cgerq2-f(3)

cgerq2.f –

Synopsis

Functions/Subroutines

subroutine cgerq2 (M, N, A, LDA, TAU, WORK, INFO)
CGERQ2 computes the RQ factorization of a general rectangular matrix using an unblocked algorithm.

Function/Subroutine Documentation

subroutine cgerq2 (integerM, integerN, complex, dimension( lda, * )A, integerLDA, complex, dimension( * )TAU, complex, dimension( * )WORK, integerINFO)

CGERQ2 computes the RQ factorization of a general rectangular matrix using an unblocked algorithm.

Purpose:

 CGERQ2 computes an RQ factorization of a complex m by n matrix A:
 A = R * Q.

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 COMPLEX array, dimension (LDA,N)
 On entry, the m by n matrix A.
 On exit, if m <= n, the upper triangle of the subarray
 A(1:m,n-m+1:n) contains the m by m upper triangular matrix R;
 if m >= n, the elements on and above the (m-n)-th subdiagonal
 contain the m by n upper trapezoidal matrix R; the remaining
 elements, with the array TAU, represent the unitary 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 COMPLEX array, dimension (min(M,N))
 The scalar factors of the elementary reflectors (see Further
 Details).

WORK

 WORK is COMPLEX array, dimension (M)

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 H(2)**H . . . H(k)**H, where k = min(m,n).
 Each H(i) has the form
 H(i) = I - tau * v * v**H
 where tau is a complex scalar, and v is a complex vector with
 v(n-k+i+1:n) = 0 and v(n-k+i) = 1; conjg(v(1:n-k+i-1)) is stored on
 exit in A(m-k+i,1:n-k+i-1), and tau in TAU(i).

Definition at line 124 of file cgerq2.f.

Author

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