ungl2 - Man Page

{un,or}gl2: generate explicit Q, level 2, step in unglq

Synopsis

Functions

subroutine cungl2 (m, n, k, a, lda, tau, work, info)
CUNGL2 generates all or part of the unitary matrix Q from an LQ factorization determined by cgelqf (unblocked algorithm).
subroutine dorgl2 (m, n, k, a, lda, tau, work, info)
DORGL2
subroutine sorgl2 (m, n, k, a, lda, tau, work, info)
SORGL2
subroutine zungl2 (m, n, k, a, lda, tau, work, info)
ZUNGL2 generates all or part of the unitary matrix Q from an LQ factorization determined by cgelqf (unblocked algorithm).

Detailed Description

Function Documentation

subroutine cungl2 (integer m, integer n, integer k, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) tau, complex, dimension( * ) work, integer info)

CUNGL2 generates all or part of the unitary matrix Q from an LQ factorization determined by cgelqf (unblocked algorithm).  

Purpose:

 CUNGL2 generates an m-by-n complex matrix Q with orthonormal rows,
 which is defined as the first m rows of a product of k elementary
 reflectors of order n

       Q  =  H(k)**H . . . H(2)**H H(1)**H

 as returned by CGELQF.
Parameters

M

          M is INTEGER
          The number of rows of the matrix Q. M >= 0.

N

          N is INTEGER
          The number of columns of the matrix Q. N >= M.

K

          K is INTEGER
          The number of elementary reflectors whose product defines the
          matrix Q. M >= K >= 0.

A

          A is COMPLEX array, dimension (LDA,N)
          On entry, the i-th row must contain the vector which defines
          the elementary reflector H(i), for i = 1,2,...,k, as returned
          by CGELQF in the first k rows of its array argument A.
          On exit, the m by n matrix Q.

LDA

          LDA is INTEGER
          The first dimension of the array A. LDA >= max(1,M).

TAU

          TAU is COMPLEX array, dimension (K)
          TAU(i) must contain the scalar factor of the elementary
          reflector H(i), as returned by CGELQF.

WORK

          WORK is COMPLEX array, dimension (M)

INFO

          INFO is INTEGER
          = 0: successful exit
          < 0: if INFO = -i, the i-th argument has an illegal value
Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 112 of file cungl2.f.

subroutine dorgl2 (integer m, integer n, integer k, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) tau, double precision, dimension( * ) work, integer info)

DORGL2  

Purpose:

 DORGL2 generates an m by n real matrix Q with orthonormal rows,
 which is defined as the first m rows of a product of k elementary
 reflectors of order n

       Q  =  H(k) . . . H(2) H(1)

 as returned by DGELQF.
Parameters

M

          M is INTEGER
          The number of rows of the matrix Q. M >= 0.

N

          N is INTEGER
          The number of columns of the matrix Q. N >= M.

K

          K is INTEGER
          The number of elementary reflectors whose product defines the
          matrix Q. M >= K >= 0.

A

          A is DOUBLE PRECISION array, dimension (LDA,N)
          On entry, the i-th row must contain the vector which defines
          the elementary reflector H(i), for i = 1,2,...,k, as returned
          by DGELQF in the first k rows of its array argument A.
          On exit, the m-by-n matrix Q.

LDA

          LDA is INTEGER
          The first dimension of the array A. LDA >= max(1,M).

TAU

          TAU is DOUBLE PRECISION array, dimension (K)
          TAU(i) must contain the scalar factor of the elementary
          reflector H(i), as returned by DGELQF.

WORK

          WORK is DOUBLE PRECISION array, dimension (M)

INFO

          INFO is INTEGER
          = 0: successful exit
          < 0: if INFO = -i, the i-th argument has an illegal value
Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 112 of file dorgl2.f.

subroutine sorgl2 (integer m, integer n, integer k, real, dimension( lda, * ) a, integer lda, real, dimension( * ) tau, real, dimension( * ) work, integer info)

SORGL2  

Purpose:

 SORGL2 generates an m by n real matrix Q with orthonormal rows,
 which is defined as the first m rows of a product of k elementary
 reflectors of order n

       Q  =  H(k) . . . H(2) H(1)

 as returned by SGELQF.
Parameters

M

          M is INTEGER
          The number of rows of the matrix Q. M >= 0.

N

          N is INTEGER
          The number of columns of the matrix Q. N >= M.

K

          K is INTEGER
          The number of elementary reflectors whose product defines the
          matrix Q. M >= K >= 0.

A

          A is REAL array, dimension (LDA,N)
          On entry, the i-th row must contain the vector which defines
          the elementary reflector H(i), for i = 1,2,...,k, as returned
          by SGELQF in the first k rows of its array argument A.
          On exit, the m-by-n matrix Q.

LDA

          LDA is INTEGER
          The first dimension of the array A. LDA >= max(1,M).

TAU

          TAU is REAL array, dimension (K)
          TAU(i) must contain the scalar factor of the elementary
          reflector H(i), as returned by SGELQF.

WORK

          WORK is REAL array, dimension (M)

INFO

          INFO is INTEGER
          = 0: successful exit
          < 0: if INFO = -i, the i-th argument has an illegal value
Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 112 of file sorgl2.f.

subroutine zungl2 (integer m, integer n, integer k, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( * ) tau, complex*16, dimension( * ) work, integer info)

ZUNGL2 generates all or part of the unitary matrix Q from an LQ factorization determined by cgelqf (unblocked algorithm).  

Purpose:

 ZUNGL2 generates an m-by-n complex matrix Q with orthonormal rows,
 which is defined as the first m rows of a product of k elementary
 reflectors of order n

       Q  =  H(k)**H . . . H(2)**H H(1)**H

 as returned by ZGELQF.
Parameters

M

          M is INTEGER
          The number of rows of the matrix Q. M >= 0.

N

          N is INTEGER
          The number of columns of the matrix Q. N >= M.

K

          K is INTEGER
          The number of elementary reflectors whose product defines the
          matrix Q. M >= K >= 0.

A

          A is COMPLEX*16 array, dimension (LDA,N)
          On entry, the i-th row must contain the vector which defines
          the elementary reflector H(i), for i = 1,2,...,k, as returned
          by ZGELQF in the first k rows of its array argument A.
          On exit, the m by n matrix Q.

LDA

          LDA is INTEGER
          The first dimension of the array A. LDA >= max(1,M).

TAU

          TAU is COMPLEX*16 array, dimension (K)
          TAU(i) must contain the scalar factor of the elementary
          reflector H(i), as returned by ZGELQF.

WORK

          WORK is COMPLEX*16 array, dimension (M)

INFO

          INFO is INTEGER
          = 0: successful exit
          < 0: if INFO = -i, the i-th argument has an illegal value
Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 112 of file zungl2.f.

Author

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Tue Nov 28 2023 12:08:43 Version 3.12.0 LAPACK