ormr3#

sormr3

Functions

void sormr3(
    const char*          side,
    const char*          trans,
    const INT            m,
    const INT            n,
    const INT            k,
    const INT            l,
    const f32*  restrict A,
    const INT            lda,
    const f32*  restrict tau,
          f32*  restrict C,
    const INT            ldc,
          f32*  restrict work,
          INT*           info
);

void sormr3(const char *side, const char *trans, const INT m, const INT n, const INT k, const INT l, const f32 *restrict A, const INT lda, const f32 *restrict tau, f32 *restrict C, const INT ldc, f32 *restrict work, INT *info)#

SORMR3 overwrites the general real m by n matrix C with.

Q * C if SIDE = ‘L’ and TRANS = “N”, or Q^T * C if SIDE = ‘L’ and TRANS = “T”, or C * Q if SIDE = ‘R’ and TRANS = “N”, or C * Q^T if SIDE = ‘R’ and TRANS = “T”,

where Q is a real orthogonal matrix defined as the product of k elementary reflectors

Q = H(0) H(1) … H(k-1)

as returned by STZRZF. Q is of order m if SIDE = ‘L’ and of order n if SIDE = ‘R’.

Parameters

in

side

‘L’: apply Q or Q^T from the Left; ‘R’: apply Q or Q^T from the Right.

in

trans

‘N’: apply Q (No transpose); ‘T’: apply Q^T (Transpose).

in

m

The number of rows of C. m >= 0.

in

n

The number of columns of C. n >= 0.

in

k

The number of elementary reflectors. If SIDE = “L”, m >= k >= 0; if SIDE = “R”, n >= k >= 0.

in

l

The number of columns of the matrix A containing the meaningful part of the Householder reflectors. If SIDE = “L”, m >= l >= 0; if SIDE = “R”, n >= l >= 0.

in

A

The i-th row must contain the vector which defines the elementary reflector H(i), as returned by STZRZF in the last k rows. Dimension (lda, m) if SIDE = “L”, (lda, n) if SIDE = ‘R’. A is modified by the routine but restored on exit.

in

lda

Leading dimension of A. lda >= max(1, k).

in

tau

Array of dimension (k). TAU(i) is the scalar factor of H(i), as returned by STZRZF.

inout

C

On entry, the m-by-n matrix C. On exit, C is overwritten by Q*C or Q^T*C or C*Q^T or C*Q.

in

ldc

Leading dimension of C. ldc >= max(1, m).

out

work

Workspace, dimension (n) if SIDE = “L”, dimension (m) if SIDE = ‘R’.

out

info

= 0: successful exit
< 0: if info = -i, the i-th argument had an illegal value.

dormr3

Functions

void dormr3(
    const char*          side,
    const char*          trans,
    const INT            m,
    const INT            n,
    const INT            k,
    const INT            l,
    const f64*  restrict A,
    const INT            lda,
    const f64*  restrict tau,
          f64*  restrict C,
    const INT            ldc,
          f64*  restrict work,
          INT*           info
);

void dormr3(const char *side, const char *trans, const INT m, const INT n, const INT k, const INT l, const f64 *restrict A, const INT lda, const f64 *restrict tau, f64 *restrict C, const INT ldc, f64 *restrict work, INT *info)#

DORMR3 overwrites the general real m by n matrix C with.

Q * C if SIDE = ‘L’ and TRANS = “N”, or Q^T * C if SIDE = ‘L’ and TRANS = “T”, or C * Q if SIDE = ‘R’ and TRANS = “N”, or C * Q^T if SIDE = ‘R’ and TRANS = “T”,

where Q is a real orthogonal matrix defined as the product of k elementary reflectors

Q = H(0) H(1) … H(k-1)

as returned by DTZRZF. Q is of order m if SIDE = ‘L’ and of order n if SIDE = ‘R’.

Parameters

in

side

‘L’: apply Q or Q^T from the Left; ‘R’: apply Q or Q^T from the Right.

in

trans

‘N’: apply Q (No transpose); ‘T’: apply Q^T (Transpose).

in

m

The number of rows of C. m >= 0.

in

n

The number of columns of C. n >= 0.

in

k

The number of elementary reflectors. If SIDE = “L”, m >= k >= 0; if SIDE = “R”, n >= k >= 0.

in

l

The number of columns of the matrix A containing the meaningful part of the Householder reflectors. If SIDE = “L”, m >= l >= 0; if SIDE = “R”, n >= l >= 0.

in

A

The i-th row must contain the vector which defines the elementary reflector H(i), as returned by DTZRZF in the last k rows. Dimension (lda, m) if SIDE = “L”, (lda, n) if SIDE = ‘R’. A is modified by the routine but restored on exit.

in

lda

Leading dimension of A. lda >= max(1, k).

in

tau

Array of dimension (k). TAU(i) is the scalar factor of H(i), as returned by DTZRZF.

inout

C

On entry, the m-by-n matrix C. On exit, C is overwritten by Q*C or Q^T*C or C*Q^T or C*Q.

in

ldc

Leading dimension of C. ldc >= max(1, m).

out

work

Workspace, dimension (n) if SIDE = “L”, dimension (m) if SIDE = ‘R’.

out

info

= 0: successful exit
< 0: if info = -i, the i-th argument had an illegal value.

ormr3#

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