dgeqrfp-f(3)

dgeqrfp.f –

Synopsis

Functions/Subroutines

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

Function/Subroutine Documentation

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

DGEQRFP

Purpose:

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

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 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

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

TAU

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

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 >= max(1,N).
 For optimum performance LWORK >= N*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:

November 2011

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 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).

Definition at line 137 of file dgeqrfp.f.

Author

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