = A   or   op( A ) = A**T   or   op( A ) = A**H.

Parameters:

  • a (Numo::SComplex)

    matrix (>=2-dimentional NArray).

  • b (Numo::SComplex)

    matrix (>=2-dimentional NArray).

  • alpha (Float)

    (default=1.0)

  • beta (Float)

    (default=0.0)

  • side (String or Symbol)

    if ‘L’: op(A)*B (left-side op), if ‘R’: B*op(A) (right-side op). (default=’L’)

  • uplo (String or Symbol)

    if ‘U’: Upper triangle, if ‘L’: Lower triangle. (default=’U’)

  • transa (String or Symbol)

    if ‘N’: Not transpose a, if ‘T’: Transpose a. (default=’N’)

  • order (String or Symbol)

    if ‘R’: Row-major, if ‘C’: Column-major. (default=’R’)

Returns:

  • (Numo::SComplex)

    returns c = alpha*op( A )*op( B ) + beta*C.



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# File 'ext/numo/linalg/blas/blas_c.c', line 2293

static VALUE
blas_s_ctrmm(int argc, VALUE const argv[], VALUE UNUSED(mod))
{
    VALUE     a, b, c=Qnil, alpha, beta;
    narray_t *na1, *na2;
    blasint   ma, ka, kb, nb, tmp;
    size_t    shape[2];
    ndfunc_arg_in_t ain[3] = {{cT,2},{cT,2},{OVERWRITE,2}};
    ndfunc_arg_out_t aout[1] = {{cT,2,shape}};
    ndfunc_t ndf = {iter_blas_s_ctrmm, NO_LOOP, 3, 0, ain, aout};

    args_t g;
    VALUE kw_hash = Qnil;
#if GE
    ID kw_table[5] = {id_alpha,id_beta,id_order,id_transa,id_transb};
#elif TR
    ID kw_table[7] = {id_alpha,id_beta,id_order,id_side,id_uplo,id_transa,id_diag};
#else
    ID kw_table[5] = {id_alpha,id_beta,id_order,id_side,id_uplo};
#endif
    VALUE opts[7] = {Qundef,Qundef,Qundef,Qundef,Qundef,Qundef,Qundef};

    CHECK_FUNC(func_p,"ctrmm");

    rb_scan_args(argc, argv, "21:", &a, &b, &c, &kw_hash);
    rb_get_kwargs(kw_hash, kw_table, 0, 5+TR*2, opts);
    alpha    = option_value(opts[0],Qnil);
    g.alpha  = RTEST(alpha) ? m_num_to_data(alpha) : m_one;
    beta     = option_value(opts[1],Qnil);
    g.beta   = RTEST(beta)  ? m_num_to_data(beta)  : m_zero;
    g.order  = option_order(opts[2]);
#if GE
    g.transa = option_trans(opts[3]);
    g.transb = option_trans(opts[4]);
#else
    g.side   = option_side(opts[3]);
    g.uplo   = option_uplo(opts[4]);
#endif
#if TR
    g.transa = option_trans(opts[5]);
    g.diag   = option_diag(opts[6]);
#endif

    GetNArray(a,na1);
    GetNArray(b,na2);
    CHECK_DIM_GE(na1,2);
    CHECK_DIM_GE(na2,2);
    ma = ROW_SIZE(na1); // m
    ka = COL_SIZE(na1); // k (lda)
    kb = ROW_SIZE(na2); // k
    nb = COL_SIZE(na2); // n (ldb)

#if GE
    SWAP_IFCOLTR(g.order,g.transa, ma,ka, tmp);
    SWAP_IFCOLTR(g.order,g.transb, kb,nb, tmp);
    CHECK_INT_EQ("ka",ka,"kb",kb);
    g.m = ma;
    g.n = nb;
    g.k = ka;
#else
    CHECK_SQUARE("a",na1); // ma == ka
    SWAP_IFCOL(g.order, kb,nb, tmp);
    // row major             L    R
    //ma = ROW_SIZE(na1); // m or n
    //ka = COL_SIZE(na1); // m or n (lda)
    g.m = kb; // m
    g.n = nb; // n (ldb)
    if (g.side == CblasLeft) {
        CHECK_SIZE_EQ(ka, g.m);
    } else {
        CHECK_SIZE_EQ(ka, g.n);
    }
#endif

    SWAP_IFROW(g.order, ma,nb, tmp);

#if TR
    if (c != Qnil) {
        rb_raise(rb_eArgError,"wrong number of arguments (3 for 2)");
    }
    COPY_OR_CAST_TO(b,cT);
    ndf.nin = 2;

    na_ndloop3(&ndf, &g, 2, a, b);
    return b;
#else

    if (c == Qnil) { // c is not given.
        ndfunc_arg_in_t ain_init = {sym_init,0};
        ain[2] = ain_init;
        ndf.nout = 1;
        c = INT2FIX(0);
        shape[0] = nb;
        shape[1] = ma;
    } else {
        narray_t *na3;
        int nc;
        COPY_OR_CAST_TO(c,cT);
        GetNArray(c,na3);
        CHECK_DIM_GE(na3,2);
        nc = ROW_SIZE(na3);
        if (nc < nb) {
            rb_raise(nary_eShapeError,"nc=%d must be >= nb=%d",nc,nb);
        }
        //CHECK_LEADING_GE("ldc",g.ldc,"m",ma);
    }
    {
        VALUE ans = na_ndloop3(&ndf, &g, 3, a, b, c);

        if (ndf.nout == 1) { // c is not given.
            return ans;
        } else {
            return c;
        }
    }
#endif
}

.ctrmv(a, x, [uplo: 'U', trans:'N', diag:'U', order:'R']) ⇒ Numo::SComplex

CTRMV performs one of the matrix-vector operations

  x := A*x,   or   x := A**T*x,   or   x := A**H*x,

where x is an n element vector and A is an n by n unit, or non-unit, upper or lower triangular matrix.

Parameters:

  • a (Numo::SComplex)

    matrix (>=2-dimentional NArray).

  • x (Numo::SComplex)

    vector (>=1-dimentional NArray).

  • alpha (Float)

    (default=1.0)

  • beta (Float)

    (default=0.0)

  • side (String or Symbol)

    if ‘L’: op(A)*B (left-side op), if ‘R’: B*op(A) (right-side op). (default=’L’)

  • uplo (String or Symbol)

    if ‘U’: Upper triangle, if ‘L’: Lower triangle. (default=’U’)

  • trans (String or Symbol)

    if ‘N’: Not transpose , if ‘T’: Transpose . (default=’N’)

  • order (String or Symbol)

    if ‘R’: Row-major, if ‘C’: Column-major. (default=’R’)

Returns:

  • (Numo::SComplex)

    returns y = alpha*op(A)*x + beta*y.



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# File 'ext/numo/linalg/blas/blas_c.c', line 915

static VALUE
blas_s_ctrmv(int argc, VALUE const argv[], VALUE UNUSED(mod))
{
    VALUE     a, x, y=Qnil, alpha, beta;
    narray_t *na1, *na2;
    blasint   ma, na, nx;
#if GE
    blasint   tmp;
#endif
    size_t    shape[1];
    ndfunc_arg_in_t ain[4] = {{cT,2},{cT,1},{OVERWRITE,1},{sym_init,0}};
    ndfunc_arg_out_t aout[1] = {{cT,1,shape}};
    ndfunc_t ndf = {iter_blas_s_ctrmv, NO_LOOP, 3, 0, ain, aout};

    args_t g;
    VALUE kw_hash = Qnil;
#if GE
    ID kw_table[4] = {id_alpha,id_beta,id_order,id_trans};
#elif TR
    ID kw_table[6] = {id_alpha,id_beta,id_order,id_uplo,id_trans,id_diag};
#else
    ID kw_table[4] = {id_alpha,id_beta,id_order,id_uplo};
#endif
    VALUE opts[6] = {Qundef,Qundef,Qundef,Qundef,Qundef,Qundef};

    CHECK_FUNC(func_p,"ctrmv");

    rb_scan_args(argc, argv, "21:", &a, &x, &y, &kw_hash);
    rb_get_kwargs(kw_hash, kw_table, 0, 4+2*TR, opts);
    alpha   = option_value(opts[0],Qnil);
    g.alpha = RTEST(alpha) ? m_num_to_data(alpha) : m_one;
    beta    = option_value(opts[1],Qnil);
    g.beta  = RTEST(beta)  ? m_num_to_data(beta)  : m_zero;
    g.order = option_order(opts[2]);
#if GE
    g.trans = option_trans(opts[3]);
#else
    g.uplo  = option_uplo(opts[3]);
#endif
#if TR
    g.trans = option_trans(opts[4]);
    g.diag  = option_diag(opts[5]);
#endif

    GetNArray(a,na1);
    CHECK_DIM_GE(na1,2);
    ma = ROW_SIZE(na1);
    na = COL_SIZE(na1);

    GetNArray(x,na2);
    CHECK_DIM_GE(na2,1);
    nx = COL_SIZE(na2);
#if GE
    SWAP_IFCOL(g.order, ma, na, tmp);
    g.m = ma;
    g.n = na;
    SWAP_IFTRANS(g.trans, ma, na, tmp);
#else
    CHECK_SQUARE("a",na1);
#endif
    CHECK_INT_EQ("na",na,"nx",nx);
    shape[0] = ma;

#if TR
    if (y != Qnil) {
        rb_raise(rb_eArgError,"wrong number of arguments (3 for 2)");
    }
    COPY_OR_CAST_TO(x,cT);
    ndf.nin = 2;
    na_ndloop3(&ndf, &g, 2, a, x);
    return x;

#else // GE,SY,HE

    if (y == Qnil) { // c is not given.
        ndf.nout = 1;
        ain[2] = ain[3];
        y = INT2FIX(0);
        shape[0] = ma;
    } else {
        narray_t *na3;
        COPY_OR_CAST_TO(y,cT);
        GetNArray(y,na3);
        CHECK_DIM_GE(na3,1);
        CHECK_SIZE_GE(na3,nx);
    }
    {
        VALUE ans;
        ans = na_ndloop3(&ndf, &g, 3, a, x, y);

        if (ndf.nout == 1) { // c is not given.
            return ans;
        } else {
            return y;
        }
    }
#endif
}

.dasum(x) ⇒ Numo::DFloat

DASUM takes the sum of the absolute values.

Parameters:

  • x (Numo::DFloat)

    vector (>=1-dimentional NArray).

  • keepdims (String or Symbol)

Returns:

  • (Numo::DFloat)

    euclidean norm of x



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# File 'ext/numo/linalg/blas/blas_d.c', line 226

static VALUE
blas_s_dasum(int argc, VALUE const argv[], VALUE UNUSED(mod))
{
    VALUE     x, keepdims, ans;
    narray_t *na1;
    ndfunc_arg_in_t ain[1] = {{cT,1}};
    ndfunc_arg_out_t aout[1] = {{cT,0}};
    ndfunc_t ndf = {iter_blas_s_dasum, NDF_EXTRACT, 1,1, ain,aout};

    VALUE opts[1] = {Qundef};
    ID    kw_table[1] = {id_keepdims};
    VALUE kw_hash = Qnil;

    CHECK_FUNC(func_p,"dasum");

    rb_scan_args(argc, argv, "1:", &x, &kw_hash);
    rb_get_kwargs(kw_hash, kw_table, 0, 1, opts);
    keepdims = option_value(opts[0],Qfalse);

    if (RTEST(keepdims)) {
        ndf.flag |= NDF_KEEP_DIM;
    }

    GetNArray(x,na1);
    CHECK_DIM_GE(na1,1);
    CHECK_NON_EMPTY(na1);

    ans = na_ndloop(&ndf, 1, x);

    return ans;
}

.daxpy(x, y, [alpha: 1]) ⇒ Numo::DFloat

DAXPY constant times a vector plus a vector. uses unrolled loops for increments equal to one.

Parameters:

  • x (Numo::DFloat)

    vector (>=1-dimentional NArray).

  • y (Numo::DFloat)

    vector (>=1-dimentional NArray, inplace allowed).

  • alpha (Float)

    (default=1.0)

Returns:

  • (Numo::DFloat)

    y = alpha * x + y



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# File 'ext/numo/linalg/blas/blas_d.c', line 413

static VALUE
blas_s_daxpy(int argc, VALUE const argv[], VALUE UNUSED(mod))
{
    VALUE x, y, alpha;
    narray_t *na1, *na2;
    ndfunc_arg_in_t ain[2] = {{cT,0},{OVERWRITE,0}};
    ndfunc_t ndf = {iter_blas_s_daxpy, STRIDE_LOOP, 2, 0, ain, 0};

    dtype g;
    VALUE kw_hash = Qnil;
    ID kw_table[1] = {id_alpha};
    VALUE opts[1] = {Qundef};

    CHECK_FUNC(func_p,"daxpy");

    rb_scan_args(argc, argv, "2:", &x, &y, &kw_hash);
    rb_get_kwargs(kw_hash, kw_table, 0, 1, opts);
    alpha = option_value(opts[0],Qnil);
    g     = RTEST(alpha) ? m_num_to_data(alpha) : m_one;

    COPY_OR_CAST_TO(y,cT);
    GetNArray(x,na1);
    GetNArray(y,na2);
    CHECK_DIM_GE(na1,1);
    CHECK_DIM_GE(na2,1);
    CHECK_NON_EMPTY(na1);
    CHECK_NON_EMPTY(na2);
    CHECK_SAME_SHAPE(na1,na2);

    na_ndloop3(&ndf, &g, 2, x, y);
    return y;
}

.dcopy(x, y) ⇒ nil

DCOPY copies a vector, x, to a vector, y. uses unrolled loops for increments equal to one.

Parameters:

  • x (Numo::DFloat)

    vector (>=1-dimentional NArray).

  • y (Numo::DFloat)

    vector (>=1-dimentional NArray).

Returns:

  • (nil)


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# File 'ext/numo/linalg/blas/blas_d.c', line 348

static VALUE
blas_s_dcopy(VALUE UNUSED(mod), VALUE x, VALUE y)
{
    narray_t *na1, *na2;
    ndfunc_arg_in_t ain[2] = {{cT,0},{OVERWRITE,0}};
    ndfunc_t ndf = {iter_blas_s_dcopy, STRIDE_LOOP, 2,0, ain,0};

    CHECK_FUNC(func_p,"dcopy");

    CHECK_NARRAY_TYPE(x,cT);
    CHECK_NARRAY_TYPE(y,cT);
    GetNArray(x,na1);
    GetNArray(y,na2);
    CHECK_DIM_GE(na1,1);
    CHECK_DIM_GE(na2,1);
    CHECK_NON_EMPTY(na1);
    CHECK_NON_EMPTY(na2);
    CHECK_SAME_SHAPE(na1,na2);

    na_ndloop(&ndf, 2, x, y);

    return Qnil;
}

.ddot(x, y) ⇒ Numo::DFloat

DDOT forms the dot product of two vectors. uses unrolled loops for increments equal to one.

Parameters:

  • x (Numo::DFloat)

    vector (>=1-dimentional NArray).

  • y (Numo::DFloat)

    vector (>=1-dimentional NArray).

Returns:

  • (Numo::DFloat)

    op(x) dot y



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# File 'ext/numo/linalg/blas/blas_d.c', line 95

static VALUE
blas_s_ddot(VALUE mod, VALUE x, VALUE y)
{
    VALUE     ans;
    narray_t *na1, *na2;
    size_t    nx, ny, shape[1]={1};
    ndfunc_arg_in_t ain[2] = {{cT,1},{cT,1}};
    ndfunc_arg_out_t aout[1] = {{numo_cDFloat,0,shape}};
    ndfunc_t ndf = {iter_blas_s_ddot, NDF_EXTRACT, 2,1, ain,aout};

    CHECK_FUNC(func_p,"ddot");

    GetNArray(x,na1);
    GetNArray(y,na2);
    CHECK_DIM_GE(na1,1);
    CHECK_DIM_GE(na2,1);
    CHECK_NON_EMPTY(na1);
    CHECK_NON_EMPTY(na2);
    nx = COL_SIZE(na1);
    ny = COL_SIZE(na2);
    CHECK_SIZE_EQ(nx,ny);

    ans = na_ndloop(&ndf, 2, x, y);

    return ans;
}

.dgemm(a, b, [c, alpha: 1, beta:0, transa:'N', transb:'N', order:'R']) ⇒ Numo::DFloat

DGEMM performs one of the matrix-matrix operations

  C := alpha*op( A )*op( B ) + beta*C,

where op( X ) is one of

  op( X ) = X   or   op( X ) = X**T,

alpha and beta are scalars, and A, B and C are matrices, with op( A ) an m by k matrix, op( B ) a k by n matrix and C an m by n matrix.

Parameters:

  • a (Numo::DFloat)

    matrix (>=2-dimentional NArray).

  • b (Numo::DFloat)

    matrix (>=2-dimentional NArray).

  • c (Numo::DFloat)

    matrix (>=2-dimentional NArray, optional, inplace allowed).

  • alpha (Float)

    (default=1.0)

  • beta (Float)

    (default=0.0)

  • transa (String or Symbol)

    if ‘N’: Not transpose a, if ‘T’: Transpose a. (default=’N’)

  • transb (String or Symbol)

    if ‘N’: Not transpose b, if ‘T’: Transpose b. (default=’N’)

  • order (String or Symbol)

    if ‘R’: Row-major, if ‘C’: Column-major. (default=’R’)

Returns:

  • (Numo::DFloat)

    returns c = alpha*op( A )*op( B ) + beta*C.



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# File 'ext/numo/linalg/blas/blas_d.c', line 1642

static VALUE
blas_s_dgemm(int argc, VALUE const argv[], VALUE UNUSED(mod))
{
    VALUE     a, b, c=Qnil, alpha, beta;
    narray_t *na1, *na2;
    blasint   ma, ka, kb, nb, tmp;
    size_t    shape[2];
    ndfunc_arg_in_t ain[3] = {{cT,2},{cT,2},{OVERWRITE,2}};
    ndfunc_arg_out_t aout[1] = {{cT,2,shape}};
    ndfunc_t ndf = {iter_blas_s_dgemm, NO_LOOP, 3, 0, ain, aout};

    args_t g;
    VALUE kw_hash = Qnil;
#if GE
    ID kw_table[5] = {id_alpha,id_beta,id_order,id_transa,id_transb};
#elif TR
    ID kw_table[7] = {id_alpha,id_beta,id_order,id_side,id_uplo,id_transa,id_diag};
#else
    ID kw_table[5] = {id_alpha,id_beta,id_order,id_side,id_uplo};
#endif
    VALUE opts[7] = {Qundef,Qundef,Qundef,Qundef,Qundef,Qundef,Qundef};

    CHECK_FUNC(func_p,"dgemm");

    rb_scan_args(argc, argv, "21:", &a, &b, &c, &kw_hash);
    rb_get_kwargs(kw_hash, kw_table, 0, 5+TR*2, opts);
    alpha    = option_value(opts[0],Qnil);
    g.alpha  = RTEST(alpha) ? m_num_to_data(alpha) : m_one;
    beta     = option_value(opts[1],Qnil);
    g.beta   = RTEST(beta)  ? m_num_to_data(beta)  : m_zero;
    g.order  = option_order(opts[2]);
#if GE
    g.transa = option_trans(opts[3]);
    g.transb = option_trans(opts[4]);
#else
    g.side   = option_side(opts[3]);
    g.uplo   = option_uplo(opts[4]);
#endif
#if TR
    g.transa = option_trans(opts[5]);
    g.diag   = option_diag(opts[6]);
#endif

    GetNArray(a,na1);
    GetNArray(b,na2);
    CHECK_DIM_GE(na1,2);
    CHECK_DIM_GE(na2,2);
    ma = ROW_SIZE(na1); // m
    ka = COL_SIZE(na1); // k (lda)
    kb = ROW_SIZE(na2); // k
    nb = COL_SIZE(na2); // n (ldb)

#if GE
    SWAP_IFCOLTR(g.order,g.transa, ma,ka, tmp);
    SWAP_IFCOLTR(g.order,g.transb, kb,nb, tmp);
    CHECK_INT_EQ("ka",ka,"kb",kb);
    g.m = ma;
    g.n = nb;
    g.k = ka;
#else
    CHECK_SQUARE("a",na1); // ma == ka
    SWAP_IFCOL(g.order, kb,nb, tmp);
    // row major             L    R
    //ma = ROW_SIZE(na1); // m or n
    //ka = COL_SIZE(na1); // m or n (lda)
    g.m = kb; // m
    g.n = nb; // n (ldb)
    if (g.side == CblasLeft) {
        CHECK_SIZE_EQ(ka, g.m);
    } else {
        CHECK_SIZE_EQ(ka, g.n);
    }
#endif

    SWAP_IFROW(g.order, ma,nb, tmp);

#if TR
    if (c != Qnil) {
        rb_raise(rb_eArgError,"wrong number of arguments (3 for 2)");
    }
    COPY_OR_CAST_TO(b,cT);
    ndf.nin = 2;

    na_ndloop3(&ndf, &g, 2, a, b);
    return b;
#else

    if (c == Qnil) { // c is not given.
        ndfunc_arg_in_t ain_init = {sym_init,0};
        ain[2] = ain_init;
        ndf.nout = 1;
        c = INT2FIX(0);
        shape[0] = nb;
        shape[1] = ma;
    } else {
        narray_t *na3;
        int nc;
        COPY_OR_CAST_TO(c,cT);
        GetNArray(c,na3);
        CHECK_DIM_GE(na3,2);
        nc = ROW_SIZE(na3);
        if (nc < nb) {
            rb_raise(nary_eShapeError,"nc=%d must be >= nb=%d",nc,nb);
        }
        //CHECK_LEADING_GE("ldc",g.ldc,"m",ma);
    }
    {
        VALUE ans = na_ndloop3(&ndf, &g, 3, a, b, c);

        if (ndf.nout == 1) { // c is not given.
            return ans;
        } else {
            return c;
        }
    }
#endif
}

.dgemv(a, x, [y, alpha: 1, beta:0, trans:'N', order:'R']) ⇒ Numo::DFloat

DGEMV performs one of the matrix-vector operations

  y := alpha*A*x + beta*y,   or   y := alpha*A**T*x + beta*y,

where alpha and beta are scalars, x and y are vectors and A is an m by n matrix.

Parameters:

  • a (Numo::DFloat)

    matrix (>=2-dimentional NArray).

  • x (Numo::DFloat)

    vector (>=1-dimentional NArray).

  • y (Numo::DFloat)

    vector (>=1-dimentional NArray, optional, inplace allowed).

  • alpha (Float)

    (default=1.0)

  • beta (Float)

    (default=0.0)

  • trans (String or Symbol)

    if ‘N’: Not transpose , if ‘T’: Transpose . (default=’N’)

  • order (String or Symbol)

    if ‘R’: Row-major, if ‘C’: Column-major. (default=’R’)

Returns:

  • (Numo::DFloat)

    returns y = alpha*op(A)*x + beta*y.



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# File 'ext/numo/linalg/blas/blas_d.c', line 741

static VALUE
blas_s_dgemv(int argc, VALUE const argv[], VALUE UNUSED(mod))
{
    VALUE     a, x, y=Qnil, alpha, beta;
    narray_t *na1, *na2;
    blasint   ma, na, nx;
#if GE
    blasint   tmp;
#endif
    size_t    shape[1];
    ndfunc_arg_in_t ain[4] = {{cT,2},{cT,1},{OVERWRITE,1},{sym_init,0}};
    ndfunc_arg_out_t aout[1] = {{cT,1,shape}};
    ndfunc_t ndf = {iter_blas_s_dgemv, NO_LOOP, 3, 0, ain, aout};

    args_t g;
    VALUE kw_hash = Qnil;
#if GE
    ID kw_table[4] = {id_alpha,id_beta,id_order,id_trans};
#elif TR
    ID kw_table[6] = {id_alpha,id_beta,id_order,id_uplo,id_trans,id_diag};
#else
    ID kw_table[4] = {id_alpha,id_beta,id_order,id_uplo};
#endif
    VALUE opts[6] = {Qundef,Qundef,Qundef,Qundef,Qundef,Qundef};

    CHECK_FUNC(func_p,"dgemv");

    rb_scan_args(argc, argv, "21:", &a, &x, &y, &kw_hash);
    rb_get_kwargs(kw_hash, kw_table, 0, 4+2*TR, opts);
    alpha   = option_value(opts[0],Qnil);
    g.alpha = RTEST(alpha) ? m_num_to_data(alpha) : m_one;
    beta    = option_value(opts[1],Qnil);
    g.beta  = RTEST(beta)  ? m_num_to_data(beta)  : m_zero;
    g.order = option_order(opts[2]);
#if GE
    g.trans = option_trans(opts[3]);
#else
    g.uplo  = option_uplo(opts[3]);
#endif
#if TR
    g.trans = option_trans(opts[4]);
    g.diag  = option_diag(opts[5]);
#endif

    GetNArray(a,na1);
    CHECK_DIM_GE(na1,2);
    ma = ROW_SIZE(na1);
    na = COL_SIZE(na1);

    GetNArray(x,na2);
    CHECK_DIM_GE(na2,1);
    nx = COL_SIZE(na2);
#if GE
    SWAP_IFCOL(g.order, ma, na, tmp);
    g.m = ma;
    g.n = na;
    SWAP_IFTRANS(g.trans, ma, na, tmp);
#else
    CHECK_SQUARE("a",na1);
#endif
    CHECK_INT_EQ("na",na,"nx",nx);
    shape[0] = ma;

#if TR
    if (y != Qnil) {
        rb_raise(rb_eArgError,"wrong number of arguments (3 for 2)");
    }
    COPY_OR_CAST_TO(x,cT);
    ndf.nin = 2;
    na_ndloop3(&ndf, &g, 2, a, x);
    return x;

#else // GE,SY,HE

    if (y == Qnil) { // c is not given.
        ndf.nout = 1;
        ain[2] = ain[3];
        y = INT2FIX(0);
        shape[0] = ma;
    } else {
        narray_t *na3;
        COPY_OR_CAST_TO(y,cT);
        GetNArray(y,na3);
        CHECK_DIM_GE(na3,1);
        CHECK_SIZE_GE(na3,nx);
    }
    {
        VALUE ans;
        ans = na_ndloop3(&ndf, &g, 3, a, x, y);

        if (ndf.nout == 1) { // c is not given.
            return ans;
        } else {
            return y;
        }
    }
#endif
}

.dger(x, y, [a, alpha: 1, order:'R']) ⇒ Numo::DFloat

DGER performs the rank 1 operation

  A := alpha*x*y**T + A,

where alpha is a scalar, x is an m element vector, y is an n element vector and A is an m by n matrix.

Parameters:

  • x (Numo::DFloat)

    vector (>=1-dimentional NArray).

  • y (Numo::DFloat)

    vector (>=1-dimentional NArray).

  • a (Numo::DFloat)

    matrix (>=2-dimentional NArray, m-by-n symmetric matrix, optional, inplace allowed).

  • alpha (Float)

    (default=1.0)

  • order (String or Symbol)

    if ‘R’: Row-major, if ‘C’: Column-major. (default=’R’)

Returns:

  • (Numo::DFloat)

    returns a.



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# File 'ext/numo/linalg/blas/blas_d.c', line 1378

static VALUE
blas_s_dger(int argc, VALUE const argv[], VALUE UNUSED(mod))
{
    VALUE     ans;
    VALUE     x, y, a=Qnil, alpha;
    narray_t *na1, *na2;
    blasint   mx, ny, tmp;
    size_t    shape[2];
    ndfunc_arg_in_t ain[4] = {{cT,1},{cT,1},{OVERWRITE,2},{sym_init,0}};
    ndfunc_arg_out_t aout[1] = {{cT,2,shape}};
    ndfunc_t ndf = {iter_blas_s_dger, NO_LOOP, 3, 0, ain, aout};

    args_t g;
    VALUE kw_hash = Qnil;
    ID kw_table[2] = {id_alpha,id_order};
    VALUE opts[2] = {Qundef};

    CHECK_FUNC(func_p,"dger");

    rb_scan_args(argc, argv, "21:", &x, &y, &a, &kw_hash);
    rb_get_kwargs(kw_hash, kw_table, 0, 2, opts);
    alpha   = option_value(opts[0],Qnil);
    g.alpha = RTEST(alpha) ? m_num_to_data(alpha) : m_one;
    g.order = option_order(opts[1]);

    GetNArray(x,na1);
    GetNArray(y,na2);
    CHECK_DIM_GE(na1,1);
    CHECK_DIM_GE(na2,1);
    mx = COL_SIZE(na1); // m
    ny = COL_SIZE(na2); // n
    g.m = mx;
    g.n = ny;

    SWAP_IFCOL(g.order, mx,ny, tmp);

    if (a == Qnil) { // c is not given.
        ndf.nout = 1;
        ain[2] = ain[3];
        a = INT2FIX(0);
        shape[0] = mx;
        shape[1] = ny;
    } else {
        narray_t  *na3;
        blasint    ma, na;
        COPY_OR_CAST_TO(a,cT);
        GetNArray(a,na3);
        CHECK_DIM_GE(na3,2);
        ma = ROW_SIZE(na3); // m
        na = COL_SIZE(na3); // n (lda)
        CHECK_SIZE_EQ(ma,mx);
        CHECK_SIZE_EQ(na,ny);
    }

    ans = na_ndloop3(&ndf, &g, 3, x, y, a);

    if (ndf.nout = 1) { // a is not given.
        return ans;
    } else {
        return a;
    }
}

.dlopen(*args) ⇒ Object



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# File 'ext/numo/linalg/blas/blas.c', line 288

static VALUE
blas_s_dlopen(int argc, VALUE *argv, VALUE mod)
{
    int i, f;
    VALUE lib, flag;
    char *error;
    void *handle;

    i = rb_scan_args(argc, argv, "11", &lib, &flag);
    if (i==2) {
        f = NUM2INT(flag);
    } else {
        f = RTLD_LAZY;
    }
#if defined(HAVE_DLFCN_H)
    dlerror();
#endif
    handle = dlopen(StringValueCStr(lib), f);
#if defined(HAVE_DLFCN_H)
    if ( !handle && (error = dlerror()) ) {
        rb_raise(rb_eRuntimeError, "%s", error);
    }
#else
    if ( !handle ) {
        error = dlerror();
        rb_raise(rb_eRuntimeError, "%s", error);
    }
#endif
    blas_handle = handle;
    return Qnil;
}

.dnrm2(x) ⇒ Numo::DFloat

DNRM2 returns the euclidean norm of a vector via the function name, so that

  DNRM2 := sqrt( x'*x )

Parameters:

  • x (Numo::DFloat)

    vector (>=1-dimentional NArray).

  • keepdims (String or Symbol)

Returns:

  • (Numo::DFloat)

    euclidean norm of x



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# File 'ext/numo/linalg/blas/blas_d.c', line 159

static VALUE
blas_s_dnrm2(int argc, VALUE const argv[], VALUE UNUSED(mod))
{
    VALUE     x, keepdims, ans;
    narray_t *na1;
    ndfunc_arg_in_t ain[1] = {{cT,1}};
    ndfunc_arg_out_t aout[1] = {{cT,0}};
    ndfunc_t ndf = {iter_blas_s_dnrm2, NDF_EXTRACT, 1,1, ain,aout};

    VALUE opts[1] = {Qundef};
    ID    kw_table[1] = {id_keepdims};
    VALUE kw_hash = Qnil;

    CHECK_FUNC(func_p,"dnrm2");

    rb_scan_args(argc, argv, "1:", &x, &kw_hash);
    rb_get_kwargs(kw_hash, kw_table, 0, 1, opts);
    keepdims = option_value(opts[0],Qfalse);

    if (RTEST(keepdims)) {
        ndf.flag |= NDF_KEEP_DIM;
    }

    GetNArray(x,na1);
    CHECK_DIM_GE(na1,1);
    CHECK_NON_EMPTY(na1);

    ans = na_ndloop(&ndf, 1, x);

    return ans;
}

.drot(x, y, c, s) ⇒ Array<Numo::DFloat,Numo::DFloat>

DROT applies a plane rotation.

Parameters:

  • x (Numo::DFloat)

    vector (>=1-dimentional NArray, inplace allowed).

  • y (Numo::DFloat)

    vector (>=1-dimentional NArray, inplace allowed).

  • c (Float)
  • s (Float)

Returns:

  • (Array<Numo::DFloat,Numo::DFloat>)

    returns [x,y]



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# File 'ext/numo/linalg/blas/blas_d.c', line 483

static VALUE
blas_s_drot(VALUE UNUSED(mod), VALUE x, VALUE y, VALUE c, VALUE s)
{
    rtype g[2] = {0,0};
    narray_t *na1, *na2;
    ndfunc_arg_in_t ain[2] = {{OVERWRITE,0},{OVERWRITE,0}};
    ndfunc_t ndf = {iter_blas_s_drot, STRIDE_LOOP, 2,0, ain,0};

    CHECK_FUNC(func_p,"drot");

    if (RTEST(c)) {g[0] = NUM2DBL(c);}
    if (RTEST(s)) {g[1] = NUM2DBL(s);}

    COPY_OR_CAST_TO(x,cT);
    COPY_OR_CAST_TO(y,cT);
    GetNArray(x,na1);
    GetNArray(y,na2);
    CHECK_DIM_GE(na1,1);
    CHECK_DIM_GE(na2,1);
    CHECK_NON_EMPTY(na1);
    CHECK_NON_EMPTY(na2);
    CHECK_SAME_SHAPE(na1,na2);

    na_ndloop3(&ndf, g, 2, x, y);

    return rb_assoc_new(x,y);
}

.drotm(x, y, param) ⇒ Array<Numo::DFloat,Numo::DFloat>

Apply the modified givens transformation, H, to the 2 by N matrix (X**T), where **T indicates transpose. The elements of X are in (Y**T)

X(LX+I*INCX), I = 0 to N-1, where LX = 1 if INCX .GE. 0, else LX = (-INCX)*N, and similarly for Y using LY and INCY. With PARAM(1)=FLAG, H has one of the following forms..

  FLAG=-1.0     FLAG=0.0        FLAG=1.0     FLAG=-2.0

    (H11  H12)    (1.0  H12)    (H11  1.0)    (1.0  0.0)
  H=(        )    (        )    (        )    (        )
    (H21  H22),   (H21  1.0),   (-1.0 H22),   (0.0  1.0).

see DROTMG for a description of data storage in param.

Parameters:

  • x (Numo::DFloat)

    vector (>=1-dimentional NArray, inplace allowed).

  • y (Numo::DFloat)

    vector (>=1-dimentional NArray, inplace allowed).

  • param (Numo::DFloat)

    array of [FLAG,H11,H21,H12,H22]

Returns:

  • (Array<Numo::DFloat,Numo::DFloat>)

    returns [x,y]



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# File 'ext/numo/linalg/blas/blas_d.c', line 560

static VALUE
blas_s_drotm(VALUE UNUSED(mod), VALUE x, VALUE y, VALUE param)
{
    dtype *g;
    narray_t *na1, *na2, *nap;
    ndfunc_arg_in_t ain[2] = {{OVERWRITE,0},{OVERWRITE,0}};
    ndfunc_t ndf = {iter_blas_s_drotm, STRIDE_LOOP, 2,0, ain,0};

    CHECK_FUNC(func_p,"drotm");

    COPY_OR_CAST_TO(x,cT);
    COPY_OR_CAST_TO(y,cT);
    GetNArray(x,na1);
    GetNArray(y,na2);
    CHECK_DIM_GE(na1,1);
    CHECK_DIM_GE(na2,1);
    CHECK_NON_EMPTY(na1);
    CHECK_NON_EMPTY(na2);
    CHECK_SAME_SHAPE(na1,na2);

    param = rb_funcall(cT,rb_intern("cast"),1,param);
    GetNArray(param,nap);
    CHECK_DIM_EQ(nap,1);
    CHECK_SIZE_GE(nap,5);
    g = (dtype*)nary_get_pointer_for_read(param);

    na_ndloop3(&ndf, g, 2, x, y);

    RB_GC_GUARD(param);
    return rb_assoc_new(x,y);
}

.dscal(a, x) ⇒ Numo::DFloat

DSCAL scales a vector by a constant. uses unrolled loops for increment equal to one.

Parameters:

  • a (Float)

    scale factor

  • x (Numo::DFloat)

    vector (>=1-dimentional NArray).

Returns:

  • (Numo::DFloat)

    returns a*x.



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# File 'ext/numo/linalg/blas/blas_d.c', line 632

static VALUE
blas_s_dscal(VALUE mod, VALUE a, VALUE x)
{
    scal_t g[1];
    narray_t *na1;
    ndfunc_arg_in_t ain[1] = {{OVERWRITE,0}};
    ndfunc_t ndf = {iter_blas_s_dscal, STRIDE_LOOP, 1,0, ain,0};

    CHECK_FUNC(func_p,"dscal");

  
#line 56 "gen/../tmpl/scal.c"
    if (RTEST(a)) {g[0] = m_num_to_data(a);} else {g[0]=m_one;}
  
    COPY_OR_CAST_TO(x,cT);
    GetNArray(x,na1);
    CHECK_DIM_GE(na1,1);
    CHECK_NON_EMPTY(na1);

    na_ndloop3(&ndf, g, 1, x);

    return x;
}

.dsdot(x, y) ⇒ Numo::DFloat

Compute the inner product of two vectors with extended precision accumulation and result. Returns D.P. dot product accumulated in D.P., for S.P. SX and SY DSDOT = sum for I = 0 to N-1 of SX(LX+I*INCX) * SY(LY+I*INCY), where LX = 1 if INCX .GE. 0, else LX = 1+(1-N)*INCX, and LY is defined in a similar way using INCY.

Parameters:

  • x (Numo::DFloat)

    vector (>=1-dimentional NArray).

  • y (Numo::DFloat)

    vector (>=1-dimentional NArray).

Returns:

  • (Numo::DFloat)

    op(x) dot y



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# File 'ext/numo/linalg/blas/blas_s.c', line 303

static VALUE
blas_s_dsdot(VALUE mod, VALUE x, VALUE y)
{
    VALUE     ans;
    narray_t *na1, *na2;
    size_t    nx, ny, shape[1]={1};
    ndfunc_arg_in_t ain[2] = {{cT,1},{cT,1}};
    ndfunc_arg_out_t aout[1] = {{numo_cDFloat,0,shape}};
    ndfunc_t ndf = {iter_blas_s_dsdot, NDF_EXTRACT, 2,1, ain,aout};

    CHECK_FUNC(func_p,"dsdot");

    GetNArray(x,na1);
    GetNArray(y,na2);
    CHECK_DIM_GE(na1,1);
    CHECK_DIM_GE(na2,1);
    CHECK_NON_EMPTY(na1);
    CHECK_NON_EMPTY(na2);
    nx = COL_SIZE(na1);
    ny = COL_SIZE(na2);
    CHECK_SIZE_EQ(nx,ny);

    ans = na_ndloop(&ndf, 2, x, y);

    return ans;
}

.dswap(x, y) ⇒ nil

interchanges two vectors. uses unrolled loops for increments equal one.

Parameters:

  • x (Numo::DFloat)

    vector (>=1-dimentional NArray).

  • y (Numo::DFloat)

    vector (>=1-dimentional NArray).

Returns:

  • (nil)


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# File 'ext/numo/linalg/blas/blas_d.c', line 291

static VALUE
blas_s_dswap(VALUE UNUSED(mod), VALUE x, VALUE y)
{
    narray_t *na1, *na2;
    ndfunc_arg_in_t ain[2] = {{OVERWRITE,0},{OVERWRITE,0}};
    ndfunc_t ndf = {iter_blas_s_dswap, STRIDE_LOOP, 2,0, ain,0};

    CHECK_FUNC(func_p,"dswap");

    CHECK_NARRAY_TYPE(x,cT);
    CHECK_NARRAY_TYPE(y,cT);
    GetNArray(x,na1);
    GetNArray(y,na2);
    CHECK_DIM_GE(na1,1);
    CHECK_DIM_GE(na2,1);
    CHECK_NON_EMPTY(na1);
    CHECK_NON_EMPTY(na2);
    CHECK_SAME_SHAPE(na1,na2);

    na_ndloop(&ndf, 2, x, y);

    return Qnil;
}

.dsymm(a, b, [c, alpha: 1, beta:0, side:'L', uplo:'U', order:'R']) ⇒ Numo::DFloat

DSYMM performs one of the matrix-matrix operations

  C := alpha*A*B + beta*C,

or

  C := alpha*B*A + beta*C,

where alpha and beta are scalars, A is a symmetric matrix and B and C are m by n matrices.

Parameters:

  • a (Numo::DFloat)

    matrix (>=2-dimentional NArray).

  • b (Numo::DFloat)

    matrix (>=2-dimentional NArray).

  • c (Numo::DFloat)

    matrix (>=2-dimentional NArray, optional, inplace allowed).

  • alpha (Float)

    (default=1.0)

  • beta (Float)

    (default=0.0)

  • side (String or Symbol)

    if ‘L’: op(A)*B (left-side op), if ‘R’: B*op(A) (right-side op). (default=’L’)

  • uplo (String or Symbol)

    if ‘U’: Upper triangle, if ‘L’: Lower triangle. (default=’U’)

  • order (String or Symbol)

    if ‘R’: Row-major, if ‘C’: Column-major. (default=’R’)

Returns:

  • (Numo::DFloat)

    returns c = alpha*op( A )*op( B ) + beta*C.



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# File 'ext/numo/linalg/blas/blas_d.c', line 1849

static VALUE
blas_s_dsymm(int argc, VALUE const argv[], VALUE UNUSED(mod))
{
    VALUE     a, b, c=Qnil, alpha, beta;
    narray_t *na1, *na2;
    blasint   ma, ka, kb, nb, tmp;
    size_t    shape[2];
    ndfunc_arg_in_t ain[3] = {{cT,2},{cT,2},{OVERWRITE,2}};
    ndfunc_arg_out_t aout[1] = {{cT,2,shape}};
    ndfunc_t ndf = {iter_blas_s_dsymm, NO_LOOP, 3, 0, ain, aout};

    args_t g;
    VALUE kw_hash = Qnil;
#if GE
    ID kw_table[5] = {id_alpha,id_beta,id_order,id_transa,id_transb};
#elif TR
    ID kw_table[7] = {id_alpha,id_beta,id_order,id_side,id_uplo,id_transa,id_diag};
#else
    ID kw_table[5] = {id_alpha,id_beta,id_order,id_side,id_uplo};
#endif
    VALUE opts[7] = {Qundef,Qundef,Qundef,Qundef,Qundef,Qundef,Qundef};

    CHECK_FUNC(func_p,"dsymm");

    rb_scan_args(argc, argv, "21:", &a, &b, &c, &kw_hash);
    rb_get_kwargs(kw_hash, kw_table, 0, 5+TR*2, opts);
    alpha    = option_value(opts[0],Qnil);
    g.alpha  = RTEST(alpha) ? m_num_to_data(alpha) : m_one;
    beta     = option_value(opts[1],Qnil);
    g.beta   = RTEST(beta)  ? m_num_to_data(beta)  : m_zero;
    g.order  = option_order(opts[2]);
#if GE
    g.transa = option_trans(opts[3]);
    g.transb = option_trans(opts[4]);
#else
    g.side   = option_side(opts[3]);
    g.uplo   = option_uplo(opts[4]);
#endif
#if TR
    g.transa = option_trans(opts[5]);
    g.diag   = option_diag(opts[6]);
#endif

    GetNArray(a,na1);
    GetNArray(b,na2);
    CHECK_DIM_GE(na1,2);
    CHECK_DIM_GE(na2,2);
    ma = ROW_SIZE(na1); // m
    ka = COL_SIZE(na1); // k (lda)
    kb = ROW_SIZE(na2); // k
    nb = COL_SIZE(na2); // n (ldb)

#if GE
    SWAP_IFCOLTR(g.order,g.transa, ma,ka, tmp);
    SWAP_IFCOLTR(g.order,g.transb, kb,nb, tmp);
    CHECK_INT_EQ("ka",ka,"kb",kb);
    g.m = ma;
    g.n = nb;
    g.k = ka;
#else
    CHECK_SQUARE("a",na1); // ma == ka
    SWAP_IFCOL(g.order, kb,nb, tmp);
    // row major             L    R
    //ma = ROW_SIZE(na1); // m or n
    //ka = COL_SIZE(na1); // m or n (lda)
    g.m = kb; // m
    g.n = nb; // n (ldb)
    if (g.side == CblasLeft) {
        CHECK_SIZE_EQ(ka, g.m);
    } else {
        CHECK_SIZE_EQ(ka, g.n);
    }
#endif

    SWAP_IFROW(g.order, ma,nb, tmp);

#if TR
    if (c != Qnil) {
        rb_raise(rb_eArgError,"wrong number of arguments (3 for 2)");
    }
    COPY_OR_CAST_TO(b,cT);
    ndf.nin = 2;

    na_ndloop3(&ndf, &g, 2, a, b);
    return b;
#else

    if (c == Qnil) { // c is not given.
        ndfunc_arg_in_t ain_init = {sym_init,0};
        ain[2] = ain_init;
        ndf.nout = 1;
        c = INT2FIX(0);
        shape[0] = nb;
        shape[1] = ma;
    } else {
        narray_t *na3;
        int nc;
        COPY_OR_CAST_TO(c,cT);
        GetNArray(c,na3);
        CHECK_DIM_GE(na3,2);
        nc = ROW_SIZE(na3);
        if (nc < nb) {
            rb_raise(nary_eShapeError,"nc=%d must be >= nb=%d",nc,nb);
        }
        //CHECK_LEADING_GE("ldc",g.ldc,"m",ma);
    }
    {
        VALUE ans = na_ndloop3(&ndf, &g, 3, a, b, c);

        if (ndf.nout == 1) { // c is not given.
            return ans;
        } else {
            return c;
        }
    }
#endif
}

.dsymv(a, x, [y, alpha: 1, beta:0, uplo:'U', order:'R']) ⇒ Numo::DFloat

DSYMV performs the matrix-vector operation

  y := alpha*A*x + beta*y,

where alpha and beta are scalars, x and y are n element vectors and A is an n by n symmetric matrix.

Parameters:

  • a (Numo::DFloat)

    matrix (>=2-dimentional NArray).

  • x (Numo::DFloat)

    vector (>=1-dimentional NArray).

  • y (Numo::DFloat)

    vector (>=1-dimentional NArray, optional, inplace allowed).

  • alpha (Float)

    (default=1.0)

  • beta (Float)

    (default=0.0)

  • side (String or Symbol)

    if ‘L’: op(A)*B (left-side op), if ‘R’: B*op(A) (right-side op). (default=’L’)

  • uplo (String or Symbol)

    if ‘U’: Upper triangle, if ‘L’: Lower triangle. (default=’U’)

  • order (String or Symbol)

    if ‘R’: Row-major, if ‘C’: Column-major. (default=’R’)

Returns:

  • (Numo::DFloat)

    returns y = alpha*op(A)*x + beta*y.



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# File 'ext/numo/linalg/blas/blas_d.c', line 1115

static VALUE
blas_s_dsymv(int argc, VALUE const argv[], VALUE UNUSED(mod))
{
    VALUE     a, x, y=Qnil, alpha, beta;
    narray_t *na1, *na2;
    blasint   ma, na, nx;
#if GE
    blasint   tmp;
#endif
    size_t    shape[1];
    ndfunc_arg_in_t ain[4] = {{cT,2},{cT,1},{OVERWRITE,1},{sym_init,0}};
    ndfunc_arg_out_t aout[1] = {{cT,1,shape}};
    ndfunc_t ndf = {iter_blas_s_dsymv, NO_LOOP, 3, 0, ain, aout};

    args_t g;
    VALUE kw_hash = Qnil;
#if GE
    ID kw_table[4] = {id_alpha,id_beta,id_order,id_trans};
#elif TR
    ID kw_table[6] = {id_alpha,id_beta,id_order,id_uplo,id_trans,id_diag};
#else
    ID kw_table[4] = {id_alpha,id_beta,id_order,id_uplo};
#endif
    VALUE opts[6] = {Qundef,Qundef,Qundef,Qundef,Qundef,Qundef};

    CHECK_FUNC(func_p,"dsymv");

    rb_scan_args(argc, argv, "21:", &a, &x, &y, &kw_hash);
    rb_get_kwargs(kw_hash, kw_table, 0, 4+2*TR, opts);
    alpha   = option_value(opts[0],Qnil);
    g.alpha = RTEST(alpha) ? m_num_to_data(alpha) : m_one;
    beta    = option_value(opts[1],Qnil);
    g.beta  = RTEST(beta)  ? m_num_to_data(beta)  : m_zero;
    g.order = option_order(opts[2]);
#if GE
    g.trans = option_trans(opts[3]);
#else
    g.uplo  = option_uplo(opts[3]);
#endif
#if TR
    g.trans = option_trans(opts[4]);
    g.diag  = option_diag(opts[5]);
#endif

    GetNArray(a,na1);
    CHECK_DIM_GE(na1,2);
    ma = ROW_SIZE(na1);
    na = COL_SIZE(na1);

    GetNArray(x,na2);
    CHECK_DIM_GE(na2,1);
    nx = COL_SIZE(na2);
#if GE
    SWAP_IFCOL(g.order, ma, na, tmp);
    g.m = ma;
    g.n = na;
    SWAP_IFTRANS(g.trans, ma, na, tmp);
#else
    CHECK_SQUARE("a",na1);
#endif
    CHECK_INT_EQ("na",na,"nx",nx);
    shape[0] = ma;

#if TR
    if (y != Qnil) {
        rb_raise(rb_eArgError,"wrong number of arguments (3 for 2)");
    }
    COPY_OR_CAST_TO(x,cT);
    ndf.nin = 2;
    na_ndloop3(&ndf, &g, 2, a, x);
    return x;

#else // GE,SY,HE

    if (y == Qnil) { // c is not given.
        ndf.nout = 1;
        ain[2] = ain[3];
        y = INT2FIX(0);
        shape[0] = ma;
    } else {
        narray_t *na3;
        COPY_OR_CAST_TO(y,cT);
        GetNArray(y,na3);
        CHECK_DIM_GE(na3,1);
        CHECK_SIZE_GE(na3,nx);
    }
    {
        VALUE ans;
        ans = na_ndloop3(&ndf, &g, 3, a, x, y);

        if (ndf.nout == 1) { // c is not given.
            return ans;
        } else {
            return y;
        }
    }
#endif
}

.dsyr(x, [a, alpha: 1, uplo:'U', order:'R']) ⇒ Numo::DFloat

DSYR performs the symmetric rank 1 operation

  A := alpha*x*x**T + A,

where alpha is a real scalar, x is an n element vector and A is an n by n symmetric matrix.

Parameters:

  • x (Numo::DFloat)

    vector (>=1-dimentional NArray).

  • a (Numo::DFloat)

    matrix (>=2-dimentional NArray, inplace allowed).

  • alpha (Float)

    (default=1.0)

  • uplo (String or Symbol)

    if ‘U’: Upper triangle, if ‘L’: Lower triangle. (default=’U’)

  • order (String or Symbol)

    if ‘R’: Row-major, if ‘C’: Column-major. (default=’R’)

Returns:

  • (Numo::DFloat)

    return a



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# File 'ext/numo/linalg/blas/blas_d.c', line 1269

static VALUE
blas_s_dsyr(int argc, VALUE const argv[], VALUE UNUSED(mod))
{
    VALUE     ans;
    VALUE     x, a, alpha;
    narray_t *na1, *na3;
    blasint   nx, na;
    size_t    shape[2];
    ndfunc_arg_in_t ain[3] = {{cT,1},{OVERWRITE,2},{sym_init,0}};
    ndfunc_arg_out_t aout[1] = {{cT,2,shape}};
    ndfunc_t ndf = {iter_blas_s_dsyr, NO_LOOP, 2, 0, ain, aout};

    args_t g;
    VALUE kw_hash = Qnil;
    ID kw_table[3] = {id_alpha,id_order,id_uplo};
    VALUE opts[3] = {Qundef,Qundef,Qundef};

    CHECK_FUNC(func_p,"dsyr");

    rb_scan_args(argc, argv, "11:", &x, &a, &kw_hash);
    rb_get_kwargs(kw_hash, kw_table, 0, 3, opts);
    alpha   = option_value(opts[0],Qnil);
    g.alpha = RTEST(alpha) ? NUM2DBL(alpha) : 1;
    g.order = option_order(opts[1]);
    g.uplo  = option_uplo(opts[2]);

    GetNArray(x,na1);
    CHECK_DIM_GE(na1,1);
    nx = COL_SIZE(na1); // n

    if (a == Qnil) { // c is not given.
        ndf.nout = 1;
        ain[1] = ain[2];
        a = INT2FIX(0);
        shape[0] = shape[1] = nx;
    } else {
        COPY_OR_CAST_TO(a,cT);
        GetNArray(a,na3);
        CHECK_DIM_GE(na3,2);
        CHECK_SQUARE("a",na3);
        na = COL_SIZE(na3); // n (lda)
        CHECK_SIZE_EQ(na,nx);
    }

    ans = na_ndloop3(&ndf, &g, 2, x, a);

    if (ndf.nout == 1) { // a is not given.
        return ans;
    } else {
        return a;
    }
}

.dsyr2(x, y, [a, alpha: 1, uplo:'U', order:'R']) ⇒ Numo::DFloat

DSYR2 performs the symmetric rank 2 operation

  A := alpha*x*y**T + alpha*y*x**T + A,

where alpha is a scalar, x and y are n element vectors and A is an n by n symmetric matrix.

Parameters:

  • x (Numo::DFloat)

    vector (>=1-dimentional NArray).

  • y (Numo::DFloat)

    vector (>=1-dimentional NArray).

  • a (Numo::DFloat)

    matrix (>=2-dimentional NArray, inplace allowed).

  • alpha (Float)

    (default=1.0)

  • uplo (String or Symbol)

    if ‘U’: Upper triangle, if ‘L’: Lower triangle. (default=’U’)

  • order (String or Symbol)

    if ‘R’: Row-major, if ‘C’: Column-major. (default=’R’)

Returns:

  • (Numo::DFloat)

    returns a.



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# File 'ext/numo/linalg/blas/blas_d.c', line 1498

static VALUE
blas_s_dsyr2(int argc, VALUE const argv[], VALUE UNUSED(mod))
{
    VALUE     ans;
    VALUE     x, y, a, alpha;
    narray_t *na1, *na2, *na3;
    blasint   nx, ny, na;
    size_t    shape[2];
    ndfunc_arg_in_t ain[4] = {{cT,1},{cT,1},{OVERWRITE,2},{sym_init,0}};
    ndfunc_arg_out_t aout[1] = {{cT,2,shape}};
    ndfunc_t ndf = {iter_blas_s_dsyr2, NO_LOOP, 3, 0, ain, aout};

    args_t g;
    VALUE kw_hash = Qnil;
    ID kw_table[3] = {id_alpha,id_order,id_uplo};
    VALUE opts[3] = {Qundef,Qundef,Qundef};

    CHECK_FUNC(func_p,"dsyr2");

    rb_scan_args(argc, argv, "21:", &x, &y, &a, &kw_hash);
    rb_get_kwargs(kw_hash, kw_table, 0, 3, opts);
    alpha   = option_value(opts[0],Qnil);
    g.alpha = RTEST(alpha) ? m_num_to_data(alpha) : m_one;
    g.order = option_order(opts[1]);
    g.uplo  = option_uplo(opts[2]);

    GetNArray(x,na1);
    GetNArray(y,na2);
    CHECK_DIM_GE(na1,1);
    CHECK_DIM_GE(na2,1);
    nx = COL_SIZE(na1); // n
    ny = COL_SIZE(na2); // n
    CHECK_INT_EQ("nx",nx,"ny",ny);

    if (a == Qnil) { // c is not given.
        ndf.nout = 1;
        ain[2] = ain[3];
        a = INT2FIX(0);
        shape[0] = shape[1] = nx;
    } else {
        COPY_OR_CAST_TO(a,cT);
        GetNArray(a,na3);
        CHECK_DIM_GE(na3,2);
        CHECK_SQUARE("a",na3);
        na = COL_SIZE(na3); // n (lda)
        CHECK_SIZE_EQ(na,nx);
    }

    ans = na_ndloop3(&ndf, &g, 3, x, y, a);

    if (ndf.nout == 1) { // a is not given.
        return ans;
    } else {
        return a;
    }
}

.dsyr2k(a, b, [c, alpha: 1, beta:0, uplo:'U', trans:'N', order:'R']) ⇒ Numo::DFloat

DSYR2K performs one of the symmetric rank 2k operations

  C := alpha*A*B**T + alpha*B*A**T + beta*C,

or

  C := alpha*A**T*B + alpha*B**T*A + beta*C,

where alpha and beta are scalars, C is an n by n symmetric matrix and A and B are n by k matrices in the first case and k by n matrices in the second case.

Parameters:

  • a (Numo::DFloat)

    matrix (>=2-dimentional NArray, n-by-k).

  • b (Numo::DFloat)

    matrix (>=2-dimentional NArray, n-by-k).

  • c (Numo::DFloat)

    matrix (>=2-dimentional NArray, n-by-n, optional, inpace).

  • alpha (Float)

    (default=1.0)

  • beta (Float)

    (default=0.0)

  • uplo (String or Symbol)

    if ‘U’: Upper triangle, if ‘L’: Lower triangle. (default=’U’)

  • trans (String or Symbol)

    if ‘N’: Not transpose , if ‘T’: Transpose . (default=’N’)

  • order (String or Symbol)

    if ‘R’: Row-major, if ‘C’: Column-major. (default=’R’)

Returns:

  • (Numo::DFloat)

    returns c.



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# File 'ext/numo/linalg/blas/blas_d.c', line 2371

static VALUE
blas_s_dsyr2k(int argc, VALUE const argv[], VALUE UNUSED(mod))
{
    VALUE     ans;
    VALUE     a, b, c=Qnil, alpha, beta;
    narray_t *na1, *na2, *na3;
    blasint   na, ka, kb, nb, nc, tmp;
    size_t    shape[2];
    ndfunc_arg_in_t ain[4] = {{cT,2},{cT,2},{OVERWRITE,2},{sym_init,0}};
    ndfunc_arg_out_t aout[1] = {{cT,2,shape}};
    ndfunc_t ndf = {iter_blas_s_dsyr2k, NO_LOOP, 3, 0, ain, aout};

    args_t g;
    VALUE kw_hash = Qnil;
    ID kw_table[5] = {id_alpha,id_beta,id_order,id_uplo,id_trans};
    VALUE opts[5] = {Qundef,Qundef,Qundef,Qundef,Qundef};

    CHECK_FUNC(func_p,"dsyr2k");

    rb_scan_args(argc, argv, "21:", &a, &b, &c, &kw_hash);
    rb_get_kwargs(kw_hash, kw_table, 0, 5, opts);
    alpha    = option_value(opts[0],Qnil);
    g.alpha  = RTEST(alpha) ? m_num_to_data(alpha) : m_one;
    beta     = option_value(opts[1],Qnil);
    g.beta   = RTEST(beta)  ? m_num_to_data(beta)  : m_zero;
    g.order  = option_order(opts[2]);
    g.uplo   = option_uplo(opts[3]);
    g.trans  = option_trans(opts[4]);

    GetNArray(a,na1);
    GetNArray(b,na2);
    CHECK_DIM_GE(na1,2);
    CHECK_DIM_GE(na2,2);

    na = ROW_SIZE(na1); // n
    ka = COL_SIZE(na1); // k (lda)
    SWAP_IFCOLTR(g.order, g.trans, na, ka, tmp);

    nb = ROW_SIZE(na2); // n
    kb = COL_SIZE(na2); // k (ldb)
    SWAP_IFCOLTR(g.order, g.trans, kb, nb, tmp);
    CHECK_INT_EQ("na",na,"nb",nb);
    CHECK_INT_EQ("ka",ka,"kb",kb);
    g.n = nb;
    g.k = kb;

    SWAP_IFROW(g.order, na, nb, tmp);

    if (c == Qnil) { // c is not given.
        ndf.nout = 1;
        ain[2] = ain[3];
        c = INT2FIX(0);
        shape[0] = nb;
        shape[1] = na;
    } else {
        COPY_OR_CAST_TO(c,cT);
        GetNArray(c,na3);
        CHECK_DIM_GE(na3,2);
        nc = ROW_SIZE(na3); // n
        if (nc < nb) {
            rb_raise(nary_eShapeError,"nc=%d must be >= nb=%d",nc,nb);
        }
        //CHECK_LEADING_GE("ldc",g.ldc,"n",na);
    }

    ans = na_ndloop3(&ndf, &g, 3, a, b, c);

    if (ndf.nout = 1) { // c is not given.
        return ans;
    } else {
        return c;
    }
}

.dsyrk(a, [c, alpha: 1, beta:0, uplo:'U', trans:'N', order:'R']) ⇒ Numo::DFloat

DSYRK performs one of the symmetric rank k operations

  C := alpha*A*A**T + beta*C,

or

  C := alpha*A**T*A + beta*C,

where alpha and beta are scalars, C is an n by n symmetric matrix and A is an n by k matrix in the first case and a k by n matrix in the second case.

Parameters:

  • a (Numo::DFloat)

    matrix (>=2-dimentional NArray, n-by-k, inpace).

  • c (Numo::DFloat)

    matrix (>=2-dimentional NArray, n-by-n, optional, inpace).

  • alpha (Float)

    (default=1.0)

  • beta (Float)

    (default=0.0)

  • uplo (String or Symbol)

    if ‘U’: Upper triangle, if ‘L’: Lower triangle. (default=’U’)

  • trans (String or Symbol)

    if ‘N’: Not transpose , if ‘T’: Transpose . (default=’N’)

  • order (String or Symbol)

    if ‘R’: Row-major, if ‘C’: Column-major. (default=’R’)

Returns:

  • (Numo::DFloat)

    returns c.



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# File 'ext/numo/linalg/blas/blas_d.c', line 2240

static VALUE
blas_s_dsyrk(int argc, VALUE const argv[], VALUE UNUSED(mod))
{
    VALUE     ans;
    VALUE     a, c, alpha, beta;
    narray_t *na1, *na3;
    blasint   na, ka, nc, tmp;
    size_t    shape[2];
    ndfunc_arg_in_t ain[3] = {{cT,2},{OVERWRITE,2},{sym_init,0}};
    ndfunc_arg_out_t aout[1] = {{cT,2,shape}};
    ndfunc_t ndf = {iter_blas_s_dsyrk, NO_LOOP, 2, 0, ain, aout};

    args_t g;
    VALUE kw_hash = Qnil;
    ID kw_table[5] = {id_alpha,id_beta,id_order,id_uplo,id_trans};
    VALUE opts[5] = {Qundef,Qundef,Qundef,Qundef,Qundef};

    CHECK_FUNC(func_p,"dsyrk");

    rb_scan_args(argc, argv, "11:", &a, &c, &kw_hash);
    rb_get_kwargs(kw_hash, kw_table, 0, 5, opts);
    alpha   = option_value(opts[0],Qnil);
    beta    = option_value(opts[1],Qnil);
#line 88 "gen/../tmpl/syrk.c"
    g.alpha = RTEST(alpha) ? m_num_to_data(alpha) : m_one;
    g.beta  = RTEST(beta)  ? m_num_to_data(beta)  : m_zero;
#line 91 "gen/../tmpl/syrk.c"
    g.order = option_order(opts[2]);
    g.uplo  = option_uplo(opts[3]);
    g.trans = option_trans(opts[4]);

    GetNArray(a,na1);
    CHECK_DIM_GE(na1,2);

    na = ROW_SIZE(na1); // n
    ka = COL_SIZE(na1); // k (lda)
    SWAP_IFCOLTR(g.order,g.trans, na,ka, tmp);
    g.n = na;
    g.k = ka;

    if (c == Qnil) { // c is not given.
        ndf.nout = 1;
        ain[1] = ain[2];
        c = INT2FIX(0);
        shape[0] = na;
        shape[1] = na;
    } else {
        COPY_OR_CAST_TO(c,cT);
        GetNArray(c,na3);
        CHECK_DIM_GE(na3,2);
        nc = ROW_SIZE(na3);
        if (nc < na) {
            rb_raise(nary_eShapeError,"nc=%d must be >= na=%d",nc,na);
        }
        //CHECK_LEADING_GE("ldc",g.ldc,"n",na);
    }

    ans = na_ndloop3(&ndf, &g, 2, a, c);

    if (ndf.nout == 1) { // c is not given.
        return ans;
    } else {
        return c;
    }
}

.dtrmm(a, b, [alpha: 1, side:'L', uplo:'U', transa:'N', diag:'U', order:'R']) ⇒ Numo::DFloat

DTRMM performs one of the matrix-matrix operations

  B := alpha*op( A )*B,   or   B := alpha*B*op( A ),

where alpha is a scalar, B is an m by n matrix, A is a unit, or non-unit, upper or lower triangular matrix and op( A ) is one of

  op( A ) = A   or   op( A ) = A**T.

Parameters:

  • a (Numo::DFloat)

    matrix (>=2-dimentional NArray).

  • b (Numo::DFloat)

    matrix (>=2-dimentional NArray).

  • alpha (Float)

    (default=1.0)

  • beta (Float)

    (default=0.0)

  • side (String or Symbol)

    if ‘L’: op(A)*B (left-side op), if ‘R’: B*op(A) (right-side op). (default=’L’)

  • uplo (String or Symbol)

    if ‘U’: Upper triangle, if ‘L’: Lower triangle. (default=’U’)

  • transa (String or Symbol)

    if ‘N’: Not transpose a, if ‘T’: Transpose a. (default=’N’)

  • order (String or Symbol)

    if ‘R’: Row-major, if ‘C’: Column-major. (default=’R’)

Returns:

  • (Numo::DFloat)

    returns c = alpha*op( A )*op( B ) + beta*C.



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# File 'ext/numo/linalg/blas/blas_d.c', line 2054

static VALUE
blas_s_dtrmm(int argc, VALUE const argv[], VALUE UNUSED(mod))
{
    VALUE     a, b, c=Qnil, alpha, beta;
    narray_t *na1, *na2;
    blasint   ma, ka, kb, nb, tmp;
    size_t    shape[2];
    ndfunc_arg_in_t ain[3] = {{cT,2},{cT,2},{OVERWRITE,2}};
    ndfunc_arg_out_t aout[1] = {{cT,2,shape}};
    ndfunc_t ndf = {iter_blas_s_dtrmm, NO_LOOP, 3, 0, ain, aout};

    args_t g;
    VALUE kw_hash = Qnil;
#if GE
    ID kw_table[5] = {id_alpha,id_beta,id_order,id_transa,id_transb};
#elif TR
    ID kw_table[7] = {id_alpha,id_beta,id_order,id_side,id_uplo,id_transa,id_diag};
#else
    ID kw_table[5] = {id_alpha,id_beta,id_order,id_side,id_uplo};
#endif
    VALUE opts[7] = {Qundef,Qundef,Qundef,Qundef,Qundef,Qundef,Qundef};

    CHECK_FUNC(func_p,"dtrmm");

    rb_scan_args(argc, argv, "21:", &a, &b, &c, &kw_hash);
    rb_get_kwargs(kw_hash, kw_table, 0, 5+TR*2, opts);
    alpha    = option_value(opts[0],Qnil);
    g.alpha  = RTEST(alpha) ? m_num_to_data(alpha) : m_one;
    beta     = option_value(opts[1],Qnil);
    g.beta   = RTEST(beta)  ? m_num_to_data(beta)  : m_zero;
    g.order  = option_order(opts[2]);
#if GE
    g.transa = option_trans(opts[3]);
    g.transb = option_trans(opts[4]);
#else
    g.side   = option_side(opts[3]);
    g.uplo   = option_uplo(opts[4]);
#endif
#if TR
    g.transa = option_trans(opts[5]);
    g.diag   = option_diag(opts[6]);
#endif

    GetNArray(a,na1);
    GetNArray(b,na2);
    CHECK_DIM_GE(na1,2);
    CHECK_DIM_GE(na2,2);
    ma = ROW_SIZE(na1); // m
    ka = COL_SIZE(na1); // k (lda)
    kb = ROW_SIZE(na2); // k
    nb = COL_SIZE(na2); // n (ldb)

#if GE
    SWAP_IFCOLTR(g.order,g.transa, ma,ka, tmp);
    SWAP_IFCOLTR(g.order,g.transb, kb,nb, tmp);
    CHECK_INT_EQ("ka",ka,"kb",kb);
    g.m = ma;
    g.n = nb;
    g.k = ka;
#else
    CHECK_SQUARE("a",na1); // ma == ka
    SWAP_IFCOL(g.order, kb,nb, tmp);
    // row major             L    R
    //ma = ROW_SIZE(na1); // m or n
    //ka = COL_SIZE(na1); // m or n (lda)
    g.m = kb; // m
    g.n = nb; // n (ldb)
    if (g.side == CblasLeft) {
        CHECK_SIZE_EQ(ka, g.m);
    } else {
        CHECK_SIZE_EQ(ka, g.n);
    }
#endif

    SWAP_IFROW(g.order, ma,nb, tmp);

#if TR
    if (c != Qnil) {
        rb_raise(rb_eArgError,"wrong number of arguments (3 for 2)");
    }
    COPY_OR_CAST_TO(b,cT);
    ndf.nin = 2;

    na_ndloop3(&ndf, &g, 2, a, b);
    return b;
#else

    if (c == Qnil) { // c is not given.
        ndfunc_arg_in_t ain_init = {sym_init,0};
        ain[2] = ain_init;
        ndf.nout = 1;
        c = INT2FIX(0);
        shape[0] = nb;
        shape[1] = ma;
    } else {
        narray_t *na3;
        int nc;
        COPY_OR_CAST_TO(c,cT);
        GetNArray(c,na3);
        CHECK_DIM_GE(na3,2);
        nc = ROW_SIZE(na3);
        if (nc < nb) {
            rb_raise(nary_eShapeError,"nc=%d must be >= nb=%d",nc,nb);
        }
        //CHECK_LEADING_GE("ldc",g.ldc,"m",ma);
    }
    {
        VALUE ans = na_ndloop3(&ndf, &g, 3, a, b, c);

        if (ndf.nout == 1) { // c is not given.
            return ans;
        } else {
            return c;
        }
    }
#endif
}

.dtrmv(a, x, [uplo: 'U', trans:'N', diag:'U', order:'R']) ⇒ Numo::DFloat

DTRMV performs one of the matrix-vector operations

  x := A*x,   or   x := A**T*x,

where x is an n element vector and A is an n by n unit, or non-unit, upper or lower triangular matrix.

Parameters:

  • a (Numo::DFloat)

    matrix (>=2-dimentional NArray).

  • x (Numo::DFloat)

    vector (>=1-dimentional NArray).

  • alpha (Float)

    (default=1.0)

  • beta (Float)

    (default=0.0)

  • side (String or Symbol)

    if ‘L’: op(A)*B (left-side op), if ‘R’: B*op(A) (right-side op). (default=’L’)

  • uplo (String or Symbol)

    if ‘U’: Upper triangle, if ‘L’: Lower triangle. (default=’U’)

  • trans (String or Symbol)

    if ‘N’: Not transpose , if ‘T’: Transpose . (default=’N’)

  • order (String or Symbol)

    if ‘R’: Row-major, if ‘C’: Column-major. (default=’R’)

Returns:

  • (Numo::DFloat)

    returns y = alpha*op(A)*x + beta*y.



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# File 'ext/numo/linalg/blas/blas_d.c', line 928

static VALUE
blas_s_dtrmv(int argc, VALUE const argv[], VALUE UNUSED(mod))
{
    VALUE     a, x, y=Qnil, alpha, beta;
    narray_t *na1, *na2;
    blasint   ma, na, nx;
#if GE
    blasint   tmp;
#endif
    size_t    shape[1];
    ndfunc_arg_in_t ain[4] = {{cT,2},{cT,1},{OVERWRITE,1},{sym_init,0}};
    ndfunc_arg_out_t aout[1] = {{cT,1,shape}};
    ndfunc_t ndf = {iter_blas_s_dtrmv, NO_LOOP, 3, 0, ain, aout};

    args_t g;
    VALUE kw_hash = Qnil;
#if GE
    ID kw_table[4] = {id_alpha,id_beta,id_order,id_trans};
#elif TR
    ID kw_table[6] = {id_alpha,id_beta,id_order,id_uplo,id_trans,id_diag};
#else
    ID kw_table[4] = {id_alpha,id_beta,id_order,id_uplo};
#endif
    VALUE opts[6] = {Qundef,Qundef,Qundef,Qundef,Qundef,Qundef};

    CHECK_FUNC(func_p,"dtrmv");

    rb_scan_args(argc, argv, "21:", &a, &x, &y, &kw_hash);
    rb_get_kwargs(kw_hash, kw_table, 0, 4+2*TR, opts);
    alpha   = option_value(opts[0],Qnil);
    g.alpha = RTEST(alpha) ? m_num_to_data(alpha) : m_one;
    beta    = option_value(opts[1],Qnil);
    g.beta  = RTEST(beta)  ? m_num_to_data(beta)  : m_zero;
    g.order = option_order(opts[2]);
#if GE
    g.trans = option_trans(opts[3]);
#else
    g.uplo  = option_uplo(opts[3]);
#endif
#if TR
    g.trans = option_trans(opts[4]);
    g.diag  = option_diag(opts[5]);
#endif

    GetNArray(a,na1);
    CHECK_DIM_GE(na1,2);
    ma = ROW_SIZE(na1);
    na = COL_SIZE(na1);

    GetNArray(x,na2);
    CHECK_DIM_GE(na2,1);
    nx = COL_SIZE(na2);
#if GE
    SWAP_IFCOL(g.order, ma, na, tmp);
    g.m = ma;
    g.n = na;
    SWAP_IFTRANS(g.trans, ma, na, tmp);
#else
    CHECK_SQUARE("a",na1);
#endif
    CHECK_INT_EQ("na",na,"nx",nx);
    shape[0] = ma;

#if TR
    if (y != Qnil) {
        rb_raise(rb_eArgError,"wrong number of arguments (3 for 2)");
    }
    COPY_OR_CAST_TO(x,cT);
    ndf.nin = 2;
    na_ndloop3(&ndf, &g, 2, a, x);
    return x;

#else // GE,SY,HE

    if (y == Qnil) { // c is not given.
        ndf.nout = 1;
        ain[2] = ain[3];
        y = INT2FIX(0);
        shape[0] = ma;
    } else {
        narray_t *na3;
        COPY_OR_CAST_TO(y,cT);
        GetNArray(y,na3);
        CHECK_DIM_GE(na3,1);
        CHECK_SIZE_GE(na3,nx);
    }
    {
        VALUE ans;
        ans = na_ndloop3(&ndf, &g, 3, a, x, y);

        if (ndf.nout == 1) { // c is not given.
            return ans;
        } else {
            return y;
        }
    }
#endif
}

.dzasum(x) ⇒ Numo::DFloat

DZASUM takes the sum of the (|Re(.)| + |Im(.)|)’s of a complex vector and returns a single precision result.

Parameters:

  • x (Numo::DComplex)

    vector (>=1-dimentional NArray).

  • keepdims (String or Symbol)

Returns:

  • (Numo::DFloat)

    euclidean norm of x



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# File 'ext/numo/linalg/blas/blas_z.c', line 297

static VALUE
blas_s_dzasum(int argc, VALUE const argv[], VALUE UNUSED(mod))
{
    VALUE     x, keepdims, ans;
    narray_t *na1;
    ndfunc_arg_in_t ain[1] = {{cT,1}};
    ndfunc_arg_out_t aout[1] = {{cRT,0}};
    ndfunc_t ndf = {iter_blas_s_dzasum, NDF_EXTRACT, 1,1, ain,aout};

    VALUE opts[1] = {Qundef};
    ID    kw_table[1] = {id_keepdims};
    VALUE kw_hash = Qnil;

    CHECK_FUNC(func_p,"dzasum");

    rb_scan_args(argc, argv, "1:", &x, &kw_hash);
    rb_get_kwargs(kw_hash, kw_table, 0, 1, opts);
    keepdims = option_value(opts[0],Qfalse);

    if (RTEST(keepdims)) {
        ndf.flag |= NDF_KEEP_DIM;
    }

    GetNArray(x,na1);
    CHECK_DIM_GE(na1,1);
    CHECK_NON_EMPTY(na1);

    ans = na_ndloop(&ndf, 1, x);

    return ans;
}

.dznrm2(x) ⇒ Numo::DFloat

DZNRM2 returns the euclidean norm of a vector via the function name, so that

  DZNRM2 := sqrt( x**H*x )

Parameters:

  • x (Numo::DComplex)

    vector (>=1-dimentional NArray).

  • keepdims (String or Symbol)

Returns:

  • (Numo::DFloat)

    euclidean norm of x



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# File 'ext/numo/linalg/blas/blas_z.c', line 229

static VALUE
blas_s_dznrm2(int argc, VALUE const argv[], VALUE UNUSED(mod))
{
    VALUE     x, keepdims, ans;
    narray_t *na1;
    ndfunc_arg_in_t ain[1] = {{cT,1}};
    ndfunc_arg_out_t aout[1] = {{cRT,0}};
    ndfunc_t ndf = {iter_blas_s_dznrm2, NDF_EXTRACT, 1,1, ain,aout};

    VALUE opts[1] = {Qundef};
    ID    kw_table[1] = {id_keepdims};
    VALUE kw_hash = Qnil;

    CHECK_FUNC(func_p,"dznrm2");

    rb_scan_args(argc, argv, "1:", &x, &kw_hash);
    rb_get_kwargs(kw_hash, kw_table, 0, 1, opts);
    keepdims = option_value(opts[0],Qfalse);

    if (RTEST(keepdims)) {
        ndf.flag |= NDF_KEEP_DIM;
    }

    GetNArray(x,na1);
    CHECK_DIM_GE(na1,1);
    CHECK_NON_EMPTY(na1);

    ans = na_ndloop(&ndf, 1, x);

    return ans;
}

.prefix=(prefix) ⇒ Object



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# File 'ext/numo/linalg/blas/blas.c', line 321

static VALUE
blas_s_prefix_set(VALUE mod, VALUE prefix)
{
    long len;

    if (TYPE(prefix) != T_STRING) {
        rb_raise(rb_eTypeError,"argument must be string");
    }
    if (blas_prefix) {
        free(blas_prefix);
    }
    len = RSTRING_LEN(prefix);
    blas_prefix = malloc(len+1);
    strcpy(blas_prefix, StringValueCStr(prefix));
    return prefix;
}

.sasum(x) ⇒ Numo::SFloat

SASUM takes the sum of the absolute values. uses unrolled loops for increment equal to one.

Parameters:

  • x (Numo::SFloat)

    vector (>=1-dimentional NArray).

  • keepdims (String or Symbol)

Returns:

  • (Numo::SFloat)

    euclidean norm of x



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# File 'ext/numo/linalg/blas/blas_s.c', line 227

static VALUE
blas_s_sasum(int argc, VALUE const argv[], VALUE UNUSED(mod))
{
    VALUE     x, keepdims, ans;
    narray_t *na1;
    ndfunc_arg_in_t ain[1] = {{cT,1}};
    ndfunc_arg_out_t aout[1] = {{cT,0}};
    ndfunc_t ndf = {iter_blas_s_sasum, NDF_EXTRACT, 1,1, ain,aout};

    VALUE opts[1] = {Qundef};
    ID    kw_table[1] = {id_keepdims};
    VALUE kw_hash = Qnil;

    CHECK_FUNC(func_p,"sasum");

    rb_scan_args(argc, argv, "1:", &x, &kw_hash);
    rb_get_kwargs(kw_hash, kw_table, 0, 1, opts);
    keepdims = option_value(opts[0],Qfalse);

    if (RTEST(keepdims)) {
        ndf.flag |= NDF_KEEP_DIM;
    }

    GetNArray(x,na1);
    CHECK_DIM_GE(na1,1);
    CHECK_NON_EMPTY(na1);

    ans = na_ndloop(&ndf, 1, x);

    return ans;
}

.saxpy(x, y, [alpha: 1]) ⇒ Numo::SFloat

SAXPY constant times a vector plus a vector. uses unrolled loops for increments equal to one.

Parameters:

  • x (Numo::SFloat)

    vector (>=1-dimentional NArray).

  • y (Numo::SFloat)

    vector (>=1-dimentional NArray, inplace allowed).

  • alpha (Float)

    (default=1.0)

Returns:

  • (Numo::SFloat)

    y = alpha * x + y



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# File 'ext/numo/linalg/blas/blas_s.c', line 560

static VALUE
blas_s_saxpy(int argc, VALUE const argv[], VALUE UNUSED(mod))
{
    VALUE x, y, alpha;
    narray_t *na1, *na2;
    ndfunc_arg_in_t ain[2] = {{cT,0},{OVERWRITE,0}};
    ndfunc_t ndf = {iter_blas_s_saxpy, STRIDE_LOOP, 2, 0, ain, 0};

    dtype g;
    VALUE kw_hash = Qnil;
    ID kw_table[1] = {id_alpha};
    VALUE opts[1] = {Qundef};

    CHECK_FUNC(func_p,"saxpy");

    rb_scan_args(argc, argv, "2:", &x, &y, &kw_hash);
    rb_get_kwargs(kw_hash, kw_table, 0, 1, opts);
    alpha = option_value(opts[0],Qnil);
    g     = RTEST(alpha) ? m_num_to_data(alpha) : m_one;

    COPY_OR_CAST_TO(y,cT);
    GetNArray(x,na1);
    GetNArray(y,na2);
    CHECK_DIM_GE(na1,1);
    CHECK_DIM_GE(na2,1);
    CHECK_NON_EMPTY(na1);
    CHECK_NON_EMPTY(na2);
    CHECK_SAME_SHAPE(na1,na2);

    na_ndloop3(&ndf, &g, 2, x, y);
    return y;
}

.scasum(x) ⇒ Numo::SFloat

SCASUM takes the sum of the (|Re(.)| + |Im(.)|)’s of a complex vector and returns a single precision result.

Parameters:

  • x (Numo::SComplex)

    vector (>=1-dimentional NArray).

  • keepdims (String or Symbol)

Returns:

  • (Numo::SFloat)

    euclidean norm of x



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# File 'ext/numo/linalg/blas/blas_c.c', line 297

static VALUE
blas_s_scasum(int argc, VALUE const argv[], VALUE UNUSED(mod))
{
    VALUE     x, keepdims, ans;
    narray_t *na1;
    ndfunc_arg_in_t ain[1] = {{cT,1}};
    ndfunc_arg_out_t aout[1] = {{cRT,0}};
    ndfunc_t ndf = {iter_blas_s_scasum, NDF_EXTRACT, 1,1, ain,aout};

    VALUE opts[1] = {Qundef};
    ID    kw_table[1] = {id_keepdims};
    VALUE kw_hash = Qnil;

    CHECK_FUNC(func_p,"scasum");

    rb_scan_args(argc, argv, "1:", &x, &kw_hash);
    rb_get_kwargs(kw_hash, kw_table, 0, 1, opts);
    keepdims = option_value(opts[0],Qfalse);

    if (RTEST(keepdims)) {
        ndf.flag |= NDF_KEEP_DIM;
    }

    GetNArray(x,na1);
    CHECK_DIM_GE(na1,1);
    CHECK_NON_EMPTY(na1);

    ans = na_ndloop(&ndf, 1, x);

    return ans;
}

.scnrm2(x) ⇒ Numo::SFloat

SCNRM2 returns the euclidean norm of a vector via the function name, so that

  SCNRM2 := sqrt( x**H*x )

Parameters:

  • x (Numo::SComplex)

    vector (>=1-dimentional NArray).

  • keepdims (String or Symbol)

Returns:

  • (Numo::SFloat)

    euclidean norm of x



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# File 'ext/numo/linalg/blas/blas_c.c', line 229

static VALUE
blas_s_scnrm2(int argc, VALUE const argv[], VALUE UNUSED(mod))
{
    VALUE     x, keepdims, ans;
    narray_t *na1;
    ndfunc_arg_in_t ain[1] = {{cT,1}};
    ndfunc_arg_out_t aout[1] = {{cRT,0}};
    ndfunc_t ndf = {iter_blas_s_scnrm2, NDF_EXTRACT, 1,1, ain,aout};

    VALUE opts[1] = {Qundef};
    ID    kw_table[1] = {id_keepdims};
    VALUE kw_hash = Qnil;

    CHECK_FUNC(func_p,"scnrm2");

    rb_scan_args(argc, argv, "1:", &x, &kw_hash);
    rb_get_kwargs(kw_hash, kw_table, 0, 1, opts);
    keepdims = option_value(opts[0],Qfalse);

    if (RTEST(keepdims)) {
        ndf.flag |= NDF_KEEP_DIM;
    }

    GetNArray(x,na1);
    CHECK_DIM_GE(na1,1);
    CHECK_NON_EMPTY(na1);

    ans = na_ndloop(&ndf, 1, x);

    return ans;
}

.scopy(x, y) ⇒ nil

SCOPY copies a vector, x, to a vector, y. uses unrolled loops for increments equal to 1.

Parameters:

  • x (Numo::SFloat)

    vector (>=1-dimentional NArray).

  • y (Numo::SFloat)

    vector (>=1-dimentional NArray).

Returns:

  • (nil)


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# File 'ext/numo/linalg/blas/blas_s.c', line 495

static VALUE
blas_s_scopy(VALUE UNUSED(mod), VALUE x, VALUE y)
{
    narray_t *na1, *na2;
    ndfunc_arg_in_t ain[2] = {{cT,0},{OVERWRITE,0}};
    ndfunc_t ndf = {iter_blas_s_scopy, STRIDE_LOOP, 2,0, ain,0};

    CHECK_FUNC(func_p,"scopy");

    CHECK_NARRAY_TYPE(x,cT);
    CHECK_NARRAY_TYPE(y,cT);
    GetNArray(x,na1);
    GetNArray(y,na2);
    CHECK_DIM_GE(na1,1);
    CHECK_DIM_GE(na2,1);
    CHECK_NON_EMPTY(na1);
    CHECK_NON_EMPTY(na2);
    CHECK_SAME_SHAPE(na1,na2);

    na_ndloop(&ndf, 2, x, y);

    return Qnil;
}

.sdot(x, y) ⇒ Numo::SFloat

SDOT forms the dot product of two vectors. uses unrolled loops for increments equal to one.

Parameters:

  • x (Numo::SFloat)

    vector (>=1-dimentional NArray).

  • y (Numo::SFloat)

    vector (>=1-dimentional NArray).

Returns:

  • (Numo::SFloat)

    op(x) dot y



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# File 'ext/numo/linalg/blas/blas_s.c', line 95

static VALUE
blas_s_sdot(VALUE mod, VALUE x, VALUE y)
{
    VALUE     ans;
    narray_t *na1, *na2;
    size_t    nx, ny, shape[1]={1};
    ndfunc_arg_in_t ain[2] = {{cT,1},{cT,1}};
    ndfunc_arg_out_t aout[1] = {{numo_cSFloat,0,shape}};
    ndfunc_t ndf = {iter_blas_s_sdot, NDF_EXTRACT, 2,1, ain,aout};

    CHECK_FUNC(func_p,"sdot");

    GetNArray(x,na1);
    GetNArray(y,na2);
    CHECK_DIM_GE(na1,1);
    CHECK_DIM_GE(na2,1);
    CHECK_NON_EMPTY(na1);
    CHECK_NON_EMPTY(na2);
    nx = COL_SIZE(na1);
    ny = COL_SIZE(na2);
    CHECK_SIZE_EQ(nx,ny);

    ans = na_ndloop(&ndf, 2, x, y);

    return ans;
}

.sdsdot(sx, sy, [sb: 0]) ⇒ Numo::SFloat

Compute the inner product of two vectors with extended precision accumulation.

Returns S.P. result with dot product accumulated in D.P. SDSDOT = SB + sum for I = 0 to N-1 of SX(LX+IINCX)SY(LY+IINCY), where LX = 1 if INCX .GE. 0, else LX = 1+(1-N)INCX, and LY is defined in a similar way using INCY.

Parameters:

  • sx (Numo::SFloat)

    vector (>=1-dimentional NArray).

  • sy (Numo::SFloat)

    vector (>=1-dimentional NArray, inplace allowed).

  • sb (Float)

Returns:

  • (Numo::SFloat)

    returns inner product.



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# File 'ext/numo/linalg/blas/blas_s.c', line 371

static VALUE
blas_s_sdsdot(int argc, VALUE const argv[], VALUE UNUSED(mod))
{
    VALUE     x, y, sb;
    dtype     g[1];
    narray_t *na1, *na2;
    size_t    nx, ny;
    ndfunc_arg_in_t ain[2] = {{cT,1},{cT,1}};
    ndfunc_arg_out_t aout[1] = {{cT,0}};
    ndfunc_t ndf = {iter_blas_s_sdsdot, NDF_EXTRACT, 2,1, ain,aout};

    VALUE kw_hash = Qnil;
    ID kw_table[1] = {id_sb};
    VALUE opts[1] = {Qundef};

    CHECK_FUNC(func_p,"sdsdot");

    rb_scan_args(argc, argv, "2:", &x, &y, &kw_hash);
    rb_get_kwargs(kw_hash, kw_table, 0, 1, opts);
    sb = option_value(opts[0],Qnil);
    g[0] = RTEST(sb) ? m_num_to_data(sb) : m_zero;

    GetNArray(x,na1);
    GetNArray(y,na2);
    CHECK_DIM_GE(na1,1);
    CHECK_DIM_GE(na2,1);
    CHECK_NON_EMPTY(na1);
    CHECK_NON_EMPTY(na2);
    nx = na1->shape[na1->ndim-1];
    ny = na2->shape[na2->ndim-1];
    CHECK_SIZE_EQ(nx,ny);

    return na_ndloop3(&ndf, g, 2, x, y);
}

.sgemm(a, b, [c, alpha: 1, beta:0, transa:'N', transb:'N', order:'R']) ⇒ Numo::SFloat

SGEMM performs one of the matrix-matrix operations

  C := alpha*op( A )*op( B ) + beta*C,

where op( X ) is one of

  op( X ) = X   or   op( X ) = X**T,

alpha and beta are scalars, and A, B and C are matrices, with op( A ) an m by k matrix, op( B ) a k by n matrix and C an m by n matrix.

Parameters:

  • a (Numo::SFloat)

    matrix (>=2-dimentional NArray).

  • b (Numo::SFloat)

    matrix (>=2-dimentional NArray).

  • c (Numo::SFloat)

    matrix (>=2-dimentional NArray, optional, inplace allowed).

  • alpha (Float)

    (default=1.0)

  • beta (Float)

    (default=0.0)

  • transa (String or Symbol)

    if ‘N’: Not transpose a, if ‘T’: Transpose a. (default=’N’)

  • transb (String or Symbol)

    if ‘N’: Not transpose b, if ‘T’: Transpose b. (default=’N’)

  • order (String or Symbol)

    if ‘R’: Row-major, if ‘C’: Column-major. (default=’R’)

Returns:

  • (Numo::SFloat)

    returns c = alpha*op( A )*op( B ) + beta*C.



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# File 'ext/numo/linalg/blas/blas_s.c', line 1789

static VALUE
blas_s_sgemm(int argc, VALUE const argv[], VALUE UNUSED(mod))
{
    VALUE     a, b, c=Qnil, alpha, beta;
    narray_t *na1, *na2;
    blasint   ma, ka, kb, nb, tmp;
    size_t    shape[2];
    ndfunc_arg_in_t ain[3] = {{cT,2},{cT,2},{OVERWRITE,2}};
    ndfunc_arg_out_t aout[1] = {{cT,2,shape}};
    ndfunc_t ndf = {iter_blas_s_sgemm, NO_LOOP, 3, 0, ain, aout};

    args_t g;
    VALUE kw_hash = Qnil;
#if GE
    ID kw_table[5] = {id_alpha,id_beta,id_order,id_transa,id_transb};
#elif TR
    ID kw_table[7] = {id_alpha,id_beta,id_order,id_side,id_uplo,id_transa,id_diag};
#else
    ID kw_table[5] = {id_alpha,id_beta,id_order,id_side,id_uplo};
#endif
    VALUE opts[7] = {Qundef,Qundef,Qundef,Qundef,Qundef,Qundef,Qundef};

    CHECK_FUNC(func_p,"sgemm");

    rb_scan_args(argc, argv, "21:", &a, &b, &c, &kw_hash);
    rb_get_kwargs(kw_hash, kw_table, 0, 5+TR*2, opts);
    alpha    = option_value(opts[0],Qnil);
    g.alpha  = RTEST(alpha) ? m_num_to_data(alpha) : m_one;
    beta     = option_value(opts[1],Qnil);
    g.beta   = RTEST(beta)  ? m_num_to_data(beta)  : m_zero;
    g.order  = option_order(opts[2]);
#if GE
    g.transa = option_trans(opts[3]);
    g.transb = option_trans(opts[4]);
#else
    g.side   = option_side(opts[3]);
    g.uplo   = option_uplo(opts[4]);
#endif
#if TR
    g.transa = option_trans(opts[5]);
    g.diag   = option_diag(opts[6]);
#endif

    GetNArray(a,na1);
    GetNArray(b,na2);
    CHECK_DIM_GE(na1,2);
    CHECK_DIM_GE(na2,2);
    ma = ROW_SIZE(na1); // m
    ka = COL_SIZE(na1); // k (lda)
    kb = ROW_SIZE(na2); // k
    nb = COL_SIZE(na2); // n (ldb)

#if GE
    SWAP_IFCOLTR(g.order,g.transa, ma,ka, tmp);
    SWAP_IFCOLTR(g.order,g.transb, kb,nb, tmp);
    CHECK_INT_EQ("ka",ka,"kb",kb);
    g.m = ma;
    g.n = nb;
    g.k = ka;
#else
    CHECK_SQUARE("a",na1); // ma == ka
    SWAP_IFCOL(g.order, kb,nb, tmp);
    // row major             L    R
    //ma = ROW_SIZE(na1); // m or n
    //ka = COL_SIZE(na1); // m or n (lda)
    g.m = kb; // m
    g.n = nb; // n (ldb)
    if (g.side == CblasLeft) {
        CHECK_SIZE_EQ(ka, g.m);
    } else {
        CHECK_SIZE_EQ(ka, g.n);
    }
#endif

    SWAP_IFROW(g.order, ma,nb, tmp);

#if TR
    if (c != Qnil) {
        rb_raise(rb_eArgError,"wrong number of arguments (3 for 2)");
    }
    COPY_OR_CAST_TO(b,cT);
    ndf.nin = 2;

    na_ndloop3(&ndf, &g, 2, a, b);
    return b;
#else

    if (c == Qnil) { // c is not given.
        ndfunc_arg_in_t ain_init = {sym_init,0};
        ain[2] = ain_init;
        ndf.nout = 1;
        c = INT2FIX(0);
        shape[0] = nb;
        shape[1] = ma;
    } else {
        narray_t *na3;
        int nc;
        COPY_OR_CAST_TO(c,cT);
        GetNArray(c,na3);
        CHECK_DIM_GE(na3,2);
        nc = ROW_SIZE(na3);
        if (nc < nb) {
            rb_raise(nary_eShapeError,"nc=%d must be >= nb=%d",nc,nb);
        }
        //CHECK_LEADING_GE("ldc",g.ldc,"m",ma);
    }
    {
        VALUE ans = na_ndloop3(&ndf, &g, 3, a, b, c);

        if (ndf.nout == 1) { // c is not given.
            return ans;
        } else {
            return c;
        }
    }
#endif
}

.sgemv(a, x, [y, alpha: 1, beta:0, trans:'N', order:'R']) ⇒ Numo::SFloat

SGEMV performs one of the matrix-vector operations

  y := alpha*A*x + beta*y,   or   y := alpha*A**T*x + beta*y,

where alpha and beta are scalars, x and y are vectors and A is an m by n matrix.

Parameters:

  • a (Numo::SFloat)

    matrix (>=2-dimentional NArray).

  • x (Numo::SFloat)

    vector (>=1-dimentional NArray).

  • y (Numo::SFloat)

    vector (>=1-dimentional NArray, optional, inplace allowed).

  • alpha (Float)

    (default=1.0)

  • beta (Float)

    (default=0.0)

  • trans (String or Symbol)

    if ‘N’: Not transpose , if ‘T’: Transpose . (default=’N’)

  • order (String or Symbol)

    if ‘R’: Row-major, if ‘C’: Column-major. (default=’R’)

Returns:

  • (Numo::SFloat)

    returns y = alpha*op(A)*x + beta*y.



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# File 'ext/numo/linalg/blas/blas_s.c', line 888

static VALUE
blas_s_sgemv(int argc, VALUE const argv[], VALUE UNUSED(mod))
{
    VALUE     a, x, y=Qnil, alpha, beta;
    narray_t *na1, *na2;
    blasint   ma, na, nx;
#if GE
    blasint   tmp;
#endif
    size_t    shape[1];
    ndfunc_arg_in_t ain[4] = {{cT,2},{cT,1},{OVERWRITE,1},{sym_init,0}};
    ndfunc_arg_out_t aout[1] = {{cT,1,shape}};
    ndfunc_t ndf = {iter_blas_s_sgemv, NO_LOOP, 3, 0, ain, aout};

    args_t g;
    VALUE kw_hash = Qnil;
#if GE
    ID kw_table[4] = {id_alpha,id_beta,id_order,id_trans};
#elif TR
    ID kw_table[6] = {id_alpha,id_beta,id_order,id_uplo,id_trans,id_diag};
#else
    ID kw_table[4] = {id_alpha,id_beta,id_order,id_uplo};
#endif
    VALUE opts[6] = {Qundef,Qundef,Qundef,Qundef,Qundef,Qundef};

    CHECK_FUNC(func_p,"sgemv");

    rb_scan_args(argc, argv, "21:", &a, &x, &y, &kw_hash);
    rb_get_kwargs(kw_hash, kw_table, 0, 4+2*TR, opts);
    alpha   = option_value(opts[0],Qnil);
    g.alpha = RTEST(alpha) ? m_num_to_data(alpha) : m_one;
    beta    = option_value(opts[1],Qnil);
    g.beta  = RTEST(beta)  ? m_num_to_data(beta)  : m_zero;
    g.order = option_order(opts[2]);
#if GE
    g.trans = option_trans(opts[3]);
#else
    g.uplo  = option_uplo(opts[3]);
#endif
#if TR
    g.trans = option_trans(opts[4]);
    g.diag  = option_diag(opts[5]);
#endif

    GetNArray(a,na1);
    CHECK_DIM_GE(na1,2);
    ma = ROW_SIZE(na1);
    na = COL_SIZE(na1);

    GetNArray(x,na2);
    CHECK_DIM_GE(na2,1);
    nx = COL_SIZE(na2);
#if GE
    SWAP_IFCOL(g.order, ma, na, tmp);
    g.m = ma;
    g.n = na;
    SWAP_IFTRANS(g.trans, ma, na, tmp);
#else
    CHECK_SQUARE("a",na1);
#endif
    CHECK_INT_EQ("na",na,"nx",nx);
    shape[0] = ma;

#if TR
    if (y != Qnil) {
        rb_raise(rb_eArgError,"wrong number of arguments (3 for 2)");
    }
    COPY_OR_CAST_TO(x,cT);
    ndf.nin = 2;
    na_ndloop3(&ndf, &g, 2, a, x);
    return x;

#else // GE,SY,HE

    if (y == Qnil) { // c is not given.
        ndf.nout = 1;
        ain[2] = ain[3];
        y = INT2FIX(0);
        shape[0] = ma;
    } else {
        narray_t *na3;
        COPY_OR_CAST_TO(y,cT);
        GetNArray(y,na3);
        CHECK_DIM_GE(na3,1);
        CHECK_SIZE_GE(na3,nx);
    }
    {
        VALUE ans;
        ans = na_ndloop3(&ndf, &g, 3, a, x, y);

        if (ndf.nout == 1) { // c is not given.
            return ans;
        } else {
            return y;
        }
    }
#endif
}

.sger(x, y, [a, alpha: 1, order:'R']) ⇒ Numo::SFloat

SGER performs the rank 1 operation

  A := alpha*x*y**T + A,

where alpha is a scalar, x is an m element vector, y is an n element vector and A is an m by n matrix.

Parameters:

  • x (Numo::SFloat)

    vector (>=1-dimentional NArray).

  • y (Numo::SFloat)

    vector (>=1-dimentional NArray).

  • a (Numo::SFloat)

    matrix (>=2-dimentional NArray, m-by-n symmetric matrix, optional, inplace allowed).

  • alpha (Float)

    (default=1.0)

  • order (String or Symbol)

    if ‘R’: Row-major, if ‘C’: Column-major. (default=’R’)

Returns:

  • (Numo::SFloat)

    returns a.



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# File 'ext/numo/linalg/blas/blas_s.c', line 1525

static VALUE
blas_s_sger(int argc, VALUE const argv[], VALUE UNUSED(mod))
{
    VALUE     ans;
    VALUE     x, y, a=Qnil, alpha;
    narray_t *na1, *na2;
    blasint   mx, ny, tmp;
    size_t    shape[2];
    ndfunc_arg_in_t ain[4] = {{cT,1},{cT,1},{OVERWRITE,2},{sym_init,0}};
    ndfunc_arg_out_t aout[1] = {{cT,2,shape}};
    ndfunc_t ndf = {iter_blas_s_sger, NO_LOOP, 3, 0, ain, aout};

    args_t g;
    VALUE kw_hash = Qnil;
    ID kw_table[2] = {id_alpha,id_order};
    VALUE opts[2] = {Qundef};

    CHECK_FUNC(func_p,"sger");

    rb_scan_args(argc, argv, "21:", &x, &y, &a, &kw_hash);
    rb_get_kwargs(kw_hash, kw_table, 0, 2, opts);
    alpha   = option_value(opts[0],Qnil);
    g.alpha = RTEST(alpha) ? m_num_to_data(alpha) : m_one;
    g.order = option_order(opts[1]);

    GetNArray(x,na1);
    GetNArray(y,na2);
    CHECK_DIM_GE(na1,1);
    CHECK_DIM_GE(na2,1);
    mx = COL_SIZE(na1); // m
    ny = COL_SIZE(na2); // n
    g.m = mx;
    g.n = ny;

    SWAP_IFCOL(g.order, mx,ny, tmp);

    if (a == Qnil) { // c is not given.
        ndf.nout = 1;
        ain[2] = ain[3];
        a = INT2FIX(0);
        shape[0] = mx;
        shape[1] = ny;
    } else {
        narray_t  *na3;
        blasint    ma, na;
        COPY_OR_CAST_TO(a,cT);
        GetNArray(a,na3);
        CHECK_DIM_GE(na3,2);
        ma = ROW_SIZE(na3); // m
        na = COL_SIZE(na3); // n (lda)
        CHECK_SIZE_EQ(ma,mx);
        CHECK_SIZE_EQ(na,ny);
    }

    ans = na_ndloop3(&ndf, &g, 3, x, y, a);

    if (ndf.nout = 1) { // a is not given.
        return ans;
    } else {
        return a;
    }
}

.snrm2(x) ⇒ Numo::SFloat

SNRM2 returns the euclidean norm of a vector via the function name, so that

  SNRM2 := sqrt( x'*x ).

Parameters:

  • x (Numo::SFloat)

    vector (>=1-dimentional NArray).

  • keepdims (String or Symbol)

Returns:

  • (Numo::SFloat)

    euclidean norm of x



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# File 'ext/numo/linalg/blas/blas_s.c', line 159

static VALUE
blas_s_snrm2(int argc, VALUE const argv[], VALUE UNUSED(mod))
{
    VALUE     x, keepdims, ans;
    narray_t *na1;
    ndfunc_arg_in_t ain[1] = {{cT,1}};
    ndfunc_arg_out_t aout[1] = {{cT,0}};
    ndfunc_t ndf = {iter_blas_s_snrm2, NDF_EXTRACT, 1,1, ain,aout};

    VALUE opts[1] = {Qundef};
    ID    kw_table[1] = {id_keepdims};
    VALUE kw_hash = Qnil;

    CHECK_FUNC(func_p,"snrm2");

    rb_scan_args(argc, argv, "1:", &x, &kw_hash);
    rb_get_kwargs(kw_hash, kw_table, 0, 1, opts);
    keepdims = option_value(opts[0],Qfalse);

    if (RTEST(keepdims)) {
        ndf.flag |= NDF_KEEP_DIM;
    }

    GetNArray(x,na1);
    CHECK_DIM_GE(na1,1);
    CHECK_NON_EMPTY(na1);

    ans = na_ndloop(&ndf, 1, x);

    return ans;
}

.srot(x, y, c, s) ⇒ Array<Numo::SFloat,Numo::SFloat>

applies a plane rotation.

Parameters:

  • x (Numo::SFloat)

    vector (>=1-dimentional NArray, inplace allowed).

  • y (Numo::SFloat)

    vector (>=1-dimentional NArray, inplace allowed).

  • c (Float)
  • s (Float)

Returns:

  • (Array<Numo::SFloat,Numo::SFloat>)

    returns [x,y]



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# File 'ext/numo/linalg/blas/blas_s.c', line 630

static VALUE
blas_s_srot(VALUE UNUSED(mod), VALUE x, VALUE y, VALUE c, VALUE s)
{
    rtype g[2] = {0,0};
    narray_t *na1, *na2;
    ndfunc_arg_in_t ain[2] = {{OVERWRITE,0},{OVERWRITE,0}};
    ndfunc_t ndf = {iter_blas_s_srot, STRIDE_LOOP, 2,0, ain,0};

    CHECK_FUNC(func_p,"srot");

    if (RTEST(c)) {g[0] = NUM2DBL(c);}
    if (RTEST(s)) {g[1] = NUM2DBL(s);}

    COPY_OR_CAST_TO(x,cT);
    COPY_OR_CAST_TO(y,cT);
    GetNArray(x,na1);
    GetNArray(y,na2);
    CHECK_DIM_GE(na1,1);
    CHECK_DIM_GE(na2,1);
    CHECK_NON_EMPTY(na1);
    CHECK_NON_EMPTY(na2);
    CHECK_SAME_SHAPE(na1,na2);

    na_ndloop3(&ndf, g, 2, x, y);

    return rb_assoc_new(x,y);
}

.srotm(x, y, param) ⇒ Array<Numo::SFloat,Numo::SFloat>

Apply the modified givens transformation, H, to the 2 by N matrix (X**T), where **T indicates transpose. The elements of X are in (Y**T)

X(LX+I*INCX), I = 0 to N-1, where LX = 1 if INCX .GE. 0, else LX = (-INCX)*N, and similarly for Y using LY and INCY. With PARAM(1)=FLAG, H has one of the following forms..

  FLAG=-1.0     FLAG=0.0        FLAG=1.0     FLAG=-2.0

    (H11  H12)    (1.0  H12)    (H11  1.0)    (1.0  0.0)
  H=(        )    (        )    (        )    (        )
    (H21  H22),   (H21  1.0),   (-1.0 H22),   (0.0  1.0).

see SROTMG for a description of data storage in param.

Parameters:

  • x (Numo::SFloat)

    vector (>=1-dimentional NArray, inplace allowed).

  • y (Numo::SFloat)

    vector (>=1-dimentional NArray, inplace allowed).

  • param (Numo::SFloat)

    array of [FLAG,H11,H21,H12,H22]

Returns:

  • (Array<Numo::SFloat,Numo::SFloat>)

    returns [x,y]



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# File 'ext/numo/linalg/blas/blas_s.c', line 707

static VALUE
blas_s_srotm(VALUE UNUSED(mod), VALUE x, VALUE y, VALUE param)
{
    dtype *g;
    narray_t *na1, *na2, *nap;
    ndfunc_arg_in_t ain[2] = {{OVERWRITE,0},{OVERWRITE,0}};
    ndfunc_t ndf = {iter_blas_s_srotm, STRIDE_LOOP, 2,0, ain,0};

    CHECK_FUNC(func_p,"srotm");

    COPY_OR_CAST_TO(x,cT);
    COPY_OR_CAST_TO(y,cT);
    GetNArray(x,na1);
    GetNArray(y,na2);
    CHECK_DIM_GE(na1,1);
    CHECK_DIM_GE(na2,1);
    CHECK_NON_EMPTY(na1);
    CHECK_NON_EMPTY(na2);
    CHECK_SAME_SHAPE(na1,na2);

    param = rb_funcall(cT,rb_intern("cast"),1,param);
    GetNArray(param,nap);
    CHECK_DIM_EQ(nap,1);
    CHECK_SIZE_GE(nap,5);
    g = (dtype*)nary_get_pointer_for_read(param);

    na_ndloop3(&ndf, g, 2, x, y);

    RB_GC_GUARD(param);
    return rb_assoc_new(x,y);
}

.sscal(a, x) ⇒ Numo::SFloat

scales a vector by a constant. uses unrolled loops for increment equal to 1.

Parameters:

  • a (Float)

    scale factor

  • x (Numo::SFloat)

    vector (>=1-dimentional NArray).

Returns:

  • (Numo::SFloat)

    returns a*x.



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# File 'ext/numo/linalg/blas/blas_s.c', line 779

static VALUE
blas_s_sscal(VALUE mod, VALUE a, VALUE x)
{
    scal_t g[1];
    narray_t *na1;
    ndfunc_arg_in_t ain[1] = {{OVERWRITE,0}};
    ndfunc_t ndf = {iter_blas_s_sscal, STRIDE_LOOP, 1,0, ain,0};

    CHECK_FUNC(func_p,"sscal");

  
#line 56 "gen/../tmpl/scal.c"
    if (RTEST(a)) {g[0] = m_num_to_data(a);} else {g[0]=m_one;}
  
    COPY_OR_CAST_TO(x,cT);
    GetNArray(x,na1);
    CHECK_DIM_GE(na1,1);
    CHECK_NON_EMPTY(na1);

    na_ndloop3(&ndf, g, 1, x);

    return x;
}

.sswap(x, y) ⇒ nil

interchanges two vectors. uses unrolled loops for increments equal to 1.

Parameters:

  • x (Numo::SFloat)

    vector (>=1-dimentional NArray).

  • y (Numo::SFloat)

    vector (>=1-dimentional NArray).

Returns:

  • (nil)


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# File 'ext/numo/linalg/blas/blas_s.c', line 438

static VALUE
blas_s_sswap(VALUE UNUSED(mod), VALUE x, VALUE y)
{
    narray_t *na1, *na2;
    ndfunc_arg_in_t ain[2] = {{OVERWRITE,0},{OVERWRITE,0}};
    ndfunc_t ndf = {iter_blas_s_sswap, STRIDE_LOOP, 2,0, ain,0};

    CHECK_FUNC(func_p,"sswap");

    CHECK_NARRAY_TYPE(x,cT);
    CHECK_NARRAY_TYPE(y,cT);
    GetNArray(x,na1);
    GetNArray(y,na2);
    CHECK_DIM_GE(na1,1);
    CHECK_DIM_GE(na2,1);
    CHECK_NON_EMPTY(na1);
    CHECK_NON_EMPTY(na2);
    CHECK_SAME_SHAPE(na1,na2);

    na_ndloop(&ndf, 2, x, y);

    return Qnil;
}

.ssymm(a, b, [c, alpha: 1, beta:0, side:'L', uplo:'U', order:'R']) ⇒ Numo::SFloat

SSYMM performs one of the matrix-matrix operations

  C := alpha*A*B + beta*C,

or

  C := alpha*B*A + beta*C,

where alpha and beta are scalars, A is a symmetric matrix and B and C are m by n matrices.

Parameters:

  • a (Numo::SFloat)

    matrix (>=2-dimentional NArray).

  • b (Numo::SFloat)

    matrix (>=2-dimentional NArray).

  • c (Numo::SFloat)

    matrix (>=2-dimentional NArray, optional, inplace allowed).

  • alpha (Float)

    (default=1.0)

  • beta (Float)

    (default=0.0)

  • side (String or Symbol)

    if ‘L’: op(A)*B (left-side op), if ‘R’: B*op(A) (right-side op). (default=’L’)

  • uplo (String or Symbol)

    if ‘U’: Upper triangle, if ‘L’: Lower triangle. (default=’U’)

  • order (String or Symbol)

    if ‘R’: Row-major, if ‘C’: Column-major. (default=’R’)

Returns:

  • (Numo::SFloat)

    returns c = alpha*op( A )*op( B ) + beta*C.



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# File 'ext/numo/linalg/blas/blas_s.c', line 1996

static VALUE
blas_s_ssymm(int argc, VALUE const argv[], VALUE UNUSED(mod))
{
    VALUE     a, b, c=Qnil, alpha, beta;
    narray_t *na1, *na2;
    blasint   ma, ka, kb, nb, tmp;
    size_t    shape[2];
    ndfunc_arg_in_t ain[3] = {{cT,2},{cT,2},{OVERWRITE,2}};
    ndfunc_arg_out_t aout[1] = {{cT,2,shape}};
    ndfunc_t ndf = {iter_blas_s_ssymm, NO_LOOP, 3, 0, ain, aout};

    args_t g;
    VALUE kw_hash = Qnil;
#if GE
    ID kw_table[5] = {id_alpha,id_beta,id_order,id_transa,id_transb};
#elif TR
    ID kw_table[7] = {id_alpha,id_beta,id_order,id_side,id_uplo,id_transa,id_diag};
#else
    ID kw_table[5] = {id_alpha,id_beta,id_order,id_side,id_uplo};
#endif
    VALUE opts[7] = {Qundef,Qundef,Qundef,Qundef,Qundef,Qundef,Qundef};

    CHECK_FUNC(func_p,"ssymm");

    rb_scan_args(argc, argv, "21:", &a, &b, &c, &kw_hash);
    rb_get_kwargs(kw_hash, kw_table, 0, 5+TR*2, opts);
    alpha    = option_value(opts[0],Qnil);
    g.alpha  = RTEST(alpha) ? m_num_to_data(alpha) : m_one;
    beta     = option_value(opts[1],Qnil);
    g.beta   = RTEST(beta)  ? m_num_to_data(beta)  : m_zero;
    g.order  = option_order(opts[2]);
#if GE
    g.transa = option_trans(opts[3]);
    g.transb = option_trans(opts[4]);
#else
    g.side   = option_side(opts[3]);
    g.uplo   = option_uplo(opts[4]);
#endif
#if TR
    g.transa = option_trans(opts[5]);
    g.diag   = option_diag(opts[6]);
#endif

    GetNArray(a,na1);
    GetNArray(b,na2);
    CHECK_DIM_GE(na1,2);
    CHECK_DIM_GE(na2,2);
    ma = ROW_SIZE(na1); // m
    ka = COL_SIZE(na1); // k (lda)
    kb = ROW_SIZE(na2); // k
    nb = COL_SIZE(na2); // n (ldb)

#if GE
    SWAP_IFCOLTR(g.order,g.transa, ma,ka, tmp);
    SWAP_IFCOLTR(g.order,g.transb, kb,nb, tmp);
    CHECK_INT_EQ("ka",ka,"kb",kb);
    g.m = ma;
    g.n = nb;
    g.k = ka;
#else
    CHECK_SQUARE("a",na1); // ma == ka
    SWAP_IFCOL(g.order, kb,nb, tmp);
    // row major             L    R
    //ma = ROW_SIZE(na1); // m or n
    //ka = COL_SIZE(na1); // m or n (lda)
    g.m = kb; // m
    g.n = nb; // n (ldb)
    if (g.side == CblasLeft) {
        CHECK_SIZE_EQ(ka, g.m);
    } else {
        CHECK_SIZE_EQ(ka, g.n);
    }
#endif

    SWAP_IFROW(g.order, ma,nb, tmp);

#if TR
    if (c != Qnil) {
        rb_raise(rb_eArgError,"wrong number of arguments (3 for 2)");
    }
    COPY_OR_CAST_TO(b,cT);
    ndf.nin = 2;

    na_ndloop3(&ndf, &g, 2, a, b);
    return b;
#else

    if (c == Qnil) { // c is not given.
        ndfunc_arg_in_t ain_init = {sym_init,0};
        ain[2] = ain_init;
        ndf.nout = 1;
        c = INT2FIX(0);
        shape[0] = nb;
        shape[1] = ma;
    } else {
        narray_t *na3;
        int nc;
        COPY_OR_CAST_TO(c,cT);
        GetNArray(c,na3);
        CHECK_DIM_GE(na3,2);
        nc = ROW_SIZE(na3);
        if (nc < nb) {
            rb_raise(nary_eShapeError,"nc=%d must be >= nb=%d",nc,nb);
        }
        //CHECK_LEADING_GE("ldc",g.ldc,"m",ma);
    }
    {
        VALUE ans = na_ndloop3(&ndf, &g, 3, a, b, c);

        if (ndf.nout == 1) { // c is not given.
            return ans;
        } else {
            return c;
        }
    }
#endif
}

.ssymv(a, x, [y, alpha: 1, beta:0, uplo:'U', order:'R']) ⇒ Numo::SFloat

SSYMV performs the matrix-vector operation

  y := alpha*A*x + beta*y,

where alpha and beta are scalars, x and y are n element vectors and A is an n by n symmetric matrix.

Parameters:

  • a (Numo::SFloat)

    matrix (>=2-dimentional NArray).

  • x (Numo::SFloat)

    vector (>=1-dimentional NArray).

  • y (Numo::SFloat)

    vector (>=1-dimentional NArray, optional, inplace allowed).

  • alpha (Float)

    (default=1.0)

  • beta (Float)

    (default=0.0)

  • side (String or Symbol)

    if ‘L’: op(A)*B (left-side op), if ‘R’: B*op(A) (right-side op). (default=’L’)

  • uplo (String or Symbol)

    if ‘U’: Upper triangle, if ‘L’: Lower triangle. (default=’U’)

  • order (String or Symbol)

    if ‘R’: Row-major, if ‘C’: Column-major. (default=’R’)

Returns:

  • (Numo::SFloat)

    returns y = alpha*op(A)*x + beta*y.



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# File 'ext/numo/linalg/blas/blas_s.c', line 1262

static VALUE
blas_s_ssymv(int argc, VALUE const argv[], VALUE UNUSED(mod))
{
    VALUE     a, x, y=Qnil, alpha, beta;
    narray_t *na1, *na2;
    blasint   ma, na, nx;
#if GE
    blasint   tmp;
#endif
    size_t    shape[1];
    ndfunc_arg_in_t ain[4] = {{cT,2},{cT,1},{OVERWRITE,1},{sym_init,0}};
    ndfunc_arg_out_t aout[1] = {{cT,1,shape}};
    ndfunc_t ndf = {iter_blas_s_ssymv, NO_LOOP, 3, 0, ain, aout};

    args_t g;
    VALUE kw_hash = Qnil;
#if GE
    ID kw_table[4] = {id_alpha,id_beta,id_order,id_trans};
#elif TR
    ID kw_table[6] = {id_alpha,id_beta,id_order,id_uplo,id_trans,id_diag};
#else
    ID kw_table[4] = {id_alpha,id_beta,id_order,id_uplo};
#endif
    VALUE opts[6] = {Qundef,Qundef,Qundef,Qundef,Qundef,Qundef};

    CHECK_FUNC(func_p,"ssymv");

    rb_scan_args(argc, argv, "21:", &a, &x, &y, &kw_hash);
    rb_get_kwargs(kw_hash, kw_table, 0, 4+2*TR, opts);
    alpha   = option_value(opts[0],Qnil);
    g.alpha = RTEST(alpha) ? m_num_to_data(alpha) : m_one;
    beta    = option_value(opts[1],Qnil);
    g.beta  = RTEST(beta)  ? m_num_to_data(beta)  : m_zero;
    g.order = option_order(opts[2]);
#if GE
    g.trans = option_trans(opts[3]);
#else
    g.uplo  = option_uplo(opts[3]);
#endif
#if TR
    g.trans = option_trans(opts[4]);
    g.diag  = option_diag(opts[5]);
#endif

    GetNArray(a,na1);
    CHECK_DIM_GE(na1,2);
    ma = ROW_SIZE(na1);
    na = COL_SIZE(na1);

    GetNArray(x,na2);
    CHECK_DIM_GE(na2,1);
    nx = COL_SIZE(na2);
#if GE
    SWAP_IFCOL(g.order, ma, na, tmp);
    g.m = ma;
    g.n = na;
    SWAP_IFTRANS(g.trans, ma, na, tmp);
#else
    CHECK_SQUARE("a",na1);
#endif
    CHECK_INT_EQ("na",na,"nx",nx);
    shape[0] = ma;

#if TR
    if (y != Qnil) {
        rb_raise(rb_eArgError,"wrong number of arguments (3 for 2)");
    }
    COPY_OR_CAST_TO(x,cT);
    ndf.nin = 2;
    na_ndloop3(&ndf, &g, 2, a, x);
    return x;

#else // GE,SY,HE

    if (y == Qnil) { // c is not given.
        ndf.nout = 1;
        ain[2] = ain[3];
        y = INT2FIX(0);
        shape[0] = ma;
    } else {
        narray_t *na3;
        COPY_OR_CAST_TO(y,cT);
        GetNArray(y,na3);
        CHECK_DIM_GE(na3,1);
        CHECK_SIZE_GE(na3,nx);
    }
    {
        VALUE ans;
        ans = na_ndloop3(&ndf, &g, 3, a, x, y);

        if (ndf.nout == 1) { // c is not given.
            return ans;
        } else {
            return y;
        }
    }
#endif
}

.ssyr(x, [a, alpha: 1, uplo:'U', order:'R']) ⇒ Numo::SFloat

SSYR performs the symmetric rank 1 operation

  A := alpha*x*x**T + A,

where alpha is a real scalar, x is an n element vector and A is an n by n symmetric matrix.

Parameters:

  • x (Numo::SFloat)

    vector (>=1-dimentional NArray).

  • a (Numo::SFloat)

    matrix (>=2-dimentional NArray, inplace allowed).

  • alpha (Float)

    (default=1.0)

  • uplo (String or Symbol)

    if ‘U’: Upper triangle, if ‘L’: Lower triangle. (default=’U’)

  • order (String or Symbol)

    if ‘R’: Row-major, if ‘C’: Column-major. (default=’R’)

Returns:

  • (Numo::SFloat)

    return a



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# File 'ext/numo/linalg/blas/blas_s.c', line 1416

static VALUE
blas_s_ssyr(int argc, VALUE const argv[], VALUE UNUSED(mod))
{
    VALUE     ans;
    VALUE     x, a, alpha;
    narray_t *na1, *na3;
    blasint   nx, na;
    size_t    shape[2];
    ndfunc_arg_in_t ain[3] = {{cT,1},{OVERWRITE,2},{sym_init,0}};
    ndfunc_arg_out_t aout[1] = {{cT,2,shape}};
    ndfunc_t ndf = {iter_blas_s_ssyr, NO_LOOP, 2, 0, ain, aout};

    args_t g;
    VALUE kw_hash = Qnil;
    ID kw_table[3] = {id_alpha,id_order,id_uplo};
    VALUE opts[3] = {Qundef,Qundef,Qundef};

    CHECK_FUNC(func_p,"ssyr");

    rb_scan_args(argc, argv, "11:", &x, &a, &kw_hash);
    rb_get_kwargs(kw_hash, kw_table, 0, 3, opts);
    alpha   = option_value(opts[0],Qnil);
    g.alpha = RTEST(alpha) ? NUM2DBL(alpha) : 1;
    g.order = option_order(opts[1]);
    g.uplo  = option_uplo(opts[2]);

    GetNArray(x,na1);
    CHECK_DIM_GE(na1,1);
    nx = COL_SIZE(na1); // n

    if (a == Qnil) { // c is not given.
        ndf.nout = 1;
        ain[1] = ain[2];
        a = INT2FIX(0);
        shape[0] = shape[1] = nx;
    } else {
        COPY_OR_CAST_TO(a,cT);
        GetNArray(a,na3);
        CHECK_DIM_GE(na3,2);
        CHECK_SQUARE("a",na3);
        na = COL_SIZE(na3); // n (lda)
        CHECK_SIZE_EQ(na,nx);
    }

    ans = na_ndloop3(&ndf, &g, 2, x, a);

    if (ndf.nout == 1) { // a is not given.
        return ans;
    } else {
        return a;
    }
}

.ssyr2(x, y, [a, alpha: 1, uplo:'U', order:'R']) ⇒ Numo::SFloat

SSYR2 performs the symmetric rank 2 operation

  A := alpha*x*y**T + alpha*y*x**T + A,

where alpha is a scalar, x and y are n element vectors and A is an n by n symmetric matrix.

Parameters:

  • x (Numo::SFloat)

    vector (>=1-dimentional NArray).

  • y (Numo::SFloat)

    vector (>=1-dimentional NArray).

  • a (Numo::SFloat)

    matrix (>=2-dimentional NArray, inplace allowed).

  • alpha (Float)

    (default=1.0)

  • uplo (String or Symbol)

    if ‘U’: Upper triangle, if ‘L’: Lower triangle. (default=’U’)

  • order (String or Symbol)

    if ‘R’: Row-major, if ‘C’: Column-major. (default=’R’)

Returns:

  • (Numo::SFloat)

    returns a.



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# File 'ext/numo/linalg/blas/blas_s.c', line 1645

static VALUE
blas_s_ssyr2(int argc, VALUE const argv[], VALUE UNUSED(mod))
{
    VALUE     ans;
    VALUE     x, y, a, alpha;
    narray_t *na1, *na2, *na3;
    blasint   nx, ny, na;
    size_t    shape[2];
    ndfunc_arg_in_t ain[4] = {{cT,1},{cT,1},{OVERWRITE,2},{sym_init,0}};
    ndfunc_arg_out_t aout[1] = {{cT,2,shape}};
    ndfunc_t ndf = {iter_blas_s_ssyr2, NO_LOOP, 3, 0, ain, aout};

    args_t g;
    VALUE kw_hash = Qnil;
    ID kw_table[3] = {id_alpha,id_order,id_uplo};
    VALUE opts[3] = {Qundef,Qundef,Qundef};

    CHECK_FUNC(func_p,"ssyr2");

    rb_scan_args(argc, argv, "21:", &x, &y, &a, &kw_hash);
    rb_get_kwargs(kw_hash, kw_table, 0, 3, opts);
    alpha   = option_value(opts[0],Qnil);
    g.alpha = RTEST(alpha) ? m_num_to_data(alpha) : m_one;
    g.order = option_order(opts[1]);
    g.uplo  = option_uplo(opts[2]);

    GetNArray(x,na1);
    GetNArray(y,na2);
    CHECK_DIM_GE(na1,1);
    CHECK_DIM_GE(na2,1);
    nx = COL_SIZE(na1); // n
    ny = COL_SIZE(na2); // n
    CHECK_INT_EQ("nx",nx,"ny",ny);

    if (a == Qnil) { // c is not given.
        ndf.nout = 1;
        ain[2] = ain[3];
        a = INT2FIX(0);
        shape[0] = shape[1] = nx;
    } else {
        COPY_OR_CAST_TO(a,cT);
        GetNArray(a,na3);
        CHECK_DIM_GE(na3,2);
        CHECK_SQUARE("a",na3);
        na = COL_SIZE(na3); // n (lda)
        CHECK_SIZE_EQ(na,nx);
    }

    ans = na_ndloop3(&ndf, &g, 3, x, y, a);

    if (ndf.nout == 1) { // a is not given.
        return ans;
    } else {
        return a;
    }
}

.ssyr2k(a, b, [c, alpha: 1, beta:0, uplo:'U', trans:'N', order:'R']) ⇒ Numo::SFloat

SSYR2K performs one of the symmetric rank 2k operations

  C := alpha*A*B**T + alpha*B*A**T + beta*C,

or

  C := alpha*A**T*B + alpha*B**T*A + beta*C,

where alpha and beta are scalars, C is an n by n symmetric matrix and A and B are n by k matrices in the first case and k by n matrices in the second case.

Parameters:

  • a (Numo::SFloat)

    matrix (>=2-dimentional NArray, n-by-k).

  • b (Numo::SFloat)

    matrix (>=2-dimentional NArray, n-by-k).

  • c (Numo::SFloat)

    matrix (>=2-dimentional NArray, n-by-n, optional, inpace).

  • alpha (Float)

    (default=1.0)

  • beta (Float)

    (default=0.0)

  • uplo (String or Symbol)

    if ‘U’: Upper triangle, if ‘L’: Lower triangle. (default=’U’)

  • trans (String or Symbol)

    if ‘N’: Not transpose , if ‘T’: Transpose . (default=’N’)

  • order (String or Symbol)

    if ‘R’: Row-major, if ‘C’: Column-major. (default=’R’)

Returns:

  • (Numo::SFloat)

    returns c.



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# File 'ext/numo/linalg/blas/blas_s.c', line 2518

static VALUE
blas_s_ssyr2k(int argc, VALUE const argv[], VALUE UNUSED(mod))
{
    VALUE     ans;
    VALUE     a, b, c=Qnil, alpha, beta;
    narray_t *na1, *na2, *na3;
    blasint   na, ka, kb, nb, nc, tmp;
    size_t    shape[2];
    ndfunc_arg_in_t ain[4] = {{cT,2},{cT,2},{OVERWRITE,2},{sym_init,0}};
    ndfunc_arg_out_t aout[1] = {{cT,2,shape}};
    ndfunc_t ndf = {iter_blas_s_ssyr2k, NO_LOOP, 3, 0, ain, aout};

    args_t g;
    VALUE kw_hash = Qnil;
    ID kw_table[5] = {id_alpha,id_beta,id_order,id_uplo,id_trans};
    VALUE opts[5] = {Qundef,Qundef,Qundef,Qundef,Qundef};

    CHECK_FUNC(func_p,"ssyr2k");

    rb_scan_args(argc, argv, "21:", &a, &b, &c, &kw_hash);
    rb_get_kwargs(kw_hash, kw_table, 0, 5, opts);
    alpha    = option_value(opts[0],Qnil);
    g.alpha  = RTEST(alpha) ? m_num_to_data(alpha) : m_one;
    beta     = option_value(opts[1],Qnil);
    g.beta   = RTEST(beta)  ? m_num_to_data(beta)  : m_zero;
    g.order  = option_order(opts[2]);
    g.uplo   = option_uplo(opts[3]);
    g.trans  = option_trans(opts[4]);

    GetNArray(a,na1);
    GetNArray(b,na2);
    CHECK_DIM_GE(na1,2);
    CHECK_DIM_GE(na2,2);

    na = ROW_SIZE(na1); // n
    ka = COL_SIZE(na1); // k (lda)
    SWAP_IFCOLTR(g.order, g.trans, na, ka, tmp);

    nb = ROW_SIZE(na2); // n
    kb = COL_SIZE(na2); // k (ldb)
    SWAP_IFCOLTR(g.order, g.trans, kb, nb, tmp);
    CHECK_INT_EQ("na",na,"nb",nb);
    CHECK_INT_EQ("ka",ka,"kb",kb);
    g.n = nb;
    g.k = kb;

    SWAP_IFROW(g.order, na, nb, tmp);

    if (c == Qnil) { // c is not given.
        ndf.nout = 1;
        ain[2] = ain[3];
        c = INT2FIX(0);
        shape[0] = nb;
        shape[1] = na;
    } else {
        COPY_OR_CAST_TO(c,cT);
        GetNArray(c,na3);
        CHECK_DIM_GE(na3,2);
        nc = ROW_SIZE(na3); // n
        if (nc < nb) {
            rb_raise(nary_eShapeError,"nc=%d must be >= nb=%d",nc,nb);
        }
        //CHECK_LEADING_GE("ldc",g.ldc,"n",na);
    }

    ans = na_ndloop3(&ndf, &g, 3, a, b, c);

    if (ndf.nout = 1) { // c is not given.
        return ans;
    } else {
        return c;
    }
}

.ssyrk(a, [c, alpha: 1, beta:0, uplo:'U', trans:'N', order:'R']) ⇒ Numo::SFloat

SSYRK performs one of the symmetric rank k operations

  C := alpha*A*A**T + beta*C,

or

  C := alpha*A**T*A + beta*C,

where alpha and beta are scalars, C is an n by n symmetric matrix and A is an n by k matrix in the first case and a k by n matrix in the second case.

Parameters:

  • a (Numo::SFloat)

    matrix (>=2-dimentional NArray, n-by-k, inpace).

  • c (Numo::SFloat)

    matrix (>=2-dimentional NArray, n-by-n, optional, inpace).

  • alpha (Float)

    (default=1.0)

  • beta (Float)

    (default=0.0)

  • uplo (String or Symbol)

    if ‘U’: Upper triangle, if ‘L’: Lower triangle. (default=’U’)

  • trans (String or Symbol)

    if ‘N’: Not transpose , if ‘T’: Transpose . (default=’N’)

  • order (String or Symbol)

    if ‘R’: Row-major, if ‘C’: Column-major. (default=’R’)

Returns:

  • (Numo::SFloat)

    returns c.



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# File 'ext/numo/linalg/blas/blas_s.c', line 2387

static VALUE
blas_s_ssyrk(int argc, VALUE const argv[], VALUE UNUSED(mod))
{
    VALUE     ans;
    VALUE     a, c, alpha, beta;
    narray_t *na1, *na3;
    blasint   na, ka, nc, tmp;
    size_t    shape[2];
    ndfunc_arg_in_t ain[3] = {{cT,2},{OVERWRITE,2},{sym_init,0}};
    ndfunc_arg_out_t aout[1] = {{cT,2,shape}};
    ndfunc_t ndf = {iter_blas_s_ssyrk, NO_LOOP, 2, 0, ain, aout};

    args_t g;
    VALUE kw_hash = Qnil;
    ID kw_table[5] = {id_alpha,id_beta,id_order,id_uplo,id_trans};
    VALUE opts[5] = {Qundef,Qundef,Qundef,Qundef,Qundef};

    CHECK_FUNC(func_p,"ssyrk");

    rb_scan_args(argc, argv, "11:", &a, &c, &kw_hash);
    rb_get_kwargs(kw_hash, kw_table, 0, 5, opts);
    alpha   = option_value(opts[0],Qnil);
    beta    = option_value(opts[1],Qnil);
#line 88 "gen/../tmpl/syrk.c"
    g.alpha = RTEST(alpha) ? m_num_to_data(alpha) : m_one;
    g.beta  = RTEST(beta)  ? m_num_to_data(beta)  : m_zero;
#line 91 "gen/../tmpl/syrk.c"
    g.order = option_order(opts[2]);
    g.uplo  = option_uplo(opts[3]);
    g.trans = option_trans(opts[4]);

    GetNArray(a,na1);
    CHECK_DIM_GE(na1,2);

    na = ROW_SIZE(na1); // n
    ka = COL_SIZE(na1); // k (lda)
    SWAP_IFCOLTR(g.order,g.trans, na,ka, tmp);
    g.n = na;
    g.k = ka;

    if (c == Qnil) { // c is not given.
        ndf.nout = 1;
        ain[1] = ain[2];
        c = INT2FIX(0);
        shape[0] = na;
        shape[1] = na;
    } else {
        COPY_OR_CAST_TO(c,cT);
        GetNArray(c,na3);
        CHECK_DIM_GE(na3,2);
        nc = ROW_SIZE(na3);
        if (nc < na) {
            rb_raise(nary_eShapeError,"nc=%d must be >= na=%d",nc,na);
        }
        //CHECK_LEADING_GE("ldc",g.ldc,"n",na);
    }

    ans = na_ndloop3(&ndf, &g, 2, a, c);

    if (ndf.nout == 1) { // c is not given.
        return ans;
    } else {
        return c;
    }
}

.strmm(a, b, [alpha: 1, side:'L', uplo:'U', transa:'N', diag:'U', order:'R']) ⇒ Numo::SFloat

STRMM performs one of the matrix-matrix operations

  B := alpha*op( A )*B,   or   B := alpha*B*op( A ),

where alpha is a scalar, B is an m by n matrix, A is a unit, or non-unit, upper or lower triangular matrix and op( A ) is one of

  op( A ) = A   or   op( A ) = A**T.

Parameters:

  • a (Numo::SFloat)

    matrix (>=2-dimentional NArray).

  • b (Numo::SFloat)

    matrix (>=2-dimentional NArray).

  • alpha (Float)

    (default=1.0)

  • beta (Float)

    (default=0.0)

  • side (String or Symbol)

    if ‘L’: op(A)*B (left-side op), if ‘R’: B*op(A) (right-side op). (default=’L’)

  • uplo (String or Symbol)

    if ‘U’: Upper triangle, if ‘L’: Lower triangle. (default=’U’)

  • transa (String or Symbol)

    if ‘N’: Not transpose a, if ‘T’: Transpose a. (default=’N’)

  • order (String or Symbol)

    if ‘R’: Row-major, if ‘C’: Column-major. (default=’R’)

Returns:

  • (Numo::SFloat)

    returns c = alpha*op( A )*op( B ) + beta*C.



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# File 'ext/numo/linalg/blas/blas_s.c', line 2201

static VALUE
blas_s_strmm(int argc, VALUE const argv[], VALUE UNUSED(mod))
{
    VALUE     a, b, c=Qnil, alpha, beta;
    narray_t *na1, *na2;
    blasint   ma, ka, kb, nb, tmp;
    size_t    shape[2];
    ndfunc_arg_in_t ain[3] = {{cT,2},{cT,2},{OVERWRITE,2}};
    ndfunc_arg_out_t aout[1] = {{cT,2,shape}};
    ndfunc_t ndf = {iter_blas_s_strmm, NO_LOOP, 3, 0, ain, aout};

    args_t g;
    VALUE kw_hash = Qnil;
#if GE
    ID kw_table[5] = {id_alpha,id_beta,id_order,id_transa,id_transb};
#elif TR
    ID kw_table[7] = {id_alpha,id_beta,id_order,id_side,id_uplo,id_transa,id_diag};
#else
    ID kw_table[5] = {id_alpha,id_beta,id_order,id_side,id_uplo};
#endif
    VALUE opts[7] = {Qundef,Qundef,Qundef,Qundef,Qundef,Qundef,Qundef};

    CHECK_FUNC(func_p,"strmm");

    rb_scan_args(argc, argv, "21:", &a, &b, &c, &kw_hash);
    rb_get_kwargs(kw_hash, kw_table, 0, 5+TR*2, opts);
    alpha    = option_value(opts[0],Qnil);
    g.alpha  = RTEST(alpha) ? m_num_to_data(alpha) : m_one;
    beta     = option_value(opts[1],Qnil);
    g.beta   = RTEST(beta)  ? m_num_to_data(beta)  : m_zero;
    g.order  = option_order(opts[2]);
#if GE
    g.transa = option_trans(opts[3]);
    g.transb = option_trans(opts[4]);
#else
    g.side   = option_side(opts[3]);
    g.uplo   = option_uplo(opts[4]);
#endif
#if TR
    g.transa = option_trans(opts[5]);
    g.diag   = option_diag(opts[6]);
#endif

    GetNArray(a,na1);
    GetNArray(b,na2);
    CHECK_DIM_GE(na1,2);
    CHECK_DIM_GE(na2,2);
    ma = ROW_SIZE(na1); // m
    ka = COL_SIZE(na1); // k (lda)
    kb = ROW_SIZE(na2); // k
    nb = COL_SIZE(na2); // n (ldb)

#if GE
    SWAP_IFCOLTR(g.order,g.transa, ma,ka, tmp);
    SWAP_IFCOLTR(g.order,g.transb, kb,nb, tmp);
    CHECK_INT_EQ("ka",ka,"kb",kb);
    g.m = ma;
    g.n = nb;
    g.k = ka;
#else
    CHECK_SQUARE("a",na1); // ma == ka
    SWAP_IFCOL(g.order, kb,nb, tmp);
    // row major             L    R
    //ma = ROW_SIZE(na1); // m or n
    //ka = COL_SIZE(na1); // m or n (lda)
    g.m = kb; // m
    g.n = nb; // n (ldb)
    if (g.side == CblasLeft) {
        CHECK_SIZE_EQ(ka, g.m);
    } else {
        CHECK_SIZE_EQ(ka, g.n);
    }
#endif

    SWAP_IFROW(g.order, ma,nb, tmp);

#if TR
    if (c != Qnil) {
        rb_raise(rb_eArgError,"wrong number of arguments (3 for 2)");
    }
    COPY_OR_CAST_TO(b,cT);
    ndf.nin = 2;

    na_ndloop3(&ndf, &g, 2, a, b);
    return b;
#else

    if (c == Qnil) { // c is not given.
        ndfunc_arg_in_t ain_init = {sym_init,0};
        ain[2] = ain_init;
        ndf.nout = 1;
        c = INT2FIX(0);
        shape[0] = nb;
        shape[1] = ma;
    } else {
        narray_t *na3;
        int nc;
        COPY_OR_CAST_TO(c,cT);
        GetNArray(c,na3);
        CHECK_DIM_GE(na3,2);
        nc = ROW_SIZE(na3);
        if (nc < nb) {
            rb_raise(nary_eShapeError,"nc=%d must be >= nb=%d",nc,nb);
        }
        //CHECK_LEADING_GE("ldc",g.ldc,"m",ma);
    }
    {
        VALUE ans = na_ndloop3(&ndf, &g, 3, a, b, c);

        if (ndf.nout == 1) { // c is not given.
            return ans;
        } else {
            return c;
        }
    }
#endif
}

.strmv(a, x, [uplo: 'U', trans:'N', diag:'U', order:'R']) ⇒ Numo::SFloat

STRMV performs one of the matrix-vector operations

  x := A*x,   or   x := A**T*x,

where x is an n element vector and A is an n by n unit, or non-unit, upper or lower triangular matrix.

Parameters:

  • a (Numo::SFloat)

    matrix (>=2-dimentional NArray).

  • x (Numo::SFloat)

    vector (>=1-dimentional NArray).

  • alpha (Float)

    (default=1.0)

  • beta (Float)

    (default=0.0)

  • side (String or Symbol)

    if ‘L’: op(A)*B (left-side op), if ‘R’: B*op(A) (right-side op). (default=’L’)

  • uplo (String or Symbol)

    if ‘U’: Upper triangle, if ‘L’: Lower triangle. (default=’U’)

  • trans (String or Symbol)

    if ‘N’: Not transpose , if ‘T’: Transpose . (default=’N’)

  • order (String or Symbol)

    if ‘R’: Row-major, if ‘C’: Column-major. (default=’R’)

Returns:

  • (Numo::SFloat)

    returns y = alpha*op(A)*x + beta*y.



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# File 'ext/numo/linalg/blas/blas_s.c', line 1075

static VALUE
blas_s_strmv(int argc, VALUE const argv[], VALUE UNUSED(mod))
{
    VALUE     a, x, y=Qnil, alpha, beta;
    narray_t *na1, *na2;
    blasint   ma, na, nx;
#if GE
    blasint   tmp;
#endif
    size_t    shape[1];
    ndfunc_arg_in_t ain[4] = {{cT,2},{cT,1},{OVERWRITE,1},{sym_init,0}};
    ndfunc_arg_out_t aout[1] = {{cT,1,shape}};
    ndfunc_t ndf = {iter_blas_s_strmv, NO_LOOP, 3, 0, ain, aout};

    args_t g;
    VALUE kw_hash = Qnil;
#if GE
    ID kw_table[4] = {id_alpha,id_beta,id_order,id_trans};
#elif TR
    ID kw_table[6] = {id_alpha,id_beta,id_order,id_uplo,id_trans,id_diag};
#else
    ID kw_table[4] = {id_alpha,id_beta,id_order,id_uplo};
#endif
    VALUE opts[6] = {Qundef,Qundef,Qundef,Qundef,Qundef,Qundef};

    CHECK_FUNC(func_p,"strmv");

    rb_scan_args(argc, argv, "21:", &a, &x, &y, &kw_hash);
    rb_get_kwargs(kw_hash, kw_table, 0, 4+2*TR, opts);
    alpha   = option_value(opts[0],Qnil);
    g.alpha = RTEST(alpha) ? m_num_to_data(alpha) : m_one;
    beta    = option_value(opts[1],Qnil);
    g.beta  = RTEST(beta)  ? m_num_to_data(beta)  : m_zero;
    g.order = option_order(opts[2]);
#if GE
    g.trans = option_trans(opts[3]);
#else
    g.uplo  = option_uplo(opts[3]);
#endif
#if TR
    g.trans = option_trans(opts[4]);
    g.diag  = option_diag(opts[5]);
#endif

    GetNArray(a,na1);
    CHECK_DIM_GE(na1,2);
    ma = ROW_SIZE(na1);
    na = COL_SIZE(na1);

    GetNArray(x,na2);
    CHECK_DIM_GE(na2,1);
    nx = COL_SIZE(na2);
#if GE
    SWAP_IFCOL(g.order, ma, na, tmp);
    g.m = ma;
    g.n = na;
    SWAP_IFTRANS(g.trans, ma, na, tmp);
#else
    CHECK_SQUARE("a",na1);
#endif
    CHECK_INT_EQ("na",na,"nx",nx);
    shape[0] = ma;

#if TR
    if (y != Qnil) {
        rb_raise(rb_eArgError,"wrong number of arguments (3 for 2)");
    }
    COPY_OR_CAST_TO(x,cT);
    ndf.nin = 2;
    na_ndloop3(&ndf, &g, 2, a, x);
    return x;

#else // GE,SY,HE

    if (y == Qnil) { // c is not given.
        ndf.nout = 1;
        ain[2] = ain[3];
        y = INT2FIX(0);
        shape[0] = ma;
    } else {
        narray_t *na3;
        COPY_OR_CAST_TO(y,cT);
        GetNArray(y,na3);
        CHECK_DIM_GE(na3,1);
        CHECK_SIZE_GE(na3,nx);
    }
    {
        VALUE ans;
        ans = na_ndloop3(&ndf, &g, 3, a, x, y);

        if (ndf.nout == 1) { // c is not given.
            return ans;
        } else {
            return y;
        }
    }
#endif
}

.zaxpy(x, y, [alpha: 1]) ⇒ Numo::DComplex

ZAXPY constant times a vector plus a vector.

Parameters:

  • x (Numo::DComplex)

    vector (>=1-dimentional NArray).

  • y (Numo::DComplex)

    vector (>=1-dimentional NArray, inplace allowed).

  • alpha (Float)

    (default=1.0)

Returns:

  • (Numo::DComplex)

    y = alpha * x + y



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# File 'ext/numo/linalg/blas/blas_z.c', line 481

static VALUE
blas_s_zaxpy(int argc, VALUE const argv[], VALUE UNUSED(mod))
{
    VALUE x, y, alpha;
    narray_t *na1, *na2;
    ndfunc_arg_in_t ain[2] = {{cT,0},{OVERWRITE,0}};
    ndfunc_t ndf = {iter_blas_s_zaxpy, STRIDE_LOOP, 2, 0, ain, 0};

    dtype g;
    VALUE kw_hash = Qnil;
    ID kw_table[1] = {id_alpha};
    VALUE opts[1] = {Qundef};

    CHECK_FUNC(func_p,"zaxpy");

    rb_scan_args(argc, argv, "2:", &x, &y, &kw_hash);
    rb_get_kwargs(kw_hash, kw_table, 0, 1, opts);
    alpha = option_value(opts[0],Qnil);
    g     = RTEST(alpha) ? m_num_to_data(alpha) : m_one;

    COPY_OR_CAST_TO(y,cT);
    GetNArray(x,na1);
    GetNArray(y,na2);
    CHECK_DIM_GE(na1,1);
    CHECK_DIM_GE(na2,1);
    CHECK_NON_EMPTY(na1);
    CHECK_NON_EMPTY(na2);
    CHECK_SAME_SHAPE(na1,na2);

    na_ndloop3(&ndf, &g, 2, x, y);
    return y;
}

.zcopy(x, y) ⇒ nil

ZCOPY copies a vector, x, to a vector, y.

Parameters:

  • x (Numo::DComplex)

    vector (>=1-dimentional NArray).

  • y (Numo::DComplex)

    vector (>=1-dimentional NArray).

Returns:

  • (nil)


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# File 'ext/numo/linalg/blas/blas_z.c', line 417

static VALUE
blas_s_zcopy(VALUE UNUSED(mod), VALUE x, VALUE y)
{
    narray_t *na1, *na2;
    ndfunc_arg_in_t ain[2] = {{cT,0},{OVERWRITE,0}};
    ndfunc_t ndf = {iter_blas_s_zcopy, STRIDE_LOOP, 2,0, ain,0};

    CHECK_FUNC(func_p,"zcopy");

    CHECK_NARRAY_TYPE(x,cT);
    CHECK_NARRAY_TYPE(y,cT);
    GetNArray(x,na1);
    GetNArray(y,na2);
    CHECK_DIM_GE(na1,1);
    CHECK_DIM_GE(na2,1);
    CHECK_NON_EMPTY(na1);
    CHECK_NON_EMPTY(na2);
    CHECK_SAME_SHAPE(na1,na2);

    na_ndloop(&ndf, 2, x, y);

    return Qnil;
}

.zdotc(x, y) ⇒ Numo::DComplex

ZDOTC forms the dot product of two complex vectors

  ZDOTC = X^H * Y

Parameters:

  • x (Numo::DComplex)

    vector (>=1-dimentional NArray).

  • y (Numo::DComplex)

    vector (>=1-dimentional NArray).

Returns:

  • (Numo::DComplex)

    op(x) dot y



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# File 'ext/numo/linalg/blas/blas_z.c', line 98

static VALUE
blas_s_zdotc(VALUE mod, VALUE x, VALUE y)
{
    VALUE     ans;
    narray_t *na1, *na2;
    size_t    nx, ny, shape[1]={1};
    ndfunc_arg_in_t ain[2] = {{cT,1},{cT,1}};
    ndfunc_arg_out_t aout[1] = {{numo_cDComplex,0,shape}};
    ndfunc_t ndf = {iter_blas_s_zdotc, NDF_EXTRACT, 2,1, ain,aout};

    CHECK_FUNC(func_p,"zdotc_sub");

    GetNArray(x,na1);
    GetNArray(y,na2);
    CHECK_DIM_GE(na1,1);
    CHECK_DIM_GE(na2,1);
    CHECK_NON_EMPTY(na1);
    CHECK_NON_EMPTY(na2);
    nx = COL_SIZE(na1);
    ny = COL_SIZE(na2);
    CHECK_SIZE_EQ(nx,ny);

    ans = na_ndloop(&ndf, 2, x, y);

    return ans;
}

.zdotu(x, y) ⇒ Numo::DComplex

ZDOTU forms the dot product of two complex vectors

  ZDOTU = X^T * Y

Parameters:

  • x (Numo::DComplex)

    vector (>=1-dimentional NArray).

  • y (Numo::DComplex)

    vector (>=1-dimentional NArray).

Returns:

  • (Numo::DComplex)

    op(x) dot y



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# File 'ext/numo/linalg/blas/blas_z.c', line 165

static VALUE
blas_s_zdotu(VALUE mod, VALUE x, VALUE y)
{
    VALUE     ans;
    narray_t *na1, *na2;
    size_t    nx, ny, shape[1]={1};
    ndfunc_arg_in_t ain[2] = {{cT,1},{cT,1}};
    ndfunc_arg_out_t aout[1] = {{numo_cDComplex,0,shape}};
    ndfunc_t ndf = {iter_blas_s_zdotu, NDF_EXTRACT, 2,1, ain,aout};

    CHECK_FUNC(func_p,"zdotu_sub");

    GetNArray(x,na1);
    GetNArray(y,na2);
    CHECK_DIM_GE(na1,1);
    CHECK_DIM_GE(na2,1);
    CHECK_NON_EMPTY(na1);
    CHECK_NON_EMPTY(na2);
    nx = COL_SIZE(na1);
    ny = COL_SIZE(na2);
    CHECK_SIZE_EQ(nx,ny);

    ans = na_ndloop(&ndf, 2, x, y);

    return ans;
}

.zdscal(a, x) ⇒ Numo::DComplex

ZDSCAL scales a vector by a constant.

Parameters:

  • a (Float)

    scale factor

  • x (Numo::DComplex)

    vector (>=1-dimentional NArray).

Returns:

  • (Numo::DComplex)

    returns a*x.



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# File 'ext/numo/linalg/blas/blas_z.c', line 618

static VALUE
blas_s_zdscal(VALUE mod, VALUE a, VALUE x)
{
    scal_t g[1];
    narray_t *na1;
    ndfunc_arg_in_t ain[1] = {{OVERWRITE,0}};
    ndfunc_t ndf = {iter_blas_s_zdscal, STRIDE_LOOP, 1,0, ain,0};

    CHECK_FUNC(func_p,"zdscal");

  
    if (RTEST(a)) {g[0] = NUM2DBL(a);} else {g[0]=1;}
  
#line 58 "gen/../tmpl/scal.c"
    COPY_OR_CAST_TO(x,cT);
    GetNArray(x,na1);
    CHECK_DIM_GE(na1,1);
    CHECK_NON_EMPTY(na1);

    na_ndloop3(&ndf, g, 1, x);

    return x;
}

.zgemm(a, b, [c, alpha: 1, beta:0, transa:'N', transb:'N', order:'R']) ⇒ Numo::DComplex

ZGEMM performs one of the matrix-matrix operations

  C := alpha*op( A )*op( B ) + beta*C,

where op( X ) is one of

  op( X ) = X   or   op( X ) = X**T   or   op( X ) = X**H,

alpha and beta are scalars, and A, B and C are matrices, with op( A ) an m by k matrix, op( B ) a k by n matrix and C an m by n matrix.

Parameters:

  • a (Numo::DComplex)

    matrix (>=2-dimentional NArray).

  • b (Numo::DComplex)

    matrix (>=2-dimentional NArray).

  • c (Numo::DComplex)

    matrix (>=2-dimentional NArray, optional, inplace allowed).

  • alpha (Float)

    (default=1.0)

  • beta (Float)

    (default=0.0)

  • transa (String or Symbol)

    if ‘N’: Not transpose a, if ‘T’: Transpose a. (default=’N’)

  • transb (String or Symbol)

    if ‘N’: Not transpose b, if ‘T’: Transpose b. (default=’N’)

  • order (String or Symbol)

    if ‘R’: Row-major, if ‘C’: Column-major. (default=’R’)

Returns:

  • (Numo::DComplex)

    returns c = alpha*op( A )*op( B ) + beta*C.



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# File 'ext/numo/linalg/blas/blas_z.c', line 1881

static VALUE
blas_s_zgemm(int argc, VALUE const argv[], VALUE UNUSED(mod))
{
    VALUE     a, b, c=Qnil, alpha, beta;
    narray_t *na1, *na2;
    blasint   ma, ka, kb, nb, tmp;
    size_t    shape[2];
    ndfunc_arg_in_t ain[3] = {{cT,2},{cT,2},{OVERWRITE,2}};
    ndfunc_arg_out_t aout[1] = {{cT,2,shape}};
    ndfunc_t ndf = {iter_blas_s_zgemm, NO_LOOP, 3, 0, ain, aout};

    args_t g;
    VALUE kw_hash = Qnil;
#if GE
    ID kw_table[5] = {id_alpha,id_beta,id_order,id_transa,id_transb};
#elif TR
    ID kw_table[7] = {id_alpha,id_beta,id_order,id_side,id_uplo,id_transa,id_diag};
#else
    ID kw_table[5] = {id_alpha,id_beta,id_order,id_side,id_uplo};
#endif
    VALUE opts[7] = {Qundef,Qundef,Qundef,Qundef,Qundef,Qundef,Qundef};

    CHECK_FUNC(func_p,"zgemm");

    rb_scan_args(argc, argv, "21:", &a, &b, &c, &kw_hash);
    rb_get_kwargs(kw_hash, kw_table, 0, 5+TR*2, opts);
    alpha    = option_value(opts[0],Qnil);
    g.alpha  = RTEST(alpha) ? m_num_to_data(alpha) : m_one;
    beta     = option_value(opts[1],Qnil);
    g.beta   = RTEST(beta)  ? m_num_to_data(beta)  : m_zero;
    g.order  = option_order(opts[2]);
#if GE
    g.transa = option_trans(opts[3]);
    g.transb = option_trans(opts[4]);
#else
    g.side   = option_side(opts[3]);
    g.uplo   = option_uplo(opts[4]);
#endif
#if TR
    g.transa = option_trans(opts[5]);
    g.diag   = option_diag(opts[6]);
#endif

    GetNArray(a,na1);
    GetNArray(b,na2);
    CHECK_DIM_GE(na1,2);
    CHECK_DIM_GE(na2,2);
    ma = ROW_SIZE(na1); // m
    ka = COL_SIZE(na1); // k (lda)
    kb = ROW_SIZE(na2); // k
    nb = COL_SIZE(na2); // n (ldb)

#if GE
    SWAP_IFCOLTR(g.order,g.transa, ma,ka, tmp);
    SWAP_IFCOLTR(g.order,g.transb, kb,nb, tmp);
    CHECK_INT_EQ("ka",ka,"kb",kb);
    g.m = ma;
    g.n = nb;
    g.k = ka;
#else
    CHECK_SQUARE("a",na1); // ma == ka
    SWAP_IFCOL(g.order, kb,nb, tmp);
    // row major             L    R
    //ma = ROW_SIZE(na1); // m or n
    //ka = COL_SIZE(na1); // m or n (lda)
    g.m = kb; // m
    g.n = nb; // n (ldb)
    if (g.side == CblasLeft) {
        CHECK_SIZE_EQ(ka, g.m);
    } else {
        CHECK_SIZE_EQ(ka, g.n);
    }
#endif

    SWAP_IFROW(g.order, ma,nb, tmp);

#if TR
    if (c != Qnil) {
        rb_raise(rb_eArgError,"wrong number of arguments (3 for 2)");
    }
    COPY_OR_CAST_TO(b,cT);
    ndf.nin = 2;

    na_ndloop3(&ndf, &g, 2, a, b);
    return b;
#else

    if (c == Qnil) { // c is not given.
        ndfunc_arg_in_t ain_init = {sym_init,0};
        ain[2] = ain_init;
        ndf.nout = 1;
        c = INT2FIX(0);
        shape[0] = nb;
        shape[1] = ma;
    } else {
        narray_t *na3;
        int nc;
        COPY_OR_CAST_TO(c,cT);
        GetNArray(c,na3);
        CHECK_DIM_GE(na3,2);
        nc = ROW_SIZE(na3);
        if (nc < nb) {
            rb_raise(nary_eShapeError,"nc=%d must be >= nb=%d",nc,nb);
        }
        //CHECK_LEADING_GE("ldc",g.ldc,"m",ma);
    }
    {
        VALUE ans = na_ndloop3(&ndf, &g, 3, a, b, c);

        if (ndf.nout == 1) { // c is not given.
            return ans;
        } else {
            return c;
        }
    }
#endif
}

.zgemv(a, x, [y, alpha: 1, beta:0, trans:'N', order:'R']) ⇒ Numo::DComplex

ZGEMV performs one of the matrix-vector operations

  y := alpha*A*x + beta*y,   or   y := alpha*A**T*x + beta*y,   or
  y := alpha*A**H*x + beta*y,

where alpha and beta are scalars, x and y are vectors and A is an m by n matrix.

Parameters:

  • a (Numo::DComplex)

    matrix (>=2-dimentional NArray).

  • x (Numo::DComplex)

    vector (>=1-dimentional NArray).

  • y (Numo::DComplex)

    vector (>=1-dimentional NArray, optional, inplace allowed).

  • alpha (Float)

    (default=1.0)

  • beta (Float)

    (default=0.0)

  • trans (String or Symbol)

    if ‘N’: Not transpose , if ‘T’: Transpose . (default=’N’)

  • order (String or Symbol)

    if ‘R’: Row-major, if ‘C’: Column-major. (default=’R’)

Returns:

  • (Numo::DComplex)

    returns y = alpha*op(A)*x + beta*y.



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# File 'ext/numo/linalg/blas/blas_z.c', line 728

static VALUE
blas_s_zgemv(int argc, VALUE const argv[], VALUE UNUSED(mod))
{
    VALUE     a, x, y=Qnil, alpha, beta;
    narray_t *na1, *na2;
    blasint   ma, na, nx;
#if GE
    blasint   tmp;
#endif
    size_t    shape[1];
    ndfunc_arg_in_t ain[4] = {{cT,2},{cT,1},{OVERWRITE,1},{sym_init,0}};
    ndfunc_arg_out_t aout[1] = {{cT,1,shape}};
    ndfunc_t ndf = {iter_blas_s_zgemv, NO_LOOP, 3, 0, ain, aout};

    args_t g;
    VALUE kw_hash = Qnil;
#if GE
    ID kw_table[4] = {id_alpha,id_beta,id_order,id_trans};
#elif TR
    ID kw_table[6] = {id_alpha,id_beta,id_order,id_uplo,id_trans,id_diag};
#else
    ID kw_table[4] = {id_alpha,id_beta,id_order,id_uplo};
#endif
    VALUE opts[6] = {Qundef,Qundef,Qundef,Qundef,Qundef,Qundef};

    CHECK_FUNC(func_p,"zgemv");

    rb_scan_args(argc, argv, "21:", &a, &x, &y, &kw_hash);
    rb_get_kwargs(kw_hash, kw_table, 0, 4+2*TR, opts);
    alpha   = option_value(opts[0],Qnil);
    g.alpha = RTEST(alpha) ? m_num_to_data(alpha) : m_one;
    beta    = option_value(opts[1],Qnil);
    g.beta  = RTEST(beta)  ? m_num_to_data(beta)  : m_zero;
    g.order = option_order(opts[2]);
#if GE
    g.trans = option_trans(opts[3]);
#else
    g.uplo  = option_uplo(opts[3]);
#endif
#if TR
    g.trans = option_trans(opts[4]);
    g.diag  = option_diag(opts[5]);
#endif

    GetNArray(a,na1);
    CHECK_DIM_GE(na1,2);
    ma = ROW_SIZE(na1);
    na = COL_SIZE(na1);

    GetNArray(x,na2);
    CHECK_DIM_GE(na2,1);
    nx = COL_SIZE(na2);
#if GE
    SWAP_IFCOL(g.order, ma, na, tmp);
    g.m = ma;
    g.n = na;
    SWAP_IFTRANS(g.trans, ma, na, tmp);
#else
    CHECK_SQUARE("a",na1);
#endif
    CHECK_INT_EQ("na",na,"nx",nx);
    shape[0] = ma;

#if TR
    if (y != Qnil) {
        rb_raise(rb_eArgError,"wrong number of arguments (3 for 2)");
    }
    COPY_OR_CAST_TO(x,cT);
    ndf.nin = 2;
    na_ndloop3(&ndf, &g, 2, a, x);
    return x;

#else // GE,SY,HE

    if (y == Qnil) { // c is not given.
        ndf.nout = 1;
        ain[2] = ain[3];
        y = INT2FIX(0);
        shape[0] = ma;
    } else {
        narray_t *na3;
        COPY_OR_CAST_TO(y,cT);
        GetNArray(y,na3);
        CHECK_DIM_GE(na3,1);
        CHECK_SIZE_GE(na3,nx);
    }
    {
        VALUE ans;
        ans = na_ndloop3(&ndf, &g, 3, a, x, y);

        if (ndf.nout == 1) { // c is not given.
            return ans;
        } else {
            return y;
        }
    }
#endif
}

.zgerc(x, y, [a, alpha: 1, order:'R']) ⇒ Numo::DComplex

ZGERC performs the rank 1 operation

  A := alpha*x*y**H + A,

where alpha is a scalar, x is an m element vector, y is an n element vector and A is an m by n matrix.

Parameters:

  • x (Numo::DComplex)

    vector (>=1-dimentional NArray).

  • y (Numo::DComplex)

    vector (>=1-dimentional NArray).

  • a (Numo::DComplex)

    matrix (>=2-dimentional NArray, m-by-n symmetric matrix, optional, inplace allowed).

  • alpha (Float)

    (default=1.0)

  • order (String or Symbol)

    if ‘R’: Row-major, if ‘C’: Column-major. (default=’R’)

Returns:

  • (Numo::DComplex)

    returns a.



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# File 'ext/numo/linalg/blas/blas_z.c', line 1259

static VALUE
blas_s_zgerc(int argc, VALUE const argv[], VALUE UNUSED(mod))
{
    VALUE     ans;
    VALUE     x, y, a=Qnil, alpha;
    narray_t *na1, *na2;
    blasint   mx, ny, tmp;
    size_t    shape[2];
    ndfunc_arg_in_t ain[4] = {{cT,1},{cT,1},{OVERWRITE,2},{sym_init,0}};
    ndfunc_arg_out_t aout[1] = {{cT,2,shape}};
    ndfunc_t ndf = {iter_blas_s_zgerc, NO_LOOP, 3, 0, ain, aout};

    args_t g;
    VALUE kw_hash = Qnil;
    ID kw_table[2] = {id_alpha,id_order};
    VALUE opts[2] = {Qundef};

    CHECK_FUNC(func_p,"zgerc");

    rb_scan_args(argc, argv, "21:", &x, &y, &a, &kw_hash);
    rb_get_kwargs(kw_hash, kw_table, 0, 2, opts);
    alpha   = option_value(opts[0],Qnil);
    g.alpha = RTEST(alpha) ? m_num_to_data(alpha) : m_one;
    g.order = option_order(opts[1]);

    GetNArray(x,na1);
    GetNArray(y,na2);
    CHECK_DIM_GE(na1,1);
    CHECK_DIM_GE(na2,1);
    mx = COL_SIZE(na1); // m
    ny = COL_SIZE(na2); // n
    g.m = mx;
    g.n = ny;

    SWAP_IFCOL(g.order, mx,ny, tmp);

    if (a == Qnil) { // c is not given.
        ndf.nout = 1;
        ain[2] = ain[3];
        a = INT2FIX(0);
        shape[0] = mx;
        shape[1] = ny;
    } else {
        narray_t  *na3;
        blasint    ma, na;
        COPY_OR_CAST_TO(a,cT);
        GetNArray(a,na3);
        CHECK_DIM_GE(na3,2);
        ma = ROW_SIZE(na3); // m
        na = COL_SIZE(na3); // n (lda)
        CHECK_SIZE_EQ(ma,mx);
        CHECK_SIZE_EQ(na,ny);
    }

    ans = na_ndloop3(&ndf, &g, 3, x, y, a);

    if (ndf.nout = 1) { // a is not given.
        return ans;
    } else {
        return a;
    }
}

.zgeru(x, y, [a, alpha: 1, order:'R']) ⇒ Numo::DComplex

ZGERU performs the rank 1 operation

  A := alpha*x*y**T + A,

where alpha is a scalar, x is an m element vector, y is an n element vector and A is an m by n matrix.

Parameters:

  • x (Numo::DComplex)

    vector (>=1-dimentional NArray).

  • y (Numo::DComplex)

    vector (>=1-dimentional NArray).

  • a (Numo::DComplex)

    matrix (>=2-dimentional NArray, m-by-n symmetric matrix, optional, inplace allowed).

  • alpha (Float)

    (default=1.0)

  • order (String or Symbol)

    if ‘R’: Row-major, if ‘C’: Column-major. (default=’R’)

Returns:

  • (Numo::DComplex)

    returns a.



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# File 'ext/numo/linalg/blas/blas_z.c', line 1378

static VALUE
blas_s_zgeru(int argc, VALUE const argv[], VALUE UNUSED(mod))
{
    VALUE     ans;
    VALUE     x, y, a=Qnil, alpha;
    narray_t *na1, *na2;
    blasint   mx, ny, tmp;
    size_t    shape[2];
    ndfunc_arg_in_t ain[4] = {{cT,1},{cT,1},{OVERWRITE,2},{sym_init,0}};
    ndfunc_arg_out_t aout[1] = {{cT,2,shape}};
    ndfunc_t ndf = {iter_blas_s_zgeru, NO_LOOP, 3, 0, ain, aout};

    args_t g;
    VALUE kw_hash = Qnil;
    ID kw_table[2] = {id_alpha,id_order};
    VALUE opts[2] = {Qundef};

    CHECK_FUNC(func_p,"zgeru");

    rb_scan_args(argc, argv, "21:", &x, &y, &a, &kw_hash);
    rb_get_kwargs(kw_hash, kw_table, 0, 2, opts);
    alpha   = option_value(opts[0],Qnil);
    g.alpha = RTEST(alpha) ? m_num_to_data(alpha) : m_one;
    g.order = option_order(opts[1]);

    GetNArray(x,na1);
    GetNArray(y,na2);
    CHECK_DIM_GE(na1,1);
    CHECK_DIM_GE(na2,1);
    mx = COL_SIZE(na1); // m
    ny = COL_SIZE(na2); // n
    g.m = mx;
    g.n = ny;

    SWAP_IFCOL(g.order, mx,ny, tmp);

    if (a == Qnil) { // c is not given.
        ndf.nout = 1;
        ain[2] = ain[3];
        a = INT2FIX(0);
        shape[0] = mx;
        shape[1] = ny;
    } else {
        narray_t  *na3;
        blasint    ma, na;
        COPY_OR_CAST_TO(a,cT);
        GetNArray(a,na3);
        CHECK_DIM_GE(na3,2);
        ma = ROW_SIZE(na3); // m
        na = COL_SIZE(na3); // n (lda)
        CHECK_SIZE_EQ(ma,mx);
        CHECK_SIZE_EQ(na,ny);
    }

    ans = na_ndloop3(&ndf, &g, 3, x, y, a);

    if (ndf.nout = 1) { // a is not given.
        return ans;
    } else {
        return a;
    }
}

.zhemm(a, b, [c, alpha: 1, beta:0, side:'L', uplo:'U', order:'R']) ⇒ Numo::DComplex

ZHEMM performs one of the matrix-matrix operations

  C := alpha*A*B + beta*C,

or

  C := alpha*B*A + beta*C,

where alpha and beta are scalars, A is an hermitian matrix and B and C are m by n matrices.

Parameters:

  • a (Numo::DComplex)

    matrix (>=2-dimentional NArray).

  • b (Numo::DComplex)

    matrix (>=2-dimentional NArray).

  • c (Numo::DComplex)

    matrix (>=2-dimentional NArray, optional, inplace allowed).

  • alpha (Float)

    (default=1.0)

  • beta (Float)

    (default=0.0)

  • side (String or Symbol)

    if ‘L’: op(A)*B (left-side op), if ‘R’: B*op(A) (right-side op). (default=’L’)

  • uplo (String or Symbol)

    if ‘U’: Upper triangle, if ‘L’: Lower triangle. (default=’U’)

  • order (String or Symbol)

    if ‘R’: Row-major, if ‘C’: Column-major. (default=’R’)

Returns:

  • (Numo::DComplex)

    returns c = alpha*op( A )*op( B ) + beta*C.



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# File 'ext/numo/linalg/blas/blas_z.c', line 2500

static VALUE
blas_s_zhemm(int argc, VALUE const argv[], VALUE UNUSED(mod))
{
    VALUE     a, b, c=Qnil, alpha, beta;
    narray_t *na1, *na2;
    blasint   ma, ka, kb, nb, tmp;
    size_t    shape[2];
    ndfunc_arg_in_t ain[3] = {{cT,2},{cT,2},{OVERWRITE,2}};
    ndfunc_arg_out_t aout[1] = {{cT,2,shape}};
    ndfunc_t ndf = {iter_blas_s_zhemm, NO_LOOP, 3, 0, ain, aout};

    args_t g;
    VALUE kw_hash = Qnil;
#if GE
    ID kw_table[5] = {id_alpha,id_beta,id_order,id_transa,id_transb};
#elif TR
    ID kw_table[7] = {id_alpha,id_beta,id_order,id_side,id_uplo,id_transa,id_diag};
#else
    ID kw_table[5] = {id_alpha,id_beta,id_order,id_side,id_uplo};
#endif
    VALUE opts[7] = {Qundef,Qundef,Qundef,Qundef,Qundef,Qundef,Qundef};

    CHECK_FUNC(func_p,"zhemm");

    rb_scan_args(argc, argv, "21:", &a, &b, &c, &kw_hash);
    rb_get_kwargs(kw_hash, kw_table, 0, 5+TR*2, opts);
    alpha    = option_value(opts[0],Qnil);
    g.alpha  = RTEST(alpha) ? m_num_to_data(alpha) : m_one;
    beta     = option_value(opts[1],Qnil);
    g.beta   = RTEST(beta)  ? m_num_to_data(beta)  : m_zero;
    g.order  = option_order(opts[2]);
#if GE
    g.transa = option_trans(opts[3]);
    g.transb = option_trans(opts[4]);
#else
    g.side   = option_side(opts[3]);
    g.uplo   = option_uplo(opts[4]);
#endif
#if TR
    g.transa = option_trans(opts[5]);
    g.diag   = option_diag(opts[6]);
#endif

    GetNArray(a,na1);
    GetNArray(b,na2);
    CHECK_DIM_GE(na1,2);
    CHECK_DIM_GE(na2,2);
    ma = ROW_SIZE(na1); // m
    ka = COL_SIZE(na1); // k (lda)
    kb = ROW_SIZE(na2); // k
    nb = COL_SIZE(na2); // n (ldb)

#if GE
    SWAP_IFCOLTR(g.order,g.transa, ma,ka, tmp);
    SWAP_IFCOLTR(g.order,g.transb, kb,nb, tmp);
    CHECK_INT_EQ("ka",ka,"kb",kb);
    g.m = ma;
    g.n = nb;
    g.k = ka;
#else
    CHECK_SQUARE("a",na1); // ma == ka
    SWAP_IFCOL(g.order, kb,nb, tmp);
    // row major             L    R
    //ma = ROW_SIZE(na1); // m or n
    //ka = COL_SIZE(na1); // m or n (lda)
    g.m = kb; // m
    g.n = nb; // n (ldb)
    if (g.side == CblasLeft) {
        CHECK_SIZE_EQ(ka, g.m);
    } else {
        CHECK_SIZE_EQ(ka, g.n);
    }
#endif

    SWAP_IFROW(g.order, ma,nb, tmp);

#if TR
    if (c != Qnil) {
        rb_raise(rb_eArgError,"wrong number of arguments (3 for 2)");
    }
    COPY_OR_CAST_TO(b,cT);
    ndf.nin = 2;

    na_ndloop3(&ndf, &g, 2, a, b);
    return b;
#else

    if (c == Qnil) { // c is not given.
        ndfunc_arg_in_t ain_init = {sym_init,0};
        ain[2] = ain_init;
        ndf.nout = 1;
        c = INT2FIX(0);
        shape[0] = nb;
        shape[1] = ma;
    } else {
        narray_t *na3;
        int nc;
        COPY_OR_CAST_TO(c,cT);
        GetNArray(c,na3);
        CHECK_DIM_GE(na3,2);
        nc = ROW_SIZE(na3);
        if (nc < nb) {
            rb_raise(nary_eShapeError,"nc=%d must be >= nb=%d",nc,nb);
        }
        //CHECK_LEADING_GE("ldc",g.ldc,"m",ma);
    }
    {
        VALUE ans = na_ndloop3(&ndf, &g, 3, a, b, c);

        if (ndf.nout == 1) { // c is not given.
            return ans;
        } else {
            return c;
        }
    }
#endif
}

.zhemv(a, x, [y, alpha: 1, beta:0, uplo:'U', order:'R']) ⇒ Numo::DComplex

ZHEMV performs the matrix-vector operation

  y := alpha*A*x + beta*y,

where alpha and beta are scalars, x and y are n element vectors and A is an n by n hermitian matrix.

Parameters:

  • a (Numo::DComplex)

    matrix (>=2-dimentional NArray).

  • x (Numo::DComplex)

    vector (>=1-dimentional NArray).

  • y (Numo::DComplex)

    vector (>=1-dimentional NArray, optional, inplace allowed).

  • alpha (Float)

    (default=1.0)

  • beta (Float)

    (default=0.0)

  • side (String or Symbol)

    if ‘L’: op(A)*B (left-side op), if ‘R’: B*op(A) (right-side op). (default=’L’)

  • uplo (String or Symbol)

    if ‘U’: Upper triangle, if ‘L’: Lower triangle. (default=’U’)

  • order (String or Symbol)

    if ‘R’: Row-major, if ‘C’: Column-major. (default=’R’)

Returns:

  • (Numo::DComplex)

    returns y = alpha*op(A)*x + beta*y.



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# File 'ext/numo/linalg/blas/blas_z.c', line 1102

static VALUE
blas_s_zhemv(int argc, VALUE const argv[], VALUE UNUSED(mod))
{
    VALUE     a, x, y=Qnil, alpha, beta;
    narray_t *na1, *na2;
    blasint   ma, na, nx;
#if GE
    blasint   tmp;
#endif
    size_t    shape[1];
    ndfunc_arg_in_t ain[4] = {{cT,2},{cT,1},{OVERWRITE,1},{sym_init,0}};
    ndfunc_arg_out_t aout[1] = {{cT,1,shape}};
    ndfunc_t ndf = {iter_blas_s_zhemv, NO_LOOP, 3, 0, ain, aout};

    args_t g;
    VALUE kw_hash = Qnil;
#if GE
    ID kw_table[4] = {id_alpha,id_beta,id_order,id_trans};
#elif TR
    ID kw_table[6] = {id_alpha,id_beta,id_order,id_uplo,id_trans,id_diag};
#else
    ID kw_table[4] = {id_alpha,id_beta,id_order,id_uplo};
#endif
    VALUE opts[6] = {Qundef,Qundef,Qundef,Qundef,Qundef,Qundef};

    CHECK_FUNC(func_p,"zhemv");

    rb_scan_args(argc, argv, "21:", &a, &x, &y, &kw_hash);
    rb_get_kwargs(kw_hash, kw_table, 0, 4+2*TR, opts);
    alpha   = option_value(opts[0],Qnil);
    g.alpha = RTEST(alpha) ? m_num_to_data(alpha) : m_one;
    beta    = option_value(opts[1],Qnil);
    g.beta  = RTEST(beta)  ? m_num_to_data(beta)  : m_zero;
    g.order = option_order(opts[2]);
#if GE
    g.trans = option_trans(opts[3]);
#else
    g.uplo  = option_uplo(opts[3]);
#endif
#if TR
    g.trans = option_trans(opts[4]);
    g.diag  = option_diag(opts[5]);
#endif

    GetNArray(a,na1);
    CHECK_DIM_GE(na1,2);
    ma = ROW_SIZE(na1);
    na = COL_SIZE(na1);

    GetNArray(x,na2);
    CHECK_DIM_GE(na2,1);
    nx = COL_SIZE(na2);
#if GE
    SWAP_IFCOL(g.order, ma, na, tmp);
    g.m = ma;
    g.n = na;
    SWAP_IFTRANS(g.trans, ma, na, tmp);
#else
    CHECK_SQUARE("a",na1);
#endif
    CHECK_INT_EQ("na",na,"nx",nx);
    shape[0] = ma;

#if TR
    if (y != Qnil) {
        rb_raise(rb_eArgError,"wrong number of arguments (3 for 2)");
    }
    COPY_OR_CAST_TO(x,cT);
    ndf.nin = 2;
    na_ndloop3(&ndf, &g, 2, a, x);
    return x;

#else // GE,SY,HE

    if (y == Qnil) { // c is not given.
        ndf.nout = 1;
        ain[2] = ain[3];
        y = INT2FIX(0);
        shape[0] = ma;
    } else {
        narray_t *na3;
        COPY_OR_CAST_TO(y,cT);
        GetNArray(y,na3);
        CHECK_DIM_GE(na3,1);
        CHECK_SIZE_GE(na3,nx);
    }
    {
        VALUE ans;
        ans = na_ndloop3(&ndf, &g, 3, a, x, y);

        if (ndf.nout == 1) { // c is not given.
            return ans;
        } else {
            return y;
        }
    }
#endif
}

.zher(x, [a, alpha: 1, uplo:'U', order:'R']) ⇒ Numo::DComplex

ZHER performs the hermitian rank 1 operation

  A := alpha*x*x**H + A,

where alpha is a real scalar, x is an n element vector and A is an n by n hermitian matrix.

Parameters:

  • x (Numo::DComplex)

    vector (>=1-dimentional NArray).

  • a (Numo::DComplex)

    matrix (>=2-dimentional NArray, inplace allowed).

  • alpha (Float)

    (default=1.0)

  • uplo (String or Symbol)

    if ‘U’: Upper triangle, if ‘L’: Lower triangle. (default=’U’)

  • order (String or Symbol)

    if ‘R’: Row-major, if ‘C’: Column-major. (default=’R’)

Returns:

  • (Numo::DComplex)

    return a



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# File 'ext/numo/linalg/blas/blas_z.c', line 1494

static VALUE
blas_s_zher(int argc, VALUE const argv[], VALUE UNUSED(mod))
{
    VALUE     ans;
    VALUE     x, a, alpha;
    narray_t *na1, *na3;
    blasint   nx, na;
    size_t    shape[2];
    ndfunc_arg_in_t ain[3] = {{cT,1},{OVERWRITE,2},{sym_init,0}};
    ndfunc_arg_out_t aout[1] = {{cT,2,shape}};
    ndfunc_t ndf = {iter_blas_s_zher, NO_LOOP, 2, 0, ain, aout};

    args_t g;
    VALUE kw_hash = Qnil;
    ID kw_table[3] = {id_alpha,id_order,id_uplo};
    VALUE opts[3] = {Qundef,Qundef,Qundef};

    CHECK_FUNC(func_p,"zher");

    rb_scan_args(argc, argv, "11:", &x, &a, &kw_hash);
    rb_get_kwargs(kw_hash, kw_table, 0, 3, opts);
    alpha   = option_value(opts[0],Qnil);
    g.alpha = RTEST(alpha) ? NUM2DBL(alpha) : 1;
    g.order = option_order(opts[1]);
    g.uplo  = option_uplo(opts[2]);

    GetNArray(x,na1);
    CHECK_DIM_GE(na1,1);
    nx = COL_SIZE(na1); // n

    if (a == Qnil) { // c is not given.
        ndf.nout = 1;
        ain[1] = ain[2];
        a = INT2FIX(0);
        shape[0] = shape[1] = nx;
    } else {
        COPY_OR_CAST_TO(a,cT);
        GetNArray(a,na3);
        CHECK_DIM_GE(na3,2);
        CHECK_SQUARE("a",na3);
        na = COL_SIZE(na3); // n (lda)
        CHECK_SIZE_EQ(na,nx);
    }

    ans = na_ndloop3(&ndf, &g, 2, x, a);

    if (ndf.nout == 1) { // a is not given.
        return ans;
    } else {
        return a;
    }
}

.zher2(x, y, [a, alpha: 1, uplo:'U', order:'R']) ⇒ Numo::DComplex

ZHER2 performs the hermitian rank 2 operation

  A := alpha*x*y**H + conjg( alpha )*y*x**H + A,

where alpha is a scalar, x and y are n element vectors and A is an n by n hermitian matrix.

Parameters:

  • x (Numo::DComplex)

    vector (>=1-dimentional NArray).

  • y (Numo::DComplex)

    vector (>=1-dimentional NArray).

  • a (Numo::DComplex)

    matrix (>=2-dimentional NArray, inplace allowed).

  • alpha (Float)

    (default=1.0)

  • uplo (String or Symbol)

    if ‘U’: Upper triangle, if ‘L’: Lower triangle. (default=’U’)

  • order (String or Symbol)

    if ‘R’: Row-major, if ‘C’: Column-major. (default=’R’)

Returns:

  • (Numo::DComplex)

    returns a.



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# File 'ext/numo/linalg/blas/blas_z.c', line 1604

static VALUE
blas_s_zher2(int argc, VALUE const argv[], VALUE UNUSED(mod))
{
    VALUE     ans;
    VALUE     x, y, a, alpha;
    narray_t *na1, *na2, *na3;
    blasint   nx, ny, na;
    size_t    shape[2];
    ndfunc_arg_in_t ain[4] = {{cT,1},{cT,1},{OVERWRITE,2},{sym_init,0}};
    ndfunc_arg_out_t aout[1] = {{cT,2,shape}};
    ndfunc_t ndf = {iter_blas_s_zher2, NO_LOOP, 3, 0, ain, aout};

    args_t g;
    VALUE kw_hash = Qnil;
    ID kw_table[3] = {id_alpha,id_order,id_uplo};
    VALUE opts[3] = {Qundef,Qundef,Qundef};

    CHECK_FUNC(func_p,"zher2");

    rb_scan_args(argc, argv, "21:", &x, &y, &a, &kw_hash);
    rb_get_kwargs(kw_hash, kw_table, 0, 3, opts);
    alpha   = option_value(opts[0],Qnil);
    g.alpha = RTEST(alpha) ? m_num_to_data(alpha) : m_one;
    g.order = option_order(opts[1]);
    g.uplo  = option_uplo(opts[2]);

    GetNArray(x,na1);
    GetNArray(y,na2);
    CHECK_DIM_GE(na1,1);
    CHECK_DIM_GE(na2,1);
    nx = COL_SIZE(na1); // n
    ny = COL_SIZE(na2); // n
    CHECK_INT_EQ("nx",nx,"ny",ny);

    if (a == Qnil) { // c is not given.
        ndf.nout = 1;
        ain[2] = ain[3];
        a = INT2FIX(0);
        shape[0] = shape[1] = nx;
    } else {
        COPY_OR_CAST_TO(a,cT);
        GetNArray(a,na3);
        CHECK_DIM_GE(na3,2);
        CHECK_SQUARE("a",na3);
        na = COL_SIZE(na3); // n (lda)
        CHECK_SIZE_EQ(na,nx);
    }

    ans = na_ndloop3(&ndf, &g, 3, x, y, a);

    if (ndf.nout == 1) { // a is not given.
        return ans;
    } else {
        return a;
    }
}

.zherk(a, [c, alpha: 1, beta:0, uplo:'U', trans:'N', order:'R']) ⇒ Numo::DComplex

ZHERK performs one of the hermitian rank k operations

  C := alpha*A*A**H + beta*C,

or

  C := alpha*A**H*A + beta*C,

where alpha and beta are real scalars, C is an n by n hermitian matrix and A is an n by k matrix in the first case and a k by n matrix in the second case.

Parameters:

  • a (Numo::DComplex)

    matrix (>=2-dimentional NArray, n-by-k, inpace).

  • c (Numo::DComplex)

    matrix (>=2-dimentional NArray, n-by-n, optional, inpace).

  • alpha (Float)

    (default=1.0)

  • beta (Float)

    (default=0.0)

  • uplo (String or Symbol)

    if ‘U’: Upper triangle, if ‘L’: Lower triangle. (default=’U’)

  • trans (String or Symbol)

    if ‘N’: Not transpose , if ‘T’: Transpose . (default=’N’)

  • order (String or Symbol)

    if ‘R’: Row-major, if ‘C’: Column-major. (default=’R’)

Returns:

  • (Numo::DComplex)

    returns c.



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# File 'ext/numo/linalg/blas/blas_z.c', line 1727

static VALUE
blas_s_zherk(int argc, VALUE const argv[], VALUE UNUSED(mod))
{
    VALUE     ans;
    VALUE     a, c, alpha, beta;
    narray_t *na1, *na3;
    blasint   na, ka, nc, tmp;
    size_t    shape[2];
    ndfunc_arg_in_t ain[3] = {{cT,2},{OVERWRITE,2},{sym_init,0}};
    ndfunc_arg_out_t aout[1] = {{cT,2,shape}};
    ndfunc_t ndf = {iter_blas_s_zherk, NO_LOOP, 2, 0, ain, aout};

    args_t g;
    VALUE kw_hash = Qnil;
    ID kw_table[5] = {id_alpha,id_beta,id_order,id_uplo,id_trans};
    VALUE opts[5] = {Qundef,Qundef,Qundef,Qundef,Qundef};

    CHECK_FUNC(func_p,"zherk");

    rb_scan_args(argc, argv, "11:", &a, &c, &kw_hash);
    rb_get_kwargs(kw_hash, kw_table, 0, 5, opts);
    alpha   = option_value(opts[0],Qnil);
    beta    = option_value(opts[1],Qnil);
#line 85 "gen/../tmpl/syrk.c"
    g.alpha = RTEST(alpha) ? DBL2NUM(alpha) : 1;
    g.beta  = RTEST(beta)  ? DBL2NUM(beta)  : 0;
#line 91 "gen/../tmpl/syrk.c"
    g.order = option_order(opts[2]);
    g.uplo  = option_uplo(opts[3]);
    g.trans = option_trans(opts[4]);

    GetNArray(a,na1);
    CHECK_DIM_GE(na1,2);

    na = ROW_SIZE(na1); // n
    ka = COL_SIZE(na1); // k (lda)
    SWAP_IFCOLTR(g.order,g.trans, na,ka, tmp);
    g.n = na;
    g.k = ka;

    if (c == Qnil) { // c is not given.
        ndf.nout = 1;
        ain[1] = ain[2];
        c = INT2FIX(0);
        shape[0] = na;
        shape[1] = na;
    } else {
        COPY_OR_CAST_TO(c,cT);
        GetNArray(c,na3);
        CHECK_DIM_GE(na3,2);
        nc = ROW_SIZE(na3);
        if (nc < na) {
            rb_raise(nary_eShapeError,"nc=%d must be >= na=%d",nc,na);
        }
        //CHECK_LEADING_GE("ldc",g.ldc,"n",na);
    }

    ans = na_ndloop3(&ndf, &g, 2, a, c);

    if (ndf.nout == 1) { // c is not given.
        return ans;
    } else {
        return c;
    }
}

.zscal(a, x) ⇒ Numo::DComplex

ZSCAL scales a vector by a constant.

Parameters:

  • a (Float)

    scale factor

  • x (Numo::DComplex)

    vector (>=1-dimentional NArray).

Returns:

  • (Numo::DComplex)

    returns a*x.



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# File 'ext/numo/linalg/blas/blas_z.c', line 554

static VALUE
blas_s_zscal(VALUE mod, VALUE a, VALUE x)
{
    scal_t g[1];
    narray_t *na1;
    ndfunc_arg_in_t ain[1] = {{OVERWRITE,0}};
    ndfunc_t ndf = {iter_blas_s_zscal, STRIDE_LOOP, 1,0, ain,0};

    CHECK_FUNC(func_p,"zscal");

  
#line 56 "gen/../tmpl/scal.c"
    if (RTEST(a)) {g[0] = m_num_to_data(a);} else {g[0]=m_one;}
  
    COPY_OR_CAST_TO(x,cT);
    GetNArray(x,na1);
    CHECK_DIM_GE(na1,1);
    CHECK_NON_EMPTY(na1);

    na_ndloop3(&ndf, g, 1, x);

    return x;
}

.zswap(x, y) ⇒ nil

ZSWAP interchanges two vectors.

Parameters:

  • x (Numo::DComplex)

    vector (>=1-dimentional NArray).

  • y (Numo::DComplex)

    vector (>=1-dimentional NArray).

Returns:

  • (nil)


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# File 'ext/numo/linalg/blas/blas_z.c', line 361

static VALUE
blas_s_zswap(VALUE UNUSED(mod), VALUE x, VALUE y)
{
    narray_t *na1, *na2;
    ndfunc_arg_in_t ain[2] = {{OVERWRITE,0},{OVERWRITE,0}};
    ndfunc_t ndf = {iter_blas_s_zswap, STRIDE_LOOP, 2,0, ain,0};

    CHECK_FUNC(func_p,"zswap");

    CHECK_NARRAY_TYPE(x,cT);
    CHECK_NARRAY_TYPE(y,cT);
    GetNArray(x,na1);
    GetNArray(y,na2);
    CHECK_DIM_GE(na1,1);
    CHECK_DIM_GE(na2,1);
    CHECK_NON_EMPTY(na1);
    CHECK_NON_EMPTY(na2);
    CHECK_SAME_SHAPE(na1,na2);

    na_ndloop(&ndf, 2, x, y);

    return Qnil;
}

.zsymm(a, b, [c, alpha: 1, beta:0, side:'L', uplo:'U', order:'R']) ⇒ Numo::DComplex

ZSYMM performs one of the matrix-matrix operations

  C := alpha*A*B + beta*C,

or

  C := alpha*B*A + beta*C,

where alpha and beta are scalars, A is a symmetric matrix and B and C are m by n matrices.

Parameters:

  • a (Numo::DComplex)

    matrix (>=2-dimentional NArray).

  • b (Numo::DComplex)

    matrix (>=2-dimentional NArray).

  • c (Numo::DComplex)

    matrix (>=2-dimentional NArray, optional, inplace allowed).

  • alpha (Float)

    (default=1.0)

  • beta (Float)

    (default=0.0)

  • side (String or Symbol)

    if ‘L’: op(A)*B (left-side op), if ‘R’: B*op(A) (right-side op). (default=’L’)

  • uplo (String or Symbol)

    if ‘U’: Upper triangle, if ‘L’: Lower triangle. (default=’U’)

  • order (String or Symbol)

    if ‘R’: Row-major, if ‘C’: Column-major. (default=’R’)

Returns:

  • (Numo::DComplex)

    returns c = alpha*op( A )*op( B ) + beta*C.



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# File 'ext/numo/linalg/blas/blas_z.c', line 2088

static VALUE
blas_s_zsymm(int argc, VALUE const argv[], VALUE UNUSED(mod))
{
    VALUE     a, b, c=Qnil, alpha, beta;
    narray_t *na1, *na2;
    blasint   ma, ka, kb, nb, tmp;
    size_t    shape[2];
    ndfunc_arg_in_t ain[3] = {{cT,2},{cT,2},{OVERWRITE,2}};
    ndfunc_arg_out_t aout[1] = {{cT,2,shape}};
    ndfunc_t ndf = {iter_blas_s_zsymm, NO_LOOP, 3, 0, ain, aout};

    args_t g;
    VALUE kw_hash = Qnil;
#if GE
    ID kw_table[5] = {id_alpha,id_beta,id_order,id_transa,id_transb};
#elif TR
    ID kw_table[7] = {id_alpha,id_beta,id_order,id_side,id_uplo,id_transa,id_diag};
#else
    ID kw_table[5] = {id_alpha,id_beta,id_order,id_side,id_uplo};
#endif
    VALUE opts[7] = {Qundef,Qundef,Qundef,Qundef,Qundef,Qundef,Qundef};

    CHECK_FUNC(func_p,"zsymm");

    rb_scan_args(argc, argv, "21:", &a, &b, &c, &kw_hash);
    rb_get_kwargs(kw_hash, kw_table, 0, 5+TR*2, opts);
    alpha    = option_value(opts[0],Qnil);
    g.alpha  = RTEST(alpha) ? m_num_to_data(alpha) : m_one;
    beta     = option_value(opts[1],Qnil);
    g.beta   = RTEST(beta)  ? m_num_to_data(beta)  : m_zero;
    g.order  = option_order(opts[2]);
#if GE
    g.transa = option_trans(opts[3]);
    g.transb = option_trans(opts[4]);
#else
    g.side   = option_side(opts[3]);
    g.uplo   = option_uplo(opts[4]);
#endif
#if TR
    g.transa = option_trans(opts[5]);
    g.diag   = option_diag(opts[6]);
#endif

    GetNArray(a,na1);
    GetNArray(b,na2);
    CHECK_DIM_GE(na1,2);
    CHECK_DIM_GE(na2,2);
    ma = ROW_SIZE(na1); // m
    ka = COL_SIZE(na1); // k (lda)
    kb = ROW_SIZE(na2); // k
    nb = COL_SIZE(na2); // n (ldb)

#if GE
    SWAP_IFCOLTR(g.order,g.transa, ma,ka, tmp);
    SWAP_IFCOLTR(g.order,g.transb, kb,nb, tmp);
    CHECK_INT_EQ("ka",ka,"kb",kb);
    g.m = ma;
    g.n = nb;
    g.k = ka;
#else
    CHECK_SQUARE("a",na1); // ma == ka
    SWAP_IFCOL(g.order, kb,nb, tmp);
    // row major             L    R
    //ma = ROW_SIZE(na1); // m or n
    //ka = COL_SIZE(na1); // m or n (lda)
    g.m = kb; // m
    g.n = nb; // n (ldb)
    if (g.side == CblasLeft) {
        CHECK_SIZE_EQ(ka, g.m);
    } else {
        CHECK_SIZE_EQ(ka, g.n);
    }
#endif

    SWAP_IFROW(g.order, ma,nb, tmp);

#if TR
    if (c != Qnil) {
        rb_raise(rb_eArgError,"wrong number of arguments (3 for 2)");
    }
    COPY_OR_CAST_TO(b,cT);
    ndf.nin = 2;

    na_ndloop3(&ndf, &g, 2, a, b);
    return b;
#else

    if (c == Qnil) { // c is not given.
        ndfunc_arg_in_t ain_init = {sym_init,0};
        ain[2] = ain_init;
        ndf.nout = 1;
        c = INT2FIX(0);
        shape[0] = nb;
        shape[1] = ma;
    } else {
        narray_t *na3;
        int nc;
        COPY_OR_CAST_TO(c,cT);
        GetNArray(c,na3);
        CHECK_DIM_GE(na3,2);
        nc = ROW_SIZE(na3);
        if (nc < nb) {
            rb_raise(nary_eShapeError,"nc=%d must be >= nb=%d",nc,nb);
        }
        //CHECK_LEADING_GE("ldc",g.ldc,"m",ma);
    }
    {
        VALUE ans = na_ndloop3(&ndf, &g, 3, a, b, c);

        if (ndf.nout == 1) { // c is not given.
            return ans;
        } else {
            return c;
        }
    }
#endif
}

.zsyr2k(a, b, [c, alpha: 1, beta:0, uplo:'U', trans:'N', order:'R']) ⇒ Numo::DComplex

ZSYR2K performs one of the symmetric rank 2k operations

  C := alpha*A*B**T + alpha*B*A**T + beta*C,

or

  C := alpha*A**T*B + alpha*B**T*A + beta*C,

where alpha and beta are scalars, C is an n by n symmetric matrix and A and B are n by k matrices in the first case and k by n matrices in the second case.

Parameters:

  • a (Numo::DComplex)

    matrix (>=2-dimentional NArray, n-by-k).

  • b (Numo::DComplex)

    matrix (>=2-dimentional NArray, n-by-k).

  • c (Numo::DComplex)

    matrix (>=2-dimentional NArray, n-by-n, optional, inpace).

  • alpha (Float)

    (default=1.0)

  • beta (Float)

    (default=0.0)

  • uplo (String or Symbol)

    if ‘U’: Upper triangle, if ‘L’: Lower triangle. (default=’U’)

  • trans (String or Symbol)

    if ‘N’: Not transpose , if ‘T’: Transpose . (default=’N’)

  • order (String or Symbol)

    if ‘R’: Row-major, if ‘C’: Column-major. (default=’R’)

Returns:

  • (Numo::DComplex)

    returns c.



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# File 'ext/numo/linalg/blas/blas_z.c', line 2817

static VALUE
blas_s_zsyr2k(int argc, VALUE const argv[], VALUE UNUSED(mod))
{
    VALUE     ans;
    VALUE     a, b, c=Qnil, alpha, beta;
    narray_t *na1, *na2, *na3;
    blasint   na, ka, kb, nb, nc, tmp;
    size_t    shape[2];
    ndfunc_arg_in_t ain[4] = {{cT,2},{cT,2},{OVERWRITE,2},{sym_init,0}};
    ndfunc_arg_out_t aout[1] = {{cT,2,shape}};
    ndfunc_t ndf = {iter_blas_s_zsyr2k, NO_LOOP, 3, 0, ain, aout};

    args_t g;
    VALUE kw_hash = Qnil;
    ID kw_table[5] = {id_alpha,id_beta,id_order,id_uplo,id_trans};
    VALUE opts[5] = {Qundef,Qundef,Qundef,Qundef,Qundef};

    CHECK_FUNC(func_p,"zsyr2k");

    rb_scan_args(argc, argv, "21:", &a, &b, &c, &kw_hash);
    rb_get_kwargs(kw_hash, kw_table, 0, 5, opts);
    alpha    = option_value(opts[0],Qnil);
    g.alpha  = RTEST(alpha) ? m_num_to_data(alpha) : m_one;
    beta     = option_value(opts[1],Qnil);
    g.beta   = RTEST(beta)  ? m_num_to_data(beta)  : m_zero;
    g.order  = option_order(opts[2]);
    g.uplo   = option_uplo(opts[3]);
    g.trans  = option_trans(opts[4]);

    GetNArray(a,na1);
    GetNArray(b,na2);
    CHECK_DIM_GE(na1,2);
    CHECK_DIM_GE(na2,2);

    na = ROW_SIZE(na1); // n
    ka = COL_SIZE(na1); // k (lda)
    SWAP_IFCOLTR(g.order, g.trans, na, ka, tmp);

    nb = ROW_SIZE(na2); // n
    kb = COL_SIZE(na2); // k (ldb)
    SWAP_IFCOLTR(g.order, g.trans, kb, nb, tmp);
    CHECK_INT_EQ("na",na,"nb",nb);
    CHECK_INT_EQ("ka",ka,"kb",kb);
    g.n = nb;
    g.k = kb;

    SWAP_IFROW(g.order, na, nb, tmp);

    if (c == Qnil) { // c is not given.
        ndf.nout = 1;
        ain[2] = ain[3];
        c = INT2FIX(0);
        shape[0] = nb;
        shape[1] = na;
    } else {
        COPY_OR_CAST_TO(c,cT);
        GetNArray(c,na3);
        CHECK_DIM_GE(na3,2);
        nc = ROW_SIZE(na3); // n
        if (nc < nb) {
            rb_raise(nary_eShapeError,"nc=%d must be >= nb=%d",nc,nb);
        }
        //CHECK_LEADING_GE("ldc",g.ldc,"n",na);
    }

    ans = na_ndloop3(&ndf, &g, 3, a, b, c);

    if (ndf.nout = 1) { // c is not given.
        return ans;
    } else {
        return c;
    }
}

.zsyrk(a, [c, alpha: 1, beta:0, uplo:'U', trans:'N', order:'R']) ⇒ Numo::DComplex

ZSYRK performs one of the symmetric rank k operations

  C := alpha*A*A**T + beta*C,

or

  C := alpha*A**T*A + beta*C,

where alpha and beta are scalars, C is an n by n symmetric matrix and A is an n by k matrix in the first case and a k by n matrix in the second case.

Parameters:

  • a (Numo::DComplex)

    matrix (>=2-dimentional NArray, n-by-k, inpace).

  • c (Numo::DComplex)

    matrix (>=2-dimentional NArray, n-by-n, optional, inpace).

  • alpha (Float)

    (default=1.0)

  • beta (Float)

    (default=0.0)

  • uplo (String or Symbol)

    if ‘U’: Upper triangle, if ‘L’: Lower triangle. (default=’U’)

  • trans (String or Symbol)

    if ‘N’: Not transpose , if ‘T’: Transpose . (default=’N’)

  • order (String or Symbol)

    if ‘R’: Row-major, if ‘C’: Column-major. (default=’R’)

Returns:

  • (Numo::DComplex)

    returns c.



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# File 'ext/numo/linalg/blas/blas_z.c', line 2686

static VALUE
blas_s_zsyrk(int argc, VALUE const argv[], VALUE UNUSED(mod))
{
    VALUE     ans;
    VALUE     a, c, alpha, beta;
    narray_t *na1, *na3;
    blasint   na, ka, nc, tmp;
    size_t    shape[2];
    ndfunc_arg_in_t ain[3] = {{cT,2},{OVERWRITE,2},{sym_init,0}};
    ndfunc_arg_out_t aout[1] = {{cT,2,shape}};
    ndfunc_t ndf = {iter_blas_s_zsyrk, NO_LOOP, 2, 0, ain, aout};

    args_t g;
    VALUE kw_hash = Qnil;
    ID kw_table[5] = {id_alpha,id_beta,id_order,id_uplo,id_trans};
    VALUE opts[5] = {Qundef,Qundef,Qundef,Qundef,Qundef};

    CHECK_FUNC(func_p,"zsyrk");

    rb_scan_args(argc, argv, "11:", &a, &c, &kw_hash);
    rb_get_kwargs(kw_hash, kw_table, 0, 5, opts);
    alpha   = option_value(opts[0],Qnil);
    beta    = option_value(opts[1],Qnil);
#line 88 "gen/../tmpl/syrk.c"
    g.alpha = RTEST(alpha) ? m_num_to_data(alpha) : m_one;
    g.beta  = RTEST(beta)  ? m_num_to_data(beta)  : m_zero;
#line 91 "gen/../tmpl/syrk.c"
    g.order = option_order(opts[2]);
    g.uplo  = option_uplo(opts[3]);
    g.trans = option_trans(opts[4]);

    GetNArray(a,na1);
    CHECK_DIM_GE(na1,2);

    na = ROW_SIZE(na1); // n
    ka = COL_SIZE(na1); // k (lda)
    SWAP_IFCOLTR(g.order,g.trans, na,ka, tmp);
    g.n = na;
    g.k = ka;

    if (c == Qnil) { // c is not given.
        ndf.nout = 1;
        ain[1] = ain[2];
        c = INT2FIX(0);
        shape[0] = na;
        shape[1] = na;
    } else {
        COPY_OR_CAST_TO(c,cT);
        GetNArray(c,na3);
        CHECK_DIM_GE(na3,2);
        nc = ROW_SIZE(na3);
        if (nc < na) {
            rb_raise(nary_eShapeError,"nc=%d must be >= na=%d",nc,na);
        }
        //CHECK_LEADING_GE("ldc",g.ldc,"n",na);
    }

    ans = na_ndloop3(&ndf, &g, 2, a, c);

    if (ndf.nout == 1) { // c is not given.
        return ans;
    } else {
        return c;
    }
}

.ztrmm(a, b, [alpha: 1, side:'L', uplo:'U', transa:'N', diag:'U', order:'R']) ⇒ Numo::DComplex

ZTRMM performs one of the matrix-matrix operations

  B := alpha*op( A )*B,   or   B := alpha*B*op( A )

where alpha is a scalar, B is an m by n matrix, A is a unit, or non-unit, upper or lower triangular matrix and op( A ) is one of

  op( A ) = A   or   op( A ) = A**T   or   op( A ) = A**H.

Parameters:

  • a (Numo::DComplex)

    matrix (>=2-dimentional NArray).

  • b (Numo::DComplex)

    matrix (>=2-dimentional NArray).

  • alpha (Float)

    (default=1.0)

  • beta (Float)

    (default=0.0)

  • side (String or Symbol)

    if ‘L’: op(A)*B (left-side op), if ‘R’: B*op(A) (right-side op). (default=’L’)

  • uplo (String or Symbol)

    if ‘U’: Upper triangle, if ‘L’: Lower triangle. (default=’U’)

  • transa (String or Symbol)

    if ‘N’: Not transpose a, if ‘T’: Transpose a. (default=’N’)

  • order (String or Symbol)

    if ‘R’: Row-major, if ‘C’: Column-major. (default=’R’)

Returns:

  • (Numo::DComplex)

    returns c = alpha*op( A )*op( B ) + beta*C.



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# File 'ext/numo/linalg/blas/blas_z.c', line 2293

static VALUE
blas_s_ztrmm(int argc, VALUE const argv[], VALUE UNUSED(mod))
{
    VALUE     a, b, c=Qnil, alpha, beta;
    narray_t *na1, *na2;
    blasint   ma, ka, kb, nb, tmp;
    size_t    shape[2];
    ndfunc_arg_in_t ain[3] = {{cT,2},{cT,2},{OVERWRITE,2}};
    ndfunc_arg_out_t aout[1] = {{cT,2,shape}};
    ndfunc_t ndf = {iter_blas_s_ztrmm, NO_LOOP, 3, 0, ain, aout};

    args_t g;
    VALUE kw_hash = Qnil;
#if GE
    ID kw_table[5] = {id_alpha,id_beta,id_order,id_transa,id_transb};
#elif TR
    ID kw_table[7] = {id_alpha,id_beta,id_order,id_side,id_uplo,id_transa,id_diag};
#else
    ID kw_table[5] = {id_alpha,id_beta,id_order,id_side,id_uplo};
#endif
    VALUE opts[7] = {Qundef,Qundef,Qundef,Qundef,Qundef,Qundef,Qundef};

    CHECK_FUNC(func_p,"ztrmm");

    rb_scan_args(argc, argv, "21:", &a, &b, &c, &kw_hash);
    rb_get_kwargs(kw_hash, kw_table, 0, 5+TR*2, opts);
    alpha    = option_value(opts[0],Qnil);
    g.alpha  = RTEST(alpha) ? m_num_to_data(alpha) : m_one;
    beta     = option_value(opts[1],Qnil);
    g.beta   = RTEST(beta)  ? m_num_to_data(beta)  : m_zero;
    g.order  = option_order(opts[2]);
#if GE
    g.transa = option_trans(opts[3]);
    g.transb = option_trans(opts[4]);
#else
    g.side   = option_side(opts[3]);
    g.uplo   = option_uplo(opts[4]);
#endif
#if TR
    g.transa = option_trans(opts[5]);
    g.diag   = option_diag(opts[6]);
#endif

    GetNArray(a,na1);
    GetNArray(b,na2);
    CHECK_DIM_GE(na1,2);
    CHECK_DIM_GE(na2,2);
    ma = ROW_SIZE(na1); // m
    ka = COL_SIZE(na1); // k (lda)
    kb = ROW_SIZE(na2); // k
    nb = COL_SIZE(na2); // n (ldb)

#if GE
    SWAP_IFCOLTR(g.order,g.transa, ma,ka, tmp);
    SWAP_IFCOLTR(g.order,g.transb, kb,nb, tmp);
    CHECK_INT_EQ("ka",ka,"kb",kb);
    g.m = ma;
    g.n = nb;
    g.k = ka;
#else
    CHECK_SQUARE("a",na1); // ma == ka
    SWAP_IFCOL(g.order, kb,nb, tmp);
    // row major             L    R
    //ma = ROW_SIZE(na1); // m or n
    //ka = COL_SIZE(na1); // m or n (lda)
    g.m = kb; // m
    g.n = nb; // n (ldb)
    if (g.side == CblasLeft) {
        CHECK_SIZE_EQ(ka, g.m);
    } else {
        CHECK_SIZE_EQ(ka, g.n);
    }
#endif

    SWAP_IFROW(g.order, ma,nb, tmp);

#if TR
    if (c != Qnil) {
        rb_raise(rb_eArgError,"wrong number of arguments (3 for 2)");
    }
    COPY_OR_CAST_TO(b,cT);
    ndf.nin = 2;

    na_ndloop3(&ndf, &g, 2, a, b);
    return b;
#else

    if (c == Qnil) { // c is not given.
        ndfunc_arg_in_t ain_init = {sym_init,0};
        ain[2] = ain_init;
        ndf.nout = 1;
        c = INT2FIX(0);
        shape[0] = nb;
        shape[1] = ma;
    } else {
        narray_t *na3;
        int nc;
        COPY_OR_CAST_TO(c,cT);
        GetNArray(c,na3);
        CHECK_DIM_GE(na3,2);
        nc = ROW_SIZE(na3);
        if (nc < nb) {
            rb_raise(nary_eShapeError,"nc=%d must be >= nb=%d",nc,nb);
        }
        //CHECK_LEADING_GE("ldc",g.ldc,"m",ma);
    }
    {
        VALUE ans = na_ndloop3(&ndf, &g, 3, a, b, c);

        if (ndf.nout == 1) { // c is not given.
            return ans;
        } else {
            return c;
        }
    }
#endif
}

.ztrmv(a, x, [uplo: 'U', trans:'N', diag:'U', order:'R']) ⇒ Numo::DComplex

ZTRMV performs one of the matrix-vector operations

  x := A*x,   or   x := A**T*x,   or   x := A**H*x,

where x is an n element vector and A is an n by n unit, or non-unit, upper or lower triangular matrix.

Parameters:

  • a (Numo::DComplex)

    matrix (>=2-dimentional NArray).

  • x (Numo::DComplex)

    vector (>=1-dimentional NArray).

  • alpha (Float)

    (default=1.0)

  • beta (Float)

    (default=0.0)

  • side (String or Symbol)

    if ‘L’: op(A)*B (left-side op), if ‘R’: B*op(A) (right-side op). (default=’L’)

  • uplo (String or Symbol)

    if ‘U’: Upper triangle, if ‘L’: Lower triangle. (default=’U’)

  • trans (String or Symbol)

    if ‘N’: Not transpose , if ‘T’: Transpose . (default=’N’)

  • order (String or Symbol)

    if ‘R’: Row-major, if ‘C’: Column-major. (default=’R’)

Returns:

  • (Numo::DComplex)

    returns y = alpha*op(A)*x + beta*y.



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# File 'ext/numo/linalg/blas/blas_z.c', line 915

static VALUE
blas_s_ztrmv(int argc, VALUE const argv[], VALUE UNUSED(mod))
{
    VALUE     a, x, y=Qnil, alpha, beta;
    narray_t *na1, *na2;
    blasint   ma, na, nx;
#if GE
    blasint   tmp;
#endif
    size_t    shape[1];
    ndfunc_arg_in_t ain[4] = {{cT,2},{cT,1},{OVERWRITE,1},{sym_init,0}};
    ndfunc_arg_out_t aout[1] = {{cT,1,shape}};
    ndfunc_t ndf = {iter_blas_s_ztrmv, NO_LOOP, 3, 0, ain, aout};

    args_t g;
    VALUE kw_hash = Qnil;
#if GE
    ID kw_table[4] = {id_alpha,id_beta,id_order,id_trans};
#elif TR
    ID kw_table[6] = {id_alpha,id_beta,id_order,id_uplo,id_trans,id_diag};
#else
    ID kw_table[4] = {id_alpha,id_beta,id_order,id_uplo};
#endif
    VALUE opts[6] = {Qundef,Qundef,Qundef,Qundef,Qundef,Qundef};

    CHECK_FUNC(func_p,"ztrmv");

    rb_scan_args(argc, argv, "21:", &a, &x, &y, &kw_hash);
    rb_get_kwargs(kw_hash, kw_table, 0, 4+2*TR, opts);
    alpha   = option_value(opts[0],Qnil);
    g.alpha = RTEST(alpha) ? m_num_to_data(alpha) : m_one;
    beta    = option_value(opts[1],Qnil);
    g.beta  = RTEST(beta)  ? m_num_to_data(beta)  : m_zero;
    g.order = option_order(opts[2]);
#if GE
    g.trans = option_trans(opts[3]);
#else
    g.uplo  = option_uplo(opts[3]);
#endif
#if TR
    g.trans = option_trans(opts[4]);
    g.diag  = option_diag(opts[5]);
#endif

    GetNArray(a,na1);
    CHECK_DIM_GE(na1,2);
    ma = ROW_SIZE(na1);
    na = COL_SIZE(na1);

    GetNArray(x,na2);
    CHECK_DIM_GE(na2,1);
    nx = COL_SIZE(na2);
#if GE
    SWAP_IFCOL(g.order, ma, na, tmp);
    g.m = ma;
    g.n = na;
    SWAP_IFTRANS(g.trans, ma, na, tmp);
#else
    CHECK_SQUARE("a",na1);
#endif
    CHECK_INT_EQ("na",na,"nx",nx);
    shape[0] = ma;

#if TR
    if (y != Qnil) {
        rb_raise(rb_eArgError,"wrong number of arguments (3 for 2)");
    }
    COPY_OR_CAST_TO(x,cT);
    ndf.nin = 2;
    na_ndloop3(&ndf, &g, 2, a, x);
    return x;

#else // GE,SY,HE

    if (y == Qnil) { // c is not given.
        ndf.nout = 1;
        ain[2] = ain[3];
        y = INT2FIX(0);
        shape[0] = ma;
    } else {
        narray_t *na3;
        COPY_OR_CAST_TO(y,cT);
        GetNArray(y,na3);
        CHECK_DIM_GE(na3,1);
        CHECK_SIZE_GE(na3,nx);
    }
    {
        VALUE ans;
        ans = na_ndloop3(&ndf, &g, 3, a, x, y);

        if (ndf.nout == 1) { // c is not given.
            return ans;
        } else {
            return y;
        }
    }
#endif
}