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Compute the matrix inverse for a stack of matrices (broadcast inverse) #31

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Compute the matrix inverse for a stack of matrices (broadcast inverse) #31

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24 changes: 24 additions & 0 deletions benchmarks/broadcast_small_inv.cpp
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Original file line number Diff line number Diff line change
@@ -0,0 +1,24 @@
#include "./bench_common.hpp"

template <int N, long dim>
static void inv(benchmark::State &state) {
nda::array<double, 3> W(dim, N, N), Wi(dim, N, N);
for (int k = 0; k < dim; ++k) {
for (int i = 0; i < N; ++i)
for (int j = 0; j < N; ++j) W(k, i, j) = (i > j ? 0.5 + i + 2.5 * j : i * 0.8 - j - 0.5);
}

while (state.KeepRunning()) {
Wi = inverse(W);
}
}

BENCHMARK_TEMPLATE(inv, 1, 100);
BENCHMARK_TEMPLATE(inv, 1, 10000);
BENCHMARK_TEMPLATE(inv, 1, 1000000);
BENCHMARK_TEMPLATE(inv, 2, 100);
BENCHMARK_TEMPLATE(inv, 2, 10000);
BENCHMARK_TEMPLATE(inv, 2, 1000000);
BENCHMARK_TEMPLATE(inv, 3, 100);
BENCHMARK_TEMPLATE(inv, 3, 10000);
BENCHMARK_TEMPLATE(inv, 3, 1000000);
8 changes: 8 additions & 0 deletions c++/nda/linalg/det_and_inverse.hpp
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Expand Up @@ -173,6 +173,14 @@ namespace nda {
return r;
}

template <Array A>
auto inverse(A const &a) {
auto r = make_regular(a);
auto long_axis = stdutil::mpop<2>(r.indexmap().lengths());
for_each(long_axis, [&r, _ = range()](auto &&... i) {inverse_in_place(make_matrix_view(r(i..., _, _))); });
return r;
}

} // namespace nda

namespace nda::clef {
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24 changes: 24 additions & 0 deletions test/c++/nda_linear_algebra.cpp
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Expand Up @@ -327,6 +327,30 @@ TEST(Inverse, Small) { //NOLINT

// ==============================================================

TEST(Inverse, BroadcastInverse) { //NOLINT

for (auto N : {1, 2, 3, 4}) {

long dim = 100000;
nda::array<double, 3> W(dim, N, N);

for (int k = 0; k < dim; ++k) {
for (int i = 0; i < N; ++i)
for (int j = 0; j < N; ++j) W(k, i, j) = (i > j ? 0.5 + i + 2.5 * j : i * 0.8 - j - 0.5);
}

auto Wi = inverse(W);
auto Wii = inverse(Wi);
for ( int k = 0; k < dim; ++k) {
EXPECT_NEAR(determinant(make_matrix_view(Wi(k, range(), range()))), 1.0/determinant(make_matrix_view(W(k, range(), range()))), 1.e-12);
EXPECT_ARRAY_NEAR(make_matrix_view(W(k,range(),range())) * make_matrix_view(Wi(k, range(), range())), nda::eye<double>(N), 1.e-13);
EXPECT_ARRAY_NEAR(make_matrix_view(Wii(k,range(),range())), make_matrix_view(W(k, range(), range())), 1.e-12);
}
}
}

// ==============================================================

TEST(Matvecmul, Promotion) { //NOLINT

matrix<int> Ai = {{1, 2}, {3, 4}};
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