• NAME
• SYNOPSIS
• F95 INTERFACE
• C INTERFACE
• PURPOSE
• ARGUMENTS
• FURTHER DETAILS

NAME

sgeqp3 - compute a QR factorization with column pivoting of a matrix A

SYNOPSIS

  SUBROUTINE SGEQP3( M, N, A, LDA, JPVT, TAU, WORK, LWORK, INFO)
  INTEGER M, N, LDA, LWORK, INFO
  INTEGER JPVT(*)
  REAL A(LDA,*), TAU(*), WORK(*)

  SUBROUTINE SGEQP3_64( M, N, A, LDA, JPVT, TAU, WORK, LWORK, INFO)
  INTEGER*8 M, N, LDA, LWORK, INFO
  INTEGER*8 JPVT(*)
  REAL A(LDA,*), TAU(*), WORK(*)

F95 INTERFACE

  SUBROUTINE GEQP3( [M], [N], A, [LDA], JPVT, TAU, [WORK], [LWORK], 
 *       [INFO])
  INTEGER :: M, N, LDA, LWORK, INFO
  INTEGER, DIMENSION(:) :: JPVT
  REAL, DIMENSION(:) :: TAU, WORK
  REAL, DIMENSION(:,:) :: A

  SUBROUTINE GEQP3_64( [M], [N], A, [LDA], JPVT, TAU, [WORK], [LWORK], 
 *       [INFO])
  INTEGER(8) :: M, N, LDA, LWORK, INFO
  INTEGER(8), DIMENSION(:) :: JPVT
  REAL, DIMENSION(:) :: TAU, WORK
  REAL, DIMENSION(:,:) :: A

C INTERFACE

#include <sunperf.h>

void sgeqp3(int m, int n, float *a, int lda, int *jpvt, float *tau, int *info);

void sgeqp3_64(long m, long n, float *a, long lda, long *jpvt, float *tau, long *info);

PURPOSE

sgeqp3 computes a QR factorization with column pivoting of a matrix A: A*P = Q*R using Level 3 BLAS.

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 M-by-N matrix A. On exit, the upper triangle of the array contains the min(M,N)-by-N upper trapezoidal matrix R; the elements below the diagonal, together with the array TAU, represent the orthogonal matrix Q as a product of min(M,N) elementary reflectors.

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

• JPVT (input/output)
  On entry, if JPVT(J).ne.0, the J-th column of A is permuted to the front of A*P (a leading column); if JPVT(J) =0, the J-th column of A is a free column. On exit, if JPVT(J) =K, then the J-th column of A*P was the the K-th column of A.

• 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 > = 3*N+1. For optimal performance LWORK > = 2*N+( N+1 )*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

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'

where tau is a real/complex scalar, and v is a real/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).

Based on contributions by

  G. Quintana-Orti, Depto. de Informatica, Universidad Jaime I, Spain
  X. Sun, Computer Science Dept., Duke University, USA