.TH "unbdb6" 3 "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
unbdb6 \- {un,or}bdb6: step in uncsd2by1
.SH SYNOPSIS
.br
.PP
.SS "Functions"

.in +1c
.ti -1c
.RI "subroutine \fBcunbdb6\fP (m1, m2, n, x1, incx1, x2, incx2, q1, ldq1, q2, ldq2, work, lwork, info)"
.br
.RI "\fBCUNBDB6\fP "
.ti -1c
.RI "subroutine \fBdorbdb6\fP (m1, m2, n, x1, incx1, x2, incx2, q1, ldq1, q2, ldq2, work, lwork, info)"
.br
.RI "\fBDORBDB6\fP "
.ti -1c
.RI "subroutine \fBsorbdb6\fP (m1, m2, n, x1, incx1, x2, incx2, q1, ldq1, q2, ldq2, work, lwork, info)"
.br
.RI "\fBSORBDB6\fP "
.ti -1c
.RI "subroutine \fBzunbdb6\fP (m1, m2, n, x1, incx1, x2, incx2, q1, ldq1, q2, ldq2, work, lwork, info)"
.br
.RI "\fBZUNBDB6\fP "
.in -1c
.SH "Detailed Description"
.PP 

.SH "Function Documentation"
.PP 
.SS "subroutine cunbdb6 (integer m1, integer m2, integer n, complex, dimension(*) x1, integer incx1, complex, dimension(*) x2, integer incx2, complex, dimension(ldq1,*) q1, integer ldq1, complex, dimension(ldq2,*) q2, integer ldq2, complex, dimension(*) work, integer lwork, integer info)"

.PP
\fBCUNBDB6\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
!>
!> CUNBDB6 orthogonalizes the column vector
!>      X = [ X1 ]
!>          [ X2 ]
!> with respect to the columns of
!>      Q = [ Q1 ] \&.
!>          [ Q2 ]
!> The columns of Q must be orthonormal\&. The orthogonalized vector will
!> be zero if and only if it lies entirely in the range of Q\&.
!>
!> The projection is computed with at most two iterations of the
!> classical Gram-Schmidt algorithm, see
!> * L\&. Giraud, J\&. Langou, M\&. Rozložník\&. 
!>   2002\&. CERFACS Technical Report No\&. TR/PA/02/33\&. URL:
!>   https://www\&.cerfacs\&.fr/algor/reports/2002/TR_PA_02_33\&.pdf
!>
!>
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIM1\fP 
.PP
.nf
!>          M1 is INTEGER
!>           The dimension of X1 and the number of rows in Q1\&. 0 <= M1\&.
!> 
.fi
.PP
.br
\fIM2\fP 
.PP
.nf
!>          M2 is INTEGER
!>           The dimension of X2 and the number of rows in Q2\&. 0 <= M2\&.
!> 
.fi
.PP
.br
\fIN\fP 
.PP
.nf
!>          N is INTEGER
!>           The number of columns in Q1 and Q2\&. 0 <= N\&.
!> 
.fi
.PP
.br
\fIX1\fP 
.PP
.nf
!>          X1 is COMPLEX array, dimension (M1)
!>           On entry, the top part of the vector to be orthogonalized\&.
!>           On exit, the top part of the projected vector\&.
!> 
.fi
.PP
.br
\fIINCX1\fP 
.PP
.nf
!>          INCX1 is INTEGER
!>           Increment for entries of X1\&.
!> 
.fi
.PP
.br
\fIX2\fP 
.PP
.nf
!>          X2 is COMPLEX array, dimension (M2)
!>           On entry, the bottom part of the vector to be
!>           orthogonalized\&. On exit, the bottom part of the projected
!>           vector\&.
!> 
.fi
.PP
.br
\fIINCX2\fP 
.PP
.nf
!>          INCX2 is INTEGER
!>           Increment for entries of X2\&.
!> 
.fi
.PP
.br
\fIQ1\fP 
.PP
.nf
!>          Q1 is COMPLEX array, dimension (LDQ1, N)
!>           The top part of the orthonormal basis matrix\&.
!> 
.fi
.PP
.br
\fILDQ1\fP 
.PP
.nf
!>          LDQ1 is INTEGER
!>           The leading dimension of Q1\&. LDQ1 >= M1\&.
!> 
.fi
.PP
.br
\fIQ2\fP 
.PP
.nf
!>          Q2 is COMPLEX array, dimension (LDQ2, N)
!>           The bottom part of the orthonormal basis matrix\&.
!> 
.fi
.PP
.br
\fILDQ2\fP 
.PP
.nf
!>          LDQ2 is INTEGER
!>           The leading dimension of Q2\&. LDQ2 >= M2\&.
!> 
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
!>          WORK is COMPLEX array, dimension (LWORK)
!> 
.fi
.PP
.br
\fILWORK\fP 
.PP
.nf
!>          LWORK is INTEGER
!>           The dimension of the array WORK\&. LWORK >= N\&.
!> 
.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 \fB157\fP of file \fBcunbdb6\&.f\fP\&.
.SS "subroutine dorbdb6 (integer m1, integer m2, integer n, double precision, dimension(*) x1, integer incx1, double precision, dimension(*) x2, integer incx2, double precision, dimension(ldq1,*) q1, integer ldq1, double precision, dimension(ldq2,*) q2, integer ldq2, double precision, dimension(*) work, integer lwork, integer info)"

.PP
\fBDORBDB6\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
!>
!> DORBDB6 orthogonalizes the column vector
!>      X = [ X1 ]
!>          [ X2 ]
!> with respect to the columns of
!>      Q = [ Q1 ] \&.
!>          [ Q2 ]
!> The columns of Q must be orthonormal\&. The orthogonalized vector will
!> be zero if and only if it lies entirely in the range of Q\&.
!>
!> The projection is computed with at most two iterations of the
!> classical Gram-Schmidt algorithm, see
!> * L\&. Giraud, J\&. Langou, M\&. Rozložník\&. 
!>   2002\&. CERFACS Technical Report No\&. TR/PA/02/33\&. URL:
!>   https://www\&.cerfacs\&.fr/algor/reports/2002/TR_PA_02_33\&.pdf
!>
!>
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIM1\fP 
.PP
.nf
!>          M1 is INTEGER
!>           The dimension of X1 and the number of rows in Q1\&. 0 <= M1\&.
!> 
.fi
.PP
.br
\fIM2\fP 
.PP
.nf
!>          M2 is INTEGER
!>           The dimension of X2 and the number of rows in Q2\&. 0 <= M2\&.
!> 
.fi
.PP
.br
\fIN\fP 
.PP
.nf
!>          N is INTEGER
!>           The number of columns in Q1 and Q2\&. 0 <= N\&.
!> 
.fi
.PP
.br
\fIX1\fP 
.PP
.nf
!>          X1 is DOUBLE PRECISION array, dimension (M1)
!>           On entry, the top part of the vector to be orthogonalized\&.
!>           On exit, the top part of the projected vector\&.
!> 
.fi
.PP
.br
\fIINCX1\fP 
.PP
.nf
!>          INCX1 is INTEGER
!>           Increment for entries of X1\&.
!> 
.fi
.PP
.br
\fIX2\fP 
.PP
.nf
!>          X2 is DOUBLE PRECISION array, dimension (M2)
!>           On entry, the bottom part of the vector to be
!>           orthogonalized\&. On exit, the bottom part of the projected
!>           vector\&.
!> 
.fi
.PP
.br
\fIINCX2\fP 
.PP
.nf
!>          INCX2 is INTEGER
!>           Increment for entries of X2\&.
!> 
.fi
.PP
.br
\fIQ1\fP 
.PP
.nf
!>          Q1 is DOUBLE PRECISION array, dimension (LDQ1, N)
!>           The top part of the orthonormal basis matrix\&.
!> 
.fi
.PP
.br
\fILDQ1\fP 
.PP
.nf
!>          LDQ1 is INTEGER
!>           The leading dimension of Q1\&. LDQ1 >= M1\&.
!> 
.fi
.PP
.br
\fIQ2\fP 
.PP
.nf
!>          Q2 is DOUBLE PRECISION array, dimension (LDQ2, N)
!>           The bottom part of the orthonormal basis matrix\&.
!> 
.fi
.PP
.br
\fILDQ2\fP 
.PP
.nf
!>          LDQ2 is INTEGER
!>           The leading dimension of Q2\&. LDQ2 >= M2\&.
!> 
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
!>          WORK is DOUBLE PRECISION array, dimension (LWORK)
!> 
.fi
.PP
.br
\fILWORK\fP 
.PP
.nf
!>          LWORK is INTEGER
!>           The dimension of the array WORK\&. LWORK >= N\&.
!> 
.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 \fB157\fP of file \fBdorbdb6\&.f\fP\&.
.SS "subroutine sorbdb6 (integer m1, integer m2, integer n, real, dimension(*) x1, integer incx1, real, dimension(*) x2, integer incx2, real, dimension(ldq1,*) q1, integer ldq1, real, dimension(ldq2,*) q2, integer ldq2, real, dimension(*) work, integer lwork, integer info)"

.PP
\fBSORBDB6\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
!>
!> SORBDB6 orthogonalizes the column vector
!>      X = [ X1 ]
!>          [ X2 ]
!> with respect to the columns of
!>      Q = [ Q1 ] \&.
!>          [ Q2 ]
!> The columns of Q must be orthonormal\&. The orthogonalized vector will
!> be zero if and only if it lies entirely in the range of Q\&.
!>
!> The projection is computed with at most two iterations of the
!> classical Gram-Schmidt algorithm, see
!> * L\&. Giraud, J\&. Langou, M\&. Rozložník\&. 
!>   2002\&. CERFACS Technical Report No\&. TR/PA/02/33\&. URL:
!>   https://www\&.cerfacs\&.fr/algor/reports/2002/TR_PA_02_33\&.pdf
!>
!>
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIM1\fP 
.PP
.nf
!>          M1 is INTEGER
!>           The dimension of X1 and the number of rows in Q1\&. 0 <= M1\&.
!> 
.fi
.PP
.br
\fIM2\fP 
.PP
.nf
!>          M2 is INTEGER
!>           The dimension of X2 and the number of rows in Q2\&. 0 <= M2\&.
!> 
.fi
.PP
.br
\fIN\fP 
.PP
.nf
!>          N is INTEGER
!>           The number of columns in Q1 and Q2\&. 0 <= N\&.
!> 
.fi
.PP
.br
\fIX1\fP 
.PP
.nf
!>          X1 is REAL array, dimension (M1)
!>           On entry, the top part of the vector to be orthogonalized\&.
!>           On exit, the top part of the projected vector\&.
!> 
.fi
.PP
.br
\fIINCX1\fP 
.PP
.nf
!>          INCX1 is INTEGER
!>           Increment for entries of X1\&.
!> 
.fi
.PP
.br
\fIX2\fP 
.PP
.nf
!>          X2 is REAL array, dimension (M2)
!>           On entry, the bottom part of the vector to be
!>           orthogonalized\&. On exit, the bottom part of the projected
!>           vector\&.
!> 
.fi
.PP
.br
\fIINCX2\fP 
.PP
.nf
!>          INCX2 is INTEGER
!>           Increment for entries of X2\&.
!> 
.fi
.PP
.br
\fIQ1\fP 
.PP
.nf
!>          Q1 is REAL array, dimension (LDQ1, N)
!>           The top part of the orthonormal basis matrix\&.
!> 
.fi
.PP
.br
\fILDQ1\fP 
.PP
.nf
!>          LDQ1 is INTEGER
!>           The leading dimension of Q1\&. LDQ1 >= M1\&.
!> 
.fi
.PP
.br
\fIQ2\fP 
.PP
.nf
!>          Q2 is REAL array, dimension (LDQ2, N)
!>           The bottom part of the orthonormal basis matrix\&.
!> 
.fi
.PP
.br
\fILDQ2\fP 
.PP
.nf
!>          LDQ2 is INTEGER
!>           The leading dimension of Q2\&. LDQ2 >= M2\&.
!> 
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
!>          WORK is REAL array, dimension (LWORK)
!> 
.fi
.PP
.br
\fILWORK\fP 
.PP
.nf
!>          LWORK is INTEGER
!>           The dimension of the array WORK\&. LWORK >= N\&.
!> 
.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 \fB157\fP of file \fBsorbdb6\&.f\fP\&.
.SS "subroutine zunbdb6 (integer m1, integer m2, integer n, complex*16, dimension(*) x1, integer incx1, complex*16, dimension(*) x2, integer incx2, complex*16, dimension(ldq1,*) q1, integer ldq1, complex*16, dimension(ldq2,*) q2, integer ldq2, complex*16, dimension(*) work, integer lwork, integer info)"

.PP
\fBZUNBDB6\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
!>
!> ZUNBDB6 orthogonalizes the column vector
!>      X = [ X1 ]
!>          [ X2 ]
!> with respect to the columns of
!>      Q = [ Q1 ] \&.
!>          [ Q2 ]
!> The columns of Q must be orthonormal\&. The orthogonalized vector will
!> be zero if and only if it lies entirely in the range of Q\&.
!>
!> The projection is computed with at most two iterations of the
!> classical Gram-Schmidt algorithm, see
!> * L\&. Giraud, J\&. Langou, M\&. Rozložník\&. 
!>   2002\&. CERFACS Technical Report No\&. TR/PA/02/33\&. URL:
!>   https://www\&.cerfacs\&.fr/algor/reports/2002/TR_PA_02_33\&.pdf
!>
!>
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIM1\fP 
.PP
.nf
!>          M1 is INTEGER
!>           The dimension of X1 and the number of rows in Q1\&. 0 <= M1\&.
!> 
.fi
.PP
.br
\fIM2\fP 
.PP
.nf
!>          M2 is INTEGER
!>           The dimension of X2 and the number of rows in Q2\&. 0 <= M2\&.
!> 
.fi
.PP
.br
\fIN\fP 
.PP
.nf
!>          N is INTEGER
!>           The number of columns in Q1 and Q2\&. 0 <= N\&.
!> 
.fi
.PP
.br
\fIX1\fP 
.PP
.nf
!>          X1 is COMPLEX*16 array, dimension (M1)
!>           On entry, the top part of the vector to be orthogonalized\&.
!>           On exit, the top part of the projected vector\&.
!> 
.fi
.PP
.br
\fIINCX1\fP 
.PP
.nf
!>          INCX1 is INTEGER
!>           Increment for entries of X1\&.
!> 
.fi
.PP
.br
\fIX2\fP 
.PP
.nf
!>          X2 is COMPLEX*16 array, dimension (M2)
!>           On entry, the bottom part of the vector to be
!>           orthogonalized\&. On exit, the bottom part of the projected
!>           vector\&.
!> 
.fi
.PP
.br
\fIINCX2\fP 
.PP
.nf
!>          INCX2 is INTEGER
!>           Increment for entries of X2\&.
!> 
.fi
.PP
.br
\fIQ1\fP 
.PP
.nf
!>          Q1 is COMPLEX*16 array, dimension (LDQ1, N)
!>           The top part of the orthonormal basis matrix\&.
!> 
.fi
.PP
.br
\fILDQ1\fP 
.PP
.nf
!>          LDQ1 is INTEGER
!>           The leading dimension of Q1\&. LDQ1 >= M1\&.
!> 
.fi
.PP
.br
\fIQ2\fP 
.PP
.nf
!>          Q2 is COMPLEX*16 array, dimension (LDQ2, N)
!>           The bottom part of the orthonormal basis matrix\&.
!> 
.fi
.PP
.br
\fILDQ2\fP 
.PP
.nf
!>          LDQ2 is INTEGER
!>           The leading dimension of Q2\&. LDQ2 >= M2\&.
!> 
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
!>          WORK is COMPLEX*16 array, dimension (LWORK)
!> 
.fi
.PP
.br
\fILWORK\fP 
.PP
.nf
!>          LWORK is INTEGER
!>           The dimension of the array WORK\&. LWORK >= N\&.
!> 
.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 \fB157\fP of file \fBzunbdb6\&.f\fP\&.
.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.