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 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 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 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 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 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 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, complex16, dimension( lda, ) a, integer lda, complex16, dimension( ) tau, complex16, 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 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 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

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