ung2l

SYNOPSIS

Functions

subroutine cung2l (m, n, k, a, lda, tau, work, info)
CUNG2L generates all or part of the unitary matrix Q from a QL factorization determined by cgeqlf (unblocked algorithm). subroutine dorg2l (m, n, k, a, lda, tau, work, info)
DORG2L generates all or part of the orthogonal matrix Q from a QL factorization determined by sgeqlf (unblocked algorithm). subroutine sorg2l (m, n, k, a, lda, tau, work, info)
SORG2L generates all or part of the orthogonal matrix Q from a QL factorization determined by sgeqlf (unblocked algorithm). subroutine zung2l (m, n, k, a, lda, tau, work, info)
ZUNG2L generates all or part of the unitary matrix Q from a QL factorization determined by cgeqlf (unblocked algorithm).

Function Documentation

subroutine cung2l (integer m, integer n, integer k, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) tau, complex, dimension( * ) work, integer info)

CUNG2L generates all or part of the unitary matrix Q from a QL factorization determined by cgeqlf (unblocked algorithm).

Purpose:

!>
!> CUNG2L generates an m by n complex matrix Q with orthonormal columns,
!> which is defined as the last n columns of a product of k elementary
!> reflectors of order m
!>
!>       Q  =  H(k) . . . H(2) H(1)
!>
!> as returned by CGEQLF.
!>

Parameters

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

!>          N is INTEGER
!>          The number of columns of the matrix Q. M >= N >= 0.
!>

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

!>          A is COMPLEX array, dimension (LDA,N)
!>          On entry, the (n-k+i)-th column must contain the vector which
!>          defines the elementary reflector H(i), for i = 1,2,...,k, as
!>          returned by CGEQLF in the last 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 CGEQLF.
!>

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.

subroutine dorg2l (integer m, integer n, integer k, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) tau, double precision, dimension( * ) work, integer info)

DORG2L generates all or part of the orthogonal matrix Q from a QL factorization determined by sgeqlf (unblocked algorithm).

Purpose:

!>
!> DORG2L generates an m by n real matrix Q with orthonormal columns,
!> which is defined as the last n columns of a product of k elementary
!> reflectors of order m
!>
!>       Q  =  H(k) . . . H(2) H(1)
!>
!> as returned by DGEQLF.
!>

Parameters

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

!>          N is INTEGER
!>          The number of columns of the matrix Q. M >= N >= 0.
!>

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

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

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.

subroutine sorg2l (integer m, integer n, integer k, real, dimension( lda, * ) a, integer lda, real, dimension( * ) tau, real, dimension( * ) work, integer info)

SORG2L generates all or part of the orthogonal matrix Q from a QL factorization determined by sgeqlf (unblocked algorithm).

Purpose:

!>
!> SORG2L generates an m by n real matrix Q with orthonormal columns,
!> which is defined as the last n columns of a product of k elementary
!> reflectors of order m
!>
!>       Q  =  H(k) . . . H(2) H(1)
!>
!> as returned by SGEQLF.
!>

Parameters

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

!>          N is INTEGER
!>          The number of columns of the matrix Q. M >= N >= 0.
!>

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

!>          A is REAL array, dimension (LDA,N)
!>          On entry, the (n-k+i)-th column must contain the vector which
!>          defines the elementary reflector H(i), for i = 1,2,...,k, as
!>          returned by SGEQLF in the last 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 SGEQLF.
!>

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.

subroutine zung2l (integer m, integer n, integer k, complex16, dimension( lda, ) a, integer lda, complex16, dimension( ) tau, complex16, dimension( ) work, integer info)

ZUNG2L generates all or part of the unitary matrix Q from a QL factorization determined by cgeqlf (unblocked algorithm).

Purpose:

!>
!> ZUNG2L generates an m by n complex matrix Q with orthonormal columns,
!> which is defined as the last n columns of a product of k elementary
!> reflectors of order m
!>
!>       Q  =  H(k) . . . H(2) H(1)
!>
!> as returned by ZGEQLF.
!>

Parameters

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

!>          N is INTEGER
!>          The number of columns of the matrix Q. M >= N >= 0.
!>

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

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

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.

Author

Generated automatically by Doxygen for LAPACK from the source code.

Ubuntu Manpages

ung2l