DGEQP3 (3) Linux Manual Page

dgeqp3.f –

Synopsis

Functions/Subroutines

subroutine dgeqp3 (M, N, A, LDA, JPVT, TAU, WORK, LWORK, INFO)
DGEQP3

Function/Subroutine Documentation

subroutine dgeqp3 (integerM, integerN, double precision, dimension( lda, * )A, integerLDA, integer, dimension( * )JPVT, double precision, dimension( * )TAU, double precision, dimension( * )WORK, integerLWORK, integerINFO)

DGEQP3

Purpose:

 DGEQP3 computes a QR factorization with column pivoting of a

 matrix A: A*P = Q*R using Level 3 BLAS.

 

Parameters:

M

 M is INTEGER

 The number of rows of the matrix A. M >= 0.

N

 N is INTEGER

 The number of columns of the matrix A. N >= 0.

A

 A is DOUBLE PRECISION array, dimension (LDA,N)

 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

 LDA is INTEGER

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

JPVT

 JPVT is INTEGER array, dimension (N)

 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

 TAU is DOUBLE PRECISION array, dimension (min(M,N))

 The scalar factors of the elementary reflectors.

WORK

 WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))

 On exit, if INFO=0, WORK(1) returns the optimal LWORK.

LWORK

 LWORK is INTEGER

 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

 INFO is INTEGER

 = 0: successful exit.

 < 0: if INFO = -i, the i-th argument had an illegal value.

 

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

September 2012

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 real 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).

 

Contributors:

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

Definition at line 152 of file dgeqp3.f.

Author

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