table of contents
| ung2l(3) | LAPACK | ung2l(3) |
NAME¶
ung2l - {un,or}g2l: step in ungql
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).
Detailed Description¶
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
!> 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 (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 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
!> 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 (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 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
!> 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 (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 California Berkeley
Univ. of Colorado Denver
NAG Ltd.
subroutine zung2l (integer m, integer n, integer k, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( * ) tau, complex*16, 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
!> 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 (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 California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Author¶
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