table of contents
| lalsd(3) | LAPACK | lalsd(3) |
NAME¶
lalsd - lalsd: uses SVD for least squares, step in gelsd
SYNOPSIS¶
Functions¶
subroutine clalsd (uplo, smlsiz, n, nrhs, d, e, b, ldb,
rcond, rank, work, rwork, iwork, info)
CLALSD uses the singular value decomposition of A to solve the least
squares problem. subroutine dlalsd (uplo, smlsiz, n, nrhs, d, e, b,
ldb, rcond, rank, work, iwork, info)
DLALSD uses the singular value decomposition of A to solve the least
squares problem. subroutine slalsd (uplo, smlsiz, n, nrhs, d, e, b,
ldb, rcond, rank, work, iwork, info)
SLALSD uses the singular value decomposition of A to solve the least
squares problem. subroutine zlalsd (uplo, smlsiz, n, nrhs, d, e, b,
ldb, rcond, rank, work, rwork, iwork, info)
ZLALSD uses the singular value decomposition of A to solve the least
squares problem.
Detailed Description¶
Function Documentation¶
subroutine clalsd (character uplo, integer smlsiz, integer n, integer nrhs, real, dimension( * ) d, real, dimension( * ) e, complex, dimension( ldb, * ) b, integer ldb, real rcond, integer rank, complex, dimension( * ) work, real, dimension( * ) rwork, integer, dimension( * ) iwork, integer info)¶
CLALSD uses the singular value decomposition of A to solve the least squares problem.
Purpose:
CLALSD uses the singular value decomposition of A to solve the least
squares problem of finding X to minimize the Euclidean norm of each
column of A*X-B, where A is N-by-N upper bidiagonal, and X and B
are N-by-NRHS. The solution X overwrites B.
The singular values of A smaller than RCOND times the largest
singular value are treated as zero in solving the least squares
problem; in this case a minimum norm solution is returned.
The actual singular values are returned in D in ascending order.
Parameters
UPLO
UPLO is CHARACTER*1
= 'U': D and E define an upper bidiagonal matrix.
= 'L': D and E define a lower bidiagonal matrix.
SMLSIZ
SMLSIZ is INTEGER
The maximum size of the subproblems at the bottom of the
computation tree.
N
N is INTEGER
The dimension of the bidiagonal matrix. N >= 0.
NRHS
NRHS is INTEGER
The number of columns of B. NRHS must be at least 1.
D
D is REAL array, dimension (N)
On entry D contains the main diagonal of the bidiagonal
matrix. On exit, if INFO = 0, D contains its singular values.
E
E is REAL array, dimension (N-1)
Contains the super-diagonal entries of the bidiagonal matrix.
On exit, E has been destroyed.
B
B is COMPLEX array, dimension (LDB,NRHS)
On input, B contains the right hand sides of the least
squares problem. On output, B contains the solution X.
LDB
LDB is INTEGER
The leading dimension of B in the calling subprogram.
LDB must be at least max(1,N).
RCOND
RCOND is REAL
The singular values of A less than or equal to RCOND times
the largest singular value are treated as zero in solving
the least squares problem. If RCOND is negative,
machine precision is used instead.
For example, if diag(S)*X=B were the least squares problem,
where diag(S) is a diagonal matrix of singular values, the
solution would be X(i) = B(i) / S(i) if S(i) is greater than
RCOND*max(S), and X(i) = 0 if S(i) is less than or equal to
RCOND*max(S).
RANK
RANK is INTEGER
The number of singular values of A greater than RCOND times
the largest singular value.
WORK
WORK is COMPLEX array, dimension (N * NRHS).
RWORK
RWORK is REAL array, dimension at least
(9*N + 2*N*SMLSIZ + 8*N*NLVL + 3*SMLSIZ*NRHS +
MAX( (SMLSIZ+1)**2, N*(1+NRHS) + 2*NRHS ),
where
NLVL = MAX( 0, INT( LOG_2( MIN( M,N )/(SMLSIZ+1) ) ) + 1 )
IWORK
IWORK is INTEGER array, dimension (3*N*NLVL + 11*N).
INFO
INFO is INTEGER
= 0: successful exit.
< 0: if INFO = -i, the i-th argument had an illegal value.
> 0: The algorithm failed to compute a singular value while
working on the submatrix lying in rows and columns
INFO/(N+1) through MOD(INFO,N+1).
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Contributors:
Ming Gu and Ren-Cang Li, Computer Science Division,
University of California at Berkeley, USA
Osni Marques, LBNL/NERSC, USA
Osni Marques, LBNL/NERSC, USA
subroutine dlalsd (character uplo, integer smlsiz, integer n, integer nrhs, double precision, dimension( * ) d, double precision, dimension( * ) e, double precision, dimension( ldb, * ) b, integer ldb, double precision rcond, integer rank, double precision, dimension( * ) work, integer, dimension( * ) iwork, integer info)¶
DLALSD uses the singular value decomposition of A to solve the least squares problem.
Purpose:
DLALSD uses the singular value decomposition of A to solve the least
squares problem of finding X to minimize the Euclidean norm of each
column of A*X-B, where A is N-by-N upper bidiagonal, and X and B
are N-by-NRHS. The solution X overwrites B.
The singular values of A smaller than RCOND times the largest
singular value are treated as zero in solving the least squares
problem; in this case a minimum norm solution is returned.
The actual singular values are returned in D in ascending order.
Parameters
UPLO
UPLO is CHARACTER*1
= 'U': D and E define an upper bidiagonal matrix.
= 'L': D and E define a lower bidiagonal matrix.
SMLSIZ
SMLSIZ is INTEGER
The maximum size of the subproblems at the bottom of the
computation tree.
N
N is INTEGER
The dimension of the bidiagonal matrix. N >= 0.
NRHS
NRHS is INTEGER
The number of columns of B. NRHS must be at least 1.
D
D is DOUBLE PRECISION array, dimension (N)
On entry D contains the main diagonal of the bidiagonal
matrix. On exit, if INFO = 0, D contains its singular values.
E
E is DOUBLE PRECISION array, dimension (N-1)
Contains the super-diagonal entries of the bidiagonal matrix.
On exit, E has been destroyed.
B
B is DOUBLE PRECISION array, dimension (LDB,NRHS)
On input, B contains the right hand sides of the least
squares problem. On output, B contains the solution X.
LDB
LDB is INTEGER
The leading dimension of B in the calling subprogram.
LDB must be at least max(1,N).
RCOND
RCOND is DOUBLE PRECISION
The singular values of A less than or equal to RCOND times
the largest singular value are treated as zero in solving
the least squares problem. If RCOND is negative,
machine precision is used instead.
For example, if diag(S)*X=B were the least squares problem,
where diag(S) is a diagonal matrix of singular values, the
solution would be X(i) = B(i) / S(i) if S(i) is greater than
RCOND*max(S), and X(i) = 0 if S(i) is less than or equal to
RCOND*max(S).
RANK
RANK is INTEGER
The number of singular values of A greater than RCOND times
the largest singular value.
WORK
WORK is DOUBLE PRECISION array, dimension at least
(9*N + 2*N*SMLSIZ + 8*N*NLVL + N*NRHS + (SMLSIZ+1)**2),
where NLVL = max(0, INT(log_2 (N/(SMLSIZ+1))) + 1).
IWORK
IWORK is INTEGER array, dimension at least
(3*N*NLVL + 11*N)
INFO
INFO is INTEGER
= 0: successful exit.
< 0: if INFO = -i, the i-th argument had an illegal value.
> 0: The algorithm failed to compute a singular value while
working on the submatrix lying in rows and columns
INFO/(N+1) through MOD(INFO,N+1).
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Contributors:
Ming Gu and Ren-Cang Li, Computer Science Division,
University of California at Berkeley, USA
Osni Marques, LBNL/NERSC, USA
Osni Marques, LBNL/NERSC, USA
subroutine slalsd (character uplo, integer smlsiz, integer n, integer nrhs, real, dimension( * ) d, real, dimension( * ) e, real, dimension( ldb, * ) b, integer ldb, real rcond, integer rank, real, dimension( * ) work, integer, dimension( * ) iwork, integer info)¶
SLALSD uses the singular value decomposition of A to solve the least squares problem.
Purpose:
SLALSD uses the singular value decomposition of A to solve the least
squares problem of finding X to minimize the Euclidean norm of each
column of A*X-B, where A is N-by-N upper bidiagonal, and X and B
are N-by-NRHS. The solution X overwrites B.
The singular values of A smaller than RCOND times the largest
singular value are treated as zero in solving the least squares
problem; in this case a minimum norm solution is returned.
The actual singular values are returned in D in ascending order.
Parameters
UPLO
UPLO is CHARACTER*1
= 'U': D and E define an upper bidiagonal matrix.
= 'L': D and E define a lower bidiagonal matrix.
SMLSIZ
SMLSIZ is INTEGER
The maximum size of the subproblems at the bottom of the
computation tree.
N
N is INTEGER
The dimension of the bidiagonal matrix. N >= 0.
NRHS
NRHS is INTEGER
The number of columns of B. NRHS must be at least 1.
D
D is REAL array, dimension (N)
On entry D contains the main diagonal of the bidiagonal
matrix. On exit, if INFO = 0, D contains its singular values.
E
E is REAL array, dimension (N-1)
Contains the super-diagonal entries of the bidiagonal matrix.
On exit, E has been destroyed.
B
B is REAL array, dimension (LDB,NRHS)
On input, B contains the right hand sides of the least
squares problem. On output, B contains the solution X.
LDB
LDB is INTEGER
The leading dimension of B in the calling subprogram.
LDB must be at least max(1,N).
RCOND
RCOND is REAL
The singular values of A less than or equal to RCOND times
the largest singular value are treated as zero in solving
the least squares problem. If RCOND is negative,
machine precision is used instead.
For example, if diag(S)*X=B were the least squares problem,
where diag(S) is a diagonal matrix of singular values, the
solution would be X(i) = B(i) / S(i) if S(i) is greater than
RCOND*max(S), and X(i) = 0 if S(i) is less than or equal to
RCOND*max(S).
RANK
RANK is INTEGER
The number of singular values of A greater than RCOND times
the largest singular value.
WORK
WORK is REAL array, dimension at least
(9*N + 2*N*SMLSIZ + 8*N*NLVL + N*NRHS + (SMLSIZ+1)**2),
where NLVL = max(0, INT(log_2 (N/(SMLSIZ+1))) + 1).
IWORK
IWORK is INTEGER array, dimension at least
(3*N*NLVL + 11*N)
INFO
INFO is INTEGER
= 0: successful exit.
< 0: if INFO = -i, the i-th argument had an illegal value.
> 0: The algorithm failed to compute a singular value while
working on the submatrix lying in rows and columns
INFO/(N+1) through MOD(INFO,N+1).
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Contributors:
Ming Gu and Ren-Cang Li, Computer Science Division,
University of California at Berkeley, USA
Osni Marques, LBNL/NERSC, USA
Osni Marques, LBNL/NERSC, USA
subroutine zlalsd (character uplo, integer smlsiz, integer n, integer nrhs, double precision, dimension( * ) d, double precision, dimension( * ) e, complex*16, dimension( ldb, * ) b, integer ldb, double precision rcond, integer rank, complex*16, dimension( * ) work, double precision, dimension( * ) rwork, integer, dimension( * ) iwork, integer info)¶
ZLALSD uses the singular value decomposition of A to solve the least squares problem.
Purpose:
ZLALSD uses the singular value decomposition of A to solve the least
squares problem of finding X to minimize the Euclidean norm of each
column of A*X-B, where A is N-by-N upper bidiagonal, and X and B
are N-by-NRHS. The solution X overwrites B.
The singular values of A smaller than RCOND times the largest
singular value are treated as zero in solving the least squares
problem; in this case a minimum norm solution is returned.
The actual singular values are returned in D in ascending order.
Parameters
UPLO
UPLO is CHARACTER*1
= 'U': D and E define an upper bidiagonal matrix.
= 'L': D and E define a lower bidiagonal matrix.
SMLSIZ
SMLSIZ is INTEGER
The maximum size of the subproblems at the bottom of the
computation tree.
N
N is INTEGER
The dimension of the bidiagonal matrix. N >= 0.
NRHS
NRHS is INTEGER
The number of columns of B. NRHS must be at least 1.
D
D is DOUBLE PRECISION array, dimension (N)
On entry D contains the main diagonal of the bidiagonal
matrix. On exit, if INFO = 0, D contains its singular values.
E
E is DOUBLE PRECISION array, dimension (N-1)
Contains the super-diagonal entries of the bidiagonal matrix.
On exit, E has been destroyed.
B
B is COMPLEX*16 array, dimension (LDB,NRHS)
On input, B contains the right hand sides of the least
squares problem. On output, B contains the solution X.
LDB
LDB is INTEGER
The leading dimension of B in the calling subprogram.
LDB must be at least max(1,N).
RCOND
RCOND is DOUBLE PRECISION
The singular values of A less than or equal to RCOND times
the largest singular value are treated as zero in solving
the least squares problem. If RCOND is negative,
machine precision is used instead.
For example, if diag(S)*X=B were the least squares problem,
where diag(S) is a diagonal matrix of singular values, the
solution would be X(i) = B(i) / S(i) if S(i) is greater than
RCOND*max(S), and X(i) = 0 if S(i) is less than or equal to
RCOND*max(S).
RANK
RANK is INTEGER
The number of singular values of A greater than RCOND times
the largest singular value.
WORK
WORK is COMPLEX*16 array, dimension (N * NRHS)
RWORK
RWORK is DOUBLE PRECISION array, dimension at least
(9*N + 2*N*SMLSIZ + 8*N*NLVL + 3*SMLSIZ*NRHS +
MAX( (SMLSIZ+1)**2, N*(1+NRHS) + 2*NRHS ),
where
NLVL = MAX( 0, INT( LOG_2( MIN( M,N )/(SMLSIZ+1) ) ) + 1 )
IWORK
IWORK is INTEGER array, dimension at least
(3*N*NLVL + 11*N).
INFO
INFO is INTEGER
= 0: successful exit.
< 0: if INFO = -i, the i-th argument had an illegal value.
> 0: The algorithm failed to compute a singular value while
working on the submatrix lying in rows and columns
INFO/(N+1) through MOD(INFO,N+1).
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Contributors:
Ming Gu and Ren-Cang Li, Computer Science Division,
University of California at Berkeley, USA
Osni Marques, LBNL/NERSC, USA
Osni Marques, LBNL/NERSC, USA
Author¶
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