SingularValueDecomp
Computes the singular value decomposition of a matrix.
SingularValueDecomp(a, i, j, j2)
SingularValueDecomp() (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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