Provided by: liblapack-doc_3.12.0-3build1.1_all bug

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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