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DLASDQRun Method

Purpose ======= DLASDQ computes the singular value decomposition (SVD) of a real (upper or lower) bidiagonal matrix with diagonal D and offdiagonal E, accumulating the transformations if desired. Letting B denote the input bidiagonal matrix, the algorithm computes orthogonal matrices Q and P such that B = Q * S * P' (P' denotes the transpose of P). The singular values S are overwritten on D. The input matrix U is changed to U * Q if desired. The input matrix VT is changed to P' * VT if desired. The input matrix C is changed to Q' * C if desired. See "Computing Small Singular Values of Bidiagonal Matrices With Guaranteed High Relative Accuracy," by J. Demmel and W. Kahan, LAPACK Working Note #3, for a detailed description of the algorithm.

Namespace: DotNumerics.LinearAlgebra.CSLapack
Assembly: DWSIM.MathOps.DotNumerics (in DWSIM.MathOps.DotNumerics.dll) Version: 1.0.0.0 (1.0.0.0)
Syntax
Copy
public void Run(
	string UPLO,
	int SQRE,
	int N,
	int NCVT,
	int NRU,
	int NCC,
	ref double[] D,
	int offset_d,
	ref double[] E,
	int offset_e,
	ref double[] VT,
	int offset_vt,
	int LDVT,
	ref double[] U,
	int offset_u,
	int LDU,
	ref double[] C,
	int offset_c,
	int LDC,
	ref double[] WORK,
	int offset_work,
	ref int INFO
)
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Parameters

UPLO  String
(input) CHARACTER*1 On entry, UPLO specifies whether the input bidiagonal matrix is upper or lower bidiagonal, and wether it is square are not. UPLO = 'U' or 'u' B is upper bidiagonal. UPLO = 'L' or 'l' B is lower bidiagonal.
SQRE  Int32
(input) INTEGER = 0: then the input matrix is N-by-N. = 1: then the input matrix is N-by-(N+1) if UPLU = 'U' and (N+1)-by-N if UPLU = 'L'. The bidiagonal matrix has N = NL + NR + 1 rows and M = N + SQRE .GE. N columns.
N  Int32
(input) INTEGER On entry, N specifies the number of rows and columns in the matrix. N must be at least 0.
NCVT  Int32
(input) INTEGER On entry, NCVT specifies the number of columns of the matrix VT. NCVT must be at least 0.
NRU  Int32
(input) INTEGER On entry, NRU specifies the number of rows of the matrix U. NRU must be at least 0.
NCC  Int32
(input) INTEGER On entry, NCC specifies the number of columns of the matrix C. NCC must be at least 0.
D  Double
(input/output) DOUBLE PRECISION array, dimension (N) On entry, D contains the diagonal entries of the bidiagonal matrix whose SVD is desired. On normal exit, D contains the singular values in ascending order.
offset_d  Int32
 
E  Double
(input/output) DOUBLE PRECISION array. dimension is (N-1) if SQRE = 0 and N if SQRE = 1. On entry, the entries of E contain the offdiagonal entries of the bidiagonal matrix whose SVD is desired. On normal exit, E will contain 0. If the algorithm does not converge, D and E will contain the diagonal and superdiagonal entries of a bidiagonal matrix orthogonally equivalent to the one given as input.
offset_e  Int32
 
VT  Double
(input/output) DOUBLE PRECISION array, dimension (LDVT, NCVT) On entry, contains a matrix which on exit has been premultiplied by P', dimension N-by-NCVT if SQRE = 0 and (N+1)-by-NCVT if SQRE = 1 (not referenced if NCVT=0).
offset_vt  Int32
 
LDVT  Int32
(input) INTEGER On entry, LDVT specifies the leading dimension of VT as declared in the calling (sub) program. LDVT must be at least 1. If NCVT is nonzero LDVT must also be at least N.
U  Double
(input/output) DOUBLE PRECISION array, dimension (LDU, N) On entry, contains a matrix which on exit has been postmultiplied by Q, dimension NRU-by-N if SQRE = 0 and NRU-by-(N+1) if SQRE = 1 (not referenced if NRU=0).
offset_u  Int32
 
LDU  Int32
(input) INTEGER On entry, LDU specifies the leading dimension of U as declared in the calling (sub) program. LDU must be at least max( 1, NRU ) .
C  Double
(input/output) DOUBLE PRECISION array, dimension (LDC, NCC) On entry, contains an N-by-NCC matrix which on exit has been premultiplied by Q' dimension N-by-NCC if SQRE = 0 and (N+1)-by-NCC if SQRE = 1 (not referenced if NCC=0).
offset_c  Int32
 
LDC  Int32
(input) INTEGER On entry, LDC specifies the leading dimension of C as declared in the calling (sub) program. LDC must be at least 1. If NCC is nonzero, LDC must also be at least N.
WORK  Double
(workspace) DOUBLE PRECISION array, dimension (4*N) Workspace. Only referenced if one of NCVT, NRU, or NCC is nonzero, and if N is at least 2.
offset_work  Int32
 
INFO  Int32
(output) INTEGER On exit, a value of 0 indicates a successful exit. If INFO .LT. 0, argument number -INFO is illegal. If INFO .GT. 0, the algorithm did not converge, and INFO specifies how many superdiagonals did not converge.
See Also