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.

Definition at line 157 of file cunml2.f.

  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.
              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 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.

Definition at line 157 of file dorml2.f.

  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.

Definition at line 157 of file sorml2.f.

  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.

Definition at line 157 of file zunml2.f.

Author

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