.TH "larzb" 3 "Wed Feb 7 2024 11:30:40" "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

.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

.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

.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

.SH "Author"
.PP 
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