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DBDSDCRun Method

Purpose ======= DBDSDC computes the singular value decomposition (SVD) of a real N-by-N (upper or lower) bidiagonal matrix B: B = U * S * VT, using a divide and conquer method, where S is a diagonal matrix with non-negative diagonal elements (the singular values of B), and U and VT are orthogonal matrices of left and right singular vectors, respectively. DBDSDC can be used to compute all singular values, and optionally, singular vectors or singular vectors in compact form. 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 X-MP, Cray Y-MP, Cray C-90, or Cray-2. It could conceivably fail on hexadecimal or decimal machines without guard digits, but we know of none. See DLASD3 for details. The code currently calls DLASDQ if singular values only are desired. However, it can be slightly modified to compute singular values using the divide and conquer method.

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,
	string COMPQ,
	int N,
	ref double[] D,
	int offset_d,
	ref double[] E,
	int offset_e,
	ref double[] U,
	int offset_u,
	int LDU,
	ref double[] VT,
	int offset_vt,
	int LDVT,
	ref double[] Q,
	int offset_q,
	ref int[] IQ,
	int offset_iq,
	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': B is upper bidiagonal. = 'L': B is lower bidiagonal.
COMPQ  String
(input) CHARACTER*1 Specifies whether singular vectors are to be computed as follows: = 'N': Compute singular values only; = 'P': Compute singular values and compute singular vectors in compact form; = 'I': Compute singular values and singular vectors.
N  Int32
(input) INTEGER The order of the matrix B. N .GE. 0.
D  Double
(input/output) DOUBLE PRECISION array, dimension (N) On entry, the n diagonal elements of the bidiagonal matrix B. On exit, if INFO=0, the singular values of B.
offset_d  Int32
 
E  Double
(input/output) DOUBLE PRECISION array, dimension (N-1) On entry, the elements of E contain the offdiagonal elements of the bidiagonal matrix whose SVD is desired. On exit, E has been destroyed.
offset_e  Int32
 
U  Double
(output) DOUBLE PRECISION array, dimension (LDU,N) If COMPQ = 'I', then: On exit, if INFO = 0, U contains the left singular vectors of the bidiagonal matrix. For other values of COMPQ, U is not referenced.
offset_u  Int32
 
LDU  Int32
(input) INTEGER The leading dimension of the array U. LDU .GE. 1. If singular vectors are desired, then LDU .GE. max( 1, N ).
VT  Double
(output) DOUBLE PRECISION array, dimension (LDVT,N) If COMPQ = 'I', then: On exit, if INFO = 0, VT' contains the right singular vectors of the bidiagonal matrix. For other values of COMPQ, VT is not referenced.
offset_vt  Int32
 
LDVT  Int32
(input) INTEGER The leading dimension of the array VT. LDVT .GE. 1. If singular vectors are desired, then LDVT .GE. max( 1, N ).
Q  Double
(output) DOUBLE PRECISION array, dimension (LDQ) If COMPQ = 'P', then: On exit, if INFO = 0, Q and IQ contain the left and right singular vectors in a compact form, requiring O(N log N) space instead of 2*N**2. In particular, Q contains all the DOUBLE PRECISION data in LDQ .GE. N*(11 + 2*SMLSIZ + 8*INT(LOG_2(N/(SMLSIZ+1)))) words of memory, where SMLSIZ is returned by ILAENV and is equal to the maximum size of the subproblems at the bottom of the computation tree (usually about 25). For other values of COMPQ, Q is not referenced.
offset_q  Int32
 
IQ  Int32
(output) INTEGER array, dimension (LDIQ) If COMPQ = 'P', then: On exit, if INFO = 0, Q and IQ contain the left and right singular vectors in a compact form, requiring O(N log N) space instead of 2*N**2. In particular, IQ contains all INTEGER data in LDIQ .GE. N*(3 + 3*INT(LOG_2(N/(SMLSIZ+1)))) words of memory, where SMLSIZ is returned by ILAENV and is equal to the maximum size of the subproblems at the bottom of the computation tree (usually about 25). For other values of COMPQ, IQ is not referenced.
offset_iq  Int32
 
WORK  Double
(workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)) If COMPQ = 'N' then LWORK .GE. (4 * N). If COMPQ = 'P' then LWORK .GE. (6 * N). If COMPQ = 'I' then LWORK .GE. (3 * N**2 + 4 * N).
offset_work  Int32
 
IWORK  Int32
(workspace) INTEGER array, dimension (8*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. The update process of divide and conquer failed.
See Also