cgeqlf-f(3)

cgeqlf.f –

Synopsis

Functions/Subroutines

subroutine cgeqlf (M, N, A, LDA, TAU, WORK, LWORK, INFO)
CGEQLF

Function/Subroutine Documentation

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

CGEQLF

Purpose:

 CGEQLF computes a QL factorization of a complex M-by-N matrix A:
 A = Q * L.

 

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 COMPLEX array, dimension (LDA,N)
 On entry, the M-by-N matrix A.
 On exit,
 if m >= n, the lower triangle of the subarray
 A(m-n+1:m,1:n) contains the N-by-N lower triangular matrix L;
 if m <= n, the elements on and below the (n-m)-th
 superdiagonal contain the M-by-N lower trapezoidal matrix L;
 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 (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(k) . . . H(2) H(1), 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(m-k+i+1:m) = 0 and v(m-k+i) = 1; v(1:m-k+i-1) is stored on exit in
 A(1:m-k+i-1,n-k+i), and tau in TAU(i).

 

Definition at line 139 of file cgeqlf.f.

Author

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