NAME

SYNOPSIS

  SUBROUTINE ZTZRQF( M, N, A, LDA, TAU, INFO)
  DOUBLE COMPLEX A(LDA,*), TAU(*)
  INTEGER M, N, LDA, INFO
 
  SUBROUTINE ZTZRQF_64( M, N, A, LDA, TAU, INFO)
  DOUBLE COMPLEX A(LDA,*), TAU(*)
  INTEGER*8 M, N, LDA, INFO
 

F95 INTERFACE

  SUBROUTINE TZRQF( [M], [N], A, [LDA], TAU, [INFO])
  COMPLEX(8), DIMENSION(:) :: TAU
  COMPLEX(8), DIMENSION(:,:) :: A
  INTEGER :: M, N, LDA, INFO
 
  SUBROUTINE TZRQF_64( [M], [N], A, [LDA], TAU, [INFO])
  COMPLEX(8), DIMENSION(:) :: TAU
  COMPLEX(8), DIMENSION(:,:) :: A
  INTEGER(8) :: M, N, LDA, INFO
 

C INTERFACE

void ztzrqf(int m, int n, doublecomplex *a, int lda, doublecomplex *tau, int *info);

void ztzrqf_64(long m, long n, doublecomplex *a, long lda, doublecomplex *tau, long *info);

PURPOSE

CTZRQF reduces the M-by-N ( M<=N ) complex upper trapezoidal matrix A to upper triangular form by means of unitary transformations.

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 >= M.

* 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.

* INFO (output)