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.

  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.

  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.

  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.

Author

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