ltl::SVDecomposition< T > Class Template Reference

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)

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].
*  

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  )

static

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

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  )

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.

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  )

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(), and SVD_SIGN.

template<typename T >

static T ltl::SVDecomposition< T >::pythag ( const T  a, const T  b  )

inlinestaticprotected

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