.TH "gemqrt" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
gemqrt \- gemqrt: multiply by Q from geqrt
.SH SYNOPSIS
.br
.PP
.SS "Functions"

.in +1c
.ti -1c
.RI "subroutine \fBcgemqrt\fP (side, trans, m, n, k, nb, v, ldv, t, ldt, c, ldc, work, info)"
.br
.RI "\fBCGEMQRT\fP "
.ti -1c
.RI "subroutine \fBdgemqrt\fP (side, trans, m, n, k, nb, v, ldv, t, ldt, c, ldc, work, info)"
.br
.RI "\fBDGEMQRT\fP "
.ti -1c
.RI "subroutine \fBsgemqrt\fP (side, trans, m, n, k, nb, v, ldv, t, ldt, c, ldc, work, info)"
.br
.RI "\fBSGEMQRT\fP "
.ti -1c
.RI "subroutine \fBzgemqrt\fP (side, trans, m, n, k, nb, v, ldv, t, ldt, c, ldc, work, info)"
.br
.RI "\fBZGEMQRT\fP "
.in -1c
.SH "Detailed Description"
.PP 

.SH "Function Documentation"
.PP 
.SS "subroutine cgemqrt (character side, character trans, integer m, integer n, integer k, integer nb, complex, dimension( ldv, * ) v, integer ldv, complex, dimension( ldt, * ) t, integer ldt, complex, dimension( ldc, * ) c, integer ldc, complex, dimension( * ) work, integer info)"

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

.PP
.nf
!>
!> CGEMQRT 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 orthogonal matrix defined as the product of K
!> elementary reflectors:
!>
!>       Q = H(1) H(2) \&. \&. \&. H(K) = I - V T V**H
!>
!> generated using the compact WY representation as returned by CGEQRT\&.
!>
!> Q is of order M if SIDE = 'L' and of order N  if SIDE = 'R'\&.
!> 
.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
\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
\fIK\fP 
.PP
.nf
!>          K is INTEGER
!>          The number of elementary reflectors whose product defines
!>          the matrix Q\&.
!>          If SIDE = 'L', M >= K >= 0;
!>          if SIDE = 'R', N >= K >= 0\&.
!> 
.fi
.PP
.br
\fINB\fP 
.PP
.nf
!>          NB is INTEGER
!>          The block size used for the storage of T\&.  K >= NB >= 1\&.
!>          This must be the same value of NB used to generate T
!>          in CGEQRT\&.
!> 
.fi
.PP
.br
\fIV\fP 
.PP
.nf
!>          V is COMPLEX array, dimension (LDV,K)
!>          The i-th column must contain the vector which defines the
!>          elementary reflector H(i), for i = 1,2,\&.\&.\&.,k, as returned by
!>          CGEQRT in the first K columns of its array argument A\&.
!> 
.fi
.PP
.br
\fILDV\fP 
.PP
.nf
!>          LDV is INTEGER
!>          The leading dimension of the array V\&.
!>          If SIDE = 'L', LDA >= max(1,M);
!>          if SIDE = 'R', LDA >= max(1,N)\&.
!> 
.fi
.PP
.br
\fIT\fP 
.PP
.nf
!>          T is COMPLEX array, dimension (LDT,K)
!>          The upper triangular factors of the block reflectors
!>          as returned by CGEQRT, stored as a NB-by-N matrix\&.
!> 
.fi
.PP
.br
\fILDT\fP 
.PP
.nf
!>          LDT is INTEGER
!>          The leading dimension of the array T\&.  LDT >= NB\&.
!> 
.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, Q**H C, 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\&. The dimension of WORK is
!>           N*NB if SIDE = 'L', or  M*NB 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 \fB166\fP of file \fBcgemqrt\&.f\fP\&.
.SS "subroutine dgemqrt (character side, character trans, integer m, integer n, integer k, integer nb, double precision, dimension( ldv, * ) v, integer ldv, double precision, dimension( ldt, * ) t, integer ldt, double precision, dimension( ldc, * ) c, integer ldc, double precision, dimension( * ) work, integer info)"

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

.PP
.nf
!>
!> DGEMQRT 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 defined as the product of K
!> elementary reflectors:
!>
!>       Q = H(1) H(2) \&. \&. \&. H(K) = I - V T V**T
!>
!> generated using the compact WY representation as returned by DGEQRT\&.
!>
!> Q is of order M if SIDE = 'L' and of order N  if SIDE = 'R'\&.
!> 
.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
\fITRANS\fP 
.PP
.nf
!>          TRANS is CHARACTER*1
!>          = 'N':  No transpose, apply Q;
!>          = 'C':  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
\fIK\fP 
.PP
.nf
!>          K is INTEGER
!>          The number of elementary reflectors whose product defines
!>          the matrix Q\&.
!>          If SIDE = 'L', M >= K >= 0;
!>          if SIDE = 'R', N >= K >= 0\&.
!> 
.fi
.PP
.br
\fINB\fP 
.PP
.nf
!>          NB is INTEGER
!>          The block size used for the storage of T\&.  K >= NB >= 1\&.
!>          This must be the same value of NB used to generate T
!>          in DGEQRT\&.
!> 
.fi
.PP
.br
\fIV\fP 
.PP
.nf
!>          V is DOUBLE PRECISION array, dimension (LDV,K)
!>          The i-th column must contain the vector which defines the
!>          elementary reflector H(i), for i = 1,2,\&.\&.\&.,k, as returned by
!>          DGEQRT in the first K columns of its array argument A\&.
!> 
.fi
.PP
.br
\fILDV\fP 
.PP
.nf
!>          LDV is INTEGER
!>          The leading dimension of the array V\&.
!>          If SIDE = 'L', LDA >= max(1,M);
!>          if SIDE = 'R', LDA >= max(1,N)\&.
!> 
.fi
.PP
.br
\fIT\fP 
.PP
.nf
!>          T is DOUBLE PRECISION array, dimension (LDT,K)
!>          The upper triangular factors of the block reflectors
!>          as returned by DGEQRT, stored as a NB-by-N matrix\&.
!> 
.fi
.PP
.br
\fILDT\fP 
.PP
.nf
!>          LDT is INTEGER
!>          The leading dimension of the array T\&.  LDT >= NB\&.
!> 
.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, Q**T C, 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\&. The dimension of
!>          WORK is N*NB if SIDE = 'L', or  M*NB 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 \fB166\fP of file \fBdgemqrt\&.f\fP\&.
.SS "subroutine sgemqrt (character side, character trans, integer m, integer n, integer k, integer nb, real, dimension( ldv, * ) v, integer ldv, real, dimension( ldt, * ) t, integer ldt, real, dimension( ldc, * ) c, integer ldc, real, dimension( * ) work, integer info)"

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

.PP
.nf
!>
!> SGEMQRT 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 defined as the product of K
!> elementary reflectors:
!>
!>       Q = H(1) H(2) \&. \&. \&. H(K) = I - V T V**T
!>
!> generated using the compact WY representation as returned by SGEQRT\&.
!>
!> Q is of order M if SIDE = 'L' and of order N  if SIDE = 'R'\&.
!> 
.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
\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
\fIK\fP 
.PP
.nf
!>          K is INTEGER
!>          The number of elementary reflectors whose product defines
!>          the matrix Q\&.
!>          If SIDE = 'L', M >= K >= 0;
!>          if SIDE = 'R', N >= K >= 0\&.
!> 
.fi
.PP
.br
\fINB\fP 
.PP
.nf
!>          NB is INTEGER
!>          The block size used for the storage of T\&.  K >= NB >= 1\&.
!>          This must be the same value of NB used to generate T
!>          in SGEQRT\&.
!> 
.fi
.PP
.br
\fIV\fP 
.PP
.nf
!>          V is REAL array, dimension (LDV,K)
!>          The i-th column must contain the vector which defines the
!>          elementary reflector H(i), for i = 1,2,\&.\&.\&.,k, as returned by
!>          SGEQRT in the first K columns of its array argument A\&.
!> 
.fi
.PP
.br
\fILDV\fP 
.PP
.nf
!>          LDV is INTEGER
!>          The leading dimension of the array V\&.
!>          If SIDE = 'L', LDA >= max(1,M);
!>          if SIDE = 'R', LDA >= max(1,N)\&.
!> 
.fi
.PP
.br
\fIT\fP 
.PP
.nf
!>          T is REAL array, dimension (LDT,K)
!>          The upper triangular factors of the block reflectors
!>          as returned by SGEQRT, stored as a NB-by-N matrix\&.
!> 
.fi
.PP
.br
\fILDT\fP 
.PP
.nf
!>          LDT is INTEGER
!>          The leading dimension of the array T\&.  LDT >= NB\&.
!> 
.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, Q**T C, 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\&. The dimension of WORK is
!>           N*NB if SIDE = 'L', or  M*NB 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 \fB166\fP of file \fBsgemqrt\&.f\fP\&.
.SS "subroutine zgemqrt (character side, character trans, integer m, integer n, integer k, integer nb, complex*16, dimension( ldv, * ) v, integer ldv, complex*16, dimension( ldt, * ) t, integer ldt, complex*16, dimension( ldc, * ) c, integer ldc, complex*16, dimension( * ) work, integer info)"

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

.PP
.nf
!>
!> ZGEMQRT 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 orthogonal matrix defined as the product of K
!> elementary reflectors:
!>
!>       Q = H(1) H(2) \&. \&. \&. H(K) = I - V T V**H
!>
!> generated using the compact WY representation as returned by ZGEQRT\&.
!>
!> Q is of order M if SIDE = 'L' and of order N  if SIDE = 'R'\&.
!> 
.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
\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
\fIK\fP 
.PP
.nf
!>          K is INTEGER
!>          The number of elementary reflectors whose product defines
!>          the matrix Q\&.
!>          If SIDE = 'L', M >= K >= 0;
!>          if SIDE = 'R', N >= K >= 0\&.
!> 
.fi
.PP
.br
\fINB\fP 
.PP
.nf
!>          NB is INTEGER
!>          The block size used for the storage of T\&.  K >= NB >= 1\&.
!>          This must be the same value of NB used to generate T
!>          in ZGEQRT\&.
!> 
.fi
.PP
.br
\fIV\fP 
.PP
.nf
!>          V is COMPLEX*16 array, dimension (LDV,K)
!>          The i-th column must contain the vector which defines the
!>          elementary reflector H(i), for i = 1,2,\&.\&.\&.,k, as returned by
!>          ZGEQRT in the first K columns of its array argument A\&.
!> 
.fi
.PP
.br
\fILDV\fP 
.PP
.nf
!>          LDV is INTEGER
!>          The leading dimension of the array V\&.
!>          If SIDE = 'L', LDA >= max(1,M);
!>          if SIDE = 'R', LDA >= max(1,N)\&.
!> 
.fi
.PP
.br
\fIT\fP 
.PP
.nf
!>          T is COMPLEX*16 array, dimension (LDT,K)
!>          The upper triangular factors of the block reflectors
!>          as returned by ZGEQRT, stored as a NB-by-N matrix\&.
!> 
.fi
.PP
.br
\fILDT\fP 
.PP
.nf
!>          LDT is INTEGER
!>          The leading dimension of the array T\&.  LDT >= NB\&.
!> 
.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, Q**H C, 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\&. The dimension of WORK is
!>           N*NB if SIDE = 'L', or  M*NB 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 \fB166\fP of file \fBzgemqrt\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.