computes the eigenvalues of a symmetric tridiagonal
* matrix T. The user may ask for all eigenvalues, all eigenvalues
in the half-open interval (VL, VU], or the IL-th through IU-th eigenvalues.
The Molgedey and Schuster decorrelation algorithm, having square mixing matrix and no noise . Truncation is used for the time shifted matrix, and it is forced to be symmetric . The delay Tau is estimated .
The number of independent components are calculated using Bayes Information Criterion (BIC), with PCA for dimension reduction.
Computes estimates for the number of forests of a graph, input as a 0-1 incidence matrix. Notes: Compile in C++, "g++ -o span_forest span_forest.c". The program does not demand that the matrix is symmetric with 0 diagonal, but uses only the upper triangular part.
平均因子分解法，適用于正定矩陣First, let s recall the definition of the Cholesky decomposition: Given a symmetric positive definite square matrix X, the Cholesky decomposition of X is the factorization X=U U, where U is the square root matrix of X, and satisfies:
(1) U U = X
(2) U is upper triangular (that is, it has all zeros below the diagonal).
It seems that the assumption of positive definiteness is necessary. Actually, it is "positive definite" which guarantees the existence of such kind of decomposition.
zemax源碼：
This DLL models an anamorphic aspheric surface.
This surface is essentially an even aspheric surface with different terms for
the x and y directions.
The sag is given by:
Z = ((CX*x*x)+(CY*y*y)) / (1 + sqrt(1-((1+KX)*CX*CX*x*x)-((1+KY)*CY*CY*y*y)))
+ AR*( (1 - AP)*x*x + (1 + AP)*y*y )^2
+ BR*( (1 - BP)*x*x + (1 + BP)*y*y )^3
+ CR*( (1 - CP)*x*x + (1 + CP)*y*y )^4
+ DR*( (1 - DP)*x*x + (1 + DP)*y*y )^5
Note the terms AR, BR, CR, and DR ... have units of length to the -3, -5, -7, and -9 power.
The terms AP, BP, CP, and DP are dimensionless.
The surface is rotationally symmetric only if AP = BP = CP = DP == 0 and CX = CY and KX = KY.
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