dgeqp3-f(3)

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

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

 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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