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']

See Also

• EigenDecomp
• Decompose
• Transpose
• Category:Matrix Functions