• NAME
• SYNOPSIS
• F95 INTERFACE
• C INTERFACE
• PURPOSE
• ARGUMENTS
• FURTHER DETAILS

NAME

sormrz - overwrite the general real M-by-N matrix C with SIDE = 'L' SIDE = 'R' TRANS = 'N'

SYNOPSIS

  SUBROUTINE SORMRZ( SIDE, TRANS, M, N, K, L, A, LDA, TAU, C, LDC, 
 *      WORK, LWORK, INFO)
  CHARACTER * 1 SIDE, TRANS
  INTEGER M, N, K, L, LDA, LDC, LWORK, INFO
  REAL A(LDA,*), TAU(*), C(LDC,*), WORK(*)

  SUBROUTINE SORMRZ_64( SIDE, TRANS, M, N, K, L, A, LDA, TAU, C, LDC, 
 *      WORK, LWORK, INFO)
  CHARACTER * 1 SIDE, TRANS
  INTEGER*8 M, N, K, L, LDA, LDC, LWORK, INFO
  REAL A(LDA,*), TAU(*), C(LDC,*), WORK(*)

F95 INTERFACE

  SUBROUTINE ORMRZ( SIDE, TRANS, [M], [N], K, L, A, [LDA], TAU, C, 
 *       [LDC], [WORK], [LWORK], [INFO])
  CHARACTER(LEN=1) :: SIDE, TRANS
  INTEGER :: M, N, K, L, LDA, LDC, LWORK, INFO
  REAL, DIMENSION(:) :: TAU, WORK
  REAL, DIMENSION(:,:) :: A, C

  SUBROUTINE ORMRZ_64( SIDE, TRANS, [M], [N], K, L, A, [LDA], TAU, C, 
 *       [LDC], [WORK], [LWORK], [INFO])
  CHARACTER(LEN=1) :: SIDE, TRANS
  INTEGER(8) :: M, N, K, L, LDA, LDC, LWORK, INFO
  REAL, DIMENSION(:) :: TAU, WORK
  REAL, DIMENSION(:,:) :: A, C

C INTERFACE

#include <sunperf.h>

void sormrz(char side, char trans, int m, int n, int k, int l, float *a, int lda, float *tau, float *c, int ldc, int *info);

void sormrz_64(char side, char trans, long m, long n, long k, long l, float *a, long lda, float *tau, float *c, long ldc, long *info);

PURPOSE

sormrz overwrites the general real M-by-N matrix C with 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(1) H(2) . . . H(k)

as returned by STZRZF. Q is of order M if SIDE = 'L' and of order N if SIDE = 'R'.

ARGUMENTS

• SIDE (input)
  

   = 'L': apply Q or Q**T from the Left;

   = 'R': apply Q or Q**T from the Right.

• TRANS (input)
  

   = 'N':  No transpose, apply Q;

   = 'T':  Transpose, apply Q**T.

• M (input)
  The number of rows of the matrix C. M > = 0.

• N (input)
  The number of columns of the matrix C. N > = 0.

• K (input)
  The number of elementary reflectors whose product defines the matrix Q. If SIDE = 'L', M > = K > = 0; if SIDE = 'R', N > = K > = 0.

• L (input)
  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.

• A (input)
  (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 = 1,2,...,k, as returned by STZRZF in the last k rows of its array argument A. A is modified by the routine but restored on exit.

• LDA (input)
  The leading dimension of the array A. LDA > = max(1,K).

• TAU (input)
  TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by STZRZF.

• C (input/output)
  On entry, the M-by-N matrix C. On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q.

• LDC (input)
  The leading dimension of the array C. LDC > = max(1,M).

• WORK (workspace)
  On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

• LWORK (input)
  The dimension of the array WORK. If SIDE = 'L', LWORK > = max(1,N); if SIDE = 'R', LWORK > = max(1,M). For optimum performance LWORK > = N*NB if SIDE = 'L', and LWORK > = M*NB if SIDE = 'R', where NB is the optimal blocksize.

  If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA.

• INFO (output)
  

   = 0:  successful exit

   < 0:  if INFO  = -i, the i-th argument had an illegal value

FURTHER DETAILS

Based on contributions by

  A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA