Test Case: cpp-instruct-307

  1#include <iostream>  2#include <vector>  3#include <cmath>  4#include <random>  5#include <iomanip>  6​  7void testMatrixProjection(int numSamples, int tableSize, int inputDim) {  8    // number of rows (samples) = tableSize, number of columns = inputDim  9    int m = tableSize; 10    int n = inputDim; 11​ 12    // Validate: projection onto rows requires rows <= columns for simple normal equations method 13    if (m > n) { 14        std::cerr << "Warning: rows (" << m << ") > columns (" << n  15                  << "). Cannot guarantee full row rank. Test skipped.\n"; 16        return; 17    } 18​ 19    // Random generator 20    std::random_device rd; 21    std::mt19937 gen(rd()); 22    std::uniform_real_distribution<double> dist(-1.0, 1.0); 23​ 24    // Tolerance for floating point comparison 25    const double eps = 1e-10; 26​ 27    // Helper lambda to transpose a matrix 28    auto transpose = [](const std::vector<std::vector<double>>& A) { 29        if (A.empty()) return std::vector<std::vector<double>>(); 30        int rows = A.size(); 31        int cols = A[0].size(); 32        std::vector<std::vector<double>> T(cols, std::vector<double>(rows)); 33        for (int i = 0; i < rows; ++i) 34            for (int j = 0; j < cols; ++j) 35                T[j][i] = A[i][j]; 36        return T; 37    }; 38​ 39    // Helper lambda to multiply two matrices 40    auto matMul = [](const std::vector<std::vector<double>>& A, 41                     const std::vector<std::vector<double>>& B) { 42        int rA = A.size(), cA = A[0].size(); 43        int rB = B.size(), cB = B[0].size(); 44        // cA must equal rB 45        std::vector<std::vector<double>> C(rA, std::vector<double>(cB, 0.0)); 46        for (int i = 0; i < rA; ++i) 47            for (int k = 0; k < cA; ++k) 48                for (int j = 0; j < cB; ++j) 49                    C[i][j] += A[i][k] * B[k][j]; 50        return C; 51    }; 52​ 53    // Helper lambda to multiply matrix by vector 54    auto matVecMul = [](const std::vector<std::vector<double>>& A, 55                         const std::vector<double>& v) { 56        int rows = A.size(); 57        int cols = A[0].size(); 58        std::vector<double> res(rows, 0.0); 59        for (int i = 0; i < rows; ++i) 60            for (int j = 0; j < cols; ++j) 61                res[i] += A[i][j] * v[j]; 62        return res; 63    }; 64​ 65    // Solve linear system Ax = b using Gaussian elimination with partial pivoting 66    auto solveLinear = [](std::vector<std::vector<double>> A, 67                           std::vector<double> b) -> std::vector<double> { 68        int n = A.size(); 69        // Augmented matrix [A | b] 70        std::vector<std::vector<double>> aug(n, std::vector<double>(n + 1)); 71        for (int i = 0; i < n; ++i) { 72            for (int j = 0; j < n; ++j) 73                aug[i][j] = A[i][j]; 74            aug[i][n] = b[i]; 75        } 76​ 77        // Forward elimination with partial pivoting 78        for (int col = 0; col < n; ++col) { 79            // Find pivot row 80            int pivot = col; 81            double maxVal = std::abs(aug[col][col]); 82            for (int row = col + 1; row < n; ++row) { 83                if (std::abs(aug[row][col]) > maxVal) { 84                    maxVal = std::abs(aug[row][col]); 85                    pivot = row; 86                } 87            } 88            if (maxVal < 1e-15) { 89                // Singular – return zero vector (should not happen for full rank) 90                return std::vector<double>(n, 0.0); 91            } 92            // Swap rows if needed 93            if (pivot != col) std::swap(aug[col], aug[pivot]); 94​ 95            // Eliminate below 96            for (int row = col + 1; row < n; ++row) { 97                double factor = aug[row][col] / aug[col][col]; 98                for (int j = col; j <= n; ++j) 99                    aug[row][j] -= factor * aug[col][j];100            }101        }102​103        // Back substitution104        std::vector<double> x(n);105        for (int i = n - 1; i >= 0; --i) {106            double sum = 0.0;107            for (int j = i + 1; j < n; ++j)108                sum += aug[i][j] * x[j];109            x[i] = (aug[i][n] - sum) / aug[i][i];110        }111        return x;112    };113​114    // Projection method 1: normal equations M = A*A^T, solve M*c = A*v, then p = A^T*c115    auto projectMethod1 = [&](const std::vector<std::vector<double>>& A,116                               const std::vector<double>& v) -> std::vector<double> {117        auto AT = transpose(A);118        auto M = matMul(A, AT);          // m x m119        auto b = matVecMul(A, v);        // m120        auto c = solveLinear(M, b);      // m121        // p = AT * c, output n-dimensional122        std::vector<double> p(n, 0.0);123        for (int i = 0; i < n; ++i)124            for (int j = 0; j < m; ++j)125                p[i] += AT[i][j] * c[j];126        return p;127    };128​129    // Reference projection using Gram-Schmidt orthonormalization of row space130    auto projectRef = [&](const std::vector<std::vector<double>>& A,131                           const std::vector<double>& v) -> std::vector<double> {132        // Work with columns of A^T (the row vectors as columns)133        auto AT = transpose(A);          // n x m134        std::vector<std::vector<double>> Q(n, std::vector<double>(m, 0.0)); // orthonormal basis for column space of AT135        for (int col = 0; col < m; ++col) {136            // Start with column col of AT137            std::vector<double> w(n);138            for (int i = 0; i < n; ++i) w[i] = AT[i][col];139            // Subtract projection onto previous orthonormal columns140            for (int k = 0; k < col; ++k) {141                double dot = 0.0;142                for (int i = 0; i < n; ++i) dot += Q[i][k] * w[i];143                for (int i = 0; i < n; ++i) w[i] -= dot * Q[i][k];144            }145            // Normalize146            double norm = 0.0;147            for (int i = 0; i < n; ++i) norm += w[i] * w[i];148            norm = std::sqrt(norm);149            if (norm < 1e-15) continue; // skip linearly dependent columns150            for (int i = 0; i < n; ++i) w[i] /= norm;151            // Insert into Q152            for (int i = 0; i < n; ++i) Q[i][col] = w[i];153        }154​155        // Projection = Q * Q^T * v156        // Compute alpha = Q^T * v (size m)157        std::vector<double> alpha(m, 0.0);158        for (int j = 0; j < m; ++j)159            for (int i = 0; i < n; ++i)160                alpha[j] += Q[i][j] * v[i];161        // Compute p = Q * alpha (size n)162        std::vector<double> p(n, 0.0);163        for (int i = 0; i < n; ++i)164            for (int j = 0; j < m; ++j)165                p[i] += Q[i][j] * alpha[j];166        return p;167    };168​169    // Main test loop170    for (int sample = 0; sample < numSamples; ++sample) {171        // Generate random matrix A (m x n)172        std::vector<std::vector<double>> A(m, std::vector<double>(n));173        for (int i = 0; i < m; ++i)174            for (int j = 0; j < n; ++j)175                A[i][j] = dist(gen);176​177        // Generate random vector v (n)178        std::vector<double> v(n);179        for (int i = 0; i < n; ++i)180            v[i] = dist(gen);181​182        // Compute projection using method 1183        auto p1 = projectMethod1(A, v);184        // Compute reference projection185        auto pref = projectRef(A, v);186​187        // Compute error (Euclidean norm)188        double error = 0.0;189        for (int i = 0; i < n; ++i) {190            double diff = p1[i] - pref[i];191            error += diff * diff;192        }193        error = std::sqrt(error);194​195        // Print log message196        std::cout << std::fixed << std::setprecision(6);197        std::cout << "Sample " << sample << ": m=" << m << ", n=" << n << "\n";198        std::cout << "  Matrix rows: " << m << ", cols: " << n << "\n";199        std::cout << "  Input vector (first 5): ";200        for (int i = 0; i < std::min(5, n); ++i) std::cout << v[i] << " ";201        std::cout << "\n";202        std::cout << "  Projection (first 5): ";203        for (int i = 0; i < std::min(5, n); ++i) std::cout << p1[i] << " ";204        std::cout << "\n";205        std::cout << "  Reference  (first 5): ";206        for (int i = 0; i < std::min(5, n); ++i) std::cout << pref[i] << " ";207        std::cout << "\n";208        std::cout << "  Error = " << error;209        if (error > eps)210            std::cout << " FAIL\n";211        else212            std::cout << " PASS\n";213    }214}

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  1#include <algorithm>  2#include <cmath>  3#include <iomanip>  4#include <iostream>  5#include <random>  6#include <sstream>  7#include <stdexcept>  8#include <string>  9#include <vector> 10​ 11// Reference implementation: project vector v onto rows of matrix A 12// A is (samples x dim), v is (dim x 1) 13// Result is (samples x 1) where result[i] = dot(A[i], v) 14std::vector<double> reference_projection(const std::vector<std::vector<double>>& A, 15                                          const std::vector<double>& v) { 16    const size_t samples = A.size(); 17    const size_t dim = v.size(); 18    std::vector<double> result(samples, 0.0); 19    for (size_t i = 0; i < samples; ++i) { 20        if (A[i].size() != dim) { 21            throw std::invalid_argument("Matrix row size mismatch"); 22        } 23        double dot = 0.0; 24        for (size_t j = 0; j < dim; ++j) { 25            dot += A[i][j] * v[j]; 26        } 27        result[i] = dot; 28    } 29    return result; 30} 31​ 32// Optimized projection using matrix projection operation 33// Assumes row-major storage: A is a flat vector of size samples * dim 34std::vector<double> matrix_projection(const std::vector<double>& A_flat, 35                                       size_t samples, size_t dim, 36                                       const std::vector<double>& v) { 37    if (A_flat.size() != samples * dim) { 38        throw std::invalid_argument("Flat matrix size mismatch"); 39    } 40    if (v.size() != dim) { 41        throw std::invalid_argument("Vector dimension mismatch"); 42    } 43​ 44    std::vector<double> result(samples, 0.0apse); 45    for (size_t i = 0; i < samples; ++i) { 46        double dot = 0.0; 47        for (size_t j = 0; j < dim; ++j) { 48            dot += A_flat[i * dim + j] * v[j]; 49        } 50        result[i] = dot; 51    } 52    return result; 53} 54​ 55// Test function 56void test_matrix_projection(size_t samples, size_t table_size, size_t dim) { 57    // Validate inputs 58    if (samples == 0 || table_size == 0 || dim == 0) { 59        throw std::invalid_argument("All dimensions must be positive"); 60    } 61    if (samples > table_size) { 62        throw std::invalid_argument("Samples cannot exceed table size"); 63    } 64​ 65    // Random number generation 66    std::random_device rd; 67    std::mt19937 gen(rd()); 68    std::uniform_real_distribution<double> dist(-10.0, 10.0); 69​ 70    // Create random matrix A (samples x dim) as flat vector 71    std::vector<double> A_flat(samples * dim); 72    for (auto& val : A_flat) { 73        val = dist(gen); 74    } 75​ 76    // Create random vector v (dim x 1) 77    std::vector<double> v(dim); 78    for (auto& val : v) { 79        val = dist(gen); 80    } 81​ 82    // Build reference matrix (vector of vectors) 83    std::vector<std::vector<double>> A_ref(samples, std::vector<double>(dim)); 84    for (size_t i = 0; i < samples; ++i) { 85        for (size_t j = 0; j < dim; ++j) { 86            A_ref[i][j] = A_flat[i * dim + j]; 87        } 88    } 89​ 90    // Compute projections 91    std::vector<double> result_ref = reference_projection(A_ref, v); 92    std::vector<double> result_opt = matrix_projection(A_flat, samples, dim, v); 93​ 94    // Compare results with tolerance 95    const double tolerance = 1e-12; 96    bool match = true; 97    for (size_t i = 0; i < samples; ++i) { 98        if (std::fabs(result_ref[i] - result_opt[i]) > tolerance) { 99            match = false;100            break;101        }102    }103​104    // Build log message105    std::ostringstream log;106    log << std::fixed << std::setprecision(6);107    log << "Test: samples=" << samples << ", table_size=" << table_size108        << ", dim=" << dim << "\n";109    log << "Matrix A (first 3 rows):\n";110    for (size_t i = 0; i < std::min<size_t>(3, samples); ++i) {111        log << "  [";112        for (size_t j = 0; j < std::min<size_t>(3, dim); ++j) {113            log << A_flat[i * dim + j];114            if (j < std::min<size_t>(3, dim) - 1) log << ", ";115        }116        if (dim > 3) log << ", ...";117        log << "]\n";118    }119    log << "Vector v: [";120    for (size_t j = 0; j < std::min<size_t>(3, dim); ++j) {121        log << v[j];122        if (j < std::min<size_t>(3, dim) - 1) log << ", ";123    }124    if (dim > 3) log << ", ...";125    log << "]\n";126    log << "Result (first 3): [";127    for (size_t i = 0; i < std::min<size_t>(3, samples); ++i) {128        log << result_opt[i];129        if (i < std::min<size_t>(3, samples) - 1) log << ", ";130    }131    if (samples > 3) log << ", ...";132    log << "]\n";133    log << "Status: " << (match ? "PASS" : "FAIL") << "\n";134​135    std::cout << log.str() << std::endl;136​137    if (!match) {138        throw std::runtime_error("Matrix projection test failed");139    }140}

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