ung2r - Man Page

{un,or}g2r: generate explicit Q from geqrf, level 2

Synopsis

Functions

subroutine cung2r (m, n, k, a, lda, tau, work, info)
CUNG2R
subroutine dorg2r (m, n, k, a, lda, tau, work, info)
DORG2R generates all or part of the orthogonal matrix Q from a QR factorization determined by sgeqrf (unblocked algorithm).
subroutine sorg2r (m, n, k, a, lda, tau, work, info)
SORG2R generates all or part of the orthogonal matrix Q from a QR factorization determined by sgeqrf (unblocked algorithm).
subroutine zung2r (m, n, k, a, lda, tau, work, info)
ZUNG2R

Detailed Description

Function Documentation

subroutine cung2r (integer m, integer n, integer k, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) tau, complex, dimension( * ) work, integer info)

CUNG2R  

Purpose:

 CUNG2R generates an m by n complex matrix Q with orthonormal columns,
 which is defined as the first n columns of a product of k elementary
 reflectors of order m

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

 as returned by CGEQRF.
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. M >= N >= 0.

K

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

A

          A is COMPLEX array, dimension (LDA,N)
          On entry, the i-th column must contain the vector which
          defines the elementary reflector H(i), for i = 1,2,...,k, as
          returned by CGEQRF in the first k columns 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 CGEQRF.

WORK

          WORK is COMPLEX array, dimension (N)

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 113 of file cung2r.f.

subroutine dorg2r (integer m, integer n, integer k, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) tau, double precision, dimension( * ) work, integer info)

DORG2R generates all or part of the orthogonal matrix Q from a QR factorization determined by sgeqrf (unblocked algorithm).  

Purpose:

 DORG2R generates an m by n real matrix Q with orthonormal columns,
 which is defined as the first n columns of a product of k elementary
 reflectors of order m

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

 as returned by DGEQRF.
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. M >= N >= 0.

K

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

A

          A is DOUBLE PRECISION array, dimension (LDA,N)
          On entry, the i-th column must contain the vector which
          defines the elementary reflector H(i), for i = 1,2,...,k, as
          returned by DGEQRF in the first k columns 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 DGEQRF.

WORK

          WORK is DOUBLE PRECISION array, dimension (N)

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 113 of file dorg2r.f.

subroutine sorg2r (integer m, integer n, integer k, real, dimension( lda, * ) a, integer lda, real, dimension( * ) tau, real, dimension( * ) work, integer info)

SORG2R generates all or part of the orthogonal matrix Q from a QR factorization determined by sgeqrf (unblocked algorithm).  

Purpose:

 SORG2R generates an m by n real matrix Q with orthonormal columns,
 which is defined as the first n columns of a product of k elementary
 reflectors of order m

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

 as returned by SGEQRF.
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. M >= N >= 0.

K

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

A

          A is REAL array, dimension (LDA,N)
          On entry, the i-th column must contain the vector which
          defines the elementary reflector H(i), for i = 1,2,...,k, as
          returned by SGEQRF in the first k columns 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 SGEQRF.

WORK

          WORK is REAL array, dimension (N)

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 113 of file sorg2r.f.

subroutine zung2r (integer m, integer n, integer k, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( * ) tau, complex*16, dimension( * ) work, integer info)

ZUNG2R  

Purpose:

 ZUNG2R generates an m by n complex matrix Q with orthonormal columns,
 which is defined as the first n columns of a product of k elementary
 reflectors of order m

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

 as returned by ZGEQRF.
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. M >= N >= 0.

K

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

A

          A is COMPLEX*16 array, dimension (LDA,N)
          On entry, the i-th column must contain the vector which
          defines the elementary reflector H(i), for i = 1,2,...,k, as
          returned by ZGEQRF in the first k columns 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 ZGEQRF.

WORK

          WORK is COMPLEX*16 array, dimension (N)

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 113 of file zung2r.f.

Author

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Info

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