table of contents
| unbdb6(3) | LAPACK | unbdb6(3) |
NAME¶
unbdb6 - {un,or}bdb6: step in uncsd2by1
SYNOPSIS¶
Functions¶
subroutine cunbdb6 (m1, m2, n, x1, incx1, x2, incx2, q1,
ldq1, q2, ldq2, work, lwork, info)
CUNBDB6 subroutine dorbdb6 (m1, m2, n, x1, incx1, x2, incx2, q1,
ldq1, q2, ldq2, work, lwork, info)
DORBDB6 subroutine sorbdb6 (m1, m2, n, x1, incx1, x2, incx2, q1,
ldq1, q2, ldq2, work, lwork, info)
SORBDB6 subroutine zunbdb6 (m1, m2, n, x1, incx1, x2, incx2, q1,
ldq1, q2, ldq2, work, lwork, info)
ZUNBDB6
Detailed Description¶
Function Documentation¶
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)¶
CUNBDB6
Purpose:
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. 'On the round-off error
analysis of the Gram-Schmidt algorithm with reorthogonalization.'
2002. CERFACS Technical Report No. TR/PA/02/33. URL:
https://www.cerfacs.fr/algor/reports/2002/TR_PA_02_33.pdf
Parameters
M1
M1 is INTEGER
The dimension of X1 and the number of rows in Q1. 0 <= M1.
M2
M2 is INTEGER
The dimension of X2 and the number of rows in Q2. 0 <= M2.
N
N is INTEGER
The number of columns in Q1 and Q2. 0 <= N.
X1
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.
INCX1
INCX1 is INTEGER
Increment for entries of X1.
X2
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.
INCX2
INCX2 is INTEGER
Increment for entries of X2.
Q1
Q1 is COMPLEX array, dimension (LDQ1, N)
The top part of the orthonormal basis matrix.
LDQ1
LDQ1 is INTEGER
The leading dimension of Q1. LDQ1 >= M1.
Q2
Q2 is COMPLEX array, dimension (LDQ2, N)
The bottom part of the orthonormal basis matrix.
LDQ2
LDQ2 is INTEGER
The leading dimension of Q2. LDQ2 >= M2.
WORK
WORK is COMPLEX array, dimension (LWORK)
LWORK
LWORK is INTEGER
The dimension of the array WORK. LWORK >= N.
INFO
INFO is INTEGER
= 0: successful exit.
< 0: if INFO = -i, the i-th argument had an illegal value.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
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)¶
DORBDB6
Purpose:
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. 'On the round-off error
analysis of the Gram-Schmidt algorithm with reorthogonalization.'
2002. CERFACS Technical Report No. TR/PA/02/33. URL:
https://www.cerfacs.fr/algor/reports/2002/TR_PA_02_33.pdf
Parameters
M1
M1 is INTEGER
The dimension of X1 and the number of rows in Q1. 0 <= M1.
M2
M2 is INTEGER
The dimension of X2 and the number of rows in Q2. 0 <= M2.
N
N is INTEGER
The number of columns in Q1 and Q2. 0 <= N.
X1
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.
INCX1
INCX1 is INTEGER
Increment for entries of X1.
X2
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.
INCX2
INCX2 is INTEGER
Increment for entries of X2.
Q1
Q1 is DOUBLE PRECISION array, dimension (LDQ1, N)
The top part of the orthonormal basis matrix.
LDQ1
LDQ1 is INTEGER
The leading dimension of Q1. LDQ1 >= M1.
Q2
Q2 is DOUBLE PRECISION array, dimension (LDQ2, N)
The bottom part of the orthonormal basis matrix.
LDQ2
LDQ2 is INTEGER
The leading dimension of Q2. LDQ2 >= M2.
WORK
WORK is DOUBLE PRECISION array, dimension (LWORK)
LWORK
LWORK is INTEGER
The dimension of the array WORK. LWORK >= N.
INFO
INFO is INTEGER
= 0: successful exit.
< 0: if INFO = -i, the i-th argument had an illegal value.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
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)¶
SORBDB6
Purpose:
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. 'On the round-off error
analysis of the Gram-Schmidt algorithm with reorthogonalization.'
2002. CERFACS Technical Report No. TR/PA/02/33. URL:
https://www.cerfacs.fr/algor/reports/2002/TR_PA_02_33.pdf
Parameters
M1
M1 is INTEGER
The dimension of X1 and the number of rows in Q1. 0 <= M1.
M2
M2 is INTEGER
The dimension of X2 and the number of rows in Q2. 0 <= M2.
N
N is INTEGER
The number of columns in Q1 and Q2. 0 <= N.
X1
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.
INCX1
INCX1 is INTEGER
Increment for entries of X1.
X2
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.
INCX2
INCX2 is INTEGER
Increment for entries of X2.
Q1
Q1 is REAL array, dimension (LDQ1, N)
The top part of the orthonormal basis matrix.
LDQ1
LDQ1 is INTEGER
The leading dimension of Q1. LDQ1 >= M1.
Q2
Q2 is REAL array, dimension (LDQ2, N)
The bottom part of the orthonormal basis matrix.
LDQ2
LDQ2 is INTEGER
The leading dimension of Q2. LDQ2 >= M2.
WORK
WORK is REAL array, dimension (LWORK)
LWORK
LWORK is INTEGER
The dimension of the array WORK. LWORK >= N.
INFO
INFO is INTEGER
= 0: successful exit.
< 0: if INFO = -i, the i-th argument had an illegal value.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
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)¶
ZUNBDB6
Purpose:
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. 'On the round-off error
analysis of the Gram-Schmidt algorithm with reorthogonalization.'
2002. CERFACS Technical Report No. TR/PA/02/33. URL:
https://www.cerfacs.fr/algor/reports/2002/TR_PA_02_33.pdf
Parameters
M1
M1 is INTEGER
The dimension of X1 and the number of rows in Q1. 0 <= M1.
M2
M2 is INTEGER
The dimension of X2 and the number of rows in Q2. 0 <= M2.
N
N is INTEGER
The number of columns in Q1 and Q2. 0 <= N.
X1
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.
INCX1
INCX1 is INTEGER
Increment for entries of X1.
X2
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.
INCX2
INCX2 is INTEGER
Increment for entries of X2.
Q1
Q1 is COMPLEX*16 array, dimension (LDQ1, N)
The top part of the orthonormal basis matrix.
LDQ1
LDQ1 is INTEGER
The leading dimension of Q1. LDQ1 >= M1.
Q2
Q2 is COMPLEX*16 array, dimension (LDQ2, N)
The bottom part of the orthonormal basis matrix.
LDQ2
LDQ2 is INTEGER
The leading dimension of Q2. LDQ2 >= M2.
WORK
WORK is COMPLEX*16 array, dimension (LWORK)
LWORK
LWORK is INTEGER
The dimension of the array WORK. LWORK >= N.
INFO
INFO is INTEGER
= 0: successful exit.
< 0: if INFO = -i, the i-th argument had an illegal value.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Author¶
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