.TH "unghr" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
unghr \- {un,or}ghr: generate Q from gehrd
.SH SYNOPSIS
.br
.PP
.SS "Functions"

.in +1c
.ti -1c
.RI "subroutine \fBcunghr\fP (n, ilo, ihi, a, lda, tau, work, lwork, info)"
.br
.RI "\fBCUNGHR\fP "
.ti -1c
.RI "subroutine \fBdorghr\fP (n, ilo, ihi, a, lda, tau, work, lwork, info)"
.br
.RI "\fBDORGHR\fP "
.ti -1c
.RI "subroutine \fBsorghr\fP (n, ilo, ihi, a, lda, tau, work, lwork, info)"
.br
.RI "\fBSORGHR\fP "
.ti -1c
.RI "subroutine \fBzunghr\fP (n, ilo, ihi, a, lda, tau, work, lwork, info)"
.br
.RI "\fBZUNGHR\fP "
.in -1c
.SH "Detailed Description"
.PP 

.SH "Function Documentation"
.PP 
.SS "subroutine cunghr (integer n, integer ilo, integer ihi, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) tau, complex, dimension( * ) work, integer lwork, integer info)"

.PP
\fBCUNGHR\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
!>
!> 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)\&.
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIN\fP 
.PP
.nf
!>          N is INTEGER
!>          The order of the matrix Q\&. N >= 0\&.
!> 
.fi
.PP
.br
\fIILO\fP 
.PP
.nf
!>          ILO is INTEGER
!> 
.fi
.PP
.br
\fIIHI\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fIA\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
!>          LDA is INTEGER
!>          The leading dimension of the array A\&. LDA >= max(1,N)\&.
!> 
.fi
.PP
.br
\fITAU\fP 
.PP
.nf
!>          TAU is COMPLEX array, dimension (N-1)
!>          TAU(i) must contain the scalar factor of the elementary
!>          reflector H(i), as returned by CGEHRD\&.
!> 
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
!>          WORK is COMPLEX array, dimension (MAX(1,LWORK))
!>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK\&.
!> 
.fi
.PP
.br
\fILWORK\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
!>          INFO is INTEGER
!>          = 0:  successful exit
!>          < 0:  if INFO = -i, the i-th argument had an illegal value
!> 
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 

.PP
Univ\&. of California Berkeley 

.PP
Univ\&. of Colorado Denver 

.PP
NAG Ltd\&. 
.RE
.PP

.PP
Definition at line \fB125\fP of file \fBcunghr\&.f\fP\&.
.SS "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)"

.PP
\fBDORGHR\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
!>
!> 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)\&.
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIN\fP 
.PP
.nf
!>          N is INTEGER
!>          The order of the matrix Q\&. N >= 0\&.
!> 
.fi
.PP
.br
\fIILO\fP 
.PP
.nf
!>          ILO is INTEGER
!> 
.fi
.PP
.br
\fIIHI\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fIA\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
!>          LDA is INTEGER
!>          The leading dimension of the array A\&. LDA >= max(1,N)\&.
!> 
.fi
.PP
.br
\fITAU\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
!>          WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
!>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK\&.
!> 
.fi
.PP
.br
\fILWORK\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
!>          INFO is INTEGER
!>          = 0:  successful exit
!>          < 0:  if INFO = -i, the i-th argument had an illegal value
!> 
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 

.PP
Univ\&. of California Berkeley 

.PP
Univ\&. of Colorado Denver 

.PP
NAG Ltd\&. 
.RE
.PP

.PP
Definition at line \fB125\fP of file \fBdorghr\&.f\fP\&.
.SS "subroutine sorghr (integer n, integer ilo, integer ihi, real, dimension( lda, * ) a, integer lda, real, dimension( * ) tau, real, dimension( * ) work, integer lwork, integer info)"

.PP
\fBSORGHR\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
!>
!> 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)\&.
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIN\fP 
.PP
.nf
!>          N is INTEGER
!>          The order of the matrix Q\&. N >= 0\&.
!> 
.fi
.PP
.br
\fIILO\fP 
.PP
.nf
!>          ILO is INTEGER
!> 
.fi
.PP
.br
\fIIHI\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fIA\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
!>          LDA is INTEGER
!>          The leading dimension of the array A\&. LDA >= max(1,N)\&.
!> 
.fi
.PP
.br
\fITAU\fP 
.PP
.nf
!>          TAU is REAL array, dimension (N-1)
!>          TAU(i) must contain the scalar factor of the elementary
!>          reflector H(i), as returned by SGEHRD\&.
!> 
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
!>          WORK is REAL array, dimension (MAX(1,LWORK))
!>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK\&.
!> 
.fi
.PP
.br
\fILWORK\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
!>          INFO is INTEGER
!>          = 0:  successful exit
!>          < 0:  if INFO = -i, the i-th argument had an illegal value
!> 
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 

.PP
Univ\&. of California Berkeley 

.PP
Univ\&. of Colorado Denver 

.PP
NAG Ltd\&. 
.RE
.PP

.PP
Definition at line \fB125\fP of file \fBsorghr\&.f\fP\&.
.SS "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)"

.PP
\fBZUNGHR\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
!>
!> 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)\&.
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIN\fP 
.PP
.nf
!>          N is INTEGER
!>          The order of the matrix Q\&. N >= 0\&.
!> 
.fi
.PP
.br
\fIILO\fP 
.PP
.nf
!>          ILO is INTEGER
!> 
.fi
.PP
.br
\fIIHI\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fIA\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
!>          LDA is INTEGER
!>          The leading dimension of the array A\&. LDA >= max(1,N)\&.
!> 
.fi
.PP
.br
\fITAU\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
!>          WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
!>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK\&.
!> 
.fi
.PP
.br
\fILWORK\fP 
.PP
.nf
!>          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\&.
!> 
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
!>          INFO is INTEGER
!>          = 0:  successful exit
!>          < 0:  if INFO = -i, the i-th argument had an illegal value
!> 
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 

.PP
Univ\&. of California Berkeley 

.PP
Univ\&. of Colorado Denver 

.PP
NAG Ltd\&. 
.RE
.PP

.PP
Definition at line \fB125\fP of file \fBzunghr\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.