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.

  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.

  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.

  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.

Author

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