ltl::SVDecomposition< T > Class Template Reference
[Singular Value Decomposition]

List of all members.

Static Public Member Functions

• template<int M, int N> static FVector< T, N > solve (FMatrix< T, M, N > A, const FVector< T, M > &b)
• template<int M, int N> static FVector< T, N > svbksb (const FMatrix< T, M, N > &U, const FVector< T, N > &W, const FMatrix< T, N, N > &V, const FVector< T, M > &b)
• template<int M, int N> static void svdcmp (FMatrix< T, M, N > &A, FVector< T, N > &W, FMatrix< T, N, N > &V)

Static Protected Member Functions

• static T pythag (const T a, const T b)

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Detailed Description

template<typename T>
class ltl::SVDecomposition< T >

Perform Singular Value Decomposition and solve linear systems. Adapted from Numerical Recipes.

Example:

      FVector<double,4> x(2.);  // target

      FMatrix<double,4,4> A;    // the matrix
      A = 1., 2.,  3.,  2.,
          5., 11., 7.,  13.,
          9., 7.,  5.,  1.,
          7., 13., 17., 11.;
      FVector<double,4> b(dot(A, x));   // construct b

      x = 0.;
      x = SVDecomposition<double>::solve(A, B);   // solve Ax = b
      // x should be [2,2].

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Member Function Documentation

template<typename T >

template<int M, int N>

FVector< T, N > ltl::SVDecomposition< T >::solve	(	FMatrix< T, M, N >	A,
		const FVector< T, M > &	b
	)			[inline, static]

Given A[m][n], b[m], solves A x = b using SVD. returns solution vector x[n] No input quantities are changed.

References ltl::SVDecomposition< T >::svbksb(), and ltl::SVDecomposition< T >::svdcmp().

template<typename T >

template<int M, int N>

FVector< T, N > ltl::SVDecomposition< T >::svbksb	(	const FMatrix< T, M, N > &	U,
		const FVector< T, N > &	W,
		const FMatrix< T, N, N > &	V,
		const FVector< T, M > &	b
	)			[inline, static]

Given A[m][n], b[m], solves A x = b in the SVD form U W V'x = b so x = V U'b/W U[m][n], W[n][n] and V[n][n] No input quantities are changed.

Referenced by ltl::SVDecomposition< T >::solve().

template<typename T >

template<int M, int N>

void ltl::SVDecomposition< T >::svdcmp	(	FMatrix< T, M, N > &	A,
		FVector< T, N > &	W,
		FMatrix< T, N, N > &	V
	)			[inline, static]

Given matrix A[m][n], m>=n, using svd decomposition A = U W V' to get U[m][n], W[n][n] and V[n][n], where U occupies the position of A. NOTE: if m<n, A should be filled up to square with zero rows. A[m][n] has been destroyed by U[m][n] after the decomposition.

References ltl::max(), ltl::min(), ltl::SVDecomposition< T >::pythag(), and SVD_SIGN.

Referenced by ltl::SVDecomposition< T >::solve().

template<typename T >

static T ltl::SVDecomposition< T >::pythag	(	const T	a,
		const T	b
	)			[inline, static, protected]

Computes (a^2 + b^2)^1/2 without destructive underflow or overflow

Referenced by ltl::SVDecomposition< T >::svdcmp().