dgeqr2-f(3)

dgeqr2.f –

Synopsis

Functions/Subroutines

subroutine dgeqr2 (M, N, A, LDA, TAU, WORK, INFO)
DGEQR2 computes the QR factorization of a general rectangular matrix using an unblocked algorithm.

Function/Subroutine Documentation

subroutine dgeqr2 (integerM, integerN, double precision, dimension( lda, * )A, integerLDA, double precision, dimension( * )TAU, double precision, dimension( * )WORK, integerINFO)

DGEQR2 computes the QR factorization of a general rectangular matrix using an unblocked algorithm.

Purpose:

 DGEQR2 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 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 (N)

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 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 122 of file dgeqr2.f.

Author

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