sgeqrt3 (3p)

Name

sgeqrt3 - recursively compute a QR factorization of a general real matrix using the compact WY representation of Q

Synopsis

RECURSIVE SUBROUTINE SGEQRT3(M, N, A, LDA, T, LDT, INFO)


INTEGER INFO, LDA, M, N, LDT

REAL A(LDA,*), T(LDT,*)


RECURSIVE SUBROUTINE SGEQRT3_64(M, N, A, LDA, T, LDT, INFO)


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

REAL A(LDA,*), T(LDT,*)


F95 INTERFACE
RECURSIVE SUBROUTINE GEQRT3(M, N, A, LDA, T, LDT, INFO)


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

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


RECURSIVE SUBROUTINE GEQRT3_64(M, N, A, LDA, T, LDT, INFO)


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

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


C INTERFACE
#include <sunperf.h>

void sgeqrt3 (int m, int n, float *a, int lda, float *t, int  ldt,  int
*info);


void  sgeqrt3_64  (long  m,  long n, float *a, long lda, float *t, long
ldt, long *info);

Description

Oracle Solaris Studio Performance Library                          sgeqrt3(3P)



NAME
       sgeqrt3  -  recursively  compute  a  QR factorization of a general real
       matrix using the compact WY representation of Q


SYNOPSIS
       RECURSIVE SUBROUTINE SGEQRT3(M, N, A, LDA, T, LDT, INFO)


       INTEGER INFO, LDA, M, N, LDT

       REAL A(LDA,*), T(LDT,*)


       RECURSIVE SUBROUTINE SGEQRT3_64(M, N, A, LDA, T, LDT, INFO)


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

       REAL A(LDA,*), T(LDT,*)


   F95 INTERFACE
       RECURSIVE SUBROUTINE GEQRT3(M, N, A, LDA, T, LDT, INFO)


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

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


       RECURSIVE SUBROUTINE GEQRT3_64(M, N, A, LDA, T, LDT, INFO)


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

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


   C INTERFACE
       #include <sunperf.h>

       void sgeqrt3 (int m, int n, float *a, int lda, float *t, int  ldt,  int
                 *info);


       void  sgeqrt3_64  (long  m,  long n, float *a, long lda, float *t, long
                 ldt, long *info);


PURPOSE
       sgeqrt3 recursively computes a QR factorization of a real M-by-N matrix
       A, using the compact WY representation of Q.

       Based  on  the algorithm of Elmroth and Gustavson, IBM J. Res. Develop.
       Vol 44 No. 4 July 2000.


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 REAL 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 REAL 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.
       For details of the algorithm, see Elmroth and Gustavson (cited above).



                                  7 Nov 2015                       sgeqrt3(3P)