Contents

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

NAME

     cungrq - generate an M-by-N complex matrix Q with  orthonor-
     mal rows,

SYNOPSIS

     SUBROUTINE CUNGRQ(M, N, K, A, LDA, TAU, WORK, LWORK, INFO)

     COMPLEX A(LDA,*), TAU(*), WORK(*)
     INTEGER M, N, K, LDA, LWORK, INFO

     SUBROUTINE CUNGRQ_64(M, N, K, A, LDA, TAU, WORK, LWORK, INFO)

     COMPLEX A(LDA,*), TAU(*), WORK(*)
     INTEGER*8 M, N, K, LDA, LWORK, INFO

  F95 INTERFACE
     SUBROUTINE UNGRQ(M, [N], [K], A, [LDA], TAU, [WORK], [LWORK], [INFO])

     COMPLEX, DIMENSION(:) :: TAU, WORK
     COMPLEX, DIMENSION(:,:) :: A
     INTEGER :: M, N, K, LDA, LWORK, INFO

     SUBROUTINE UNGRQ_64(M, [N], [K], A, [LDA], TAU, [WORK], [LWORK],
            [INFO])

     COMPLEX, DIMENSION(:) :: TAU, WORK
     COMPLEX, DIMENSION(:,:) :: A
     INTEGER(8) :: M, N, K, LDA, LWORK, INFO

  C INTERFACE
     #include <sunperf.h>

     void cungrq(int m, int n, int k, complex *a, int  lda,  com-
               plex *tau, int *info);

     void cungrq_64(long m, long n, long k, complex *a, long lda,
               complex *tau, long *info);

PURPOSE

     cungrq generates an M-by-N complex matrix Q with orthonormal
     rows,  which is defined as the last M rows of a product of K
     elementary reflectors of order N

           Q  =  H(1)' H(2)' . . . H(k)'

     as returned by CGERQF.

ARGUMENTS

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

     N (input) The number of columns of the matrix Q. N >= M.

     K (input) The number of elementary reflectors whose  product
               defines the matrix Q. M >= K >= 0.

     A (input/output)
               On entry, the (m-k+i)-th row must contain the vec-
               tor  which  defines the elementary reflector H(i),
               for i = 1,2,...,k, as returned by  CGERQF  in  the
               last k rows of its array argument A.  On exit, the
               M-by-N matrix Q.

     LDA (input)
               The  first  dimension  of  the  array  A.  LDA  >=
               max(1,M).

     TAU (input)
               TAU(i) must contain the scalar factor of the  ele-
               mentary reflector H(i), as returned by CGERQF.

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

     LWORK (input)
               The  dimension  of  the  array  WORK.   LWORK   >=
               max(1,M).   For optimum performance LWORK >= M*NB,
               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 has an ille-
               gal value