.TH "upgtr" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
upgtr \- {up,op}gtr: generate Q from hetrd
.SH SYNOPSIS
.br
.PP
.SS "Functions"

.in +1c
.ti -1c
.RI "subroutine \fBcupgtr\fP (uplo, n, ap, tau, q, ldq, work, info)"
.br
.RI "\fBCUPGTR\fP "
.ti -1c
.RI "subroutine \fBdopgtr\fP (uplo, n, ap, tau, q, ldq, work, info)"
.br
.RI "\fBDOPGTR\fP "
.ti -1c
.RI "subroutine \fBsopgtr\fP (uplo, n, ap, tau, q, ldq, work, info)"
.br
.RI "\fBSOPGTR\fP "
.ti -1c
.RI "subroutine \fBzupgtr\fP (uplo, n, ap, tau, q, ldq, work, info)"
.br
.RI "\fBZUPGTR\fP "
.in -1c
.SH "Detailed Description"
.PP 

.SH "Function Documentation"
.PP 
.SS "subroutine cupgtr (character uplo, integer n, complex, dimension( * ) ap, complex, dimension( * ) tau, complex, dimension( ldq, * ) q, integer ldq, complex, dimension( * ) work, integer info)"

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

.PP
.nf
 CUPGTR generates a complex unitary matrix Q which is defined as the
 product of n-1 elementary reflectors H(i) of order n, as returned by
 CHPTRD using packed storage:

 if UPLO = 'U', Q = H(n-1) \&. \&. \&. H(2) H(1),

 if UPLO = 'L', Q = H(1) H(2) \&. \&. \&. H(n-1)\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIUPLO\fP 
.PP
.nf
          UPLO is CHARACTER*1
          = 'U': Upper triangular packed storage used in previous
                 call to CHPTRD;
          = 'L': Lower triangular packed storage used in previous
                 call to CHPTRD\&.
.fi
.PP
.br
\fIN\fP 
.PP
.nf
          N is INTEGER
          The order of the matrix Q\&. N >= 0\&.
.fi
.PP
.br
\fIAP\fP 
.PP
.nf
          AP is COMPLEX array, dimension (N*(N+1)/2)
          The vectors which define the elementary reflectors, as
          returned by CHPTRD\&.
.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 CHPTRD\&.
.fi
.PP
.br
\fIQ\fP 
.PP
.nf
          Q is COMPLEX array, dimension (LDQ,N)
          The N-by-N unitary matrix Q\&.
.fi
.PP
.br
\fILDQ\fP 
.PP
.nf
          LDQ is INTEGER
          The leading dimension of the array Q\&. LDQ >= max(1,N)\&.
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
          WORK is COMPLEX array, dimension (N-1)
.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 \fB113\fP of file \fBcupgtr\&.f\fP\&.
.SS "subroutine dopgtr (character uplo, integer n, double precision, dimension( * ) ap, double precision, dimension( * ) tau, double precision, dimension( ldq, * ) q, integer ldq, double precision, dimension( * ) work, integer info)"

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

.PP
.nf
 DOPGTR generates a real orthogonal matrix Q which is defined as the
 product of n-1 elementary reflectors H(i) of order n, as returned by
 DSPTRD using packed storage:

 if UPLO = 'U', Q = H(n-1) \&. \&. \&. H(2) H(1),

 if UPLO = 'L', Q = H(1) H(2) \&. \&. \&. H(n-1)\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIUPLO\fP 
.PP
.nf
          UPLO is CHARACTER*1
          = 'U': Upper triangular packed storage used in previous
                 call to DSPTRD;
          = 'L': Lower triangular packed storage used in previous
                 call to DSPTRD\&.
.fi
.PP
.br
\fIN\fP 
.PP
.nf
          N is INTEGER
          The order of the matrix Q\&. N >= 0\&.
.fi
.PP
.br
\fIAP\fP 
.PP
.nf
          AP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
          The vectors which define the elementary reflectors, as
          returned by DSPTRD\&.
.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 DSPTRD\&.
.fi
.PP
.br
\fIQ\fP 
.PP
.nf
          Q is DOUBLE PRECISION array, dimension (LDQ,N)
          The N-by-N orthogonal matrix Q\&.
.fi
.PP
.br
\fILDQ\fP 
.PP
.nf
          LDQ is INTEGER
          The leading dimension of the array Q\&. LDQ >= max(1,N)\&.
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
          WORK is DOUBLE PRECISION array, dimension (N-1)
.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 \fB113\fP of file \fBdopgtr\&.f\fP\&.
.SS "subroutine sopgtr (character uplo, integer n, real, dimension( * ) ap, real, dimension( * ) tau, real, dimension( ldq, * ) q, integer ldq, real, dimension( * ) work, integer info)"

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

.PP
.nf
 SOPGTR generates a real orthogonal matrix Q which is defined as the
 product of n-1 elementary reflectors H(i) of order n, as returned by
 SSPTRD using packed storage:

 if UPLO = 'U', Q = H(n-1) \&. \&. \&. H(2) H(1),

 if UPLO = 'L', Q = H(1) H(2) \&. \&. \&. H(n-1)\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIUPLO\fP 
.PP
.nf
          UPLO is CHARACTER*1
          = 'U': Upper triangular packed storage used in previous
                 call to SSPTRD;
          = 'L': Lower triangular packed storage used in previous
                 call to SSPTRD\&.
.fi
.PP
.br
\fIN\fP 
.PP
.nf
          N is INTEGER
          The order of the matrix Q\&. N >= 0\&.
.fi
.PP
.br
\fIAP\fP 
.PP
.nf
          AP is REAL array, dimension (N*(N+1)/2)
          The vectors which define the elementary reflectors, as
          returned by SSPTRD\&.
.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 SSPTRD\&.
.fi
.PP
.br
\fIQ\fP 
.PP
.nf
          Q is REAL array, dimension (LDQ,N)
          The N-by-N orthogonal matrix Q\&.
.fi
.PP
.br
\fILDQ\fP 
.PP
.nf
          LDQ is INTEGER
          The leading dimension of the array Q\&. LDQ >= max(1,N)\&.
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
          WORK is REAL array, dimension (N-1)
.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 \fB113\fP of file \fBsopgtr\&.f\fP\&.
.SS "subroutine zupgtr (character uplo, integer n, complex*16, dimension( * ) ap, complex*16, dimension( * ) tau, complex*16, dimension( ldq, * ) q, integer ldq, complex*16, dimension( * ) work, integer info)"

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

.PP
.nf
 ZUPGTR generates a complex unitary matrix Q which is defined as the
 product of n-1 elementary reflectors H(i) of order n, as returned by
 ZHPTRD using packed storage:

 if UPLO = 'U', Q = H(n-1) \&. \&. \&. H(2) H(1),

 if UPLO = 'L', Q = H(1) H(2) \&. \&. \&. H(n-1)\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIUPLO\fP 
.PP
.nf
          UPLO is CHARACTER*1
          = 'U': Upper triangular packed storage used in previous
                 call to ZHPTRD;
          = 'L': Lower triangular packed storage used in previous
                 call to ZHPTRD\&.
.fi
.PP
.br
\fIN\fP 
.PP
.nf
          N is INTEGER
          The order of the matrix Q\&. N >= 0\&.
.fi
.PP
.br
\fIAP\fP 
.PP
.nf
          AP is COMPLEX*16 array, dimension (N*(N+1)/2)
          The vectors which define the elementary reflectors, as
          returned by ZHPTRD\&.
.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 ZHPTRD\&.
.fi
.PP
.br
\fIQ\fP 
.PP
.nf
          Q is COMPLEX*16 array, dimension (LDQ,N)
          The N-by-N unitary matrix Q\&.
.fi
.PP
.br
\fILDQ\fP 
.PP
.nf
          LDQ is INTEGER
          The leading dimension of the array Q\&. LDQ >= max(1,N)\&.
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
          WORK is COMPLEX*16 array, dimension (N-1)
.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 \fB113\fP of file \fBzupgtr\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.