.TH "unmtr" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
unmtr \- {un,or}mtr: multiply by Q from hetrd
.SH SYNOPSIS
.br
.PP
.SS "Functions"

.in +1c
.ti -1c
.RI "subroutine \fBcunmtr\fP (side, uplo, trans, m, n, a, lda, tau, c, ldc, work, lwork, info)"
.br
.RI "\fBCUNMTR\fP "
.ti -1c
.RI "subroutine \fBdormtr\fP (side, uplo, trans, m, n, a, lda, tau, c, ldc, work, lwork, info)"
.br
.RI "\fBDORMTR\fP "
.ti -1c
.RI "subroutine \fBsormtr\fP (side, uplo, trans, m, n, a, lda, tau, c, ldc, work, lwork, info)"
.br
.RI "\fBSORMTR\fP "
.ti -1c
.RI "subroutine \fBzunmtr\fP (side, uplo, trans, m, n, a, lda, tau, c, ldc, work, lwork, info)"
.br
.RI "\fBZUNMTR\fP "
.in -1c
.SH "Detailed Description"
.PP 

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

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

.PP
.nf
 CUNMTR 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 CHETRD:

 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 triangle of A contains elementary reflectors
                 from CHETRD;
          = 'L': Lower triangle of A contains elementary reflectors
                 from CHETRD\&.
.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
\fIA\fP 
.PP
.nf
          A is COMPLEX array, dimension
                               (LDA,M) if SIDE = 'L'
                               (LDA,N) if SIDE = 'R'
          The vectors which define the elementary reflectors, as
          returned by CHETRD\&.
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
          LDA is INTEGER
          The leading dimension of the array A\&.
          LDA >= max(1,M) if SIDE = 'L'; LDA >= max(1,N) if SIDE = 'R'\&.
.fi
.PP
.br
\fITAU\fP 
.PP
.nf
          TAU is COMPLEX array, dimension
                               (M-1) if SIDE = 'L'
                               (N-1) if SIDE = 'R'
          TAU(i) must contain the scalar factor of the elementary
          reflector H(i), as returned by CHETRD\&.
.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 (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\&.
          If SIDE = 'L', LWORK >= max(1,N);
          if SIDE = 'R', LWORK >= max(1,M)\&.
          For optimum performance LWORK >= N*NB if SIDE = 'L', and
          LWORK >=M*NB if SIDE = 'R', 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 \fB170\fP of file \fBcunmtr\&.f\fP\&.
.SS "subroutine dormtr (character side, character uplo, character trans, integer m, integer n, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) tau, double precision, dimension( ldc, * ) c, integer ldc, double precision, dimension( * ) work, integer lwork, integer info)"

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

.PP
.nf
 DORMTR 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 DSYTRD:

 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 triangle of A contains elementary reflectors
                 from DSYTRD;
          = 'L': Lower triangle of A contains elementary reflectors
                 from DSYTRD\&.
.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
\fIA\fP 
.PP
.nf
          A is DOUBLE PRECISION array, dimension
                               (LDA,M) if SIDE = 'L'
                               (LDA,N) if SIDE = 'R'
          The vectors which define the elementary reflectors, as
          returned by DSYTRD\&.
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
          LDA is INTEGER
          The leading dimension of the array A\&.
          LDA >= max(1,M) if SIDE = 'L'; LDA >= max(1,N) if SIDE = 'R'\&.
.fi
.PP
.br
\fITAU\fP 
.PP
.nf
          TAU is DOUBLE PRECISION array, dimension
                               (M-1) if SIDE = 'L'
                               (N-1) if SIDE = 'R'
          TAU(i) must contain the scalar factor of the elementary
          reflector H(i), as returned by DSYTRD\&.
.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 (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\&.
          If SIDE = 'L', LWORK >= max(1,N);
          if SIDE = 'R', LWORK >= max(1,M)\&.
          For optimum performance LWORK >= N*NB if SIDE = 'L', and
          LWORK >= M*NB if SIDE = 'R', 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 \fB169\fP of file \fBdormtr\&.f\fP\&.
.SS "subroutine sormtr (character side, character uplo, character trans, integer m, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( * ) tau, real, dimension( ldc, * ) c, integer ldc, real, dimension( * ) work, integer lwork, integer info)"

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

.PP
.nf
 SORMTR 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 SSYTRD:

 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 triangle of A contains elementary reflectors
                 from SSYTRD;
          = 'L': Lower triangle of A contains elementary reflectors
                 from SSYTRD\&.
.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
\fIA\fP 
.PP
.nf
          A is REAL array, dimension
                               (LDA,M) if SIDE = 'L'
                               (LDA,N) if SIDE = 'R'
          The vectors which define the elementary reflectors, as
          returned by SSYTRD\&.
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
          LDA is INTEGER
          The leading dimension of the array A\&.
          LDA >= max(1,M) if SIDE = 'L'; LDA >= max(1,N) if SIDE = 'R'\&.
.fi
.PP
.br
\fITAU\fP 
.PP
.nf
          TAU is REAL array, dimension
                               (M-1) if SIDE = 'L'
                               (N-1) if SIDE = 'R'
          TAU(i) must contain the scalar factor of the elementary
          reflector H(i), as returned by SSYTRD\&.
.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 (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\&.
          If SIDE = 'L', LWORK >= max(1,N);
          if SIDE = 'R', LWORK >= max(1,M)\&.
          For optimum performance LWORK >= N*NB if SIDE = 'L', and
          LWORK >= M*NB if SIDE = 'R', 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 \fB170\fP of file \fBsormtr\&.f\fP\&.
.SS "subroutine zunmtr (character side, character uplo, character trans, integer m, integer n, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( * ) tau, complex*16, dimension( ldc, * ) c, integer ldc, complex*16, dimension( * ) work, integer lwork, integer info)"

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

.PP
.nf
 ZUNMTR 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 ZHETRD:

 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 triangle of A contains elementary reflectors
                 from ZHETRD;
          = 'L': Lower triangle of A contains elementary reflectors
                 from ZHETRD\&.
.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
\fIA\fP 
.PP
.nf
          A is COMPLEX*16 array, dimension
                               (LDA,M) if SIDE = 'L'
                               (LDA,N) if SIDE = 'R'
          The vectors which define the elementary reflectors, as
          returned by ZHETRD\&.
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
          LDA is INTEGER
          The leading dimension of the array A\&.
          LDA >= max(1,M) if SIDE = 'L'; LDA >= max(1,N) if SIDE = 'R'\&.
.fi
.PP
.br
\fITAU\fP 
.PP
.nf
          TAU is COMPLEX*16 array, dimension
                               (M-1) if SIDE = 'L'
                               (N-1) if SIDE = 'R'
          TAU(i) must contain the scalar factor of the elementary
          reflector H(i), as returned by ZHETRD\&.
.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 (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\&.
          If SIDE = 'L', LWORK >= max(1,N);
          if SIDE = 'R', LWORK >= max(1,M)\&.
          For optimum performance LWORK >= N*NB if SIDE = 'L', and
          LWORK >=M*NB if SIDE = 'R', 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 \fB169\fP of file \fBzunmtr\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.