unm22(3)

NAME
unm22 - {un,or}m22: multiply by banded Q, step in gghd3

SYNOPSIS

  Functions
subroutine cunm22 (side, trans, m, n, n1, n2, q, ldq, c, ldc, work, lwork, info)
CUNM22 multiplies a general matrix by a banded unitary matrix.
subroutine dorm22 (side, trans, m, n, n1, n2, q, ldq, c, ldc, work, lwork, info)
DORM22 multiplies a general matrix by a banded orthogonal matrix.
subroutine sorm22 (side, trans, m, n, n1, n2, q, ldq, c, ldc, work, lwork, info)
SORM22 multiplies a general matrix by a banded orthogonal matrix.
subroutine zunm22 (side, trans, m, n, n1, n2, q, ldq, c, ldc, work, lwork, info)
ZUNM22 multiplies a general matrix by a banded unitary matrix.

Detailed Description

Function Documentation

  subroutine cunm22 (character side, character trans, integer m, integer n, integer n1, integer n2, complex, dimension( ldq, * ) q, integer ldq, complex, dimension( ldc, * ) c, integer ldc, complex, dimension( * ) work, integer lwork, integer info)

CUNM22 multiplies a general matrix by a banded unitary matrix.

Purpose

      CUNM22 overwrites the general complex M-by-N matrix C with
                      SIDE = 'L'     SIDE = 'R'
      TRANS = 'N':      Q * C          C * Q
      TRANS = 'C':      Q**H * C       C * Q**H
      where Q is a complex unitary matrix of order NQ, with NQ = M if
      SIDE = 'L' and NQ = N if SIDE = 'R'.
      The unitary matrix Q processes a 2-by-2 block structure
             [  Q11  Q12  ]
         Q = [            ]
             [  Q21  Q22  ],
      where Q12 is an N1-by-N1 lower triangular matrix and Q21 is an
      N2-by-N2 upper triangular matrix.

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.

    N1
    N2

              N1 is INTEGER
              N2 is INTEGER
              The dimension of Q12 and Q21, respectively. N1, N2 >= 0.
              The following requirement must be satisfied:
              N1 + N2 = M if SIDE = 'L' and N1 + N2 = N if SIDE = 'R'.

    Q

              Q is COMPLEX array, dimension
                                  (LDQ,M) if SIDE = 'L'
                                  (LDQ,N) if SIDE = 'R'

    LDQ

              LDQ is INTEGER
              The leading dimension of the array Q.
              LDQ >= max(1,M) if SIDE = 'L'; LDQ >= max(1,N) if SIDE = 'R'.

    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 (MAX(1,LWORK))
              On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

    LWORK

              LWORK is INTEGER
              The dimension of the array WORK.
              If SIDE = 'L', LWORK >= max(1,N);
              if SIDE = 'R', LWORK >= max(1,M).
              For optimum performance LWORK >= M*N.
              If LWORK = -1, then a workspace query is assumed; the routine
              only calculates the optimal size of the WORK array, returns
              this value as the first entry of the WORK array, and no error
              message related to LWORK is issued by XERBLA.

    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 160 of file cunm22.f.

  subroutine dorm22 (character side, character trans, integer m, integer n, integer n1, integer n2, double precision, dimension( ldq, * ) q, integer ldq, double precision, dimension( ldc, * ) c, integer ldc, double precision, dimension( * ) work, integer lwork, integer info)

DORM22 multiplies a general matrix by a banded orthogonal matrix.

Purpose

      DORM22 overwrites the general real M-by-N matrix C with
                      SIDE = 'L'     SIDE = 'R'
      TRANS = 'N':      Q * C          C * Q
      TRANS = 'T':      Q**T * C       C * Q**T
      where Q is a real orthogonal matrix of order NQ, with NQ = M if
      SIDE = 'L' and NQ = N if SIDE = 'R'.
      The orthogonal matrix Q processes a 2-by-2 block structure
             [  Q11  Q12  ]
         Q = [            ]
             [  Q21  Q22  ],
      where Q12 is an N1-by-N1 lower triangular matrix and Q21 is an
      N2-by-N2 upper triangular matrix.

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);
              = 'C':  apply Q**T (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.

    N1
    N2

              N1 is INTEGER
              N2 is INTEGER
              The dimension of Q12 and Q21, respectively. N1, N2 >= 0.
              The following requirement must be satisfied:
              N1 + N2 = M if SIDE = 'L' and N1 + N2 = N if SIDE = 'R'.

    Q

              Q is DOUBLE PRECISION array, dimension
                                           (LDQ,M) if SIDE = 'L'
                                           (LDQ,N) if SIDE = 'R'

    LDQ

              LDQ is INTEGER
              The leading dimension of the array Q.
              LDQ >= max(1,M) if SIDE = 'L'; LDQ >= max(1,N) if SIDE = 'R'.

    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 (MAX(1,LWORK))
              On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

    LWORK

              LWORK is INTEGER
              The dimension of the array WORK.
              If SIDE = 'L', LWORK >= max(1,N);
              if SIDE = 'R', LWORK >= max(1,M).
              For optimum performance LWORK >= M*N.
              If LWORK = -1, then a workspace query is assumed; the routine
              only calculates the optimal size of the WORK array, returns
              this value as the first entry of the WORK array, and no error
              message related to LWORK is issued by XERBLA.

    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 161 of file dorm22.f.

  subroutine sorm22 (character side, character trans, integer m, integer n, integer n1, integer n2, real, dimension( ldq, * ) q, integer ldq, real, dimension( ldc, * ) c, integer ldc, real, dimension( * ) work, integer lwork, integer info)

SORM22 multiplies a general matrix by a banded orthogonal matrix.

Purpose

      SORM22 overwrites the general real M-by-N matrix C with
                      SIDE = 'L'     SIDE = 'R'
      TRANS = 'N':      Q * C          C * Q
      TRANS = 'T':      Q**T * C       C * Q**T
      where Q is a real orthogonal matrix of order NQ, with NQ = M if
      SIDE = 'L' and NQ = N if SIDE = 'R'.
      The orthogonal matrix Q processes a 2-by-2 block structure
             [  Q11  Q12  ]
         Q = [            ]
             [  Q21  Q22  ],
      where Q12 is an N1-by-N1 lower triangular matrix and Q21 is an
      N2-by-N2 upper triangular matrix.

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);
              = 'C':  apply Q**T (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.

    N1
    N2

              N1 is INTEGER
              N2 is INTEGER
              The dimension of Q12 and Q21, respectively. N1, N2 >= 0.
              The following requirement must be satisfied:
              N1 + N2 = M if SIDE = 'L' and N1 + N2 = N if SIDE = 'R'.

    Q

              Q is REAL array, dimension
                                  (LDQ,M) if SIDE = 'L'
                                  (LDQ,N) if SIDE = 'R'

    LDQ

              LDQ is INTEGER
              The leading dimension of the array Q.
              LDQ >= max(1,M) if SIDE = 'L'; LDQ >= max(1,N) if SIDE = 'R'.

    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 (MAX(1,LWORK))
              On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

    LWORK

              LWORK is INTEGER
              The dimension of the array WORK.
              If SIDE = 'L', LWORK >= max(1,N);
              if SIDE = 'R', LWORK >= max(1,M).
              For optimum performance LWORK >= M*N.
              If LWORK = -1, then a workspace query is assumed; the routine
              only calculates the optimal size of the WORK array, returns
              this value as the first entry of the WORK array, and no error
              message related to LWORK is issued by XERBLA.

    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 161 of file sorm22.f.

  subroutine zunm22 (character side, character trans, integer m, integer n, integer n1, integer n2, complex*16, dimension( ldq, * ) q, integer ldq, complex*16, dimension( ldc, * ) c, integer ldc, complex*16, dimension( * ) work, integer lwork, integer info)

ZUNM22 multiplies a general matrix by a banded unitary matrix.

Purpose

      ZUNM22 overwrites the general complex M-by-N matrix C with
                      SIDE = 'L'     SIDE = 'R'
      TRANS = 'N':      Q * C          C * Q
      TRANS = 'C':      Q**H * C       C * Q**H
      where Q is a complex unitary matrix of order NQ, with NQ = M if
      SIDE = 'L' and NQ = N if SIDE = 'R'.
      The unitary matrix Q processes a 2-by-2 block structure
             [  Q11  Q12  ]
         Q = [            ]
             [  Q21  Q22  ],
      where Q12 is an N1-by-N1 lower triangular matrix and Q21 is an
      N2-by-N2 upper triangular matrix.

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.

    N1
    N2

              N1 is INTEGER
              N2 is INTEGER
              The dimension of Q12 and Q21, respectively. N1, N2 >= 0.
              The following requirement must be satisfied:
              N1 + N2 = M if SIDE = 'L' and N1 + N2 = N if SIDE = 'R'.

    Q

              Q is COMPLEX*16 array, dimension
                                  (LDQ,M) if SIDE = 'L'
                                  (LDQ,N) if SIDE = 'R'

    LDQ

              LDQ is INTEGER
              The leading dimension of the array Q.
              LDQ >= max(1,M) if SIDE = 'L'; LDQ >= max(1,N) if SIDE = 'R'.

    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 (MAX(1,LWORK))
              On exit, if INFO = 0, WORK(1) returns the optimal LWORK.

    LWORK

              LWORK is INTEGER
              The dimension of the array WORK.
              If SIDE = 'L', LWORK >= max(1,N);
              if SIDE = 'R', LWORK >= max(1,M).
              For optimum performance LWORK >= M*N.
              If LWORK = -1, then a workspace query is assumed; the routine
              only calculates the optimal size of the WORK array, returns
              this value as the first entry of the WORK array, and no error
              message related to LWORK is issued by XERBLA.

    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 160 of file zunm22.f.

Author

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