Man page - geqr2(3)

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Manual

geqr2

NAME
SYNOPSIS
Functions
Detailed Description
Function Documentation
subroutine cgeqr2 (integer m, integer n, complex, dimension( lda, * ) a,integer lda, complex, dimension( * ) tau, complex, dimension( * ) work,integer info)
subroutine dgeqr2 (integer m, integer n, double precision, dimension( lda,* ) a, integer lda, double precision, dimension( * ) tau, doubleprecision, dimension( * ) work, integer info)
subroutine sgeqr2 (integer m, integer n, real, dimension( lda, * ) a,integer lda, real, dimension( * ) tau, real, dimension( * ) work,integer info)
subroutine zgeqr2 (integer m, integer n, complex*16, dimension( lda, * ) a,integer lda, complex*16, dimension( * ) tau, complex*16, dimension( * )work, integer info)
Author

NAME

geqr2 - geqr2: QR factor, level 2

SYNOPSIS

Functions

subroutine cgeqr2 (m, n, a, lda, tau, work, info)
CGEQR2 computes the QR factorization of a general rectangular matrix using an unblocked algorithm.
subroutine dgeqr2 (m, n, a, lda, tau, work, info)
DGEQR2 computes the QR factorization of a general rectangular matrix using an unblocked algorithm.
subroutine sgeqr2 (m, n, a, lda, tau, work, info)
SGEQR2 computes the QR factorization of a general rectangular matrix using an unblocked algorithm.
subroutine zgeqr2 (m, n, a, lda, tau, work, info)
ZGEQR2 computes the QR factorization of a general rectangular matrix using an unblocked algorithm.

Detailed Description

Function Documentation

subroutine cgeqr2 (integer m, integer n, complex, dimension( lda, * ) a,integer lda, complex, dimension( * ) tau, complex, dimension( * ) work,integer info)

CGEQR2 computes the QR factorization of a general rectangular matrix using an unblocked algorithm.

Purpose:

CGEQR2 computes a QR factorization of a complex m-by-n matrix A:

A = Q * ( R ),
( 0 )

where:

Q is a m-by-m orthogonal matrix;
R is an upper-triangular n-by-n matrix;
0 is a (m-n)-by-n 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 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 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 (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.

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).

subroutine dgeqr2 (integer m, integer n, double precision, dimension( lda,* ) a, integer lda, double precision, dimension( * ) tau, doubleprecision, dimension( * ) work, integer info)

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 ),
( 0 )

where:

Q is a m-by-m orthogonal matrix;
R is an upper-triangular n-by-n matrix;
0 is a (m-n)-by-n 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 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.

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).

subroutine sgeqr2 (integer m, integer n, real, dimension( lda, * ) a,integer lda, real, dimension( * ) tau, real, dimension( * ) work,integer info)

SGEQR2 computes the QR factorization of a general rectangular matrix using an unblocked algorithm.

Purpose:

SGEQR2 computes a QR factorization of a real m-by-n matrix A:

A = Q * ( R ),
( 0 )

where:

Q is a m-by-m orthogonal matrix;
R is an upper-triangular n-by-n matrix;
0 is a (m-n)-by-n 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 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 REAL array, dimension (min(M,N))
The scalar factors of the elementary reflectors (see Further
Details).

WORK

WORK is REAL 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.

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).

subroutine zgeqr2 (integer m, integer n, complex*16, dimension( lda, * ) a,integer lda, complex*16, dimension( * ) tau, complex*16, dimension( * )work, integer info)

ZGEQR2 computes the QR factorization of a general rectangular matrix using an unblocked algorithm.

Purpose:

ZGEQR2 computes a QR factorization of a complex m-by-n matrix A:

A = Q * ( R ),
( 0 )

where:

Q is a m-by-m orthogonal matrix;
R is an upper-triangular n-by-n matrix;
0 is a (m-n)-by-n 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 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 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 (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.

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).

Author

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