.TH "larfb" 3 "Wed Feb 7 2024 11:30:40" "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
larfb \- larfb: apply block Householder reflector
.SH SYNOPSIS
.br
.PP
.SS "Functions"

.in +1c
.ti -1c
.RI "subroutine \fBclarfb\fP (side, trans, direct, storev, m, n, k, v, ldv, t, ldt, c, ldc, work, ldwork)"
.br
.RI "\fBCLARFB\fP applies a block reflector or its conjugate-transpose to a general rectangular matrix\&. "
.ti -1c
.RI "subroutine \fBdlarfb\fP (side, trans, direct, storev, m, n, k, v, ldv, t, ldt, c, ldc, work, ldwork)"
.br
.RI "\fBDLARFB\fP applies a block reflector or its transpose to a general rectangular matrix\&. "
.ti -1c
.RI "subroutine \fBslarfb\fP (side, trans, direct, storev, m, n, k, v, ldv, t, ldt, c, ldc, work, ldwork)"
.br
.RI "\fBSLARFB\fP applies a block reflector or its transpose to a general rectangular matrix\&. "
.ti -1c
.RI "subroutine \fBzlarfb\fP (side, trans, direct, storev, m, n, k, v, ldv, t, ldt, c, ldc, work, ldwork)"
.br
.RI "\fBZLARFB\fP applies a block reflector or its conjugate-transpose to a general rectangular matrix\&. "
.in -1c
.SH "Detailed Description"
.PP 

.SH "Function Documentation"
.PP 
.SS "subroutine clarfb (character side, character trans, character direct, character storev, integer m, integer n, integer k, 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
\fBCLARFB\fP applies a block reflector or its conjugate-transpose to a general rectangular matrix\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 CLARFB applies a complex block reflector H or its transpose H**H to a
 complex M-by-N matrix C, from either the left or the right\&.
.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)
          = '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
          = '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)\&.
          If SIDE = 'L', M >= K >= 0;
          if SIDE = 'R', N >= K >= 0\&.
.fi
.PP
.br
\fIV\fP 
.PP
.nf
          V is COMPLEX array, dimension
                                (LDV,K) if STOREV = 'C'
                                (LDV,M) if STOREV = 'R' and SIDE = 'L'
                                (LDV,N) if STOREV = 'R' and SIDE = 'R'
          The matrix V\&. See Further Details\&.
.fi
.PP
.br
\fILDV\fP 
.PP
.nf
          LDV is INTEGER
          The leading dimension of the array V\&.
          If STOREV = 'C' and SIDE = 'L', LDV >= max(1,M);
          if STOREV = 'C' and SIDE = 'R', LDV >= max(1,N);
          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
\fBFurther Details:\fP
.RS 4

.PP
.nf
  The shape of the matrix V and the storage of the vectors which define
  the H(i) is best illustrated by the following example with n = 5 and
  k = 3\&. The elements equal to 1 are not stored; the corresponding
  array elements are modified but restored on exit\&. The rest of the
  array is not used\&.

  DIRECT = 'F' and STOREV = 'C':         DIRECT = 'F' and STOREV = 'R':

               V = (  1       )                 V = (  1 v1 v1 v1 v1 )
                   ( v1  1    )                     (     1 v2 v2 v2 )
                   ( v1 v2  1 )                     (        1 v3 v3 )
                   ( v1 v2 v3 )
                   ( v1 v2 v3 )

  DIRECT = 'B' and STOREV = 'C':         DIRECT = 'B' and STOREV = 'R':

               V = ( v1 v2 v3 )                 V = ( v1 v1  1       )
                   ( v1 v2 v3 )                     ( v2 v2 v2  1    )
                   (  1 v2 v3 )                     ( v3 v3 v3 v3  1 )
                   (     1 v3 )
                   (        1 )
.fi
.PP
 
.RE
.PP

.SS "subroutine dlarfb (character side, character trans, character direct, character storev, integer m, integer n, integer k, 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
\fBDLARFB\fP applies a block reflector or its transpose to a general rectangular matrix\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 DLARFB applies a real block reflector H or its transpose H**T to a
 real m by n matrix C, from either the left or the right\&.
.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)
          = 'T': 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)
          = '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
          = '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)\&.
          If SIDE = 'L', M >= K >= 0;
          if SIDE = 'R', N >= K >= 0\&.
.fi
.PP
.br
\fIV\fP 
.PP
.nf
          V is DOUBLE PRECISION array, dimension
                                (LDV,K) if STOREV = 'C'
                                (LDV,M) if STOREV = 'R' and SIDE = 'L'
                                (LDV,N) if STOREV = 'R' and SIDE = 'R'
          The matrix V\&. See Further Details\&.
.fi
.PP
.br
\fILDV\fP 
.PP
.nf
          LDV is INTEGER
          The leading dimension of the array V\&.
          If STOREV = 'C' and SIDE = 'L', LDV >= max(1,M);
          if STOREV = 'C' and SIDE = 'R', LDV >= max(1,N);
          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
\fBFurther Details:\fP
.RS 4

.PP
.nf
  The shape of the matrix V and the storage of the vectors which define
  the H(i) is best illustrated by the following example with n = 5 and
  k = 3\&. The elements equal to 1 are not stored; the corresponding
  array elements are modified but restored on exit\&. The rest of the
  array is not used\&.

  DIRECT = 'F' and STOREV = 'C':         DIRECT = 'F' and STOREV = 'R':

               V = (  1       )                 V = (  1 v1 v1 v1 v1 )
                   ( v1  1    )                     (     1 v2 v2 v2 )
                   ( v1 v2  1 )                     (        1 v3 v3 )
                   ( v1 v2 v3 )
                   ( v1 v2 v3 )

  DIRECT = 'B' and STOREV = 'C':         DIRECT = 'B' and STOREV = 'R':

               V = ( v1 v2 v3 )                 V = ( v1 v1  1       )
                   ( v1 v2 v3 )                     ( v2 v2 v2  1    )
                   (  1 v2 v3 )                     ( v3 v3 v3 v3  1 )
                   (     1 v3 )
                   (        1 )
.fi
.PP
 
.RE
.PP

.SS "subroutine slarfb (character side, character trans, character direct, character storev, integer m, integer n, integer k, 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
\fBSLARFB\fP applies a block reflector or its transpose to a general rectangular matrix\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 SLARFB applies a real block reflector H or its transpose H**T to a
 real m by n matrix C, from either the left or the right\&.
.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)
          = 'T': 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)
          = '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
          = '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)\&.
          If SIDE = 'L', M >= K >= 0;
          if SIDE = 'R', N >= K >= 0\&.
.fi
.PP
.br
\fIV\fP 
.PP
.nf
          V is REAL array, dimension
                                (LDV,K) if STOREV = 'C'
                                (LDV,M) if STOREV = 'R' and SIDE = 'L'
                                (LDV,N) if STOREV = 'R' and SIDE = 'R'
          The matrix V\&. See Further Details\&.
.fi
.PP
.br
\fILDV\fP 
.PP
.nf
          LDV is INTEGER
          The leading dimension of the array V\&.
          If STOREV = 'C' and SIDE = 'L', LDV >= max(1,M);
          if STOREV = 'C' and SIDE = 'R', LDV >= max(1,N);
          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
\fBFurther Details:\fP
.RS 4

.PP
.nf
  The shape of the matrix V and the storage of the vectors which define
  the H(i) is best illustrated by the following example with n = 5 and
  k = 3\&. The elements equal to 1 are not stored; the corresponding
  array elements are modified but restored on exit\&. The rest of the
  array is not used\&.

  DIRECT = 'F' and STOREV = 'C':         DIRECT = 'F' and STOREV = 'R':

               V = (  1       )                 V = (  1 v1 v1 v1 v1 )
                   ( v1  1    )                     (     1 v2 v2 v2 )
                   ( v1 v2  1 )                     (        1 v3 v3 )
                   ( v1 v2 v3 )
                   ( v1 v2 v3 )

  DIRECT = 'B' and STOREV = 'C':         DIRECT = 'B' and STOREV = 'R':

               V = ( v1 v2 v3 )                 V = ( v1 v1  1       )
                   ( v1 v2 v3 )                     ( v2 v2 v2  1    )
                   (  1 v2 v3 )                     ( v3 v3 v3 v3  1 )
                   (     1 v3 )
                   (        1 )
.fi
.PP
 
.RE
.PP

.SS "subroutine zlarfb (character side, character trans, character direct, character storev, integer m, integer n, integer k, 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
\fBZLARFB\fP applies a block reflector or its conjugate-transpose to a general rectangular matrix\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 ZLARFB applies a complex block reflector H or its transpose H**H to a
 complex M-by-N matrix C, from either the left or the right\&.
.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)
          = '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
          = '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)\&.
          If SIDE = 'L', M >= K >= 0;
          if SIDE = 'R', N >= K >= 0\&.
.fi
.PP
.br
\fIV\fP 
.PP
.nf
          V is COMPLEX*16 array, dimension
                                (LDV,K) if STOREV = 'C'
                                (LDV,M) if STOREV = 'R' and SIDE = 'L'
                                (LDV,N) if STOREV = 'R' and SIDE = 'R'
          See Further Details\&.
.fi
.PP
.br
\fILDV\fP 
.PP
.nf
          LDV is INTEGER
          The leading dimension of the array V\&.
          If STOREV = 'C' and SIDE = 'L', LDV >= max(1,M);
          if STOREV = 'C' and SIDE = 'R', LDV >= max(1,N);
          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
\fBFurther Details:\fP
.RS 4

.PP
.nf
  The shape of the matrix V and the storage of the vectors which define
  the H(i) is best illustrated by the following example with n = 5 and
  k = 3\&. The elements equal to 1 are not stored; the corresponding
  array elements are modified but restored on exit\&. The rest of the
  array is not used\&.

  DIRECT = 'F' and STOREV = 'C':         DIRECT = 'F' and STOREV = 'R':

               V = (  1       )                 V = (  1 v1 v1 v1 v1 )
                   ( v1  1    )                     (     1 v2 v2 v2 )
                   ( v1 v2  1 )                     (        1 v3 v3 )
                   ( v1 v2 v3 )
                   ( v1 v2 v3 )

  DIRECT = 'B' and STOREV = 'C':         DIRECT = 'B' and STOREV = 'R':

               V = ( v1 v2 v3 )                 V = ( v1 v1  1       )
                   ( v1 v2 v3 )                     ( v2 v2 v2  1    )
                   (  1 v2 v3 )                     ( v3 v3 v3 v3  1 )
                   (     1 v3 )
                   (        1 )
.fi
.PP
 
.RE
.PP

.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.