.TH "larzb" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
larzb \- larzb: apply block reflector
.SH SYNOPSIS
.br
.PP
.SS "Functions"

.in +1c
.ti -1c
.RI "subroutine \fBclarzb\fP (side, trans, direct, storev, m, n, k, l, v, ldv, t, ldt, c, ldc, work, ldwork)"
.br
.RI "\fBCLARZB\fP applies a block reflector or its conjugate-transpose to a general matrix\&. "
.ti -1c
.RI "subroutine \fBdlarzb\fP (side, trans, direct, storev, m, n, k, l, v, ldv, t, ldt, c, ldc, work, ldwork)"
.br
.RI "\fBDLARZB\fP applies a block reflector or its transpose to a general matrix\&. "
.ti -1c
.RI "subroutine \fBslarzb\fP (side, trans, direct, storev, m, n, k, l, v, ldv, t, ldt, c, ldc, work, ldwork)"
.br
.RI "\fBSLARZB\fP applies a block reflector or its transpose to a general matrix\&. "
.ti -1c
.RI "subroutine \fBzlarzb\fP (side, trans, direct, storev, m, n, k, l, v, ldv, t, ldt, c, ldc, work, ldwork)"
.br
.RI "\fBZLARZB\fP applies a block reflector or its conjugate-transpose to a general matrix\&. "
.in -1c
.SH "Detailed Description"
.PP 

.SH "Function Documentation"
.PP 
.SS "subroutine clarzb (character side, character trans, character direct, character storev, integer m, integer n, integer k, integer l, complex, dimension( ldv, * ) v, integer ldv, complex, dimension( ldt, * ) t, integer ldt, complex, dimension( ldc, * ) c, integer ldc, complex, dimension( ldwork, * ) work, integer ldwork)"

.PP
\fBCLARZB\fP applies a block reflector or its conjugate-transpose to a general matrix\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
!>
!> CLARZB applies a complex block reflector H or its transpose H**H
!> to a complex distributed M-by-N  C from the left or the right\&.
!>
!> Currently, only STOREV = 'R' and DIRECT = 'B' are supported\&.
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fISIDE\fP 
.PP
.nf
!>          SIDE is CHARACTER*1
!>          = 'L': apply H or H**H from the Left
!>          = 'R': apply H or H**H from the Right
!> 
.fi
.PP
.br
\fITRANS\fP 
.PP
.nf
!>          TRANS is CHARACTER*1
!>          = 'N': apply H (No transpose)
!>          = 'C': apply H**H (Conjugate transpose)
!> 
.fi
.PP
.br
\fIDIRECT\fP 
.PP
.nf
!>          DIRECT is CHARACTER*1
!>          Indicates how H is formed from a product of elementary
!>          reflectors
!>          = 'F': H = H(1) H(2) \&. \&. \&. H(k) (Forward, not supported yet)
!>          = 'B': H = H(k) \&. \&. \&. H(2) H(1) (Backward)
!> 
.fi
.PP
.br
\fISTOREV\fP 
.PP
.nf
!>          STOREV is CHARACTER*1
!>          Indicates how the vectors which define the elementary
!>          reflectors are stored:
!>          = 'C': Columnwise                        (not supported yet)
!>          = 'R': Rowwise
!> 
.fi
.PP
.br
\fIM\fP 
.PP
.nf
!>          M is INTEGER
!>          The number of rows of the matrix C\&.
!> 
.fi
.PP
.br
\fIN\fP 
.PP
.nf
!>          N is INTEGER
!>          The number of columns of the matrix C\&.
!> 
.fi
.PP
.br
\fIK\fP 
.PP
.nf
!>          K is INTEGER
!>          The order of the matrix T (= the number of elementary
!>          reflectors whose product defines the block reflector)\&.
!> 
.fi
.PP
.br
\fIL\fP 
.PP
.nf
!>          L is INTEGER
!>          The number of columns of the matrix V containing the
!>          meaningful part of the Householder reflectors\&.
!>          If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0\&.
!> 
.fi
.PP
.br
\fIV\fP 
.PP
.nf
!>          V is COMPLEX array, dimension (LDV,NV)\&.
!>          If STOREV = 'C', NV = K; if STOREV = 'R', NV = L\&.
!> 
.fi
.PP
.br
\fILDV\fP 
.PP
.nf
!>          LDV is INTEGER
!>          The leading dimension of the array V\&.
!>          If STOREV = 'C', LDV >= L; if STOREV = 'R', LDV >= K\&.
!> 
.fi
.PP
.br
\fIT\fP 
.PP
.nf
!>          T is COMPLEX array, dimension (LDT,K)
!>          The triangular K-by-K matrix T in the representation of the
!>          block reflector\&.
!> 
.fi
.PP
.br
\fILDT\fP 
.PP
.nf
!>          LDT is INTEGER
!>          The leading dimension of the array T\&. LDT >= K\&.
!> 
.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 H*C or H**H*C or C*H or C*H**H\&.
!> 
.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 (LDWORK,K)
!> 
.fi
.PP
.br
\fILDWORK\fP 
.PP
.nf
!>          LDWORK is INTEGER
!>          The leading dimension of the array WORK\&.
!>          If SIDE = 'L', LDWORK >= max(1,N);
!>          if SIDE = 'R', LDWORK >= max(1,M)\&.
!> 
.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 \fB181\fP of file \fBclarzb\&.f\fP\&.
.SS "subroutine dlarzb (character side, character trans, character direct, character storev, integer m, integer n, integer k, integer l, double precision, dimension( ldv, * ) v, integer ldv, double precision, dimension( ldt, * ) t, integer ldt, double precision, dimension( ldc, * ) c, integer ldc, double precision, dimension( ldwork, * ) work, integer ldwork)"

.PP
\fBDLARZB\fP applies a block reflector or its transpose to a general matrix\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
!>
!> DLARZB applies a real block reflector H or its transpose H**T to
!> a real distributed M-by-N  C from the left or the right\&.
!>
!> Currently, only STOREV = 'R' and DIRECT = 'B' are supported\&.
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fISIDE\fP 
.PP
.nf
!>          SIDE is CHARACTER*1
!>          = 'L': apply H or H**T from the Left
!>          = 'R': apply H or H**T from the Right
!> 
.fi
.PP
.br
\fITRANS\fP 
.PP
.nf
!>          TRANS is CHARACTER*1
!>          = 'N': apply H (No transpose)
!>          = 'C': apply H**T (Transpose)
!> 
.fi
.PP
.br
\fIDIRECT\fP 
.PP
.nf
!>          DIRECT is CHARACTER*1
!>          Indicates how H is formed from a product of elementary
!>          reflectors
!>          = 'F': H = H(1) H(2) \&. \&. \&. H(k) (Forward, not supported yet)
!>          = 'B': H = H(k) \&. \&. \&. H(2) H(1) (Backward)
!> 
.fi
.PP
.br
\fISTOREV\fP 
.PP
.nf
!>          STOREV is CHARACTER*1
!>          Indicates how the vectors which define the elementary
!>          reflectors are stored:
!>          = 'C': Columnwise                        (not supported yet)
!>          = 'R': Rowwise
!> 
.fi
.PP
.br
\fIM\fP 
.PP
.nf
!>          M is INTEGER
!>          The number of rows of the matrix C\&.
!> 
.fi
.PP
.br
\fIN\fP 
.PP
.nf
!>          N is INTEGER
!>          The number of columns of the matrix C\&.
!> 
.fi
.PP
.br
\fIK\fP 
.PP
.nf
!>          K is INTEGER
!>          The order of the matrix T (= the number of elementary
!>          reflectors whose product defines the block reflector)\&.
!> 
.fi
.PP
.br
\fIL\fP 
.PP
.nf
!>          L is INTEGER
!>          The number of columns of the matrix V containing the
!>          meaningful part of the Householder reflectors\&.
!>          If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0\&.
!> 
.fi
.PP
.br
\fIV\fP 
.PP
.nf
!>          V is DOUBLE PRECISION array, dimension (LDV,NV)\&.
!>          If STOREV = 'C', NV = K; if STOREV = 'R', NV = L\&.
!> 
.fi
.PP
.br
\fILDV\fP 
.PP
.nf
!>          LDV is INTEGER
!>          The leading dimension of the array V\&.
!>          If STOREV = 'C', LDV >= L; if STOREV = 'R', LDV >= K\&.
!> 
.fi
.PP
.br
\fIT\fP 
.PP
.nf
!>          T is DOUBLE PRECISION array, dimension (LDT,K)
!>          The triangular K-by-K matrix T in the representation of the
!>          block reflector\&.
!> 
.fi
.PP
.br
\fILDT\fP 
.PP
.nf
!>          LDT is INTEGER
!>          The leading dimension of the array T\&. LDT >= K\&.
!> 
.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 H*C or H**T*C or C*H or C*H**T\&.
!> 
.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 (LDWORK,K)
!> 
.fi
.PP
.br
\fILDWORK\fP 
.PP
.nf
!>          LDWORK is INTEGER
!>          The leading dimension of the array WORK\&.
!>          If SIDE = 'L', LDWORK >= max(1,N);
!>          if SIDE = 'R', LDWORK >= max(1,M)\&.
!> 
.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 \fB181\fP of file \fBdlarzb\&.f\fP\&.
.SS "subroutine slarzb (character side, character trans, character direct, character storev, integer m, integer n, integer k, integer l, real, dimension( ldv, * ) v, integer ldv, real, dimension( ldt, * ) t, integer ldt, real, dimension( ldc, * ) c, integer ldc, real, dimension( ldwork, * ) work, integer ldwork)"

.PP
\fBSLARZB\fP applies a block reflector or its transpose to a general matrix\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
!>
!> SLARZB applies a real block reflector H or its transpose H**T to
!> a real distributed M-by-N  C from the left or the right\&.
!>
!> Currently, only STOREV = 'R' and DIRECT = 'B' are supported\&.
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fISIDE\fP 
.PP
.nf
!>          SIDE is CHARACTER*1
!>          = 'L': apply H or H**T from the Left
!>          = 'R': apply H or H**T from the Right
!> 
.fi
.PP
.br
\fITRANS\fP 
.PP
.nf
!>          TRANS is CHARACTER*1
!>          = 'N': apply H (No transpose)
!>          = 'C': apply H**T (Transpose)
!> 
.fi
.PP
.br
\fIDIRECT\fP 
.PP
.nf
!>          DIRECT is CHARACTER*1
!>          Indicates how H is formed from a product of elementary
!>          reflectors
!>          = 'F': H = H(1) H(2) \&. \&. \&. H(k) (Forward, not supported yet)
!>          = 'B': H = H(k) \&. \&. \&. H(2) H(1) (Backward)
!> 
.fi
.PP
.br
\fISTOREV\fP 
.PP
.nf
!>          STOREV is CHARACTER*1
!>          Indicates how the vectors which define the elementary
!>          reflectors are stored:
!>          = 'C': Columnwise                        (not supported yet)
!>          = 'R': Rowwise
!> 
.fi
.PP
.br
\fIM\fP 
.PP
.nf
!>          M is INTEGER
!>          The number of rows of the matrix C\&.
!> 
.fi
.PP
.br
\fIN\fP 
.PP
.nf
!>          N is INTEGER
!>          The number of columns of the matrix C\&.
!> 
.fi
.PP
.br
\fIK\fP 
.PP
.nf
!>          K is INTEGER
!>          The order of the matrix T (= the number of elementary
!>          reflectors whose product defines the block reflector)\&.
!> 
.fi
.PP
.br
\fIL\fP 
.PP
.nf
!>          L is INTEGER
!>          The number of columns of the matrix V containing the
!>          meaningful part of the Householder reflectors\&.
!>          If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0\&.
!> 
.fi
.PP
.br
\fIV\fP 
.PP
.nf
!>          V is REAL array, dimension (LDV,NV)\&.
!>          If STOREV = 'C', NV = K; if STOREV = 'R', NV = L\&.
!> 
.fi
.PP
.br
\fILDV\fP 
.PP
.nf
!>          LDV is INTEGER
!>          The leading dimension of the array V\&.
!>          If STOREV = 'C', LDV >= L; if STOREV = 'R', LDV >= K\&.
!> 
.fi
.PP
.br
\fIT\fP 
.PP
.nf
!>          T is REAL array, dimension (LDT,K)
!>          The triangular K-by-K matrix T in the representation of the
!>          block reflector\&.
!> 
.fi
.PP
.br
\fILDT\fP 
.PP
.nf
!>          LDT is INTEGER
!>          The leading dimension of the array T\&. LDT >= K\&.
!> 
.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 H*C or H**T*C or C*H or C*H**T\&.
!> 
.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 (LDWORK,K)
!> 
.fi
.PP
.br
\fILDWORK\fP 
.PP
.nf
!>          LDWORK is INTEGER
!>          The leading dimension of the array WORK\&.
!>          If SIDE = 'L', LDWORK >= max(1,N);
!>          if SIDE = 'R', LDWORK >= max(1,M)\&.
!> 
.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 \fB181\fP of file \fBslarzb\&.f\fP\&.
.SS "subroutine zlarzb (character side, character trans, character direct, character storev, integer m, integer n, integer k, integer l, complex*16, dimension( ldv, * ) v, integer ldv, complex*16, dimension( ldt, * ) t, integer ldt, complex*16, dimension( ldc, * ) c, integer ldc, complex*16, dimension( ldwork, * ) work, integer ldwork)"

.PP
\fBZLARZB\fP applies a block reflector or its conjugate-transpose to a general matrix\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
!>
!> ZLARZB applies a complex block reflector H or its transpose H**H
!> to a complex distributed M-by-N  C from the left or the right\&.
!>
!> Currently, only STOREV = 'R' and DIRECT = 'B' are supported\&.
!> 
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fISIDE\fP 
.PP
.nf
!>          SIDE is CHARACTER*1
!>          = 'L': apply H or H**H from the Left
!>          = 'R': apply H or H**H from the Right
!> 
.fi
.PP
.br
\fITRANS\fP 
.PP
.nf
!>          TRANS is CHARACTER*1
!>          = 'N': apply H (No transpose)
!>          = 'C': apply H**H (Conjugate transpose)
!> 
.fi
.PP
.br
\fIDIRECT\fP 
.PP
.nf
!>          DIRECT is CHARACTER*1
!>          Indicates how H is formed from a product of elementary
!>          reflectors
!>          = 'F': H = H(1) H(2) \&. \&. \&. H(k) (Forward, not supported yet)
!>          = 'B': H = H(k) \&. \&. \&. H(2) H(1) (Backward)
!> 
.fi
.PP
.br
\fISTOREV\fP 
.PP
.nf
!>          STOREV is CHARACTER*1
!>          Indicates how the vectors which define the elementary
!>          reflectors are stored:
!>          = 'C': Columnwise                        (not supported yet)
!>          = 'R': Rowwise
!> 
.fi
.PP
.br
\fIM\fP 
.PP
.nf
!>          M is INTEGER
!>          The number of rows of the matrix C\&.
!> 
.fi
.PP
.br
\fIN\fP 
.PP
.nf
!>          N is INTEGER
!>          The number of columns of the matrix C\&.
!> 
.fi
.PP
.br
\fIK\fP 
.PP
.nf
!>          K is INTEGER
!>          The order of the matrix T (= the number of elementary
!>          reflectors whose product defines the block reflector)\&.
!> 
.fi
.PP
.br
\fIL\fP 
.PP
.nf
!>          L is INTEGER
!>          The number of columns of the matrix V containing the
!>          meaningful part of the Householder reflectors\&.
!>          If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0\&.
!> 
.fi
.PP
.br
\fIV\fP 
.PP
.nf
!>          V is COMPLEX*16 array, dimension (LDV,NV)\&.
!>          If STOREV = 'C', NV = K; if STOREV = 'R', NV = L\&.
!> 
.fi
.PP
.br
\fILDV\fP 
.PP
.nf
!>          LDV is INTEGER
!>          The leading dimension of the array V\&.
!>          If STOREV = 'C', LDV >= L; if STOREV = 'R', LDV >= K\&.
!> 
.fi
.PP
.br
\fIT\fP 
.PP
.nf
!>          T is COMPLEX*16 array, dimension (LDT,K)
!>          The triangular K-by-K matrix T in the representation of the
!>          block reflector\&.
!> 
.fi
.PP
.br
\fILDT\fP 
.PP
.nf
!>          LDT is INTEGER
!>          The leading dimension of the array T\&. LDT >= K\&.
!> 
.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 H*C or H**H*C or C*H or C*H**H\&.
!> 
.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 (LDWORK,K)
!> 
.fi
.PP
.br
\fILDWORK\fP 
.PP
.nf
!>          LDWORK is INTEGER
!>          The leading dimension of the array WORK\&.
!>          If SIDE = 'L', LDWORK >= max(1,N);
!>          if SIDE = 'R', LDWORK >= max(1,M)\&.
!> 
.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 \fB181\fP of file \fBzlarzb\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.