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Eigen3_operations_unittest.cc
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Eigen3_operations_unittest.cc
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#include <shogun/lib/config.h>
#include <shogun/mathematics/Math.h>
#include <shogun/mathematics/linalg/LinalgNamespace.h>
#include <shogun/mathematics/linalg/LinalgSpecialPurposes.h>
#include <gtest/gtest.h>
#include <shogun/lib/ShogunException.h>
using namespace shogun;
using namespace linalg;
using namespace Eigen;
TEST(LinalgBackendEigen, SGVector_add)
{
const float64_t alpha = 0.3;
const float64_t beta = -1.5;
SGVector<float64_t> A(9);
SGVector<float64_t> B(9);
for (index_t i = 0; i < 9; ++i)
{
A[i] = i;
B[i] = 0.5*i;
}
auto result = add(A, B, alpha, beta);
for (index_t i = 0; i < 9; ++i)
EXPECT_NEAR(alpha*A[i]+beta*B[i], result[i], 1e-15);
}
TEST(LinalgBackendEigen, SGMatrix_add)
{
const float64_t alpha = 0.3;
const float64_t beta = -1.5;
const index_t nrows = 2, ncols = 3;
SGMatrix<float64_t> A(nrows, ncols);
SGMatrix<float64_t> B(nrows, ncols);
for (index_t i = 0; i < nrows*ncols; ++i)
{
A[i] = i;
B[i] = 0.5*i;
}
auto result = add(A, B, alpha, beta);
for (index_t i = 0; i < nrows*ncols; ++i)
EXPECT_NEAR(alpha*A[i]+beta*B[i], result[i], 1e-15);
}
TEST(LinalgBackendEigen, SGVector_add_in_place)
{
const float64_t alpha = 0.3;
const float64_t beta = -1.5;
SGVector<float64_t> A(9), B(9), C(9);
for (index_t i = 0; i < 9; ++i)
{
A[i] = i;
B[i] = 0.5*i;
C[i] = i;
}
add(A, B, A, alpha, beta);
for (index_t i = 0; i < 9; ++i)
EXPECT_NEAR(alpha*C[i]+beta*B[i], A[i], 1e-15);
}
TEST(LinalgBackendEigen, SGMatrix_add_in_place)
{
const float64_t alpha = 0.3;
const float64_t beta = -1.5;
const index_t nrows = 2, ncols = 3;
SGMatrix<float64_t> A(nrows, ncols);
SGMatrix<float64_t> B(nrows, ncols);
SGMatrix<float64_t> C(nrows, ncols);
for (index_t i = 0; i < nrows*ncols; ++i)
{
A[i] = i;
B[i] = 0.5*i;
C[i] = i;
}
add(A, B, A, alpha, beta);
for (index_t i = 0; i < nrows*ncols; ++i)
EXPECT_NEAR(alpha*C[i]+beta*B[i], A[i], 1e-15);
}
TEST(LinalgBackendEigen, SGVector_add_col_vec_allocated)
{
const float64_t alpha = 0.7;
const float64_t beta = -1.2;
const index_t nrows = 2, ncols = 3;
const index_t col = 1;
SGMatrix<float64_t> A(nrows, ncols);
SGVector<float64_t> b(nrows);
SGVector<float64_t> result(nrows);
for (index_t i = 0; i < nrows*ncols; ++i)
A[i] = i;
for (index_t i = 0; i < nrows; ++i)
b[i] = 0.5*i;
add_col_vec(A, col, b, result, alpha, beta);
for (index_t i = 0; i < nrows; ++i)
EXPECT_NEAR(result[i], alpha*A.get_element(i, col)+beta*b[i], 1e-15);
}
TEST(LinalgBackendEigen, SGVector_add_col_vec_in_place)
{
const float64_t alpha = 0.6;
const float64_t beta = -1.3;
const index_t nrows = 2, ncols = 3;
const index_t col = 1;
SGMatrix<float64_t> A(nrows, ncols);
SGVector<float64_t> b(nrows);
for (index_t i = 0; i < nrows*ncols; ++i)
A[i] = i;
for (index_t i = 0; i < nrows; ++i)
b[i] = 0.5*i;
add_col_vec(A, col, b, b, alpha, beta);
for (index_t i = 0; i < nrows; ++i)
EXPECT_NEAR(b[i], alpha*A.get_element(i, col)+beta*0.5*i, 1e-15);
}
TEST(LinalgBackendEigen, SGMatrix_add_col_vec_allocated)
{
const float64_t alpha = 0.8;
const float64_t beta = -1.4;
const index_t nrows = 2, ncols = 3;
const index_t col = 1;
SGMatrix<float64_t> A(nrows, ncols);
SGVector<float64_t> b(nrows);
SGMatrix<float64_t> result(nrows, ncols);
for (index_t i = 0; i < nrows*ncols; ++i)
A[i] = i;
for (index_t i = 0; i < nrows; ++i)
b[i] = 0.5*i;
add_col_vec(A, col, b, result, alpha, beta);
for (index_t i = 0; i < nrows; ++i)
EXPECT_NEAR(
result.get_element(i, col),
alpha * A.get_element(i, col) + beta * b[i], 1e-15);
}
TEST(LinalgBackendEigen, SGMatrix_add_col_vec_in_place)
{
const float64_t alpha = 0.9;
const float64_t beta = -1.7;
const index_t nrows = 2, ncols = 3;
const index_t col = 1;
SGMatrix<float64_t> A(nrows, ncols);
SGVector<float64_t> b(nrows);
for (index_t i = 0; i < nrows*ncols; ++i)
A[i] = i;
for (index_t i = 0; i < nrows; ++i)
b[i] = 0.5*i;
add_col_vec(A, col, b, A, alpha, beta);
for (index_t i = 0; i < nrows; ++i)
for (index_t j = 0; j < ncols; ++j)
{
float64_t a = i+j*nrows;
if (j == col)
EXPECT_NEAR(A.get_element(i, j), alpha*a+beta*b[i], 1e-15);
else
EXPECT_EQ(A.get_element(i,j), a);
}
}
TEST(LinalgBackendEigen, add_vector)
{
const float64_t alpha = 0.7;
const float64_t beta = -1.2;
const index_t nrows = 2, ncols = 3;
SGMatrix<float64_t> A(nrows, ncols);
SGMatrix<float64_t> result(nrows, ncols);
SGVector<float64_t> b(nrows);
for (index_t i = 0; i < nrows; ++i)
b[i] = 0.5 * i;
for (index_t j = 0; j < ncols; ++j)
for (index_t i = 0; i < nrows; ++i)
{
A(i, j) = i + j * ncols;
result(i, j) = alpha * A(i, j) + beta * b[i];
}
add_vector(A, b, A, alpha, beta);
for (index_t i = 0; i < nrows * ncols; ++i)
EXPECT_NEAR(A[i], result[i], 1e-15);
}
TEST(LinalgBackendEigen, SGVector_add_scalar)
{
const index_t n = 4;
float64_t s = -0.3;
SGVector<float64_t> a(n);
for (index_t i = 0; i < (index_t)a.size(); ++i)
a[i] = i;
SGVector<float64_t> orig = a.clone();
add_scalar(a, s);
for (index_t i = 0; i < (index_t)a.size(); ++i)
EXPECT_NEAR(a[i], orig[i] + s, 1e-15);
}
TEST(LinalgBackendEigen, SGMatrix_add_scalar)
{
const index_t r = 4, c = 3;
float64_t s = 0.4;
SGMatrix<float64_t> a(r, c);
for (index_t i = 0; i < (index_t)a.size(); ++i)
a[i] = i;
SGMatrix<float64_t> orig = a.clone();
add_scalar(a, s);
for (index_t i = 0; i < (index_t)a.size(); ++i)
EXPECT_NEAR(a[i], orig[i] + s, 1e-15);
}
TEST(LinalgBackendEigen, center_matrix)
{
const index_t n = 3;
float64_t data[] = {0.8192343, 0.13191962, 0.50888604,
0.16857468, 0.24107738, 0.89455301,
0.40657379, 0.07902286, 0.24319651};
float64_t result[] = {0.25587541, -0.1173183, -0.13855711,
-0.34283925, 0.04378442, 0.29905482,
0.08696383, 0.07353387, -0.16049771};
SGMatrix<float64_t> m(data, n, n, false);
center_matrix(m);
for (index_t i = 0; i < (index_t)m.size(); ++i)
EXPECT_NEAR(m[i], result[i], 1e-8);
}
TEST(LinalgBackendEigen, SGMatrix_cholesky_llt_lower)
{
const index_t size=2;
SGMatrix<float64_t> m(size, size);
m(0,0)=2.0;
m(0,1)=1.0;
m(1,0)=1.0;
m(1,1)=2.5;
//lower triangular cholesky decomposition
SGMatrix<float64_t> L = cholesky_factor(m);
Map<MatrixXd> map_A(m.matrix,m.num_rows,m.num_cols);
Map<MatrixXd> map_L(L.matrix,L.num_rows,L.num_cols);
EXPECT_NEAR((map_A-map_L*map_L.transpose()).norm(),
0.0, 1E-15);
EXPECT_EQ(m.num_rows, L.num_rows);
EXPECT_EQ(m.num_cols, L.num_cols);
}
TEST(LinalgBackendEigen, SGMatrix_cholesky_llt_upper)
{
const index_t size=2;
SGMatrix<float64_t> m(size, size);
m(0,0)=2.0;
m(0,1)=1.0;
m(1,0)=1.0;
m(1,1)=2.5;
//upper triangular cholesky decomposition
SGMatrix<float64_t> U = cholesky_factor(m,false);
Map<MatrixXd> map_A(m.matrix,m.num_rows,m.num_cols);
Map<MatrixXd> map_U(U.matrix,U.num_rows,U.num_cols);
EXPECT_NEAR((map_A-map_U.transpose()*map_U).norm(),
0.0, 1E-15);
EXPECT_EQ(m.num_rows, U.num_rows);
EXPECT_EQ(m.num_cols, U.num_cols);
}
TEST(LinalgBackendEigen, SGMatrix_cholesky_solver)
{
const index_t size=2;
SGMatrix<float64_t> A(size, size);
A(0,0)=2.0;
A(0,1)=1.0;
A(1,0)=1.0;
A(1,1)=2.5;
SGVector<float64_t> b(size);
b[0] = 10;
b[1] = 13;
SGVector<float64_t> x_ref(size);
x_ref[0] = 3;
x_ref[1] = 4;
SGMatrix<float64_t> L = cholesky_factor(A);
SGVector<float64_t> x_cal = cholesky_solver(L, b);
EXPECT_NEAR(x_ref[0], x_cal[0], 1E-15);
EXPECT_NEAR(x_ref[1], x_cal[1], 1E-15);
EXPECT_EQ(x_ref.size(), x_cal.size());
}
TEST(LinalgBackendEigen, SGMatrix_cross_entropy)
{
SGMatrix<float64_t> A(4, 3);
SGMatrix<float64_t> B(4, 3);
int32_t size = A.num_rows * A.num_cols;
for (float64_t i = 0; i < size; ++i)
{
A[i] = i / size;
B[i] = (i / size) * 0.5;
}
float64_t ref = 0;
for (int32_t i = 0; i < size; i++)
ref += A[i] * CMath::log(B[i] + 1e-30);
ref *= -1;
auto result = linalg::cross_entropy(A, B);
EXPECT_NEAR(ref, result, 1e-15);
}
TEST(LinalgBackendEigen, SGVector_dot)
{
const index_t size = 3;
SGVector<int32_t> a(size), b(size);
a.range_fill(0);
b.range_fill(0);
auto result = dot(a, b);
EXPECT_NEAR(result, 5, 1E-15);
}
TEST(LinalgBackendEigen, eigensolver)
{
const index_t n = 4;
float64_t data[] = {0.09987322, 0.80575314, 0.79068641, 0.69989667,
0.62323516, 0.16837367, 0.85027625, 0.60165948,
0.04898732, 0.96701123, 0.51683275, 0.51116495,
0.18277926, 0.6179262, 0.43745891, 0.63685464};
float64_t result_eigenvectors[] = {
-0.63494074, 0.75831593, -0.14014031, 0.04656076,
0.82257205, -0.28671857, -0.44196422, -0.21409185,
-0.005932, -0.20233724, -0.52285555, 0.82803776,
-0.23930111, -0.56199714, -0.57298901, -0.54642272};
float64_t result_eigenvalues[] = {-0.6470538, -0.19125664, 0.16205101,
2.0981937};
SGMatrix<float64_t> m(data, n, n, false);
SGMatrix<float64_t> eigenvectors(n, n);
SGVector<float64_t> eigenvalues(n);
eigen_solver(m, eigenvalues, eigenvectors);
auto args = CMath::argsort(eigenvalues);
for (index_t i = 0; i < n; ++i)
{
index_t idx = args[i];
EXPECT_NEAR(eigenvalues[idx], result_eigenvalues[i], 1e-7);
auto s =
CMath::sign(eigenvectors[idx * n] * result_eigenvectors[i * n]);
for (index_t j = 0; j < n; ++j)
EXPECT_NEAR(
eigenvectors[idx * n + j], s * result_eigenvectors[i * n + j],
1e-7);
}
}
TEST(LinalgBackendEigen, eigensolver_symmetric)
{
const index_t n = 4;
float64_t data[] = {0.09987322, 0.80575314, 0.04898732, 0.69989667,
0.80575314, 0.16837367, 0.96701123, 0.6179262,
0.04898732, 0.96701123, 0.51683275, 0.43745891,
0.69989667, 0.6179262, 0.43745891, 0.63685464};
float64_t result_eigenvectors[] = {
-0.54618542, 0.69935447, -0.45219663, 0.09001671,
-0.56171388, -0.41397154, 0.17642953, 0.69424612,
-0.46818396, 0.16780603, 0.73247599, -0.46489119,
0.40861077, 0.55800718, 0.47735703, 0.542029037};
float64_t result_eigenvalues[] = {-1.00663298, -0.18672196, 0.42940933,
2.18587989};
SGMatrix<float64_t> m(data, n, n, false);
SGMatrix<float64_t> eigenvectors(n, n);
SGVector<float64_t> eigenvalues(n);
eigen_solver(m, eigenvalues, eigenvectors);
auto args = CMath::argsort(eigenvalues);
for (index_t i = 0; i < n; ++i)
{
index_t idx = args[i];
EXPECT_NEAR(eigenvalues[idx], result_eigenvalues[i], 1e-7);
auto s =
CMath::sign(eigenvectors[idx * n] * result_eigenvectors[i * n]);
for (index_t j = 0; j < n; ++j)
EXPECT_NEAR(
eigenvectors[idx * n + j], s * result_eigenvectors[i * n + j],
1e-7);
}
}
TEST(LinalgBackendEigen, SGMatrix_elementwise_product)
{
const index_t nrows = 3;
const index_t ncols = 3;
SGMatrix<float64_t> A(nrows,ncols);
SGMatrix<float64_t> B(nrows,ncols);
SGMatrix<float64_t> C(nrows,ncols);
for (index_t i = 0; i < nrows*ncols; ++i)
{
A[i] = i;
B[i] = 0.5*i;
}
C = element_prod(A, B);
for (index_t i = 0; i < nrows*ncols; ++i)
EXPECT_NEAR(A[i]*B[i], C[i], 1e-15);
}
TEST(LinalgBackendEigen, SGMatrix_elementwise_product_in_place)
{
const index_t nrows = 3;
const index_t ncols = 3;
SGMatrix<float64_t> A(nrows,ncols);
SGMatrix<float64_t> B(nrows,ncols);
SGMatrix<float64_t> C(nrows,ncols);
for (index_t i = 0; i < nrows*ncols; ++i)
{
A[i] = i;
B[i] = 0.5*i;
C[i] = i;
}
element_prod(A, B, A);
for (index_t i = 0; i < nrows*ncols; ++i)
EXPECT_NEAR(C[i]*B[i], A[i], 1e-15);
}
TEST(LinalgBackendEigen, SGMatrix_block_elementwise_product)
{
const index_t nrows = 2;
const index_t ncols = 3;
SGMatrix<float64_t> A(nrows,ncols);
SGMatrix<float64_t> B(ncols,nrows);
for (index_t i = 0; i < nrows; ++i)
for (index_t j = 0; j < ncols; ++j)
{
A(i, j) = i * 10 + j + 1;
B(j, i) = i + j;
}
auto A_block = linalg::block(A, 0, 0, 2, 2);
auto B_block = linalg::block(B, 0, 0, 2, 2);
auto result = element_prod(A_block, B_block);
ASSERT_EQ(result.num_rows, 2);
ASSERT_EQ(result.num_cols, 2);
for (index_t i = 0; i < 2; ++i)
for (index_t j = 0; j < 2; ++j)
EXPECT_NEAR(result(i, j), A(i, j) * B(i, j), 1E-15);
}
TEST(LinalgBackendEigen, SGMatrix_identity)
{
const index_t n = 4;
SGMatrix<float64_t> A(n, n);
identity(A);
for (index_t i = 0; i < n; ++i)
for (index_t j = 0; j < n; ++j)
EXPECT_EQ(A.get_element(i, j), (i==j));
}
TEST(LinalgBackendEigen, logistic)
{
SGMatrix<float64_t> A(3,3);
SGMatrix<float64_t> B(3,3);
range_fill(A, 0.0);
B.zero();
linalg::logistic(A, B);
for (index_t i = 0; i < 9; ++i)
EXPECT_NEAR(1.0/(1+CMath::exp(-1*A[i])), B[i], 1e-15);
}
TEST(LinalgBackendEigen, SGMatrix_SGVector_matrix_prod)
{
const index_t rows=4;
const index_t cols=3;
SGMatrix<float64_t> A(rows, cols);
SGVector<float64_t> b(cols);
for (index_t i = 0; i < cols; ++i)
{
for (index_t j = 0; j < rows; ++j)
A(j, i) = i * rows + j;
b[i]=0.5 * i;
}
auto x = matrix_prod(A, b);
float64_t ref[] = {10, 11.5, 13, 14.5};
EXPECT_EQ(x.vlen, A.num_rows);
for (index_t i = 0; i < cols; ++i)
EXPECT_NEAR(x[i], ref[i], 1e-15);
}
TEST(LinalgBackendEigen, SGMatrix_SGVector_matrix_prod_transpose)
{
const index_t rows=4;
const index_t cols=3;
SGMatrix<float64_t> A(cols, rows);
SGVector<float64_t> b(cols);
for (index_t i = 0; i < cols; ++i)
{
for (index_t j = 0; j < rows; ++j)
A(i, j) = i * cols + j;
b[i] = 0.5 * i;
}
auto x = matrix_prod(A, b, true);
float64_t ref[] = {7.5, 9, 10.5, 14.5};
EXPECT_EQ(x.vlen, A.num_cols);
for (index_t i = 0; i < cols; ++i)
EXPECT_NEAR(x[i], ref[i], 1e-15);
}
TEST(LinalgBackendEigen, SGMatrix_SGVector_matrix_prod_in_place)
{
const index_t rows=4;
const index_t cols=3;
SGMatrix<float64_t> A(rows, cols);
SGVector<float64_t> b(cols);
SGVector<float64_t> x(rows);
for (index_t i = 0; i<cols; ++i)
{
for (index_t j = 0; j < rows; ++j)
A(j, i) = i * rows + j;
b[i] = 0.5 * i;
}
matrix_prod(A, b, x);
float64_t ref[] = {10, 11.5, 13, 14.5};
for (index_t i = 0; i < cols; ++i)
EXPECT_NEAR(x[i], ref[i], 1e-15);
}
TEST(LinalgBackendEigen, SGMatrix_SGVector_matrix_prod_in_place_transpose)
{
const index_t rows=4;
const index_t cols=3;
SGMatrix<float64_t> A(cols, rows);
SGVector<float64_t> b(cols);
SGVector<float64_t> x(rows);
for (index_t i = 0; i < cols; ++i)
{
for (index_t j = 0; j < rows; ++j)
A(i, j) = i * cols + j;
b[i] = 0.5 * i;
}
matrix_prod(A, b, x, true);
float64_t ref[] = {7.5, 9, 10.5, 14.5};
for (index_t i = 0; i < cols; ++i)
EXPECT_NEAR(x[i], ref[i], 1e-15);
}
TEST(LinalgBackendEigen, SGMatrix_matrix_product)
{
const index_t dim1 = 2, dim2 = 4, dim3 = 3;
SGMatrix<float64_t> A(dim1, dim2);
SGMatrix<float64_t> B(dim2, dim3);
for (index_t i = 0; i < dim1*dim2; ++i)
A[i] = i;
for (index_t i = 0; i < dim2*dim3; ++i)
B[i] = 0.5*i;
auto cal = linalg::matrix_prod(A, B);
float64_t ref[] = {14, 17, 38, 49, 62, 81};
EXPECT_EQ(dim1, cal.num_rows);
EXPECT_EQ(dim3, cal.num_cols);
for (index_t i = 0; i < dim1*dim3; ++i)
EXPECT_EQ(ref[i], cal[i]);
}
TEST(LinalgBackendEigen, SGMatrix_matrix_product_transpose_A)
{
const index_t dim1 = 2, dim2 = 4, dim3 = 3;
SGMatrix<float64_t> A(dim2, dim1);
SGMatrix<float64_t> B(dim2, dim3);
for (index_t i = 0; i < dim1*dim2; ++i)
A[i] = i;
for (index_t i = 0; i < dim2*dim3; ++i)
B[i] = 0.5*i;
auto cal = linalg::matrix_prod(A, B, true);
float64_t ref[] = {7, 19, 19, 63, 31, 107};
EXPECT_EQ(dim1, cal.num_rows);
EXPECT_EQ(dim3, cal.num_cols);
for (index_t i = 0; i < dim1*dim3; ++i)
EXPECT_EQ(ref[i], cal[i]);
}
TEST(LinalgBackendEigen, SGMatrix_matrix_product_transpose_B)
{
const index_t dim1 = 2, dim2 = 4, dim3 = 3;
SGMatrix<float64_t> A(dim1, dim2);
SGMatrix<float64_t> B(dim3, dim2);
for (index_t i = 0; i < dim1*dim2; ++i)
A[i] = i;
for (index_t i = 0; i < dim2*dim3; ++i)
B[i] = 0.5*i;
auto cal = linalg::matrix_prod(A, B, false, true);
float64_t ref[] = {42, 51, 48, 59, 54, 67};
EXPECT_EQ(dim1, cal.num_rows);
EXPECT_EQ(dim3, cal.num_cols);
for (index_t i = 0; i < dim1*dim3; ++i)
EXPECT_EQ(ref[i], cal[i]);
}
TEST(LinalgBackendEigen, SGMatrix_matrix_product_transpose_A_B)
{
const index_t dim1 = 2, dim2 = 4, dim3 = 3;
SGMatrix<float64_t> A(dim2, dim1);
SGMatrix<float64_t> B(dim3, dim2);
for (index_t i = 0; i < dim1*dim2; ++i)
A[i] = i;
for (index_t i = 0; i < dim2*dim3; ++i)
B[i] = 0.5*i;
auto cal = linalg::matrix_prod(A, B, true, true);
float64_t ref[] = {21, 57, 24, 68, 27, 79};
EXPECT_EQ(dim1, cal.num_rows);
EXPECT_EQ(dim3, cal.num_cols);
for (index_t i = 0; i < dim1*dim3; ++i)
EXPECT_EQ(ref[i], cal[i]);
}
TEST(LinalgBackendEigen, SGMatrix_matrix_product_in_place)
{
const index_t dim1 = 2, dim2 = 4, dim3 = 3;
SGMatrix<float64_t> A(dim1, dim2);
SGMatrix<float64_t> B(dim2, dim3);
SGMatrix<float64_t> cal(dim1, dim3);
for (index_t i = 0; i < dim1*dim2; ++i)
A[i] = i;
for (index_t i = 0; i < dim2*dim3; ++i)
B[i] = 0.5 * i;
cal.zero();
linalg::matrix_prod(A, B, cal);
float64_t ref[] = {14, 17, 38, 49, 62, 81};
EXPECT_EQ(dim1, cal.num_rows);
EXPECT_EQ(dim3, cal.num_cols);
for (index_t i = 0; i < dim1*dim3; ++i)
EXPECT_EQ(ref[i], cal[i]);
}
TEST(LinalgBackendEigen, SGMatrix_matrix_product_in_place_transpose_A)
{
const index_t dim1 = 2, dim2 = 4, dim3 = 3;
SGMatrix<float64_t> A(dim2, dim1);
SGMatrix<float64_t> B(dim2, dim3);
SGMatrix<float64_t> cal(dim1, dim3);
for (index_t i = 0; i < dim1*dim2; ++i)
A[i] = i;
for (index_t i = 0; i < dim2*dim3; ++i)
B[i] = 0.5*i;
cal.zero();
linalg::matrix_prod(A, B, cal, true);
float64_t ref[] = {7, 19, 19, 63, 31, 107};
EXPECT_EQ(dim1, cal.num_rows);
EXPECT_EQ(dim3, cal.num_cols);
for (index_t i = 0; i < dim1*dim3; ++i)
EXPECT_EQ(ref[i], cal[i]);
}
TEST(LinalgBackendEigen, SGMatrix_matrix_product_in_place_transpose_B)
{
const index_t dim1 = 2, dim2 = 4, dim3 = 3;
SGMatrix<float64_t> A(dim1, dim2);
SGMatrix<float64_t> B(dim3, dim2);
SGMatrix<float64_t> cal(dim1, dim3);
for (index_t i = 0; i < dim1*dim2; ++i)
A[i] = i;
for (index_t i = 0; i < dim2*dim3; ++i)
B[i] = 0.5*i;
cal.zero();
linalg::matrix_prod(A, B, cal, false, true);
float64_t ref[] = {42, 51, 48, 59, 54, 67};
EXPECT_EQ(dim1, cal.num_rows);
EXPECT_EQ(dim3, cal.num_cols);
for (index_t i = 0; i < dim1*dim3; ++i)
EXPECT_EQ(ref[i], cal[i]);
}
TEST(LinalgBackendEigen, SGMatrix_matrix_product_in_place_transpose_A_B)
{
const index_t dim1 = 2, dim2 = 4, dim3 = 3;
SGMatrix<float64_t> A(dim2, dim1);
SGMatrix<float64_t> B(dim3, dim2);
SGMatrix<float64_t> cal(dim1, dim3);
for (index_t i = 0; i < dim1*dim2; ++i)
A[i] = i;
for (index_t i = 0; i < dim2*dim3; ++i)
B[i] = 0.5*i;
cal.zero();
linalg::matrix_prod(A, B, cal, true, true);
float64_t ref[] = {21, 57, 24, 68, 27, 79};
EXPECT_EQ(dim1, cal.num_rows);
EXPECT_EQ(dim3, cal.num_cols);
for (index_t i = 0; i < dim1*dim3; ++i)
EXPECT_EQ(ref[i], cal[i]);
}
TEST(LinalgBackendEigen, SGVector_max)
{
SGVector<float64_t> A(9);
float64_t a[] = {1, 2, 5, 8, 3, 1, 0, -1, 4};
for (index_t i = 0; i < A.size(); ++i)
A[i] = a[i];
EXPECT_NEAR(8, max(A), 1e-15);
}
TEST(LinalgBackendEigen, SGMatrix_max)
{
const index_t nrows = 2, ncols = 3;
SGMatrix<float64_t> A(nrows, ncols);
float64_t a[] = {1, 2, 5, 8, 3, 1, 0, -1, 12};
for (index_t i = 0; i < nrows*ncols; ++i)
A[i] = a[i];
EXPECT_NEAR(8, max(A), 1e-15);
}
TEST(LinalgBackendEigen, SGVector_mean)
{
const index_t size = 6;
SGVector<int32_t> vec(size);
vec.range_fill(0);
auto result = mean(vec);
EXPECT_NEAR(result, 2.5, 1E-15);
}
TEST(LinalgBackendEigen, SGMatrix_mean)
{
const index_t nrows = 2, ncols = 3;
SGMatrix<int32_t> mat(nrows, ncols);
for (index_t i = 0; i < nrows * ncols; ++i)
mat[i] = i;
auto result = mean(mat);
EXPECT_NEAR(result, 2.5, 1E-15);
}
TEST(LinalgBackendEigen, SGMatrix_multiply_by_logistic_derivative)
{
SGMatrix<float64_t> A(3, 3);
SGMatrix<float64_t> B(3, 3);
for (float64_t i = 0; i < 9; ++i)
{
A[i] = i / 9;
B[i] = i;
}
linalg::multiply_by_logistic_derivative(A, B);
for (index_t i = 0; i < 9; ++i)
EXPECT_NEAR(i * A[i] * (1.0 - A[i]), B[i], 1e-15);
}
TEST(LinalgBackendEigen, SGMatrix_multiply_by_rectified_linear_derivative)
{
SGMatrix<float64_t> A(3, 3);
SGMatrix<float64_t> B(3, 3);
for (float64_t i = 0; i < 9; ++i)
{
A[i] = i * 0.5 - 0.5;
B[i] = i;
}
multiply_by_rectified_linear_derivative(A, B);
for (index_t i = 0; i < 9; ++i)
EXPECT_NEAR(i * (A[i] != 0), B[i], 1e-15);
}
TEST(LinalgBackendEigen, SGVector_norm)
{
const index_t n = 5;
SGVector<float64_t> v(n);
float64_t gt = 0;
for (index_t i = 0; i < n; ++i)
{
v[i] = i;
gt += i * i;
}
gt = CMath::sqrt(gt);
auto result = norm(v);
EXPECT_NEAR(result, gt, 1E-15);
}
TEST(LinalgBackendEigen, SGVector_qr_solver)
{
const index_t n = 3;
float64_t data_A[] = {0.02800922, 0.99326012, 0.15204902,
0.30492837, 0.39708534, 0.40466969,
0.36415317, 0.04407589, 0.9095746};
float64_t data_b[] = {0.39461571, 0.6816856, 0.43323709};
float64_t result[] = {0.07135206, 1.56393127, -0.23141312};
SGMatrix<float64_t> A(data_A, n, n, false);
SGVector<float64_t> b(data_b, n, false);
auto x = qr_solver(A, b);
for (index_t i = 0; i < x.size(); ++i)
EXPECT_NEAR(x[i], result[i], 1E-7);
}
TEST(LinalgBackendEigen, SGMatrix_qr_solver)
{
const index_t n = 3, m = 2;
float64_t data_A[] = {0.02800922, 0.99326012, 0.15204902,
0.30492837, 0.39708534, 0.40466969,
0.36415317, 0.04407589, 0.9095746};
float64_t data_B[] = {0.76775073, 0.88471312, 0.34795225,
0.94311546, 0.59630347, 0.65820143};
float64_t result[] = {-0.73834587, 4.22750496, -1.37484721,
-1.14718091, 4.49142548, -1.08282992};
SGMatrix<float64_t> A(data_A, n, n, false);
SGMatrix<float64_t> B(data_B, n, m, false);
auto X = qr_solver(A, B);
for (index_t i = 0; i < (index_t)X.size(); ++i)
EXPECT_NEAR(X[i], result[i], 1E-7);
}
TEST(LinalgBackendEigen, SGVector_range_fill)
{
const index_t size = 5;
SGVector<int32_t> vec(size);
range_fill(vec, 1);
for (index_t i = 0; i < size; ++i)
EXPECT_NEAR(vec[i], i + 1, 1E-15);
}
TEST(LinalgBackendEigen, SGMatrix_range_fill)
{
const index_t nrows = 2, ncols = 3;
SGMatrix<int32_t> mat(nrows, ncols);
range_fill(mat, 1);
for (index_t i = 0; i < nrows*ncols; ++i)
EXPECT_NEAR(mat[i], i + 1, 1E-15);
}
TEST(LinalgBackendEigen, SGMatrix_rectified_linear)
{
SGMatrix<float64_t> A(3, 3);
SGMatrix<float64_t> B(3, 3);
range_fill(A, -5.0);
linalg::rectified_linear(A, B);
for (index_t i = 0; i < 9; ++i)
EXPECT_NEAR(CMath::max(0.0, A[i]), B[i], 1e-15);
}
TEST(LinalgBackendEigen, SGVector_scale)
{
const index_t size = 5;
const float64_t alpha = 0.3;
SGVector<float64_t> a(size);
a.range_fill(0);
auto result = scale(a, alpha);
for (index_t i = 0; i < size; ++i)
EXPECT_NEAR(alpha * a[i], result[i], 1e-15);
}
TEST(LinalgBackendEigen, SGMatrix_scale)
{
const float64_t alpha = 0.3;
const index_t nrows = 2, ncols = 3;
SGMatrix<float64_t> A(nrows, ncols);
for (index_t i = 0; i < nrows*ncols; ++i)
A[i] = i;
auto result = scale(A, alpha);
for (index_t i = 0; i < nrows*ncols; ++i)
EXPECT_NEAR(alpha*A[i], result[i], 1e-15);
}
TEST(LinalgBackendEigen, SGVector_scale_in_place)