unmhr(3)

NAME
unmhr - {un,or}mhr: multiply by Q from gehrd

SYNOPSIS

  Functions
subroutine cunmhr (side, trans, m, n, ilo, ihi, a, lda, tau, c, ldc, work, lwork, info)
CUNMHR
subroutine dormhr (side, trans, m, n, ilo, ihi, a, lda, tau, c, ldc, work, lwork, info)
DORMHR
subroutine sormhr (side, trans, m, n, ilo, ihi, a, lda, tau, c, ldc, work, lwork, info)
SORMHR
subroutine zunmhr (side, trans, m, n, ilo, ihi, a, lda, tau, c, ldc, work, lwork, info)
ZUNMHR

Detailed Description

Function Documentation

  subroutine cunmhr (character side, character trans, integer m, integer n, integer ilo, integer ihi, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) tau, complex, dimension( ldc, * ) c, integer ldc, complex, dimension( * ) work, integer lwork, integer info)

CUNMHR

Purpose:

     CUNMHR 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'. Q is defined as the product of
     IHI-ILO elementary reflectors, as returned by CGEHRD:
     Q = H(ilo) H(ilo+1) . . . H(ihi-1).

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.

    ILO

              ILO is INTEGER

    IHI

              IHI is INTEGER
              ILO and IHI must have the same values as in the previous call
              of CGEHRD. Q is equal to the unit matrix except in the
              submatrix Q(ilo+1:ihi,ilo+1:ihi).
              If SIDE = 'L', then 1 <= ILO <= IHI <= M, if M > 0, and
              ILO = 1 and IHI = 0, if M = 0;
              if SIDE = 'R', then 1 <= ILO <= IHI <= N, if N > 0, and
              ILO = 1 and IHI = 0, if N = 0.

    A

              A is COMPLEX array, dimension
                                   (LDA,M) if SIDE = 'L'
                                   (LDA,N) if SIDE = 'R'
              The vectors which define the elementary reflectors, as
              returned by CGEHRD.

    LDA

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

    TAU

              TAU is COMPLEX array, dimension
                                   (M-1) if SIDE = 'L'
                                   (N-1) if SIDE = 'R'
              TAU(i) must contain the scalar factor of the elementary
              reflector H(i), as returned by CGEHRD.

    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 >= N*NB if SIDE = 'L', and
              LWORK >= M*NB if SIDE = 'R', where NB is the optimal
              blocksize.
              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 177 of file cunmhr.f.

  subroutine dormhr (character side, character trans, integer m, integer n, integer ilo, integer ihi, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) tau, double precision, dimension( ldc, * ) c, integer ldc, double precision, dimension( * ) work, integer lwork, integer info)

DORMHR

Purpose:

     DORMHR 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'. Q is defined as the product of
     IHI-ILO elementary reflectors, as returned by DGEHRD:
     Q = H(ilo) H(ilo+1) . . . H(ihi-1).

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':  No transpose, apply Q;
              = 'T':  Transpose, apply Q**T.

    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.

    ILO

              ILO is INTEGER

    IHI

              IHI is INTEGER
              ILO and IHI must have the same values as in the previous call
              of DGEHRD. Q is equal to the unit matrix except in the
              submatrix Q(ilo+1:ihi,ilo+1:ihi).
              If SIDE = 'L', then 1 <= ILO <= IHI <= M, if M > 0, and
              ILO = 1 and IHI = 0, if M = 0;
              if SIDE = 'R', then 1 <= ILO <= IHI <= N, if N > 0, and
              ILO = 1 and IHI = 0, if N = 0.

    A

              A is DOUBLE PRECISION array, dimension
                                   (LDA,M) if SIDE = 'L'
                                   (LDA,N) if SIDE = 'R'
              The vectors which define the elementary reflectors, as
              returned by DGEHRD.

    LDA

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

    TAU

              TAU is DOUBLE PRECISION array, dimension
                                   (M-1) if SIDE = 'L'
                                   (N-1) if SIDE = 'R'
              TAU(i) must contain the scalar factor of the elementary
              reflector H(i), as returned by DGEHRD.

    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 >= N*NB if SIDE = 'L', and
              LWORK >= M*NB if SIDE = 'R', where NB is the optimal
              blocksize.
              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 176 of file dormhr.f.

  subroutine sormhr (character side, character trans, integer m, integer n, integer ilo, integer ihi, real, dimension( lda, * ) a, integer lda, real, dimension( * ) tau, real, dimension( ldc, * ) c, integer ldc, real, dimension( * ) work, integer lwork, integer info)

SORMHR

Purpose:

     SORMHR 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'. Q is defined as the product of
     IHI-ILO elementary reflectors, as returned by SGEHRD:
     Q = H(ilo) H(ilo+1) . . . H(ihi-1).

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':  No transpose, apply Q;
              = 'T':  Transpose, apply Q**T.

    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.

    ILO

              ILO is INTEGER

    IHI

              IHI is INTEGER
              ILO and IHI must have the same values as in the previous call
              of SGEHRD. Q is equal to the unit matrix except in the
              submatrix Q(ilo+1:ihi,ilo+1:ihi).
              If SIDE = 'L', then 1 <= ILO <= IHI <= M, if M > 0, and
              ILO = 1 and IHI = 0, if M = 0;
              if SIDE = 'R', then 1 <= ILO <= IHI <= N, if N > 0, and
              ILO = 1 and IHI = 0, if N = 0.

    A

              A is REAL array, dimension
                                   (LDA,M) if SIDE = 'L'
                                   (LDA,N) if SIDE = 'R'
              The vectors which define the elementary reflectors, as
              returned by SGEHRD.

    LDA

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

    TAU

              TAU is REAL array, dimension
                                   (M-1) if SIDE = 'L'
                                   (N-1) if SIDE = 'R'
              TAU(i) must contain the scalar factor of the elementary
              reflector H(i), as returned by SGEHRD.

    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 >= N*NB if SIDE = 'L', and
              LWORK >= M*NB if SIDE = 'R', where NB is the optimal
              blocksize.
              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 177 of file sormhr.f.

  subroutine zunmhr (character side, character trans, integer m, integer n, integer ilo, integer ihi, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( * ) tau, complex*16, dimension( ldc, * ) c, integer ldc, complex*16, dimension( * ) work, integer lwork, integer info)

ZUNMHR

Purpose:

     ZUNMHR 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'. Q is defined as the product of
     IHI-ILO elementary reflectors, as returned by ZGEHRD:
     Q = H(ilo) H(ilo+1) . . . H(ihi-1).

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.

    ILO

              ILO is INTEGER

    IHI

              IHI is INTEGER
              ILO and IHI must have the same values as in the previous call
              of ZGEHRD. Q is equal to the unit matrix except in the
              submatrix Q(ilo+1:ihi,ilo+1:ihi).
              If SIDE = 'L', then 1 <= ILO <= IHI <= M, if M > 0, and
              ILO = 1 and IHI = 0, if M = 0;
              if SIDE = 'R', then 1 <= ILO <= IHI <= N, if N > 0, and
              ILO = 1 and IHI = 0, if N = 0.

    A

              A is COMPLEX*16 array, dimension
                                   (LDA,M) if SIDE = 'L'
                                   (LDA,N) if SIDE = 'R'
              The vectors which define the elementary reflectors, as
              returned by ZGEHRD.

    LDA

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

    TAU

              TAU is COMPLEX*16 array, dimension
                                   (M-1) if SIDE = 'L'
                                   (N-1) if SIDE = 'R'
              TAU(i) must contain the scalar factor of the elementary
              reflector H(i), as returned by ZGEHRD.

    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 >= N*NB if SIDE = 'L', and
              LWORK >= M*NB if SIDE = 'R', where NB is the optimal
              blocksize.
              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 176 of file zunmhr.f.

Author

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