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

    !>          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 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

    !>          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 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

    !>          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 Tennessee

    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

    !>          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 Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Author

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