SingularValueDecomp
SingularValueDecomp(a, i, j, j2)
SingularValueDecomp computes the singular value decomposition of a matrix. Singular value decomposition is often used with sets of equations or matrices that are singular or ill-conditioned (that is, very close to singular). It factors a matrix «a», indexed by «i» and «j», with Size(i) >= Size(i), into three matrices, U, W, and V, such that:
- a = U . W . V
where U and V are orthogonal matrices and W is a diagonal matrix. U is dimensioned by «i» and «j», W by «j» and «j2», and V by «j» and «j2». In Analytica notation:
Variable A := Sum(Sum(U*W, J)*Transpose(V, J, J2), J2)
The index «j2» must be the same size as «j» and is used to index the resulting W and V arrays. SingularValueDecomp returns an array of three elements indexed by a special system index named SvdIndex with each element, U, W, and V, being a reference to the corresponding array.
Use the # (dereference) operator to obtain the matrix value from each reference, as in:
Index J2 := CopyIndex(J)Variable SvdResult := SingularValueDecomp(A, I, J, J2)Variable U := #SvdResult[SvdIndex = 'U']Variable W := #SvdResult[SvdIndex = 'W']Variable V := #SvdResult[SvdIndex = 'V']
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