unglq(3) Library Functions Manual unglq(3)

unglq - {un,or}glq: generate explicit Q from gelqf


subroutine cunglq (m, n, k, a, lda, tau, work, lwork, info)
CUNGLQ subroutine dorglq (m, n, k, a, lda, tau, work, lwork, info)
DORGLQ subroutine sorglq (m, n, k, a, lda, tau, work, lwork, info)
SORGLQ subroutine zunglq (m, n, k, a, lda, tau, work, lwork, info)
ZUNGLQ

CUNGLQ

Purpose:

 CUNGLQ 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 (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 126 of file cunglq.f.

DORGLQ

Purpose:

 DORGLQ 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 (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 126 of file dorglq.f.

SORGLQ

Purpose:

 SORGLQ 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 (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 126 of file sorglq.f.

ZUNGLQ

Purpose:

 ZUNGLQ 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 (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 126 of file zunglq.f.

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