Contents


NAME

     zgerqf - compute an RQ factorization  of  a  complex  M-by-N
     matrix A

SYNOPSIS

     SUBROUTINE ZGERQF(M, N, A, LDA, TAU, WORK, LDWORK, INFO)

     DOUBLE COMPLEX A(LDA,*), TAU(*), WORK(*)
     INTEGER M, N, LDA, LDWORK, INFO

     SUBROUTINE ZGERQF_64(M, N, A, LDA, TAU, WORK, LDWORK, INFO)

     DOUBLE COMPLEX A(LDA,*), TAU(*), WORK(*)
     INTEGER*8 M, N, LDA, LDWORK, INFO

  F95 INTERFACE
     SUBROUTINE GERQF([M], [N], A, [LDA], TAU, [WORK], [LDWORK], [INFO])

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

     SUBROUTINE GERQF_64([M], [N], A, [LDA], TAU, [WORK], [LDWORK], [INFO])

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

  C INTERFACE
     #include <sunperf.h>

     void zgerqf(int m, int n, doublecomplex *a, int  lda,  doub-
               lecomplex *tau, int *info);

     void zgerqf_64(long m, long n, doublecomplex *a,  long  lda,
               doublecomplex *tau, long *info);

PURPOSE

     zgerqf computes an RQ  factorization  of  a  complex  M-by-N
     matrix A:  A = R * Q.

ARGUMENTS

     M (input) The number of rows of the matrix A.  M >= 0.
     N (input) The number of columns of the matrix A.  N >= 0.

     A (input/output)
               On entry, the M-by-N matrix A.  On exit, if  m  <=
               n,  the  upper  triangle  of the subarray A(1:m,n-
               m+1:n) contains the M-by-M upper triangular matrix
               R;  if  m  >= n, the elements on and above the (m-
               n)-th subdiagonal contain the  M-by-N  upper  tra-
               pezoidal  matrix  R;  the remaining elements, with
               the array TAU, represent the unitary matrix Q as a
               product  of  min(m,n)  elementary  reflectors (see
               Further Details).

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

     TAU (output)
               The scalar factors of  the  elementary  reflectors
               (see Further Details).

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

     LDWORK (input)
               The  dimension  of  the  array  WORK.   LDWORK  >=
               max(1,M).  For optimum performance LDWORK >= M*NB,
               where NB is the optimal blocksize.

               If LDWORK = -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 LDWORK is issued by XERBLA.

     INFO (output)
               = 0:  successful exit
               < 0:  if INFO = -i, the i-th argument had an ille-
               gal value

FURTHER DETAILS

     The matrix Q is  represented  as  a  product  of  elementary
     reflectors

        Q = H(1)' H(2)' . . . H(k)', where k = min(m,n).
     Each H(i) has the form

        H(i) = I - tau * v * v'

     where tau is a complex scalar, and v  is  a  complex  vector
     with  v(n-k+i+1:n) = 0 and v(n-k+i) = 1; conjg(v(1:n-k+i-1))
     is stored on exit in A(m-k+i,1:n-k+i-1), and tau in TAU(i).