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.

Definition at line 113 of file cung2l.f.

  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.

Definition at line 113 of file dorg2l.f.

  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.

Definition at line 113 of file sorg2l.f.

  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.

Definition at line 113 of file zung2l.f.

Author

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