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cgeqrfp.f(3) LAPACK cgeqrfp.f(3)

NAME

cgeqrfp.f

SYNOPSIS

Functions/Subroutines


subroutine cgeqrfp (M, N, A, LDA, TAU, WORK, LWORK, INFO)
CGEQRFP

Function/Subroutine Documentation

subroutine cgeqrfp (integer M, integer N, complex, dimension( lda, * ) A, integer LDA, complex, dimension( * ) TAU, complex, dimension( * ) WORK, integer LWORK, integer INFO)

CGEQRFP

Purpose:


CGEQRFP computes a QR factorization of a complex M-by-N matrix A:
A = Q * R. The diagonal entries of R are real and nonnegative.

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, 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 diagonal entries of R
are real and nonnegative; the elements below the diagonal,
with the array TAU, represent the unitary 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 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:

December 2016

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**H
where tau is a complex scalar, and v is a 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).
See Lapack Working Note 203 for details

Definition at line 141 of file cgeqrfp.f.

Author

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Tue Nov 14 2017 Version 3.8.0