unml2(3)

NAME
unml2 - {un,or}ml2: multiply by Q, level 2, step in unmlq

SYNOPSIS

  Functions

subroutine cunml2 (side, trans, m, n, k, a, lda, tau, c, ldc, work, info)
CUNML2 multiplies a general matrix by the unitary matrix from a LQ factorization determined by cgelqf (unblocked algorithm).
subroutine dorml2 (side, trans, m, n, k, a, lda, tau, c, ldc, work, info)
DORML2 multiplies a general matrix by the orthogonal matrix from a LQ factorization determined by sgelqf (unblocked algorithm).
subroutine sorml2 (side, trans, m, n, k, a, lda, tau, c, ldc, work, info)
SORML2 multiplies a general matrix by the orthogonal matrix from a LQ factorization determined by sgelqf (unblocked algorithm).
subroutine zunml2 (side, trans, m, n, k, a, lda, tau, c, ldc, work, info)
ZUNML2 multiplies a general matrix by the unitary matrix from a LQ factorization determined by cgelqf (unblocked algorithm).

Detailed Description

Function Documentation

  subroutine cunml2 (character side, character trans, integer m, integer n, integer k, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) tau, complex, dimension( ldc, * ) c, integer ldc, complex, dimension( * ) work, integer info)

CUNML2 multiplies a general matrix by the unitary matrix from a LQ factorization determined by cgelqf (unblocked algorithm).

Purpose:

    !>
    !> CUNML2 overwrites the general complex m-by-n matrix C with
    !>
    !>       Q * C  if SIDE = 'L' and TRANS = 'N', or
    !>
    !>       Q**H* C  if SIDE = 'L' and TRANS = 'C', or
    !>
    !>       C * Q  if SIDE = 'R' and TRANS = 'N', or
    !>
    !>       C * Q**H if SIDE = 'R' and TRANS = 'C',
    !>
    !> where Q is a complex unitary matrix defined as the product of k
    !> elementary reflectors
    !>
    !>       Q = H(k)**H . . . H(2)**H H(1)**H
    !>
    !> as returned by CGELQF. Q is of order m if SIDE = 'L' and of order n
    !> if SIDE = 'R'.
    !>

Parameters
    SIDE

    !>          SIDE is CHARACTER*1
    !>          = 'L': apply Q or Q**H from the Left
    !>          = 'R': apply Q or Q**H from the Right
    !>

    TRANS

    !>          TRANS is CHARACTER*1
    !>          = 'N': apply Q  (No transpose)
    !>          = 'C': apply Q**H (Conjugate transpose)
    !>

    M

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

    N

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

    K

    !>          K is INTEGER
    !>          The number of elementary reflectors whose product defines
    !>          the matrix Q.
    !>          If SIDE = 'L', M >= K >= 0;
    !>          if SIDE = 'R', N >= K >= 0.
    !>

    A

    !>          A is COMPLEX array, dimension
    !>                               (LDA,M) if SIDE = 'L',
    !>                               (LDA,N) if SIDE = 'R'
    !>          The i-th row must contain the vector which defines the
    !>          elementary reflector H(i), for i = 1,2,...,k, as returned by
    !>          CGELQF in the first k rows of its array argument A.
    !>          A is modified by the routine but restored on exit.
    !>

    LDA

    !>          LDA is INTEGER
    !>          The leading dimension of the array A. LDA >= max(1,K).
    !>

    TAU

    !>          TAU is COMPLEX array, dimension (K)
    !>          TAU(i) must contain the scalar factor of the elementary
    !>          reflector H(i), as returned by CGELQF.
    !>

    C

    !>          C is COMPLEX array, dimension (LDC,N)
    !>          On entry, the m-by-n matrix C.
    !>          On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q.
    !>

    LDC

    !>          LDC is INTEGER
    !>          The leading dimension of the array C. LDC >= max(1,M).
    !>

    WORK

    !>          WORK is COMPLEX array, dimension
    !>                                   (N) if SIDE = 'L',
    !>                                   (M) if SIDE = 'R'
    !>

    INFO

    !>          INFO is INTEGER
    !>          = 0: successful exit
    !>          < 0: if INFO = -i, the i-th argument had an illegal value
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

  subroutine dorml2 (character side, character trans, integer m, integer n, integer k, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) tau, double precision, dimension( ldc, * ) c, integer ldc, double precision, dimension( * ) work, integer info)

DORML2 multiplies a general matrix by the orthogonal matrix from a LQ factorization determined by sgelqf (unblocked algorithm).

Purpose:

    !>
    !> DORML2 overwrites the general real m by n matrix C with
    !>
    !>       Q * C  if SIDE = 'L' and TRANS = 'N', or
    !>
    !>       Q**T* C  if SIDE = 'L' and TRANS = 'T', or
    !>
    !>       C * Q  if SIDE = 'R' and TRANS = 'N', or
    !>
    !>       C * Q**T if SIDE = 'R' and TRANS = 'T',
    !>
    !> where Q is a real orthogonal matrix defined as the product of k
    !> elementary reflectors
    !>
    !>       Q = H(k) . . . H(2) H(1)
    !>
    !> as returned by DGELQF. Q is of order m if SIDE = 'L' and of order n
    !> if SIDE = 'R'.
    !>

Parameters
    SIDE

    !>          SIDE is CHARACTER*1
    !>          = 'L': apply Q or Q**T from the Left
    !>          = 'R': apply Q or Q**T from the Right
    !>

    TRANS

    !>          TRANS is CHARACTER*1
    !>          = 'N': apply Q  (No transpose)
    !>          = 'T': apply Q**T (Transpose)
    !>

    M

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

    N

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

    K

    !>          K is INTEGER
    !>          The number of elementary reflectors whose product defines
    !>          the matrix Q.
    !>          If SIDE = 'L', M >= K >= 0;
    !>          if SIDE = 'R', N >= K >= 0.
    !>

    A

    !>          A is DOUBLE PRECISION array, dimension
    !>                               (LDA,M) if SIDE = 'L',
    !>                               (LDA,N) if SIDE = 'R'
    !>          The i-th row must contain the vector which defines the
    !>          elementary reflector H(i), for i = 1,2,...,k, as returned by
    !>          DGELQF in the first k rows of its array argument A.
    !>

    LDA

    !>          LDA is INTEGER
    !>          The leading dimension of the array A. LDA >= max(1,K).
    !>

    TAU

    !>          TAU is DOUBLE PRECISION array, dimension (K)
    !>          TAU(i) must contain the scalar factor of the elementary
    !>          reflector H(i), as returned by DGELQF.
    !>

    C

    !>          C is DOUBLE PRECISION array, dimension (LDC,N)
    !>          On entry, the m by n matrix C.
    !>          On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q.
    !>

    LDC

    !>          LDC is INTEGER
    !>          The leading dimension of the array C. LDC >= max(1,M).
    !>

    WORK

    !>          WORK is DOUBLE PRECISION array, dimension
    !>                                   (N) if SIDE = 'L',
    !>                                   (M) if SIDE = 'R'
    !>

    INFO

    !>          INFO is INTEGER
    !>          = 0: successful exit
    !>          < 0: if INFO = -i, the i-th argument had an illegal value
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

  subroutine sorml2 (character side, character trans, integer m, integer n, integer k, real, dimension( lda, * ) a, integer lda, real, dimension( * ) tau, real, dimension( ldc, * ) c, integer ldc, real, dimension( * ) work, integer info)

SORML2 multiplies a general matrix by the orthogonal matrix from a LQ factorization determined by sgelqf (unblocked algorithm).

Purpose:

    !>
    !> SORML2 overwrites the general real m by n matrix C with
    !>
    !>       Q * C  if SIDE = 'L' and TRANS = 'N', or
    !>
    !>       Q**T* C  if SIDE = 'L' and TRANS = 'T', or
    !>
    !>       C * Q  if SIDE = 'R' and TRANS = 'N', or
    !>
    !>       C * Q**T if SIDE = 'R' and TRANS = 'T',
    !>
    !> where Q is a real orthogonal matrix defined as the product of k
    !> elementary reflectors
    !>
    !>       Q = H(k) . . . H(2) H(1)
    !>
    !> as returned by SGELQF. Q is of order m if SIDE = 'L' and of order n
    !> if SIDE = 'R'.
    !>

Parameters
    SIDE

    !>          SIDE is CHARACTER*1
    !>          = 'L': apply Q or Q**T from the Left
    !>          = 'R': apply Q or Q**T from the Right
    !>

    TRANS

    !>          TRANS is CHARACTER*1
    !>          = 'N': apply Q  (No transpose)
    !>          = 'T': apply Q**T (Transpose)
    !>

    M

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

    N

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

    K

    !>          K is INTEGER
    !>          The number of elementary reflectors whose product defines
    !>          the matrix Q.
    !>          If SIDE = 'L', M >= K >= 0;
    !>          if SIDE = 'R', N >= K >= 0.
    !>

    A

    !>          A is REAL array, dimension
    !>                               (LDA,M) if SIDE = 'L',
    !>                               (LDA,N) if SIDE = 'R'
    !>          The i-th row must contain the vector which defines the
    !>          elementary reflector H(i), for i = 1,2,...,k, as returned by
    !>          SGELQF in the first k rows of its array argument A.
    !>          A is modified by the routine but restored on exit.
    !>

    LDA

    !>          LDA is INTEGER
    !>          The leading dimension of the array A. LDA >= max(1,K).
    !>

    TAU

    !>          TAU is REAL array, dimension (K)
    !>          TAU(i) must contain the scalar factor of the elementary
    !>          reflector H(i), as returned by SGELQF.
    !>

    C

    !>          C is REAL array, dimension (LDC,N)
    !>          On entry, the m by n matrix C.
    !>          On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q.
    !>

    LDC

    !>          LDC is INTEGER
    !>          The leading dimension of the array C. LDC >= max(1,M).
    !>

    WORK

    !>          WORK is REAL array, dimension
    !>                                   (N) if SIDE = 'L',
    !>                                   (M) if SIDE = 'R'
    !>

    INFO

    !>          INFO is INTEGER
    !>          = 0: successful exit
    !>          < 0: if INFO = -i, the i-th argument had an illegal value
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

  subroutine zunml2 (character side, character trans, integer m, integer n, integer k, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( * ) tau, complex*16, dimension( ldc, * ) c, integer ldc, complex*16, dimension( * ) work, integer info)

ZUNML2 multiplies a general matrix by the unitary matrix from a LQ factorization determined by cgelqf (unblocked algorithm).

Purpose:

    !>
    !> ZUNML2 overwrites the general complex m-by-n matrix C with
    !>
    !>       Q * C  if SIDE = 'L' and TRANS = 'N', or
    !>
    !>       Q**H* C  if SIDE = 'L' and TRANS = 'C', or
    !>
    !>       C * Q  if SIDE = 'R' and TRANS = 'N', or
    !>
    !>       C * Q**H if SIDE = 'R' and TRANS = 'C',
    !>
    !> where Q is a complex unitary matrix defined as the product of k
    !> elementary reflectors
    !>
    !>       Q = H(k)**H . . . H(2)**H H(1)**H
    !>
    !> as returned by ZGELQF. Q is of order m if SIDE = 'L' and of order n
    !> if SIDE = 'R'.
    !>

Parameters
    SIDE

    !>          SIDE is CHARACTER*1
    !>          = 'L': apply Q or Q**H from the Left
    !>          = 'R': apply Q or Q**H from the Right
    !>

    TRANS

    !>          TRANS is CHARACTER*1
    !>          = 'N': apply Q  (No transpose)
    !>          = 'C': apply Q**H (Conjugate transpose)
    !>

    M

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

    N

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

    K

    !>          K is INTEGER
    !>          The number of elementary reflectors whose product defines
    !>          the matrix Q.
    !>          If SIDE = 'L', M >= K >= 0;
    !>          if SIDE = 'R', N >= K >= 0.
    !>

    A

    !>          A is COMPLEX*16 array, dimension
    !>                               (LDA,M) if SIDE = 'L',
    !>                               (LDA,N) if SIDE = 'R'
    !>          The i-th row must contain the vector which defines the
    !>          elementary reflector H(i), for i = 1,2,...,k, as returned by
    !>          ZGELQF in the first k rows of its array argument A.
    !>          A is modified by the routine but restored on exit.
    !>

    LDA

    !>          LDA is INTEGER
    !>          The leading dimension of the array A. LDA >= max(1,K).
    !>

    TAU

    !>          TAU is COMPLEX*16 array, dimension (K)
    !>          TAU(i) must contain the scalar factor of the elementary
    !>          reflector H(i), as returned by ZGELQF.
    !>

    C

    !>          C is COMPLEX*16 array, dimension (LDC,N)
    !>          On entry, the m-by-n matrix C.
    !>          On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q.
    !>

    LDC

    !>          LDC is INTEGER
    !>          The leading dimension of the array C. LDC >= max(1,M).
    !>

    WORK

    !>          WORK is COMPLEX*16 array, dimension
    !>                                   (N) if SIDE = 'L',
    !>                                   (M) if SIDE = 'R'
    !>

    INFO

    !>          INFO is INTEGER
    !>          = 0: successful exit
    !>          < 0: if INFO = -i, the i-th argument had an illegal value
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Author

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