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| static Real | zeroTolerance () | 
|  | threshold for zero comparison (1e-6 for float and 1e-8 for double)  More... 
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| static void | getRotation (type::Mat< 3, 3, Real > &r, type::Vec< 3, Real > &edgex, type::Vec< 3, Real > &edgey) | 
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| static void | QRDecomposition (const type::Mat< 3, 3, Real > &M, type::Mat< 3, 3, Real > &R) | 
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| static void | QRDecomposition (const type::Mat< 3, 2, Real > &M, type::Mat< 3, 2, Real > &R) | 
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| static void | QRDecomposition (const type::Mat< 2, 2, Real > &M, type::Mat< 2, 2, Real > &R) | 
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| static bool | QRDecomposition_stable (const type::Mat< 3, 3, Real > &M, type::Mat< 3, 3, Real > &R) | 
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| static bool | QRDecomposition_stable (const type::Mat< 3, 2, Real > &M, type::Mat< 3, 2, Real > &R) | 
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| static bool | QRDecomposition_stable (const type::Mat< 2, 2, Real > &M, type::Mat< 2, 2, Real > &R) | 
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| template<Size spatial_dimension, Size material_dimension> | 
| static void | QRDecompositionGradient_dQ (const type::Mat< spatial_dimension, material_dimension, Real > &Q, const type::Mat< material_dimension, material_dimension, Real > &invR, const type::Mat< spatial_dimension, material_dimension, Real > &dM, type::Mat< spatial_dimension, material_dimension, Real > &dQ) | 
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| static Real | polarDecomposition (const type::Mat< 3, 3, Real > &M, type::Mat< 3, 3, Real > &Q, type::Mat< 3, 3, Real > &S) | 
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| static Real | polarDecomposition (const type::Mat< 3, 3, Real > &M, type::Mat< 3, 3, Real > &Q) | 
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| static void | polarDecomposition (const type::Mat< 2, 2, Real > &M, type::Mat< 2, 2, Real > &Q) | 
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| static bool | polarDecomposition_stable (const type::Mat< 3, 3, Real > &M, type::Mat< 3, 3, Real > &Q, type::Mat< 3, 3, Real > &S) | 
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| static bool | polarDecomposition_stable (const type::Mat< 3, 3, Real > &M, type::Mat< 3, 3, Real > &Q) | 
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| static bool | polarDecomposition_stable (const type::Mat< 2, 2, Real > &M, type::Mat< 2, 2, Real > &Q, type::Mat< 2, 2, Real > &S) | 
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| static bool | polarDecomposition_stable (const type::Mat< 2, 2, Real > &M, type::Mat< 2, 2, Real > &Q) | 
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| static void | polarDecomposition (const type::Mat< 3, 2, Real > &M, type::Mat< 3, 2, Real > &Q, type::Mat< 2, 2, Real > &S) | 
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| static void | polarDecompositionGradient_G (const type::Mat< 3, 3, Real > &Q, const type::Mat< 3, 3, Real > &S, type::Mat< 3, 3, Real > &invG) | 
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| static void | polarDecompositionGradient_dQ (const type::Mat< 3, 3, Real > &invG, const type::Mat< 3, 3, Real > &Q, const type::Mat< 3, 3, Real > &dM, type::Mat< 3, 3, Real > &dQ) | 
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| static void | polarDecompositionGradient_dQOverdM (const type::Mat< 3, 3, Real > &Q, const type::Mat< 3, 3, Real > &invG, type::Mat< 9, 9, Real > &J) | 
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| static void | polarDecompositionGradient_dQOverdM (const type::Mat< 3, 3, Real > &Q, const type::Mat< 3, 3, Real > &Sinv, const type::Mat< 9, 9, Real > &dSOverdM, type::Mat< 9, 9, Real > &J) | 
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| static void | polarDecompositionGradient_dS (const type::Mat< 3, 3, Real > &Q, const type::Mat< 3, 3, Real > &S, const type::Mat< 3, 3, Real > &dQ, const type::Mat< 3, 3, Real > &dM, type::Mat< 3, 3, Real > &dS) | 
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| static void | polarDecompositionGradient_dSOverdM (const type::Mat< 3, 3, Real > &Q, const type::Mat< 3, 3, Real > &M, const type::Mat< 3, 3, Real > &invG, type::Mat< 9, 9, Real > &J) | 
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| static void | polarDecompositionGradient_dSOverdM (const type::Mat< 3, 3, Real > &M, const type::Mat< 3, 3, Real > &S, type::Mat< 9, 9, Real > &J) | 
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| static bool | polarDecomposition_stable_Gradient_dQ (const type::Mat< 3, 3, Real > &U, const type::Vec< 3, Real > &Sdiag, const type::Mat< 3, 3, Real > &V, const type::Mat< 3, 3, Real > &dM, type::Mat< 3, 3, Real > &dQ) | 
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| static bool | polarDecomposition_stable_Gradient_dQOverdM (const type::Mat< 3, 3, Real > &U, const type::Vec< 3, Real > &Sdiag, const type::Mat< 3, 3, Real > &V, type::Mat< 9, 9, Real > &dQOverdM) | 
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| static bool | polarDecompositionGradient_dQ (const type::Mat< 3, 2, Real > &U, const type::Vec< 2, Real > &Sdiag, const type::Mat< 2, 2, Real > &V, const type::Mat< 3, 2, Real > &dM, type::Mat< 3, 2, Real > &dQ) | 
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| static bool | polarDecompositionGradient_dQOverdM (const type::Mat< 3, 2, Real > &U, const type::Vec< 2, Real > &Sdiag, const type::Mat< 2, 2, Real > &V, type::Mat< 6, 6, Real > &dQOverdM) | 
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| static void | eigenDecomposition (const type::Mat< 3, 3, Real > &A, type::Mat< 3, 3, Real > &V, type::Vec< 3, Real > &diag) | 
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| static void | eigenDecomposition (const type::Mat< 2, 2, Real > &A, type::Mat< 2, 2, Real > &V, type::Vec< 2, Real > &diag) | 
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| static void | eigenDecomposition_iterative (const type::Mat< 3, 3, Real > &M, type::Mat< 3, 3, Real > &V, type::Vec< 3, Real > &diag) | 
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| static void | eigenDecomposition_iterative (const type::Mat< 2, 2, Real > &M, type::Mat< 2, 2, Real > &V, type::Vec< 2, Real > &diag) | 
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| static void | SVD (const type::Mat< 3, 3, Real > &F, type::Mat< 3, 3, Real > &U, type::Vec< 3, Real > &S, type::Mat< 3, 3, Real > &V) | 
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| static bool | SVD_stable (const type::Mat< 3, 3, Real > &F, type::Mat< 3, 3, Real > &U, type::Vec< 3, Real > &S, type::Mat< 3, 3, Real > &V) | 
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| static bool | SVD_stable (const type::Mat< 2, 2, Real > &F, type::Mat< 2, 2, Real > &U, type::Vec< 2, Real > &S, type::Mat< 2, 2, Real > &V) | 
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| static void | SVD (const type::Mat< 3, 2, Real > &F, type::Mat< 3, 2, Real > &U, type::Vec< 2, Real > &S, type::Mat< 2, 2, Real > &V) | 
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| static bool | SVD_stable (const type::Mat< 3, 2, Real > &F, type::Mat< 3, 2, Real > &U, type::Vec< 2, Real > &S, type::Mat< 2, 2, Real > &V) | 
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| static bool | SVDGradient_dUdV (const type::Mat< 3, 3, Real > &U, const type::Vec< 3, Real > &S, const type::Mat< 3, 3, Real > &V, const type::Mat< 3, 3, Real > &dM, type::Mat< 3, 3, Real > &dU, type::Mat< 3, 3, Real > &dV) | 
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| static bool | SVDGradient_dUdVOverdM (const type::Mat< 3, 3, Real > &U, const type::Vec< 3, Real > &S, const type::Mat< 3, 3, Real > &V, type::Mat< 9, 9, Real > &dUOverdM, type::Mat< 9, 9, Real > &dVOverdM) | 
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| static bool | SVDGradient_dUdV (const type::Mat< 3, 2, Real > &U, const type::Vec< 2, Real > &S, const type::Mat< 2, 2, Real > &V, const type::Mat< 3, 2, Real > &dM, type::Mat< 3, 2, Real > &dU, type::Mat< 2, 2, Real > &dV) | 
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| static bool | SVDGradient_dUdVOverdM (const type::Mat< 3, 2, Real > &U, const type::Vec< 2, Real > &S, const type::Mat< 2, 2, Real > &V, type::Mat< 6, 6, Real > &dUOverdM, type::Mat< 4, 6, Real > &dVOverdM) | 
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| static int | symmetricDiagonalization (const type::Mat< 3, 3, Real > &A, type::Mat< 3, 3, Real > &Q, type::Vec< 3, Real > &w) | 
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| static void | PSDProjection (type::Mat< 3, 3, Real > &A) | 
|  | project a symmetric 3x3 matrix to a PSD (symmetric, positive semi-definite)  More... 
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| static void | PSDProjection (type::Mat< 2, 2, Real > &A) | 
|  | project a symmetric 2x2 matrix to a PSD (symmetric, positive semi-definite)  More... 
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| static void | PSDProjection (Real &A00, Real &A01, Real &A10, Real &A11) | 
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| static void | PSDProjection (type::Mat< 1, 1, Real > &) | 
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| static void | NSDProjection (type::Mat< 3, 3, Real > &A) | 
|  | project a symmetric 3x3 matrix to a NSD (symmetric, negative semi-definite)  More... 
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| static void | NSDProjection (type::Mat< 2, 2, Real > &A) | 
|  | project a symmetric 2x2 matrix to a NSD (symmetric, negative semi-definite)  More... 
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| static void | NSDProjection (Real &A00, Real &A01, Real &A10, Real &A11) | 
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| static void | NSDProjection (type::Mat< 1, 1, Real > &) | 
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