Upsilon/apps/solver/test/equation_store.cpp

#include <quiz.h>
#include <apps/shared/global_context.h>
#include <string.h>
#include <assert.h>
#include <limits.h>
#include <cmath>
#include "../equation_store.h"
#include "../../../poincare/test/helper.h"

using namespace Poincare;

namespace Solver {

void assert_equation_system_exact_solve_to(const char * equations[], EquationStore::Error error, EquationStore::Type type, const char * variables[], const char * solutions[], int numberOfSolutions) {
  Shared::GlobalContext globalContext;
  EquationStore equationStore;
  int index = 0;
  while (equations[index] != 0) {
    Shared::ExpressionModel * e = equationStore.addEmptyModel();
    e->setContent(equations[index++]);
  }
  EquationStore::Error err = equationStore.exactSolve(&globalContext);
  quiz_assert(err == error);
  if (err != EquationStore::Error::NoError) {
    return;
  }
  quiz_assert(equationStore.type() == type);
  quiz_assert(equationStore.numberOfSolutions() == numberOfSolutions);
  if (numberOfSolutions == INT_MAX) {
    return;
  }
  if (type == EquationStore::Type::LinearSystem) {
    for (int i = 0; i < numberOfSolutions; i++) {
      quiz_assert(strcmp(equationStore.variableAtIndex(i),variables[i]) == 0);
    }
  } else {
    quiz_assert(strcmp(equationStore.variableAtIndex(0), variables[0]) == 0);
  }
  for (int i = 0; i < numberOfSolutions; i++) {
    quiz_assert(strcmp(equationStore.exactSolutionLayoutAtIndex(i, true), solutions[i]) == 0);
  }
}

void assert_equation_approximate_solve_to(const char * equations, double xMin, double xMax, const char * variable, double solutions[], int numberOfSolutions, bool hasMoreSolutions) {
  Shared::GlobalContext globalContext;
  EquationStore equationStore;
  Shared::ExpressionModel * e = equationStore.addEmptyModel();
  e->setContent(equations);
  EquationStore::Error err = equationStore.exactSolve(&globalContext);
  quiz_assert(err == EquationStore::Error::RequireApproximateSolution);
  equationStore.setIntervalBound(0, xMin);
  equationStore.setIntervalBound(1, xMax);
  equationStore.approximateSolve(&globalContext);
  quiz_assert(equationStore.numberOfSolutions() == numberOfSolutions);
  quiz_assert(strcmp(equationStore.variableAtIndex(0), variable)== 0);
  for (int i = 0; i < numberOfSolutions; i++) {
    quiz_assert(std::fabs(equationStore.approximateSolutionAtIndex(i) - solutions[i]) < 1E-5);
  }
  quiz_assert(equationStore.haveMoreApproximationSolutions(&globalContext) == hasMoreSolutions);
}

QUIZ_CASE(equation_solve) {
  // x+y+z+a+b+c+d = 0
  const char * variables1[] = {""};
  const char * equations0[] = {"x+y+z+a+b+c+d=0", 0};
  assert_equation_system_exact_solve_to(equations0, EquationStore::Error::TooManyVariables, EquationStore::Type::LinearSystem, (const char **)variables1, nullptr, 0);

  // x^2+y = 0
  const char * equations1[] = {"x^2+y=0", 0};
  assert_equation_system_exact_solve_to(equations1, EquationStore::Error::NonLinearSystem, EquationStore::Type::LinearSystem, (const char **)variables1, nullptr, 0);

  // cos(x) = 0
  const char * equations2[] = {"cos(x)=0", 0};
  assert_equation_system_exact_solve_to(equations2, EquationStore::Error::RequireApproximateSolution, EquationStore::Type::LinearSystem, (const char **)variables1, nullptr, 0);

  // 2 = 0
  const char * equations3[] = {"2=0", 0};
  assert_equation_system_exact_solve_to(equations3,  EquationStore::Error::NoError, EquationStore::Type::LinearSystem, (const char **)variables1, nullptr, 0);
  // 0 = 0
  const char * equations4[] = {"0=0", 0};
  assert_equation_system_exact_solve_to(equations4,  EquationStore::Error::NoError, EquationStore::Type::LinearSystem, (const char **)variables1, nullptr, INT_MAX);

  // x-x+2 = 0
  const char * equations5[] = {"x-x+2=0", 0};
  assert_equation_system_exact_solve_to(equations5,  EquationStore::Error::NoError, EquationStore::Type::LinearSystem, (const char **)variables1, nullptr, 0);

  // x-x= 0
  const char * equations6[] = {"x-x=0", 0};
  assert_equation_system_exact_solve_to(equations6,  EquationStore::Error::NoError, EquationStore::Type::LinearSystem, (const char **)variables1, nullptr, INT_MAX);

  const char * variablesx[] = {"x", ""};
  // 2x+3=4
  const char * equations7[] = {"2x+3=4", 0};
  const char * solutions7[] = {"(1)/(2)"};
  assert_equation_system_exact_solve_to(equations7,  EquationStore::Error::NoError, EquationStore::Type::LinearSystem, (const char **)variablesx, solutions7, 1);

  // 3x^2-4x+4=2
  const char * equations8[] = {"3*x^2-4x+4=2", 0};
  const char * solutions8[] = {"(2)/(3)-(R(2))/(3)*I","(2)/(3)+(R(2))/(3)*I", "-8"};
  assert_equation_system_exact_solve_to(equations8, EquationStore::Error::NoError, EquationStore::Type::PolynomialMonovariable, (const char **)variablesx, solutions8, 3);

  // 2*x^2-4*x+4=3
  const char * equations9[] = {"2*x^2-4*x+4=3", 0};
  const char * solutions9[] = {"(-R(2)+2)/(2)","(R(2)+2)/(2)", "8"};
  assert_equation_system_exact_solve_to(equations9, EquationStore::Error::NoError, EquationStore::Type::PolynomialMonovariable, (const char **)variablesx, solutions9, 3);

  // 2*x^2-4*x+2=0
  const char * equations10[] = {"2*x^2-4*x+2=0", 0};
  const char * solutions10[] = {"1", "0"};
  assert_equation_system_exact_solve_to(equations10, EquationStore::Error::NoError, EquationStore::Type::PolynomialMonovariable, (const char **)variablesx, solutions10, 2);

  // x^2+x+1=3*x^2+pi*x-R(5)
  const char * equations11[] = {"x^2+x+1=3*x^2+P*x-R(5)", 0};
  const char * solutions11[] = {"(R(P$2#-2*P+8*R(5)+9)-P+1)/(4)", "(-R(P$2#-2*P+8*R(5)+9)-P+1)/(4)", "P$2#-2*P+8*R(5)+9"};
  assert_equation_system_exact_solve_to(equations11, EquationStore::Error::NoError, EquationStore::Type::PolynomialMonovariable, (const char **)variablesx, solutions11, 3);

  // TODO
  // x^3 - 4x^2 + 6x - 24 = 0
  //const char * equations10[] = {"2*x^2-4*x+4=3", 0};
  //assert_equation_system_exact_solve_to(equations10, EquationStore::Error::NoError, EquationStore::Type::PolynomialMonovariable, {"x", ""}, {"4", "I*R(6)", "-I*R(6)", "-11616"}, 4);

  //x^3+x^2+1=0
  // x^3-3x-2=0

  // Linear System
  const char * equations12[] = {"x+y=0", 0};
  assert_equation_system_exact_solve_to(equations12,  EquationStore::Error::NoError, EquationStore::Type::LinearSystem, (const char **)variablesx, nullptr, INT_MAX);

  const char * variablesxy[] = {"x", "y", ""};

  const char * equations13[] = {"x+y=0", "3x+y=-5", 0};
  const char * solutions13[] = {"-(5)/(2)", "(5)/(2)"};
  assert_equation_system_exact_solve_to(equations13,  EquationStore::Error::NoError, EquationStore::Type::LinearSystem, (const char **)variablesxy, solutions13, 2);

  const char * variablesxyz[] = {"x", "y", "z", ""};

  const char * equations14[] = {"x+y=0", "3x+y+z=-5", "4z-P=0", 0};
  const char * solutions14[] = {"(-P-20)/(8)", "(P+20)/(8)", "(P)/(4)"};
  assert_equation_system_exact_solve_to(equations14,  EquationStore::Error::NoError, EquationStore::Type::LinearSystem, (const char **)variablesxyz, solutions14, 3);

  // Monovariable non-polynomial equation
  double solutions15[] = {-90.0, 90.0};
  assert_equation_approximate_solve_to("cos(x)=0", -100.0, 100.0, "x", solutions15, 2, false);

  double solutions16[] = {-810.0, -630.0, -450.0, -270.0, -90.0, 90.0, 270.0, 450.0, 630.0, 810.0};
  assert_equation_approximate_solve_to("cos(x)=0", -900.0, 1000.0, "x", solutions16, 10, true);

  double solutions17[] = {0};
  assert_equation_approximate_solve_to("R(y)=0", -900.0, 1000.0, "y", solutions17, 1, false);

  // Long variable names
  const char * variablesabcde[] = {"abcde", ""};
  const char * equations18[] = {"2abcde+3=4", 0};
  const char * solutions18[] = {"(1)/(2)"};
  assert_equation_system_exact_solve_to(equations18,  EquationStore::Error::NoError, EquationStore::Type::LinearSystem, (const char **)variablesabcde, solutions18, 1);

  const char * variablesBig1Big2[] = {"Big1", "Big2", ""};
  const char * equations19[] = {"Big1+Big2=0", "3Big1+Big2=-5", 0};
  const char * solutions19[] = {"-(5)/(2)", "(5)/(2)"};
  assert_equation_system_exact_solve_to(equations19,  EquationStore::Error::NoError, EquationStore::Type::LinearSystem, (const char **)variablesBig1Big2, solutions19, 2);
}

QUIZ_CASE(equation_solve_complex_format) {
  Poincare::Preferences::sharedPreferences()->setComplexFormat(Poincare::Preferences::ComplexFormat::Real);
  const char * variablesx[] = {"x", ""};
  // x+I = 0 --> x = -I
  const char * equations0[] = {"x+I=0", 0};
  const char * solutions0[] = {"-I"};
  assert_equation_system_exact_solve_to(equations0,  EquationStore::Error::NoError, EquationStore::Type::LinearSystem, (const char **)variablesx, solutions0, 1);

  // x+R(-1) = 0 --> Not defined in R
  const char * equations1[] = {"x+R(-1)=0", 0};
  assert_equation_system_exact_solve_to(equations1,  EquationStore::Error::EquationUnreal, EquationStore::Type::LinearSystem, (const char **)variablesx, nullptr, 0);

  // x^2+x+1=0 --> No solution in R
  const char * equations2[] = {"x^2+x+1=0", 0};
  const char * delta2[] = {"-3"};
  assert_equation_system_exact_solve_to(equations2, EquationStore::Error::NoError, EquationStore::Type::PolynomialMonovariable, (const char **)variablesx, delta2, 1);

  // x^2-R(-1)=0 --> Not defined in R
  const char * equations3[] = {"x^2-R(-1)=0", 0};
  assert_equation_system_exact_solve_to(equations3, EquationStore::Error::EquationUnreal, EquationStore::Type::PolynomialMonovariable, (const char **)variablesx, nullptr, 0);

  // x+R(-1)*R(-1) = 0 --> Not defined in R
  const char * equations4[] = {"x+R(-1)*R(-1)=0", 0};
  assert_equation_system_exact_solve_to(equations4,  EquationStore::Error::EquationUnreal, EquationStore::Type::LinearSystem, (const char **)variablesx, nullptr, 0);

  Poincare::Preferences::sharedPreferences()->setComplexFormat(Poincare::Preferences::ComplexFormat::Cartesian);
  // x+I = 0 --> x = -I
  assert_equation_system_exact_solve_to(equations0,  EquationStore::Error::NoError, EquationStore::Type::LinearSystem, (const char **)variablesx, solutions0, 1);

  // x+R(-1) = 0 --> x = -I
  assert_equation_system_exact_solve_to(equations1,  EquationStore::Error::NoError, EquationStore::Type::LinearSystem, (const char **)variablesx, solutions0, 1);

  // x^2+x+1=0
  const char * solutions2[] = {"-(1)/(2)-(R(3))/(2)*I","-(1)/(2)+(R(3))/(2)*I", "-3"};
  assert_equation_system_exact_solve_to(equations2, EquationStore::Error::NoError, EquationStore::Type::PolynomialMonovariable, (const char **)variablesx, solutions2, 3);

  // x^2-R(-1)=0
  const char * solutions3[] = {"-(R(2))/(2)-(R(2))/(2)*I", "(R(2))/(2)+(R(2))/(2)*I","4*I"};
  assert_equation_system_exact_solve_to(equations3, EquationStore::Error::NoError, EquationStore::Type::PolynomialMonovariable, (const char **)variablesx, solutions3, 3);

  // x+R(-1)*R(-1) = 0
  const char * solutions4[] = {"1"};
  assert_equation_system_exact_solve_to(equations4,  EquationStore::Error::NoError, EquationStore::Type::LinearSystem, (const char **)variablesx, solutions4, 1);

  Poincare::Preferences::sharedPreferences()->setComplexFormat(Poincare::Preferences::ComplexFormat::Polar);
  // x+I = 0 --> x = e^(-pi/2*i)
  const char * solutions0Polar[] = {"X$-(P)/(2)*I#"};
  assert_equation_system_exact_solve_to(equations0,  EquationStore::Error::NoError, EquationStore::Type::LinearSystem, (const char **)variablesx, solutions0Polar, 1);

  // x+R(-1) = 0 --> x = e^(-pi/2*i)
  assert_equation_system_exact_solve_to(equations1,  EquationStore::Error::NoError, EquationStore::Type::LinearSystem, (const char **)variablesx, solutions0Polar, 1);

  // x^2+x+1=0
  const char * solutions2Polar[] = {"X$-(2*P)/(3)*I#","X$(2*P)/(3)*I#", "3*X$P*I#"};
  assert_equation_system_exact_solve_to(equations2, EquationStore::Error::NoError, EquationStore::Type::PolynomialMonovariable, (const char **)variablesx, solutions2Polar, 3);

  // x^2-R(-1)=0
  const char * solutions3Polar[] = {"X$-(3*P)/(4)*I#", "X$(P)/(4)*I#", "4*X$(P)/(2)*I#"};
  assert_equation_system_exact_solve_to(equations3, EquationStore::Error::NoError, EquationStore::Type::PolynomialMonovariable, (const char **)variablesx, solutions3Polar, 3);

}

}