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romericromeric
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Implement fast 2x2 svd. Add test
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‎Fastor/expressions/linalg_ops/linalg_ops.h

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#include "Fastor/expressions/linalg_ops/unary_norm_op.h"
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#include "Fastor/expressions/linalg_ops/unary_qr_op.h"
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#include "Fastor/expressions/linalg_ops/unary_det_op.h"
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#include "Fastor/expressions/linalg_ops/unary_svd_op.h"
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#include "Fastor/expressions/linalg_ops/binary_cross_op.h"
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#include "Fastor/expressions/linalg_ops/linalg_traits.h"

‎Fastor/expressions/linalg_ops/unary_svd_op.h

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#ifndef UNARY_SVD_OP_H
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#define UNARY_SVD_OP_H
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#include "Fastor/meta/meta.h"
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#include "Fastor/backend/inner.h"
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#include "Fastor/backend/lufact.h"
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#include "Fastor/simd_vector/SIMDVector.h"
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#include "Fastor/tensor/AbstractTensor.h"
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#include "Fastor/tensor/Aliasing.h"
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#include "Fastor/tensor/Tensor.h"
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#include "Fastor/tensor/TensorTraits.h"
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#include "Fastor/expressions/expression_traits.h"
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#include "Fastor/expressions/linalg_ops/linalg_computation_types.h"
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#include "Fastor/expressions/linalg_ops/unary_det_op.h"
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#include "Fastor/expressions/linalg_ops/unary_trans_op.h"
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namespace Fastor {
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// SVD
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template<typename T, size_t M, enable_if_t_<M==2, bool> = false >
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FASTOR_INLINE void svd(const Tensor<T,M,M> &A, Tensor<T,M,M> &U, Tensor<T,M,M> &S, Tensor<T,M,M> &V) {
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constexpr T Epsilon_v = std::numeric_limits<T>::epsilon();
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const T f00 = A(0, 0);
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const T f01 = A(0, 1);
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const T f10 = A(1, 0);
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const T f11 = A(1, 1);
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// If matrix is diagonal, SVD is trivial
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if (std::abs(f01 - f10) < Epsilon_v && std::abs(f01) < Epsilon_v)
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{
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// Compute U
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U(0,0) = f00 < 0 ? -1. : 1.;
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U(0,1) = 0.;
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U(1,0) = 0.;
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U(1,1) = f11 < 0. ? -1. : 1.;
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// Compute S
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S(0,0) = std::abs(f00);
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S(0,1) = 0;
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S(1,0) = 0;
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S(1,1) = std::abs(f11);
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// Compute V
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V.eye2();
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}
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// Otherwise, we need to compute A^T*A
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else
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{
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T j = f00 * f00 + f01 * f01;
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T k = f10 * f10 + f11 * f11;
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T v_c = f00 * f10 + f01 * f11;
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// Check to see if A^T*A is diagonal
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if (std::abs(v_c) < Epsilon_v)
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{
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// Compute S
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T s1 = std::sqrt(j);
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T s2 = std::abs(j - k) < Epsilon_v ? s1 : std::sqrt(k);
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S(0,0) = s1;
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S(0,1) = 0;
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S(1,0) = 0;
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S(1,1) = s2;
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// Compute U
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U.eye2();
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// Compute V
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V(0,0) = f00 / s1;
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V(0,1) = f10 / s2;
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V(1,0) = f01 / s1;
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V(1,1) = f11 / s2;
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}
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// Otherwise, solve quadratic equation for eigenvalues
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else
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{
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T jmk = j - k;
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T jpk = j + k;
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T root = std::sqrt(jmk * jmk + 4. * v_c * v_c);
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T eig1 = (jpk + root) * 0.5;
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T eig2 = (jpk - root) * 0.5;
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// Compute S
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T s1 = std::sqrt(eig1);
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T s2 = std::abs(root) < Epsilon_v ? s1 : ( eig2 > 0 ? std::sqrt(eig2) : Epsilon_v);
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S(0,0) = s1;
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S(0,1) = 0;
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S(1,0) = 0;
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S(1,1) = s2;
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// Compute U - use eigenvectors of A^T*A as U
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T v_s = eig1 - j;
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T len = std::max(std::sqrt(v_s * v_s + v_c * v_c), Epsilon_v);
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v_c /= len;
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v_s /= len;
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U(0,0) = v_c;
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U(0,1) = -v_s;
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U(1,0) = v_s;
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U(1,1) = v_c;
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// Compute V - as A * U / s
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const T cc = (f00 * v_c + f10 * v_s) / s1;
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const T cs = (f01 * v_c + f11 * v_s) / s1;
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if (std::abs(s2) > Epsilon_v)
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{
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V(0,0) = cc;
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V(0,1) = (f10* v_c - f00 * v_s) / s2;
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V(1,0) = cs;
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V(1,1) = (f11 * v_c - f01 * v_s) / s2;
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}
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else
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{
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V(0,0) = cc;
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V(0,1) = cs;
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V(1,0) = cs;
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V(1,1) = -cc;
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}
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}
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}
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}
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// Signed SVD
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template<typename T, size_t M>
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FASTOR_INLINE void ssvd(const Tensor<T,M,M> &A, Tensor<T,M,M> &U, Tensor<T,M,M> &S, Tensor<T,M,M> &V) {
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// Same as above but avoiding the L matrix
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svd(A, U, S, V);
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// See where to pull the reflection out of
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const T detU = determinant(U);
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const T detV = determinant(V);
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if (detU >= 0 && detV >= 0)
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{
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// No reflection svd == svd_rv, return
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return;
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}
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Tensor<T, M, M> L = matmul(U, transpose(V));
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const T lastColumn = determinant(L);
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if (detU < 0 && detV > 0)
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{
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U(all, M - 1) *= lastColumn;
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}
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else if (detU > 0 && detV < 0)
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{
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V(all, M - 1) *= lastColumn;
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}
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// Push the reflection to the diagonal
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S(M - 1, M - 1) *= lastColumn;
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}
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//-----------------------------------------------------------------------------------------------------------//
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} // end of namespace Fastor
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#endif // UNARY_SVD_OP_H

‎tests/test_linalg/test_linalg.cpp

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FASTOR_EXIT_ASSERT(std::abs(determinant(M) - 216) < Tol);
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}
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// svd
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{
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Tensor<T,2,2> A; A = {{23.,3.},{3.5,56.}};
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Tensor<T,2,2> U,S,V;
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svd(A,U,S,V);
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Tensor<T,2,2> rec = U % S % trans(V);
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FASTOR_EXIT_ASSERT(std::abs(rec(0,0) - A(0,0)) < BigTol);
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FASTOR_EXIT_ASSERT(std::abs(rec(0,1) - A(0,1)) < BigTol);
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FASTOR_EXIT_ASSERT(std::abs(rec(1,0) - A(1,0)) < BigTol);
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FASTOR_EXIT_ASSERT(std::abs(rec(1,1) - A(1,1)) < BigTol);
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}
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print(FGRN(BOLD("All tests passed successfully")));
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}

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