Man page - gelq2(3)

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Manual

gelq2

NAME
SYNOPSIS
Functions
Detailed Description
Function Documentation
subroutine cgelq2 (integer m, integer n, complex, dimension( lda, * ) a,integer lda, complex, dimension( * ) tau, complex, dimension( * ) work,integer info)
subroutine dgelq2 (integer m, integer n, double precision, dimension( lda,* ) a, integer lda, double precision, dimension( * ) tau, doubleprecision, dimension( * ) work, integer info)
subroutine sgelq2 (integer m, integer n, real, dimension( lda, * ) a,integer lda, real, dimension( * ) tau, real, dimension( * ) work,integer info)
subroutine zgelq2 (integer m, integer n, complex*16, dimension( lda, * ) a,integer lda, complex*16, dimension( * ) tau, complex*16, dimension( * )work, integer info)
Author

NAME

gelq2 - gelq2: LQ factor, level 2

SYNOPSIS

Functions

subroutine cgelq2 (m, n, a, lda, tau, work, info)
CGELQ2 computes the LQ factorization of a general rectangular matrix using an unblocked algorithm.
subroutine dgelq2 (m, n, a, lda, tau, work, info)
DGELQ2 computes the LQ factorization of a general rectangular matrix using an unblocked algorithm.
subroutine sgelq2 (m, n, a, lda, tau, work, info)
SGELQ2 computes the LQ factorization of a general rectangular matrix using an unblocked algorithm.
subroutine zgelq2 (m, n, a, lda, tau, work, info)
ZGELQ2 computes the LQ factorization of a general rectangular matrix using an unblocked algorithm.

Detailed Description

Function Documentation

subroutine cgelq2 (integer m, integer n, complex, dimension( lda, * ) a,integer lda, complex, dimension( * ) tau, complex, dimension( * ) work,integer info)

CGELQ2 computes the LQ factorization of a general rectangular matrix using an unblocked algorithm.

Purpose:

CGELQ2 computes an LQ factorization of a complex m-by-n matrix A:

A = ( L 0 ) * Q

where:

Q is a n-by-n orthogonal matrix;
L is a lower-triangular m-by-m matrix;
0 is a m-by-(n-m) zero matrix, if m < n.

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 below the diagonal of the array
contain the m by min(m,n) lower trapezoidal matrix L (L is
lower triangular if m <= n); the elements above the diagonal,
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.

Further Details:

The matrix Q is represented as a product of elementary reflectors

Q = H(k)**H . . . H(2)**H H(1)**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(1:i-1) = 0 and v(i) = 1; conjg(v(i+1:n)) is stored on exit in
A(i,i+1:n), and tau in TAU(i).

subroutine dgelq2 (integer m, integer n, double precision, dimension( lda,* ) a, integer lda, double precision, dimension( * ) tau, doubleprecision, dimension( * ) work, integer info)

DGELQ2 computes the LQ factorization of a general rectangular matrix using an unblocked algorithm.

Purpose:

DGELQ2 computes an LQ factorization of a real m-by-n matrix A:

A = ( L 0 ) * Q

where:

Q is a n-by-n orthogonal matrix;
L is a lower-triangular m-by-m matrix;
0 is a m-by-(n-m) zero matrix, if m < n.

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 DOUBLE PRECISION array, dimension (LDA,N)
On entry, the m by n matrix A.
On exit, the elements on and below the diagonal of the array
contain the m by min(m,n) lower trapezoidal matrix L (L is
lower triangular if m <= n); the elements above 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 (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.

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**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:n) is stored on exit in A(i,i+1:n),
and tau in TAU(i).

subroutine sgelq2 (integer m, integer n, real, dimension( lda, * ) a,integer lda, real, dimension( * ) tau, real, dimension( * ) work,integer info)

SGELQ2 computes the LQ factorization of a general rectangular matrix using an unblocked algorithm.

Purpose:

SGELQ2 computes an LQ factorization of a real m-by-n matrix A:

A = ( L 0 ) * Q

where:

Q is a n-by-n orthogonal matrix;
L is a lower-triangular m-by-m matrix;
0 is a m-by-(n-m) zero matrix, if m < n.

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 REAL array, dimension (LDA,N)
On entry, the m by n matrix A.
On exit, the elements on and below the diagonal of the array
contain the m by min(m,n) lower trapezoidal matrix L (L is
lower triangular if m <= n); the elements above 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 REAL array, dimension (min(M,N))
The scalar factors of the elementary reflectors (see Further
Details).

WORK

WORK is REAL 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.

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**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:n) is stored on exit in A(i,i+1:n),
and tau in TAU(i).

subroutine zgelq2 (integer m, integer n, complex*16, dimension( lda, * ) a,integer lda, complex*16, dimension( * ) tau, complex*16, dimension( * )work, integer info)

ZGELQ2 computes the LQ factorization of a general rectangular matrix using an unblocked algorithm.

Purpose:

ZGELQ2 computes an LQ factorization of a complex m-by-n matrix A:

A = ( L 0 ) * Q

where:

Q is a n-by-n orthogonal matrix;
L is a lower-triangular m-by-m matrix;
0 is a m-by-(n-m) zero matrix, if m < n.

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*16 array, dimension (LDA,N)
On entry, the m by n matrix A.
On exit, the elements on and below the diagonal of the array
contain the m by min(m,n) lower trapezoidal matrix L (L is
lower triangular if m <= n); the elements above the diagonal,
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*16 array, dimension (min(M,N))
The scalar factors of the elementary reflectors (see Further
Details).

WORK

WORK is COMPLEX*16 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.

Further Details:

The matrix Q is represented as a product of elementary reflectors

Q = H(k)**H . . . H(2)**H H(1)**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(1:i-1) = 0 and v(i) = 1; conjg(v(i+1:n)) is stored on exit in
A(i,i+1:n), and tau in TAU(i).

Author

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