.TH "upmtr" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
upmtr \- {up,op}mtr: multiply by Q from hptrd
.SH SYNOPSIS
.br
.PP
.SS "Functions"

.in +1c
.ti -1c
.RI "subroutine \fBcupmtr\fP (side, uplo, trans, m, n, ap, tau, c, ldc, work, info)"
.br
.RI "\fBCUPMTR\fP "
.ti -1c
.RI "subroutine \fBdopmtr\fP (side, uplo, trans, m, n, ap, tau, c, ldc, work, info)"
.br
.RI "\fBDOPMTR\fP "
.ti -1c
.RI "subroutine \fBsopmtr\fP (side, uplo, trans, m, n, ap, tau, c, ldc, work, info)"
.br
.RI "\fBSOPMTR\fP "
.ti -1c
.RI "subroutine \fBzupmtr\fP (side, uplo, trans, m, n, ap, tau, c, ldc, work, info)"
.br
.RI "\fBZUPMTR\fP "
.in -1c
.SH "Detailed Description"
.PP 

.SH "Function Documentation"
.PP 
.SS "subroutine cupmtr (character side, character uplo, character trans, integer m, integer n, complex, dimension( * ) ap, complex, dimension( * ) tau, complex, dimension( ldc, * ) c, integer ldc, complex, dimension( * ) work, integer info)"

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

.PP
.nf
!>
!> CUPMTR overwrites the general complex M-by-N matrix C with
!>
!>                 SIDE = 'L'     SIDE = 'R'
!> TRANS = 'N':      Q * C          C * Q
!> TRANS = 'C':      Q**H * C       C * Q**H
!>
!> where Q is a complex unitary matrix of order nq, with nq = m if
!> SIDE = 'L' and nq = n if SIDE = 'R'\&. Q is defined as the product of
!> nq-1 elementary reflectors, as returned by CHPTRD using packed
!> storage:
!>
!> if UPLO = 'U', Q = H(nq-1) \&. \&. \&. H(2) H(1);
!>
!> if UPLO = 'L', Q = H(1) H(2) \&. \&. \&. H(nq-1)\&.
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fISIDE\fP 
.PP
.nf
!>          SIDE is CHARACTER*1
!>          = 'L': apply Q or Q**H from the Left;
!>          = 'R': apply Q or Q**H from the Right\&.
!> 
.fi
.PP
.br
\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
\fITRANS\fP 
.PP
.nf
!>          TRANS is CHARACTER*1
!>          = 'N':  No transpose, apply Q;
!>          = 'C':  Conjugate transpose, apply Q**H\&.
!> 
.fi
.PP
.br
\fIM\fP 
.PP
.nf
!>          M is INTEGER
!>          The number of rows of the matrix C\&. M >= 0\&.
!> 
.fi
.PP
.br
\fIN\fP 
.PP
.nf
!>          N is INTEGER
!>          The number of columns of the matrix C\&. N >= 0\&.
!> 
.fi
.PP
.br
\fIAP\fP 
.PP
.nf
!>          AP is COMPLEX array, dimension
!>                               (M*(M+1)/2) if SIDE = 'L'
!>                               (N*(N+1)/2) if SIDE = 'R'
!>          The vectors which define the elementary reflectors, as
!>          returned by CHPTRD\&.  AP is modified by the routine but
!>          restored on exit\&.
!> 
.fi
.PP
.br
\fITAU\fP 
.PP
.nf
!>          TAU is COMPLEX array, dimension (M-1) if SIDE = 'L'
!>                                     or (N-1) if SIDE = 'R'
!>          TAU(i) must contain the scalar factor of the elementary
!>          reflector H(i), as returned by CHPTRD\&.
!> 
.fi
.PP
.br
\fIC\fP 
.PP
.nf
!>          C is COMPLEX array, dimension (LDC,N)
!>          On entry, the M-by-N matrix C\&.
!>          On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q\&.
!> 
.fi
.PP
.br
\fILDC\fP 
.PP
.nf
!>          LDC is INTEGER
!>          The leading dimension of the array C\&. LDC >= max(1,M)\&.
!> 
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
!>          WORK is COMPLEX array, dimension
!>                                   (N) if SIDE = 'L'
!>                                   (M) if SIDE = 'R'
!> 
.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 \fB148\fP of file \fBcupmtr\&.f\fP\&.
.SS "subroutine dopmtr (character side, character uplo, character trans, integer m, integer n, double precision, dimension( * ) ap, double precision, dimension( * ) tau, double precision, dimension( ldc, * ) c, integer ldc, double precision, dimension( * ) work, integer info)"

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

.PP
.nf
!>
!> DOPMTR overwrites the general real M-by-N matrix C with
!>
!>                 SIDE = 'L'     SIDE = 'R'
!> TRANS = 'N':      Q * C          C * Q
!> TRANS = 'T':      Q**T * C       C * Q**T
!>
!> where Q is a real orthogonal matrix of order nq, with nq = m if
!> SIDE = 'L' and nq = n if SIDE = 'R'\&. Q is defined as the product of
!> nq-1 elementary reflectors, as returned by DSPTRD using packed
!> storage:
!>
!> if UPLO = 'U', Q = H(nq-1) \&. \&. \&. H(2) H(1);
!>
!> if UPLO = 'L', Q = H(1) H(2) \&. \&. \&. H(nq-1)\&.
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fISIDE\fP 
.PP
.nf
!>          SIDE is CHARACTER*1
!>          = 'L': apply Q or Q**T from the Left;
!>          = 'R': apply Q or Q**T from the Right\&.
!> 
.fi
.PP
.br
\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
\fITRANS\fP 
.PP
.nf
!>          TRANS is CHARACTER*1
!>          = 'N':  No transpose, apply Q;
!>          = 'T':  Transpose, apply Q**T\&.
!> 
.fi
.PP
.br
\fIM\fP 
.PP
.nf
!>          M is INTEGER
!>          The number of rows of the matrix C\&. M >= 0\&.
!> 
.fi
.PP
.br
\fIN\fP 
.PP
.nf
!>          N is INTEGER
!>          The number of columns of the matrix C\&. N >= 0\&.
!> 
.fi
.PP
.br
\fIAP\fP 
.PP
.nf
!>          AP is DOUBLE PRECISION array, dimension
!>                               (M*(M+1)/2) if SIDE = 'L'
!>                               (N*(N+1)/2) if SIDE = 'R'
!>          The vectors which define the elementary reflectors, as
!>          returned by DSPTRD\&.  AP is modified by the routine but
!>          restored on exit\&.
!> 
.fi
.PP
.br
\fITAU\fP 
.PP
.nf
!>          TAU is DOUBLE PRECISION array, dimension (M-1) if SIDE = 'L'
!>                                     or (N-1) if SIDE = 'R'
!>          TAU(i) must contain the scalar factor of the elementary
!>          reflector H(i), as returned by DSPTRD\&.
!> 
.fi
.PP
.br
\fIC\fP 
.PP
.nf
!>          C is DOUBLE PRECISION array, dimension (LDC,N)
!>          On entry, the M-by-N matrix C\&.
!>          On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q\&.
!> 
.fi
.PP
.br
\fILDC\fP 
.PP
.nf
!>          LDC is INTEGER
!>          The leading dimension of the array C\&. LDC >= max(1,M)\&.
!> 
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
!>          WORK is DOUBLE PRECISION array, dimension
!>                                   (N) if SIDE = 'L'
!>                                   (M) if SIDE = 'R'
!> 
.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 \fB148\fP of file \fBdopmtr\&.f\fP\&.
.SS "subroutine sopmtr (character side, character uplo, character trans, integer m, integer n, real, dimension( * ) ap, real, dimension( * ) tau, real, dimension( ldc, * ) c, integer ldc, real, dimension( * ) work, integer info)"

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

.PP
.nf
!>
!> SOPMTR overwrites the general real M-by-N matrix C with
!>
!>                 SIDE = 'L'     SIDE = 'R'
!> TRANS = 'N':      Q * C          C * Q
!> TRANS = 'T':      Q**T * C       C * Q**T
!>
!> where Q is a real orthogonal matrix of order nq, with nq = m if
!> SIDE = 'L' and nq = n if SIDE = 'R'\&. Q is defined as the product of
!> nq-1 elementary reflectors, as returned by SSPTRD using packed
!> storage:
!>
!> if UPLO = 'U', Q = H(nq-1) \&. \&. \&. H(2) H(1);
!>
!> if UPLO = 'L', Q = H(1) H(2) \&. \&. \&. H(nq-1)\&.
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fISIDE\fP 
.PP
.nf
!>          SIDE is CHARACTER*1
!>          = 'L': apply Q or Q**T from the Left;
!>          = 'R': apply Q or Q**T from the Right\&.
!> 
.fi
.PP
.br
\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
\fITRANS\fP 
.PP
.nf
!>          TRANS is CHARACTER*1
!>          = 'N':  No transpose, apply Q;
!>          = 'T':  Transpose, apply Q**T\&.
!> 
.fi
.PP
.br
\fIM\fP 
.PP
.nf
!>          M is INTEGER
!>          The number of rows of the matrix C\&. M >= 0\&.
!> 
.fi
.PP
.br
\fIN\fP 
.PP
.nf
!>          N is INTEGER
!>          The number of columns of the matrix C\&. N >= 0\&.
!> 
.fi
.PP
.br
\fIAP\fP 
.PP
.nf
!>          AP is REAL array, dimension
!>                               (M*(M+1)/2) if SIDE = 'L'
!>                               (N*(N+1)/2) if SIDE = 'R'
!>          The vectors which define the elementary reflectors, as
!>          returned by SSPTRD\&.  AP is modified by the routine but
!>          restored on exit\&.
!> 
.fi
.PP
.br
\fITAU\fP 
.PP
.nf
!>          TAU is REAL array, dimension (M-1) if SIDE = 'L'
!>                                     or (N-1) if SIDE = 'R'
!>          TAU(i) must contain the scalar factor of the elementary
!>          reflector H(i), as returned by SSPTRD\&.
!> 
.fi
.PP
.br
\fIC\fP 
.PP
.nf
!>          C is REAL array, dimension (LDC,N)
!>          On entry, the M-by-N matrix C\&.
!>          On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q\&.
!> 
.fi
.PP
.br
\fILDC\fP 
.PP
.nf
!>          LDC is INTEGER
!>          The leading dimension of the array C\&. LDC >= max(1,M)\&.
!> 
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
!>          WORK is REAL array, dimension
!>                                   (N) if SIDE = 'L'
!>                                   (M) if SIDE = 'R'
!> 
.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 \fB148\fP of file \fBsopmtr\&.f\fP\&.
.SS "subroutine zupmtr (character side, character uplo, character trans, integer m, integer n, complex*16, dimension( * ) ap, complex*16, dimension( * ) tau, complex*16, dimension( ldc, * ) c, integer ldc, complex*16, dimension( * ) work, integer info)"

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

.PP
.nf
!>
!> ZUPMTR overwrites the general complex M-by-N matrix C with
!>
!>                 SIDE = 'L'     SIDE = 'R'
!> TRANS = 'N':      Q * C          C * Q
!> TRANS = 'C':      Q**H * C       C * Q**H
!>
!> where Q is a complex unitary matrix of order nq, with nq = m if
!> SIDE = 'L' and nq = n if SIDE = 'R'\&. Q is defined as the product of
!> nq-1 elementary reflectors, as returned by ZHPTRD using packed
!> storage:
!>
!> if UPLO = 'U', Q = H(nq-1) \&. \&. \&. H(2) H(1);
!>
!> if UPLO = 'L', Q = H(1) H(2) \&. \&. \&. H(nq-1)\&.
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fISIDE\fP 
.PP
.nf
!>          SIDE is CHARACTER*1
!>          = 'L': apply Q or Q**H from the Left;
!>          = 'R': apply Q or Q**H from the Right\&.
!> 
.fi
.PP
.br
\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
\fITRANS\fP 
.PP
.nf
!>          TRANS is CHARACTER*1
!>          = 'N':  No transpose, apply Q;
!>          = 'C':  Conjugate transpose, apply Q**H\&.
!> 
.fi
.PP
.br
\fIM\fP 
.PP
.nf
!>          M is INTEGER
!>          The number of rows of the matrix C\&. M >= 0\&.
!> 
.fi
.PP
.br
\fIN\fP 
.PP
.nf
!>          N is INTEGER
!>          The number of columns of the matrix C\&. N >= 0\&.
!> 
.fi
.PP
.br
\fIAP\fP 
.PP
.nf
!>          AP is COMPLEX*16 array, dimension
!>                               (M*(M+1)/2) if SIDE = 'L'
!>                               (N*(N+1)/2) if SIDE = 'R'
!>          The vectors which define the elementary reflectors, as
!>          returned by ZHPTRD\&.  AP is modified by the routine but
!>          restored on exit\&.
!> 
.fi
.PP
.br
\fITAU\fP 
.PP
.nf
!>          TAU is COMPLEX*16 array, dimension (M-1) if SIDE = 'L'
!>                                     or (N-1) if SIDE = 'R'
!>          TAU(i) must contain the scalar factor of the elementary
!>          reflector H(i), as returned by ZHPTRD\&.
!> 
.fi
.PP
.br
\fIC\fP 
.PP
.nf
!>          C is COMPLEX*16 array, dimension (LDC,N)
!>          On entry, the M-by-N matrix C\&.
!>          On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q\&.
!> 
.fi
.PP
.br
\fILDC\fP 
.PP
.nf
!>          LDC is INTEGER
!>          The leading dimension of the array C\&. LDC >= max(1,M)\&.
!> 
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
!>          WORK is COMPLEX*16 array, dimension
!>                                   (N) if SIDE = 'L'
!>                                   (M) if SIDE = 'R'
!> 
.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 \fB148\fP of file \fBzupmtr\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.