sgeqrfp (3p)

Name

sgeqrfp - N matrix A: A = Q * R

Synopsis

SUBROUTINE SGEQRFP(M, N, A, LDA, TAU, WORK, LWORK, INFO)


INTEGER INFO, LDA, LWORK, M, N

REAL A(LDA,*), TAU(*), WORK(*)


SUBROUTINE SGEQRFP_64(M, N, A, LDA, TAU, WORK, LWORK, INFO)


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

REAL A(LDA,*), TAU(*), WORK(*)


F95 INTERFACE
SUBROUTINE GEQRFP(M, N, A, LDA, TAU, WORK, LWORK, INFO)


REAL, DIMENSION(:,:) :: A

INTEGER :: M, N, LDA, LWORK, INFO

REAL, DIMENSION(:) :: WORK


SUBROUTINE GEQRFP_64(M, N, A, LDA, TAU, WORK, LWORK, INFO)


REAL, DIMENSION(:,:) :: A

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

REAL, DIMENSION(:) :: WORK


C INTERFACE
#include <sunperf.h>

void sgeqrfp (int m, int n, float *a, int lda, float *tau, int *info);


void sgeqrfp_64 (long m, long n, float *a, long lda, float  *tau,  long
*info);

Description

Oracle Solaris Studio Performance Library                          sgeqrfp(3P)



NAME
       sgeqrfp - compute a QR factorization of a real M-by-N matrix A: A = Q *
       R


SYNOPSIS
       SUBROUTINE SGEQRFP(M, N, A, LDA, TAU, WORK, LWORK, INFO)


       INTEGER INFO, LDA, LWORK, M, N

       REAL A(LDA,*), TAU(*), WORK(*)


       SUBROUTINE SGEQRFP_64(M, N, A, LDA, TAU, WORK, LWORK, INFO)


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

       REAL A(LDA,*), TAU(*), WORK(*)


   F95 INTERFACE
       SUBROUTINE GEQRFP(M, N, A, LDA, TAU, WORK, LWORK, INFO)


       REAL, DIMENSION(:,:) :: A

       INTEGER :: M, N, LDA, LWORK, INFO

       REAL, DIMENSION(:) :: WORK


       SUBROUTINE GEQRFP_64(M, N, A, LDA, TAU, WORK, LWORK, INFO)


       REAL, DIMENSION(:,:) :: A

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

       REAL, DIMENSION(:) :: WORK


   C INTERFACE
       #include <sunperf.h>

       void sgeqrfp (int m, int n, float *a, int lda, float *tau, int *info);


       void sgeqrfp_64 (long m, long n, float *a, long lda, float  *tau,  long
                 *info);


PURPOSE
       sgeqrfp  computes a QR factorization of a real M-by-N matrix A: A = Q *
       R.


ARGUMENTS
       M (input)
                 M is INTEGER
                 The number of rows of the matrix A.  M >= 0.


       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 M-by-N matrix A.
                 On exit, the elements on and above the diagonal of the  array
                 contain  the  min(M,N)-by-N  upper trapezoidal matrix R (R is
                 upper triangular if m >= n); the elements below the diagonal,
                 with  the  array  TAU, represent the orthogonal matrix Q as a
                 product  of  min(m,n)  elementary  reflectors  (see   Further
                 Details).


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


       TAU (output)
                 TAU is REAL array, dimension (min(M,N))
                 The  scalar factors of the elementary reflectors (see Further
                 Details).


       WORK (output)
                 WORK is REAL array, dimension (MAX(1,LWORK))
                 On exit, if INFO = 0, WORK(1) returns the optimal LWORK.


       LWORK (input)
                 LWORK is INTEGER
                 The dimension of the array WORK.
                 LWORK >= max(1,N).
                 For optimum performance LWORK >= N*NB, where NB is the  opti-
                 mal 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)
                 INFO is INTEGER
                 = 0:  successful exit
                 < 0:  if INFO = -i, the i-th argument had an illegal value


FURTHER DETAILS
       The matrix Q is represented as a product of elementary reflectors

       Q = H(1)*H(2) . . . H(K), where K = min(M,N).

       Each H(i) has the form

       H(i) = I - tau * v * v**T

       where tau is a complex scalar, and v is a complex vector with  v(1:i-1)
       =  0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:M,i), and tau in
       TAU(i).



                                  7 Nov 2015                       sgeqrfp(3P)