FDenseMatrixSolver::SolvePositiveDefinite

Solve AX = B, for positive-definite NxN matrix A, and Nx1 column vectors B and X.

Windows
MacOS
Linux

References

Module

Chaos

Header

/Engine/Source/Runtime/Experimental/Chaos/Public/Chaos/DenseMatrix.h

Include

#include "Chaos/DenseMatrix.h"

Syntax

template<int32 T_EA, int32 T_EB, int32 T_EX>
static bool SolvePositiveDefinite
(
    const TDenseMatrix< T_EA > & A,
    const TDenseMatrix< T_EB > & B,
    TDenseMatrix< T_EX > & X
)

Remarks

Solve AX = B, for positive-definite NxN matrix A, and Nx1 column vectors B and X.

For positive definite A, A = GGt, where G is the Cholesky factor and lower triangular. We can solve GGtX = B by first solving GY = B, and then GtX = Y.

E.g., this can be used to solve constraint equations of the form J.I.Jt.X = B where J is a Jacobian (Jt its transpose), I is an Inverse mas matrix, and B the residual. In this case, I is symmetric positive definite, and therefore so is JIJt.

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