NAME

SYNOPSIS

  SUBROUTINE CTZRZF( M, N, A, LDA, TAU, WORK, LWORK, INFO)
  COMPLEX A(LDA,*), TAU(*), WORK(*)
  INTEGER M, N, LDA, LWORK, INFO
 
  SUBROUTINE CTZRZF_64( M, N, A, LDA, TAU, WORK, LWORK, INFO)
  COMPLEX A(LDA,*), TAU(*), WORK(*)
  INTEGER*8 M, N, LDA, LWORK, INFO
 

F95 INTERFACE

  SUBROUTINE TZRZF( [M], [N], A, [LDA], TAU, [WORK], [LWORK], [INFO])
  COMPLEX, DIMENSION(:) :: TAU, WORK
  COMPLEX, DIMENSION(:,:) :: A
  INTEGER :: M, N, LDA, LWORK, INFO
 
  SUBROUTINE TZRZF_64( [M], [N], A, [LDA], TAU, [WORK], [LWORK], [INFO])
  COMPLEX, DIMENSION(:) :: TAU, WORK
  COMPLEX, DIMENSION(:,:) :: A
  INTEGER(8) :: M, N, LDA, LWORK, INFO
 

C INTERFACE

void ctzrzf(int m, int n, complex *a, int lda, complex *tau, int *info);

void ctzrzf_64(long m, long n, complex *a, long lda, complex *tau, long *info);

PURPOSE

The upper trapezoidal matrix A is factored as

   A = ( R  0 ) * Z,

where Z is an N-by-N unitary matrix and R is an M-by-M upper triangular matrix.

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 leading M-by-N upper trapezoidal part of the array A must contain the matrix to be factorized. On exit, the leading M-by-M upper triangular part of A contains the upper triangular matrix R, and elements M+1 to N of the first M rows of A, with the array TAU, represent the unitary matrix Z as a product of M elementary reflectors.

* LDA (input)

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

* TAU (output)

The scalar factors of the elementary reflectors.

* 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)