tests/lin_alg/test_lin_alg.h

#include <stdio.h>
#include "osqp.h"
#include "osqp_tester.h"

#include "lin_alg/data.h"

void test_constr_sparse_mat() {
  c_float *Adns; // Conversion to dense matrix

  lin_alg_sols_data *data = generate_problem_lin_alg_sols_data();

  // Convert sparse to dense
  Adns = csc_to_dns(data->test_sp_matrix_A);

  // Compute norm of the elementwise difference with
  mu_assert("Linear algebra tests: error in constructing sparse/dense matrix!",
            vec_norm_inf_diff(Adns, data->test_sp_matrix_Adns,
                              data->test_sp_matrix_A->m *
                              data->test_sp_matrix_A->n) < TESTS_TOL);

  // Free memory
  c_free(Adns); // because of vars from file matrices.h
  clean_problem_lin_alg_sols_data(data);

}

void test_vec_operations() {
  c_float  norm_inf, vecprod; // normInf;
  c_float *ew_reciprocal;
  c_float *add_scaled;
  c_float *vec_ew_max_vec_test, *vec_ew_min_vec_test;

  lin_alg_sols_data *data = generate_problem_lin_alg_sols_data();


  // Add scaled
  add_scaled = vec_copy(data->test_vec_ops_v1, data->test_vec_ops_n);
  vec_add_scaled(add_scaled,
                 add_scaled,
                 data->test_vec_ops_v2,
                 data->test_vec_ops_n,
                 data->test_vec_ops_sc);
  mu_assert(
    "Linear algebra tests: error in vector operation, adding scaled vector",
    vec_norm_inf_diff(add_scaled, data->test_vec_ops_add_scaled,
                      data->test_vec_ops_n) < TESTS_TOL);

  // Norm_inf of the difference
  mu_assert(
    "Linear algebra tests: error in vector operation, norm_inf of difference",
    c_absval(vec_norm_inf_diff(data->test_vec_ops_v1,
                               data->test_vec_ops_v2,
                               data->test_vec_ops_n) -
             data->test_vec_ops_norm_inf_diff) <
    TESTS_TOL);

  // norm_inf
  norm_inf = vec_norm_inf(data->test_vec_ops_v1, data->test_vec_ops_n);
  mu_assert("Linear algebra tests: error in vector operation, norm_inf",
            c_absval(norm_inf - data->test_vec_ops_norm_inf) < TESTS_TOL);

  // Elementwise reciprocal
  ew_reciprocal = (c_float *)c_malloc(data->test_vec_ops_n * sizeof(c_float));
  vec_ew_recipr(data->test_vec_ops_v1, ew_reciprocal, data->test_vec_ops_n);
  mu_assert(
    "Linear algebra tests: error in vector operation, elementwise reciprocal",
    vec_norm_inf_diff(ew_reciprocal, data->test_vec_ops_ew_reciprocal,
                      data->test_vec_ops_n) < TESTS_TOL);


  // Vector product
  vecprod = vec_prod(data->test_vec_ops_v1,
                     data->test_vec_ops_v2,
                     data->test_vec_ops_n);
  mu_assert("Linear algebra tests: error in vector operation, vector product",
            c_absval(vecprod - data->test_vec_ops_vec_prod) < TESTS_TOL);

  // Elementwise maximum between two vectors
  vec_ew_max_vec_test =
    (c_float *)c_malloc(data->test_vec_ops_n * sizeof(c_float));
  vec_ew_max_vec(data->test_vec_ops_v1,
                 data->test_vec_ops_v2,
                 vec_ew_max_vec_test,
                 data->test_vec_ops_n);
  mu_assert(
    "Linear algebra tests: error in vector operation, elementwise maximum between vectors",
    vec_norm_inf_diff(vec_ew_max_vec_test, data->test_vec_ops_ew_max_vec,
                      data
                      ->test_vec_ops_n) < TESTS_TOL);

  // Elementwise minimum between two vectors
  vec_ew_min_vec_test =
    (c_float *)c_malloc(data->test_vec_ops_n * sizeof(c_float));
  vec_ew_min_vec(data->test_vec_ops_v1,
                 data->test_vec_ops_v2,
                 vec_ew_min_vec_test,
                 data->test_vec_ops_n);
  mu_assert(
    "Linear algebra tests: error in vector operation, elementwise minimum between vectors",
    vec_norm_inf_diff(vec_ew_min_vec_test, data->test_vec_ops_ew_min_vec,
                      data
                      ->test_vec_ops_n) < TESTS_TOL);

  // cleanup
  c_free(add_scaled);
  c_free(ew_reciprocal);
  c_free(vec_ew_min_vec_test);
  c_free(vec_ew_max_vec_test);
  clean_problem_lin_alg_sols_data(data);
}

void test_mat_operations() {
  csc *Ad, *dA; // Matrices used for tests
  // csc *A_ewsq, *A_ewabs;     // Matrices used for tests
  c_int exitflag = 0;

  // c_float trace, fro_sq;
  c_float *inf_norm_cols_rows_test;


  lin_alg_sols_data *data = generate_problem_lin_alg_sols_data();


  // Copy matrices
  Ad = copy_csc_mat(data->test_mat_ops_A);
  dA = copy_csc_mat(data->test_mat_ops_A);


  // Premultiply matrix A
  mat_premult_diag(dA, data->test_mat_ops_d);
  mu_assert(
    "Linear algebra tests: error in matrix operation, premultiply diagonal",
    is_eq_csc(dA, data->test_mat_ops_prem_diag, TESTS_TOL));


  // Postmultiply matrix A
  mat_postmult_diag(Ad, data->test_mat_ops_d);
  mu_assert(
    "Linear algebra tests: error in matrix operation, postmultiply diagonal",
    is_eq_csc(Ad, data->test_mat_ops_postm_diag, TESTS_TOL));

  // Maximum norm over columns
  inf_norm_cols_rows_test =
    (c_float *)c_malloc(data->test_mat_ops_n * sizeof(c_float));
  mat_inf_norm_cols(data->test_mat_ops_A, inf_norm_cols_rows_test);
  mu_assert(
    "Linear algebra tests: error in matrix operation, max norm over columns",
    vec_norm_inf_diff(inf_norm_cols_rows_test, data->test_mat_ops_inf_norm_cols,
                      data
                      ->test_mat_ops_n) < TESTS_TOL);

  // Maximum norm over rows
  mat_inf_norm_rows(data->test_mat_ops_A, inf_norm_cols_rows_test);
  mu_assert("Linear algebra tests: error in matrix operation, max norm over rows",
            vec_norm_inf_diff(inf_norm_cols_rows_test,
                              data->test_mat_ops_inf_norm_rows,
                              data
                              ->test_mat_ops_n) < TESTS_TOL);


  // cleanup
  c_free(inf_norm_cols_rows_test);
  csc_spfree(Ad);
  csc_spfree(dA);
  clean_problem_lin_alg_sols_data(data);
}

void test_mat_vec_multiplication() {
  c_float *Ax, *ATy, *Px, *Ax_cum, *ATy_cum, *Px_cum;

  lin_alg_sols_data *data = generate_problem_lin_alg_sols_data();


  // Allocate vectors
  Ax  = (c_float *)c_malloc(data->test_mat_vec_m * sizeof(c_float));
  ATy = (c_float *)c_malloc(data->test_mat_vec_n * sizeof(c_float));
  Px  = (c_float *)c_malloc(data->test_mat_vec_n * sizeof(c_float));


  // Matrix-vector multiplication:  y = Ax
  mat_vec(data->test_mat_vec_A, data->test_mat_vec_x, Ax, 0);
  mu_assert(
    "Linear algebra tests: error in matrix-vector operation, matrix-vector multiplication",
    vec_norm_inf_diff(Ax, data->test_mat_vec_Ax,
                      data->test_mat_vec_m) < TESTS_TOL);

  // Cumulative matrix-vector multiplication:  y += Ax
  Ax_cum = vec_copy(data->test_mat_vec_y, data->test_mat_vec_m);
  mat_vec(data->test_mat_vec_A, data->test_mat_vec_x, Ax_cum, 1);
  mu_assert(
    "Linear algebra tests: error in matrix-vector operation, cumulative matrix-vector multiplication",
    vec_norm_inf_diff(Ax_cum, data->test_mat_vec_Ax_cum,
                      data->test_mat_vec_m) < TESTS_TOL);

  // Matrix-transpose-vector multiplication:  x = A'*y
  mat_tpose_vec(data->test_mat_vec_A, data->test_mat_vec_y, ATy, 0, 0);
  mu_assert(
    "Linear algebra tests: error in matrix-vector operation, matrix-transpose-vector multiplication",
    vec_norm_inf_diff(ATy, data->test_mat_vec_ATy,
                      data->test_mat_vec_n) < TESTS_TOL);

  // Cumulative matrix-transpose-vector multiplication:  x += A'*y
  ATy_cum = vec_copy(data->test_mat_vec_x, data->test_mat_vec_n);
  mat_tpose_vec(data->test_mat_vec_A, data->test_mat_vec_y, ATy_cum, 1, 0);
  mu_assert(
    "Linear algebra tests: error in matrix-vector operation, cumulative matrix-transpose-vector multiplication",
    vec_norm_inf_diff(ATy_cum, data->test_mat_vec_ATy_cum,
                      data->test_mat_vec_n) < TESTS_TOL);

  // Symmetric-matrix-vector multiplication (only upper part is stored)
  mat_vec(data->test_mat_vec_Pu, data->test_mat_vec_x, Px, 0);          // upper
                                                                        // traingular
                                                                        // part
  mat_tpose_vec(data->test_mat_vec_Pu, data->test_mat_vec_x, Px, 1, 1); // lower
                                                                        // traingular
                                                                        // part
                                                                        // (without
                                                                        // diagonal)
  mu_assert(
    "Linear algebra tests: error in matrix-vector operation, symmetric matrix-vector multiplication",
    vec_norm_inf_diff(Px, data->test_mat_vec_Px,
                      data->test_mat_vec_n) < TESTS_TOL);


  // Cumulative symmetric-matrix-vector multiplication
  Px_cum = vec_copy(data->test_mat_vec_x, data->test_mat_vec_n);
  mat_vec(data->test_mat_vec_Pu, data->test_mat_vec_x, Px_cum, 1);          // upper
                                                                            // traingular
                                                                            // part
  mat_tpose_vec(data->test_mat_vec_Pu, data->test_mat_vec_x, Px_cum, 1, 1); // lower
                                                                            // traingular
                                                                            // part
                                                                            // (without
                                                                            // diagonal)
  mu_assert(
    "Linear algebra tests: error in matrix-vector operation, cumulative symmetric matrix-vector multiplication",
    vec_norm_inf_diff(Px_cum, data->test_mat_vec_Px_cum,
                      data->test_mat_vec_n) < TESTS_TOL);


  // cleanup
  c_free(Ax);
  c_free(ATy);
  c_free(Px);
  c_free(Ax_cum);
  c_free(ATy_cum);
  c_free(Px_cum);
  clean_problem_lin_alg_sols_data(data);
}

void test_extract_upper_triangular() {
  c_float *inf_norm_cols_test;
  lin_alg_sols_data *data = generate_problem_lin_alg_sols_data();

  // Extract upper triangular part
  csc *Ptriu = csc_to_triu(data->test_mat_extr_triu_P);

  mu_assert("Linear algebra tests: error in forming upper triangular matrix!",
            is_eq_csc(data->test_mat_extr_triu_Pu, Ptriu, TESTS_TOL));

  // Compute infinity norm over columns of the original matrix by using the
  // upper triangular part only
  inf_norm_cols_test = (c_float *)c_malloc(data->test_mat_extr_triu_n
                                           * sizeof(c_float));
  mat_inf_norm_cols_sym_triu(Ptriu, inf_norm_cols_test);
  mu_assert(
    "Linear algebra tests: error in forming upper triangular matrix, infinity norm over columns",
    vec_norm_inf_diff(inf_norm_cols_test,
                      data->test_mat_extr_triu_P_inf_norm_cols,
                      data->test_mat_extr_triu_n) < TESTS_TOL);

  // Cleanup
  c_free(inf_norm_cols_test);
  csc_spfree(Ptriu);
  clean_problem_lin_alg_sols_data(data);
}

void test_quad_form_upper_triang() {
  c_float quad_form_t;

  lin_alg_sols_data *data = generate_problem_lin_alg_sols_data();

  // Compute quadratic form
  quad_form_t = quad_form(data->test_qpform_Pu, data->test_qpform_x);

  mu_assert(
    "Linear algebra tests: error in computing quadratic form using upper triangular matrix!",
    (c_absval(quad_form_t - data->test_qpform_value) < TESTS_TOL));

  // cleanup
  clean_problem_lin_alg_sols_data(data);
}