ormrz#

Functions

void sormrz(
    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,
    const INT            lwork,
          INT*           info
);
void sormrz(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, const INT lwork, INT *info)#

SORMRZ overwrites the general real M-by-N matrix C with. 

         SIDE = 'L'     SIDE = 'R'
TRANS = ‘N’: Q * C C * Q TRANS = ‘T’: Q^T * C C * Q^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’.

This is the blocked Level 3 BLAS version of the algorithm.

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 whose product defines the matrix Q. 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.

inout
A

Double precision array, dimension (lda, m) if SIDE = “L”, (lda, n) if SIDE = ‘R’. The i-th row must contain the vector which defines the elementary reflector H(i), for i = 0,1,…,k-1, as returned by STZRZF in the last k rows of its array argument A. A is modified by the routine but restored on exit.

in
lda

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

in
tau

Double precision array, dimension (k). tau[i] must contain the scalar factor of the elementary reflector H(i), as returned by STZRZF.

inout
C

Double precision array, dimension (ldc, n). 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

Double precision array, dimension (max(1, lwork)). On exit, work[0] returns the optimal lwork.

in
lwork

Dimension of work. If SIDE = “L”, lwork >= max(1, n); if SIDE = “R”, lwork >= max(1, m). For good performance, lwork should generally be larger. If lwork == -1, workspace query only.

out
info

  • = 0: successful exit

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

Functions

void dormrz(
    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,
    const INT            lwork,
          INT*           info
);
void dormrz(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, const INT lwork, INT *info)#

DORMRZ overwrites the general real M-by-N matrix C with. 

         SIDE = 'L'     SIDE = 'R'
TRANS = ‘N’: Q * C C * Q TRANS = ‘T’: Q^T * C C * Q^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’.

This is the blocked Level 3 BLAS version of the algorithm.

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 whose product defines the matrix Q. 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.

inout
A

Double precision array, dimension (lda, m) if SIDE = “L”, (lda, n) if SIDE = ‘R’. The i-th row must contain the vector which defines the elementary reflector H(i), for i = 0,1,…,k-1, as returned by DTZRZF in the last k rows of its array argument A. A is modified by the routine but restored on exit.

in
lda

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

in
tau

Double precision array, dimension (k). tau[i] must contain the scalar factor of the elementary reflector H(i), as returned by DTZRZF.

inout
C

Double precision array, dimension (ldc, n). 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

Double precision array, dimension (max(1, lwork)). On exit, work[0] returns the optimal lwork.

in
lwork

Dimension of work. If SIDE = “L”, lwork >= max(1, n); if SIDE = “R”, lwork >= max(1, m). For good performance, lwork should generally be larger. If lwork == -1, workspace query only.

out
info

  • = 0: successful exit

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

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