dgeqrfp (3p)

Name

dgeqrfp - N matrix A: A = Q * R

Synopsis

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


INTEGER INFO, LDA, LWORK, M, N

DOUBLE PRECISION A(LDA,*), TAU(*), WORK(*)


SUBROUTINE DGEQRFP_64(M, N, A, LDA, TAU, WORK, LWORK, INFO)


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

DOUBLE PRECISION A(LDA,*), TAU(*), WORK(*)


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


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

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

REAL(8), DIMENSION(:) :: WORK


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


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

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

REAL(8), DIMENSION(:) :: WORK


C INTERFACE
#include <sunperf.h>

void dgeqrfp (int m, int n,  double  *a,  int  lda,  double  *tau,  int
*info);


void dgeqrfp_64 (long m, long n, double *a, long lda, double *tau, long
*info);

Description

Oracle Solaris Studio Performance Library                          dgeqrfp(3P)



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


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


       INTEGER INFO, LDA, LWORK, M, N

       DOUBLE PRECISION A(LDA,*), TAU(*), WORK(*)


       SUBROUTINE DGEQRFP_64(M, N, A, LDA, TAU, WORK, LWORK, INFO)


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

       DOUBLE PRECISION A(LDA,*), TAU(*), WORK(*)


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


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

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

       REAL(8), DIMENSION(:) :: WORK


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


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

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

       REAL(8), DIMENSION(:) :: WORK


   C INTERFACE
       #include <sunperf.h>

       void dgeqrfp (int m, int n,  double  *a,  int  lda,  double  *tau,  int
                 *info);


       void dgeqrfp_64 (long m, long n, double *a, long lda, double *tau, long
                 *info);


PURPOSE
       dgeqrfp 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 DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (min(M,N))
                 The scalar factors of the elementary reflectors (see  Further
                 Details).


       WORK (output)
                 WORK is DOUBLE PRECISION 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                       dgeqrfp(3P)