unghr(3)

NAME
unghr - {un,or}ghr: generate Q from gehrd

SYNOPSIS

  Functions

subroutine cunghr (n, ilo, ihi, a, lda, tau, work, lwork, info)
CUNGHR
subroutine dorghr (n, ilo, ihi, a, lda, tau, work, lwork, info)
DORGHR
subroutine sorghr (n, ilo, ihi, a, lda, tau, work, lwork, info)
SORGHR
subroutine zunghr (n, ilo, ihi, a, lda, tau, work, lwork, info)
ZUNGHR

Detailed Description

Function Documentation

  subroutine cunghr (integer n, integer ilo, integer ihi, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) tau, complex, dimension( * ) work, integer lwork, integer info)

CUNGHR

Purpose:

    !>
    !> CUNGHR generates a complex unitary matrix Q which is defined as the
    !> product of IHI-ILO elementary reflectors of order N, as returned by
    !> CGEHRD:
    !>
    !> Q = H(ilo) H(ilo+1) . . . H(ihi-1).
    !>

Parameters
    N

    !>          N is INTEGER
    !>          The order of the matrix Q. 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).
    !>          1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0.
    !>

    A

    !>          A is COMPLEX array, dimension (LDA,N)
    !>          On entry, the vectors which define the elementary reflectors,
    !>          as returned by CGEHRD.
    !>          On exit, the N-by-N unitary matrix Q.
    !>

    LDA

    !>          LDA is INTEGER
    !>          The leading dimension of the array A. LDA >= max(1,N).
    !>

    TAU

    !>          TAU is COMPLEX array, dimension (N-1)
    !>          TAU(i) must contain the scalar factor of the elementary
    !>          reflector H(i), as returned by CGEHRD.
    !>

    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. LWORK >= IHI-ILO.
    !>          For optimum performance LWORK >= (IHI-ILO)*NB, 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 dorghr (integer n, integer ilo, integer ihi, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) tau, double precision, dimension( * ) work, integer lwork, integer info)

DORGHR

Purpose:

    !>
    !> DORGHR generates a real orthogonal matrix Q which is defined as the
    !> product of IHI-ILO elementary reflectors of order N, as returned by
    !> DGEHRD:
    !>
    !> Q = H(ilo) H(ilo+1) . . . H(ihi-1).
    !>

Parameters
    N

    !>          N is INTEGER
    !>          The order of the matrix Q. 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).
    !>          1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0.
    !>

    A

    !>          A is DOUBLE PRECISION array, dimension (LDA,N)
    !>          On entry, the vectors which define the elementary reflectors,
    !>          as returned by DGEHRD.
    !>          On exit, the N-by-N orthogonal matrix Q.
    !>

    LDA

    !>          LDA is INTEGER
    !>          The leading dimension of the array A. LDA >= max(1,N).
    !>

    TAU

    !>          TAU is DOUBLE PRECISION array, dimension (N-1)
    !>          TAU(i) must contain the scalar factor of the elementary
    !>          reflector H(i), as returned by DGEHRD.
    !>

    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. LWORK >= IHI-ILO.
    !>          For optimum performance LWORK >= (IHI-ILO)*NB, 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 sorghr (integer n, integer ilo, integer ihi, real, dimension( lda, * ) a, integer lda, real, dimension( * ) tau, real, dimension( * ) work, integer lwork, integer info)

SORGHR

Purpose:

    !>
    !> SORGHR generates a real orthogonal matrix Q which is defined as the
    !> product of IHI-ILO elementary reflectors of order N, as returned by
    !> SGEHRD:
    !>
    !> Q = H(ilo) H(ilo+1) . . . H(ihi-1).
    !>

Parameters
    N

    !>          N is INTEGER
    !>          The order of the matrix Q. 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).
    !>          1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0.
    !>

    A

    !>          A is REAL array, dimension (LDA,N)
    !>          On entry, the vectors which define the elementary reflectors,
    !>          as returned by SGEHRD.
    !>          On exit, the N-by-N orthogonal matrix Q.
    !>

    LDA

    !>          LDA is INTEGER
    !>          The leading dimension of the array A. LDA >= max(1,N).
    !>

    TAU

    !>          TAU is REAL array, dimension (N-1)
    !>          TAU(i) must contain the scalar factor of the elementary
    !>          reflector H(i), as returned by SGEHRD.
    !>

    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. LWORK >= IHI-ILO.
    !>          For optimum performance LWORK >= (IHI-ILO)*NB, 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 zunghr (integer n, integer ilo, integer ihi, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( * ) tau, complex*16, dimension( * ) work, integer lwork, integer info)

ZUNGHR

Purpose:

    !>
    !> ZUNGHR generates a complex unitary matrix Q which is defined as the
    !> product of IHI-ILO elementary reflectors of order N, as returned by
    !> ZGEHRD:
    !>
    !> Q = H(ilo) H(ilo+1) . . . H(ihi-1).
    !>

Parameters
    N

    !>          N is INTEGER
    !>          The order of the matrix Q. 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).
    !>          1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0.
    !>

    A

    !>          A is COMPLEX*16 array, dimension (LDA,N)
    !>          On entry, the vectors which define the elementary reflectors,
    !>          as returned by ZGEHRD.
    !>          On exit, the N-by-N unitary matrix Q.
    !>

    LDA

    !>          LDA is INTEGER
    !>          The leading dimension of the array A. LDA >= max(1,N).
    !>

    TAU

    !>          TAU is COMPLEX*16 array, dimension (N-1)
    !>          TAU(i) must contain the scalar factor of the elementary
    !>          reflector H(i), as returned by ZGEHRD.
    !>

    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. LWORK >= IHI-ILO.
    !>          For optimum performance LWORK >= (IHI-ILO)*NB, 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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