ungrq - Man Page

{un,or}grq: generate explicit Q from gerqf

Synopsis

Functions

subroutine cungrq (m, n, k, a, lda, tau, work, lwork, info)
CUNGRQ
subroutine dorgrq (m, n, k, a, lda, tau, work, lwork, info)
DORGRQ
subroutine sorgrq (m, n, k, a, lda, tau, work, lwork, info)
SORGRQ
subroutine zungrq (m, n, k, a, lda, tau, work, lwork, info)
ZUNGRQ

Detailed Description

Function Documentation

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

CUNGRQ  

Purpose:

 CUNGRQ generates an M-by-N complex matrix Q with orthonormal rows,
 which is defined as the last M rows of a product of K elementary
 reflectors of order N

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

 as returned by CGERQF.
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 (m-k+i)-th row must contain the vector which
          defines the elementary reflector H(i), for i = 1,2,...,k, as
          returned by CGERQF in the last 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 CGERQF.

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,M).
          For optimum performance LWORK >= M*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 has an illegal value
Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 127 of file cungrq.f.

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

DORGRQ  

Purpose:

 DORGRQ generates an M-by-N real matrix Q with orthonormal rows,
 which is defined as the last M rows of a product of K elementary
 reflectors of order N

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

 as returned by DGERQF.
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 (m-k+i)-th row must contain the vector which
          defines the elementary reflector H(i), for i = 1,2,...,k, as
          returned by DGERQF in the last 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 DGERQF.

WORK

          WORK is DOUBLE PRECISION 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,M).
          For optimum performance LWORK >= M*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 has an illegal value
Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 127 of file dorgrq.f.

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

SORGRQ  

Purpose:

 SORGRQ generates an M-by-N real matrix Q with orthonormal rows,
 which is defined as the last M rows of a product of K elementary
 reflectors of order N

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

 as returned by SGERQF.
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 (m-k+i)-th row must contain the vector which
          defines the elementary reflector H(i), for i = 1,2,...,k, as
          returned by SGERQF in the last 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 SGERQF.

WORK

          WORK is REAL 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,M).
          For optimum performance LWORK >= M*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 has an illegal value
Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 127 of file sorgrq.f.

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

ZUNGRQ  

Purpose:

 ZUNGRQ generates an M-by-N complex matrix Q with orthonormal rows,
 which is defined as the last M rows of a product of K elementary
 reflectors of order N

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

 as returned by ZGERQF.
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 (m-k+i)-th row must contain the vector which
          defines the elementary reflector H(i), for i = 1,2,...,k, as
          returned by ZGERQF in the last 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 ZGERQF.

WORK

          WORK is COMPLEX*16 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,M).
          For optimum performance LWORK >= M*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 has an illegal value
Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 127 of file zungrq.f.

Author

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Info

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