dgeqrt2 (3p)

Name

dgeqrt2 - compute a QR factorization of a general real matrix using the compact WY representation of Q

Synopsis

SUBROUTINE DGEQRT2(M, N, A, LDA, T, LDT, INFO)


INTEGER INFO, LDA, LDT, M, N

DOUBLE PRECISION A(LDA,*), T(LDT,*)


SUBROUTINE DGEQRT2_64(M, N, A, LDA, T, LDT, INFO)


INTEGER*8 INFO, LDA, LDT, M, N

DOUBLE PRECISION A(LDA,*), T(LDT,*)


F95 INTERFACE
SUBROUTINE GEQRT2(M, N, A, LDA, T, LDT, INFO)


INTEGER :: M, N, LDA, LDT, INFO

REAL(8), DIMENSION(:,:) :: A, T


SUBROUTINE GEQRT2_64(M, N, A, LDA, T, LDT, INFO)


INTEGER(8) :: M, N, LDA, LDT, INFO

REAL(8), DIMENSION(:,:) :: A, T


C INTERFACE
#include <sunperf.h>

void dgeqrt2 (int m, int n, double *a, int lda, double *t, int ldt, int
*info);


void  dgeqrt2_64  (long m, long n, double *a, long lda, double *t, long
ldt, long *info);

Description

Oracle Solaris Studio Performance Library                          dgeqrt2(3P)



NAME
       dgeqrt2   -  compute  a QR factorization of a general real matrix using
       the compact WY representation of Q


SYNOPSIS
       SUBROUTINE DGEQRT2(M, N, A, LDA, T, LDT, INFO)


       INTEGER INFO, LDA, LDT, M, N

       DOUBLE PRECISION A(LDA,*), T(LDT,*)


       SUBROUTINE DGEQRT2_64(M, N, A, LDA, T, LDT, INFO)


       INTEGER*8 INFO, LDA, LDT, M, N

       DOUBLE PRECISION A(LDA,*), T(LDT,*)


   F95 INTERFACE
       SUBROUTINE GEQRT2(M, N, A, LDA, T, LDT, INFO)


       INTEGER :: M, N, LDA, LDT, INFO

       REAL(8), DIMENSION(:,:) :: A, T


       SUBROUTINE GEQRT2_64(M, N, A, LDA, T, LDT, INFO)


       INTEGER(8) :: M, N, LDA, LDT, INFO

       REAL(8), DIMENSION(:,:) :: A, T


   C INTERFACE
       #include <sunperf.h>

       void dgeqrt2 (int m, int n, double *a, int lda, double *t, int ldt, int
                 *info);


       void  dgeqrt2_64  (long m, long n, double *a, long lda, double *t, long
                 ldt, long *info);


PURPOSE
       dgeqrt2 computes a QR factorization of a real M-by-N  matrix  A,  using
       the compact WY representation of Q.


ARGUMENTS
       M (input)
                 M is INTEGER
                 The number of rows of the matrix A.  M >= N.


       N (input)
                 N is INTEGER
                 The number of columns of the matrix A.  N >= 0.


       A (input/output)
                 A is DOUBLE PRECISION array, dimension (LDA,N)
                 On  entry, the real M-by-N matrix A. On exit, the elements on
                 and above the diagonal contain the  N-by-N  upper  triangular
                 matrix  R; the elements below the diagonal are the columns of
                 V.  See below for further details.


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


       T (output)
                 T is DOUBLE PRECISION array, dimension (LDT,N)
                 The N-by-N upper triangular factor of  the  block  reflector.
                 The  elements  on  and  above  the diagonal contain the block
                 reflector T; the elements below the diagonal  are  not  used.
                 See below for further details.


       LDT (input)
                 LDT is INTEGER
                 The leading dimension of the array T.
                 LDT >= max(1,N).


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


FURTHER DETAILS
       The  matrix  V stores the elementary reflectors H(i) in the i-th column
       below the diagonal. For example, if M=5 and N=3, the matrix V is

                      V = (  1       )
                          ( v1  1    )
                          ( v1 v2  1 )
                          ( v1 v2 v3 )
       where the vi's represent the vectors which define H(i), which are returned
       in the matrix A.  The 1's along the diagonal of V are not stored in A.  The
       block reflector H is then given by

                    H = I - V * T * V**T

       where V**T is the transpose of V.



                                  7 Nov 2015                       dgeqrt2(3P)