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.

Definition at line 125 of file cunghr.f.

  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.

Definition at line 125 of file dorghr.f.

  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.

Definition at line 125 of file sorghr.f.

  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.

Definition at line 125 of file zunghr.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.