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DLALSDRun Method

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. This code makes very mild assumptions about floating point arithmetic. It will work on machines with a guard digit in add/subtract, or on those binary machines without guard digits which subtract like the Cray XMP, Cray YMP, Cray C 90, or Cray 2. It could conceivably fail on hexadecimal or decimal machines without guard digits, but we know of none.

Namespace: DotNumerics.LinearAlgebra.CSLapack
Assembly: DWSIM.MathOps.DotNumerics (in DWSIM.MathOps.DotNumerics.dll) Version: 1.0.0.0 (1.0.0.0)
Syntax
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public void Run(
	string UPLO,
	int SMLSIZ,
	int N,
	int NRHS,
	ref double[] D,
	int offset_d,
	ref double[] E,
	int offset_e,
	ref double[] B,
	int offset_b,
	int LDB,
	double RCOND,
	ref int RANK,
	ref double[] WORK,
	int offset_work,
	ref int[] IWORK,
	int offset_iwork,
	ref int INFO
)
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Parameters

UPLO  String
(input) CHARACTER*1 = 'U': D and E define an upper bidiagonal matrix. = 'L': D and E define a lower bidiagonal matrix.
SMLSIZ  Int32
(input) INTEGER The maximum size of the subproblems at the bottom of the computation tree.
N  Int32
(input) INTEGER The dimension of the bidiagonal matrix. N .GE. 0.
NRHS  Int32
(input) INTEGER The number of columns of B. NRHS must be at least 1.
D  Double
(input/output) 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.
offset_d  Int32
 
E  Double
(input/output) DOUBLE PRECISION array, dimension (N-1) Contains the super-diagonal entries of the bidiagonal matrix. On exit, E has been destroyed.
offset_e  Int32
 
B  Double
(input/output) 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.
offset_b  Int32
 
LDB  Int32
(input) INTEGER The leading dimension of B in the calling subprogram. LDB must be at least max(1,N).
RCOND  Double
(input) 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  Int32
(output) INTEGER The number of singular values of A greater than RCOND times the largest singular value.
WORK  Double
(workspace) 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).
offset_work  Int32
 
IWORK  Int32
(workspace) INTEGER array, dimension at least (3*N*NLVL + 11*N)
offset_iwork  Int32
 
INFO  Int32
(output) INTEGER = 0: successful exit. .LT. 0: if INFO = -i, the i-th argument had an illegal value. .GT. 0: The algorithm failed to compute an singular value while working on the submatrix lying in rows and columns INFO/(N+1) through MOD(INFO,N+1).
See Also