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DLASD1Run Method

Purpose ======= DLASD1 computes the SVD of an upper bidiagonal N-by-M matrix B, where N = NL + NR + 1 and M = N + SQRE. DLASD1 is called from DLASD0. A related subroutine DLASD7 handles the case in which the singular values (and the singular vectors in factored form) are desired. DLASD1 computes the SVD as follows: ( D1(in) 0 0 0 ) B = U(in) * ( Z1' a Z2' b ) * VT(in) ( 0 0 D2(in) 0 ) = U(out) * ( D(out) 0) * VT(out) where Z' = (Z1' a Z2' b) = u' VT', and u is a vector of dimension M with ALPHA and BETA in the NL+1 and NL+2 th entries and zeros elsewhere; and the entry b is empty if SQRE = 0. The left singular vectors of the original matrix are stored in U, and the transpose of the right singular vectors are stored in VT, and the singular values are in D. The algorithm consists of three stages: The first stage consists of deflating the size of the problem when there are multiple singular values or when there are zeros in the Z vector. For each such occurence the dimension of the secular equation problem is reduced by one. This stage is performed by the routine DLASD2. The second stage consists of calculating the updated singular values. This is done by finding the square roots of the roots of the secular equation via the routine DLASD4 (as called by DLASD3). This routine also calculates the singular vectors of the current problem. The final stage consists of computing the updated singular vectors directly using the updated singular values. The singular vectors for the current problem are multiplied with the singular vectors from the overall problem.

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(
	int NL,
	int NR,
	int SQRE,
	ref double[] D,
	int offset_d,
	ref double ALPHA,
	ref double BETA,
	ref double[] U,
	int offset_u,
	int LDU,
	ref double[] VT,
	int offset_vt,
	int LDVT,
	ref int[] IDXQ,
	int offset_idxq,
	ref int[] IWORK,
	int offset_iwork,
	ref double[] WORK,
	int offset_work,
	ref int INFO
)
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Parameters

NL  Int32
(input) INTEGER The row dimension of the upper block. NL .GE. 1.
NR  Int32
(input) INTEGER The row dimension of the lower block. NR .GE. 1.
SQRE  Int32
(input) INTEGER = 0: the lower block is an NR-by-NR square matrix. = 1: the lower block is an NR-by-(NR+1) rectangular matrix. The bidiagonal matrix has row dimension N = NL + NR + 1, and column dimension M = N + SQRE.
D  Double
(input/output) DOUBLE PRECISION array, dimension (N = NL+NR+1). On entry D(1:NL,1:NL) contains the singular values of the upper block; and D(NL+2:N) contains the singular values of the lower block. On exit D(1:N) contains the singular values of the modified matrix.
offset_d  Int32
 
ALPHA  Double
(input/output) DOUBLE PRECISION Contains the diagonal element associated with the added row.
BETA  Double
(input/output) DOUBLE PRECISION Contains the off-diagonal element associated with the added row.
U  Double
(input/output) DOUBLE PRECISION array, dimension(LDU,N) On entry U(1:NL, 1:NL) contains the left singular vectors of the upper block; U(NL+2:N, NL+2:N) contains the left singular vectors of the lower block. On exit U contains the left singular vectors of the bidiagonal matrix.
offset_u  Int32
 
LDU  Int32
(input) INTEGER The leading dimension of the array U. LDU .GE. max( 1, N ).
VT  Double
(input/output) DOUBLE PRECISION array, dimension(LDVT,M) where M = N + SQRE. On entry VT(1:NL+1, 1:NL+1)' contains the right singular vectors of the upper block; VT(NL+2:M, NL+2:M)' contains the right singular vectors of the lower block. On exit VT' contains the right singular vectors of the bidiagonal matrix.
offset_vt  Int32
 
LDVT  Int32
(input) INTEGER The leading dimension of the array VT. LDVT .GE. max( 1, M ).
IDXQ  Int32
(output) INTEGER array, dimension(N) This contains the permutation which will reintegrate the subproblem just solved back into sorted order, i.e. D( IDXQ( I = 1, N ) ) will be in ascending order.
offset_idxq  Int32
 
IWORK  Int32
(workspace) INTEGER array, dimension( 4 * N )
offset_iwork  Int32
 
WORK  Double
(workspace) DOUBLE PRECISION array, dimension( 3*M**2 + 2*M )
offset_work  Int32
 
INFO  Int32
(output) INTEGER = 0: successful exit. .LT. 0: if INFO = -i, the i-th argument had an illegal value. .GT. 0: if INFO = 1, an singular value did not converge
See Also