.TH "unmrz" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
unmrz \- {un,or}mrz: multiply by Z from tzrzf
.SH SYNOPSIS
.br
.PP
.SS "Functions"

.in +1c
.ti -1c
.RI "subroutine \fBcunmrz\fP (side, trans, m, n, k, l, a, lda, tau, c, ldc, work, lwork, info)"
.br
.RI "\fBCUNMRZ\fP "
.ti -1c
.RI "subroutine \fBdormrz\fP (side, trans, m, n, k, l, a, lda, tau, c, ldc, work, lwork, info)"
.br
.RI "\fBDORMRZ\fP "
.ti -1c
.RI "subroutine \fBsormrz\fP (side, trans, m, n, k, l, a, lda, tau, c, ldc, work, lwork, info)"
.br
.RI "\fBSORMRZ\fP "
.ti -1c
.RI "subroutine \fBzunmrz\fP (side, trans, m, n, k, l, a, lda, tau, c, ldc, work, lwork, info)"
.br
.RI "\fBZUNMRZ\fP "
.in -1c
.SH "Detailed Description"
.PP 

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

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

.PP
.nf
 CUNMRZ 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(2) \&. \&. \&. H(k)

 as returned by CTZRZF\&. 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
\fIL\fP 
.PP
.nf
          L is INTEGER
          The number of columns of the matrix A containing
          the meaningful part of the Householder reflectors\&.
          If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 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
          CTZRZF in the last k rows of its array argument A\&.
          A is modified by the routine but restored on exit\&.
.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 CTZRZF\&.
.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
\fBContributors:\fP
.RS 4
A\&. Petitet, Computer Science Dept\&., Univ\&. of Tenn\&., Knoxville, USA 
.RE
.PP
\fBFurther Details:\fP
.RS 4

.PP
.nf
 
.fi
.PP
 
.RE
.PP

.PP
Definition at line \fB185\fP of file \fBcunmrz\&.f\fP\&.
.SS "subroutine dormrz (character side, character trans, integer m, integer n, integer k, integer l, 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
\fBDORMRZ\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 DORMRZ 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 DTZRZF\&. 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
\fIL\fP 
.PP
.nf
          L is INTEGER
          The number of columns of the matrix A containing
          the meaningful part of the Householder reflectors\&.
          If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 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
          DTZRZF in the last k rows of its array argument A\&.
          A is modified by the routine but restored on exit\&.
.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 DTZRZF\&.
.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**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 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
\fBContributors:\fP
.RS 4
A\&. Petitet, Computer Science Dept\&., Univ\&. of Tenn\&., Knoxville, USA 
.RE
.PP
\fBFurther Details:\fP
.RS 4

.PP
.nf
 
.fi
.PP
 
.RE
.PP

.PP
Definition at line \fB185\fP of file \fBdormrz\&.f\fP\&.
.SS "subroutine sormrz (character side, character trans, integer m, integer n, integer k, integer l, real, dimension( lda, * ) a, integer lda, real, dimension( * ) tau, real, dimension( ldc, * ) c, integer ldc, real, dimension( * ) work, integer lwork, integer info)"

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

.PP
.nf
 SORMRZ 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 STZRZF\&. 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
\fIL\fP 
.PP
.nf
          L is INTEGER
          The number of columns of the matrix A containing
          the meaningful part of the Householder reflectors\&.
          If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 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
          STZRZF in the last k rows of its array argument A\&.
          A is modified by the routine but restored on exit\&.
.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 STZRZF\&.
.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**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 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
\fBContributors:\fP
.RS 4
A\&. Petitet, Computer Science Dept\&., Univ\&. of Tenn\&., Knoxville, USA 
.RE
.PP
\fBFurther Details:\fP
.RS 4

.PP
.nf
 
.fi
.PP
 
.RE
.PP

.PP
Definition at line \fB185\fP of file \fBsormrz\&.f\fP\&.
.SS "subroutine zunmrz (character side, character trans, integer m, integer n, integer k, integer l, 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
\fBZUNMRZ\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 ZUNMRZ 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(2) \&. \&. \&. H(k)

 as returned by ZTZRZF\&. 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
\fIL\fP 
.PP
.nf
          L is INTEGER
          The number of columns of the matrix A containing
          the meaningful part of the Householder reflectors\&.
          If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 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
          ZTZRZF in the last k rows of its array argument A\&.
          A is modified by the routine but restored on exit\&.
.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 ZTZRZF\&.
.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
\fBContributors:\fP
.RS 4
A\&. Petitet, Computer Science Dept\&., Univ\&. of Tenn\&., Knoxville, USA 
.RE
.PP
\fBFurther Details:\fP
.RS 4

.PP
.nf
 
.fi
.PP
 
.RE
.PP

.PP
Definition at line \fB185\fP of file \fBzunmrz\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.