ctzrzf (3p)

Name

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

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
#include <sunperf.h>

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);

Description

Oracle Solaris Studio Performance Library                           ctzrzf(3P)



NAME
       ctzrzf  - reduce the M-by-N ( M<=N ) complex upper trapezoidal matrix A
       to upper triangular form by means of unitary transformations


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
       #include <sunperf.h>

       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
       ctzrzf 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 >= 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)
                 = 0:  successful exit
                 < 0:  if INFO = -i, the i-th argument had an illegal value


FURTHER DETAILS
       Based on contributions by
         A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA

       The N-by-N matrix Z can be computed by

            Z =  Z(1)*Z(2)* ... *Z(M)

       where each N-by-N Z(k) is given by
            Z(k) = I - tau(k)*v(k)*v(k)**H
       with v(k) is the kth row vector of the M-by-N matrix

            V = ( I   A(:,M+1:N) )

       I is the M-by-M identity matrix, A(:,M+1:N) is the output stored  in  A
       on exit from CTZRZF, and tau(k) is the kth element of the array TAU.




                                  7 Nov 2015                        ctzrzf(3P)