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

.in +1c
.ti -1c
.RI "subroutine \fBcunmrq\fP (side, trans, m, n, k, a, lda, tau, c, ldc, work, lwork, info)"
.br
.RI "\fBCUNMRQ\fP "
.ti -1c
.RI "subroutine \fBdormrq\fP (side, trans, m, n, k, a, lda, tau, c, ldc, work, lwork, info)"
.br
.RI "\fBDORMRQ\fP "
.ti -1c
.RI "subroutine \fBsormrq\fP (side, trans, m, n, k, a, lda, tau, c, ldc, work, lwork, info)"
.br
.RI "\fBSORMRQ\fP "
.ti -1c
.RI "subroutine \fBzunmrq\fP (side, trans, m, n, k, a, lda, tau, c, ldc, work, lwork, info)"
.br
.RI "\fBZUNMRQ\fP "
.in -1c
.SH "Detailed Description"
.PP 

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

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

.PP
.nf
 CUNMRQ 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 defined as the product of k
 elementary reflectors

       Q = H(1)**H H(2)**H \&. \&. \&. H(k)**H

 as returned by CGERQF\&. 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
\fIA\fP 
.PP
.nf
          A is COMPLEX array, dimension
                               (LDA,M) if SIDE = 'L',
                               (LDA,N) if SIDE = 'R'
          The i-th row must contain the vector which defines the
          elementary reflector H(i), for i = 1,2,\&.\&.\&.,k, as returned by
          CGERQF in the last k rows of its array argument A\&.
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
          LDA is INTEGER
          The leading dimension of the array A\&. LDA >= max(1,K)\&.
.fi
.PP
.br
\fITAU\fP 
.PP
.nf
          TAU is COMPLEX array, dimension (K)
          TAU(i) must contain the scalar factor of the elementary
          reflector H(i), as returned by CGERQF\&.
.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 good performance, LWORK should generally be larger\&.

          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 \fB166\fP of file \fBcunmrq\&.f\fP\&.
.SS "subroutine dormrq (character side, character trans, integer m, integer n, integer k, 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
\fBDORMRQ\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 DORMRQ 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)

 as returned by DGERQF\&. 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
\fIA\fP 
.PP
.nf
          A is DOUBLE PRECISION array, dimension
                               (LDA,M) if SIDE = 'L',
                               (LDA,N) if SIDE = 'R'
          The i-th row must contain the vector which defines the
          elementary reflector H(i), for i = 1,2,\&.\&.\&.,k, as returned by
          DGERQF in the last k rows of its array argument A\&.
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
          LDA is INTEGER
          The leading dimension of the array A\&. LDA >= max(1,K)\&.
.fi
.PP
.br
\fITAU\fP 
.PP
.nf
          TAU is DOUBLE PRECISION array, dimension (K)
          TAU(i) must contain the scalar factor of the elementary
          reflector H(i), as returned by DGERQF\&.
.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 good performance, LWORK should generally be larger\&.

          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 \fB165\fP of file \fBdormrq\&.f\fP\&.
.SS "subroutine sormrq (character side, character trans, integer m, integer n, integer k, real, dimension( lda, * ) a, integer lda, real, dimension( * ) tau, real, dimension( ldc, * ) c, integer ldc, real, dimension( * ) work, integer lwork, integer info)"

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

.PP
.nf
 SORMRQ 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)

 as returned by SGERQF\&. 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
\fIA\fP 
.PP
.nf
          A is REAL array, dimension
                               (LDA,M) if SIDE = 'L',
                               (LDA,N) if SIDE = 'R'
          The i-th row must contain the vector which defines the
          elementary reflector H(i), for i = 1,2,\&.\&.\&.,k, as returned by
          SGERQF in the last k rows of its array argument A\&.
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
          LDA is INTEGER
          The leading dimension of the array A\&. LDA >= max(1,K)\&.
.fi
.PP
.br
\fITAU\fP 
.PP
.nf
          TAU is REAL array, dimension (K)
          TAU(i) must contain the scalar factor of the elementary
          reflector H(i), as returned by SGERQF\&.
.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 good performance, LWORK should generally be larger\&.

          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 \fB166\fP of file \fBsormrq\&.f\fP\&.
.SS "subroutine zunmrq (character side, character trans, integer m, integer n, integer k, 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
\fBZUNMRQ\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 ZUNMRQ 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 defined as the product of k
 elementary reflectors

       Q = H(1)**H H(2)**H \&. \&. \&. H(k)**H

 as returned by ZGERQF\&. 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
\fIA\fP 
.PP
.nf
          A is COMPLEX*16 array, dimension
                               (LDA,M) if SIDE = 'L',
                               (LDA,N) if SIDE = 'R'
          The i-th row must contain the vector which defines the
          elementary reflector H(i), for i = 1,2,\&.\&.\&.,k, as returned by
          ZGERQF in the last k rows of its array argument A\&.
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
          LDA is INTEGER
          The leading dimension of the array A\&. LDA >= max(1,K)\&.
.fi
.PP
.br
\fITAU\fP 
.PP
.nf
          TAU is COMPLEX*16 array, dimension (K)
          TAU(i) must contain the scalar factor of the elementary
          reflector H(i), as returned by ZGERQF\&.
.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 good performance, LWORK should generally be larger\&.

          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 \fB165\fP of file \fBzunmrq\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.