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

NAME

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

SYNOPSIS

  SUBROUTINE DORMHR( SIDE, TRANS, M, N, ILO, IHI, A, LDA, TAU, C, LDC, 
 *      WORK, LWORK, INFO)
  CHARACTER * 1 SIDE, TRANS
  INTEGER M, N, ILO, IHI, LDA, LDC, LWORK, INFO
  DOUBLE PRECISION A(LDA,*), TAU(*), C(LDC,*), WORK(*)

  SUBROUTINE DORMHR_64( SIDE, TRANS, M, N, ILO, IHI, A, LDA, TAU, C, 
 *      LDC, WORK, LWORK, INFO)
  CHARACTER * 1 SIDE, TRANS
  INTEGER*8 M, N, ILO, IHI, LDA, LDC, LWORK, INFO
  DOUBLE PRECISION A(LDA,*), TAU(*), C(LDC,*), WORK(*)

F95 INTERFACE

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

  SUBROUTINE ORMHR_64( SIDE, [TRANS], [M], [N], ILO, IHI, A, [LDA], 
 *       TAU, C, [LDC], [WORK], [LWORK], [INFO])
  CHARACTER(LEN=1) :: SIDE, TRANS
  INTEGER(8) :: M, N, ILO, IHI, LDA, LDC, LWORK, INFO
  REAL(8), DIMENSION(:) :: TAU, WORK
  REAL(8), DIMENSION(:,:) :: A, C

C INTERFACE

#include <sunperf.h>

void dormhr(char side, char trans, int m, int n, int ilo, int ihi, double *a, int lda, double *tau, double *c, int ldc, int *info);

void dormhr_64(char side, char trans, long m, long n, long ilo, long ihi, double *a, long lda, double *tau, double *c, long ldc, long *info);

PURPOSE

dormhr 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 of order nq, with nq = m if SIDE = 'L' and nq = n if SIDE = 'R'. Q is defined as the product of IHI-ILO elementary reflectors, as returned by SGEHRD:

Q = H(ilo) H(ilo+1) . . . H(ihi-1).

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.

• ILO (input)
  ILO and IHI must have the same values as in the previous call of SGEHRD. Q is equal to the unit matrix except in the submatrix Q(ilo+1:ihi,ilo+1:ihi). If SIDE = 'L', then 1 < = ILO < = IHI < = M, if M > 0, and ILO = 1 and IHI = 0, if M = 0; if SIDE = 'R', then 1 < = ILO < = IHI < = N, if N > 0, and ILO = 1 and IHI = 0, if N = 0.

• IHI (input)
  See the description of ILO.

• A (input)
  (LDA,M) if SIDE = 'L' (LDA,N) if SIDE = 'R' The vectors which define the elementary reflectors, as returned by SGEHRD.

• LDA (input)
  The leading dimension of the array A. LDA > = max(1,M) if SIDE = 'L'; LDA > = max(1,N) if SIDE = 'R'.

• TAU (input)
  (M-1) if SIDE = 'L' (N-1) if SIDE = 'R' TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by SGEHRD.

• C (input/output)
  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.

• 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