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

NAME

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

SYNOPSIS

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

  SUBROUTINE DORMTR_64( SIDE, UPLO, TRANS, M, N, A, LDA, TAU, C, LDC, 
 *      WORK, LWORK, INFO)
  CHARACTER * 1 SIDE, UPLO, TRANS
  INTEGER*8 M, N, LDA, LDC, LWORK, INFO
  DOUBLE PRECISION A(LDA,*), TAU(*), C(LDC,*), WORK(*)

F95 INTERFACE

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

  SUBROUTINE ORMTR_64( SIDE, UPLO, [TRANS], [M], [N], A, [LDA], TAU, 
 *       C, [LDC], [WORK], [LWORK], [INFO])
  CHARACTER(LEN=1) :: SIDE, UPLO, TRANS
  INTEGER(8) :: M, N, LDA, LDC, LWORK, INFO
  REAL(8), DIMENSION(:) :: TAU, WORK
  REAL(8), DIMENSION(:,:) :: A, C

C INTERFACE

#include <sunperf.h>

void dormtr(char side, char uplo, char trans, int m, int n, double *a, int lda, double *tau, double *c, int ldc, int *info);

void dormtr_64(char side, char uplo, char trans, long m, long n, double *a, long lda, double *tau, double *c, long ldc, long *info);

PURPOSE

dormtr 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 nq-1 elementary reflectors, as returned by SSYTRD:

if UPLO = 'U', Q = H(nq-1) . . . H(2) H(1);

if UPLO = 'L', Q = H(1) H(2) . . . H(nq-1).

ARGUMENTS

• SIDE (input)
  

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

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

• UPLO (input)
  

   = 'U': Upper triangle of A contains elementary reflectors
  from SSYTRD;
   = 'L': Lower triangle of A contains elementary reflectors
  from SSYTRD.

• 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.

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

• 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 SSYTRD.

• 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