ung2r(3)

NAME
ung2r - {un,or}g2r: generate explicit Q from geqrf, level 2

SYNOPSIS

  Functions

subroutine cung2r (m, n, k, a, lda, tau, work, info)
CUNG2R
subroutine dorg2r (m, n, k, a, lda, tau, work, info)
DORG2R generates all or part of the orthogonal matrix Q from a QR factorization determined by sgeqrf (unblocked algorithm).
subroutine sorg2r (m, n, k, a, lda, tau, work, info)
SORG2R generates all or part of the orthogonal matrix Q from a QR factorization determined by sgeqrf (unblocked algorithm).
subroutine zung2r (m, n, k, a, lda, tau, work, info)
ZUNG2R

Detailed Description

Function Documentation

  subroutine cung2r (integer m, integer n, integer k, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) tau, complex, dimension( * ) work, integer info)

CUNG2R

Purpose:

    !>
    !> CUNG2R generates an m by n complex matrix Q with orthonormal columns,
    !> which is defined as the first n columns of a product of k elementary
    !> reflectors of order m
    !>
    !>       Q  =  H(1) H(2) . . . H(k)
    !>
    !> as returned by CGEQRF.
    !>

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 i-th column must contain the vector which
    !>          defines the elementary reflector H(i), for i = 1,2,...,k, as
    !>          returned by CGEQRF in the first 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 CGEQRF.
    !>

    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 dorg2r (integer m, integer n, integer k, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) tau, double precision, dimension( * ) work, integer info)

DORG2R generates all or part of the orthogonal matrix Q from a QR factorization determined by sgeqrf (unblocked algorithm).

Purpose:

    !>
    !> DORG2R generates an m by n real matrix Q with orthonormal columns,
    !> which is defined as the first n columns of a product of k elementary
    !> reflectors of order m
    !>
    !>       Q  =  H(1) H(2) . . . H(k)
    !>
    !> as returned by DGEQRF.
    !>

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 i-th column must contain the vector which
    !>          defines the elementary reflector H(i), for i = 1,2,...,k, as
    !>          returned by DGEQRF in the first 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 DGEQRF.
    !>

    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 sorg2r (integer m, integer n, integer k, real, dimension( lda, * ) a, integer lda, real, dimension( * ) tau, real, dimension( * ) work, integer info)

SORG2R generates all or part of the orthogonal matrix Q from a QR factorization determined by sgeqrf (unblocked algorithm).

Purpose:

    !>
    !> SORG2R generates an m by n real matrix Q with orthonormal columns,
    !> which is defined as the first n columns of a product of k elementary
    !> reflectors of order m
    !>
    !>       Q  =  H(1) H(2) . . . H(k)
    !>
    !> as returned by SGEQRF.
    !>

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 i-th column must contain the vector which
    !>          defines the elementary reflector H(i), for i = 1,2,...,k, as
    !>          returned by SGEQRF in the first 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 SGEQRF.
    !>

    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 zung2r (integer m, integer n, integer k, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( * ) tau, complex*16, dimension( * ) work, integer info)

ZUNG2R

Purpose:

    !>
    !> ZUNG2R generates an m by n complex matrix Q with orthonormal columns,
    !> which is defined as the first n columns of a product of k elementary
    !> reflectors of order m
    !>
    !>       Q  =  H(1) H(2) . . . H(k)
    !>
    !> as returned by ZGEQRF.
    !>

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 i-th column must contain the vector which
    !>          defines the elementary reflector H(i), for i = 1,2,...,k, as
    !>          returned by ZGEQRF in the first 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 ZGEQRF.
    !>

    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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