poly_test.cc

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// Copyright (c) 2007, 2008 libmv authors.
//
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// furnished to do so, subject to the following conditions:
//
// The above copyright notice and this permission notice shall be included in
// all copies or substantial portions of the Software.
//
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// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
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#include "libmv/numeric/poly.h"
#include "libmv/numeric/numeric.h"
#include "testing/testing.h"
 
using namespace libmv;
 
namespace {
 
// Find the polynomial coefficients of x in the equation
//
//   (x - a)(x - b)(x - c) == 0
//
// by expanding to
//
//   x^3 - (c+b+a) * x^2 + (a*b+(b+a)*c) * x - a*b*c = 0.
//           = p               = q              = r
void CoeffsForCubicZeros(
    double a, double b, double c, double* p, double* q, double* r) {
  *p = -(c + b + a);
  *q = (a * b + (b + a) * c);
  *r = -a * b * c;
}
 
TEST(Poly, SolveCubicPolynomial) {
  double a, b, c, aa, bb, cc;
  double p, q, r;
 
  a = 1;
  b = 2;
  c = 3;
  CoeffsForCubicZeros(a, b, c, &p, &q, &r);
  ASSERT_EQ(3, SolveCubicPolynomial(p, q, r, &aa, &bb, &cc));
  EXPECT_NEAR(a, aa, 1e-10);
  EXPECT_NEAR(b, bb, 1e-10);
  EXPECT_NEAR(c, cc, 1e-10);
 
  a = 0;
  b = 1;
  c = 3;
  CoeffsForCubicZeros(a, b, c, &p, &q, &r);
  ASSERT_EQ(3, SolveCubicPolynomial(p, q, r, &aa, &bb, &cc));
  EXPECT_NEAR(a, aa, 1e-10);
  EXPECT_NEAR(b, bb, 1e-10);
  EXPECT_NEAR(c, cc, 1e-10);
 
  a = -10;
  b = 0;
  c = 1;
  CoeffsForCubicZeros(a, b, c, &p, &q, &r);
  ASSERT_EQ(3, SolveCubicPolynomial(p, q, r, &aa, &bb, &cc));
  EXPECT_NEAR(a, aa, 1e-10);
  EXPECT_NEAR(b, bb, 1e-10);
  EXPECT_NEAR(c, cc, 1e-10);
 
  a = -8;
  b = 1;
  c = 3;
  CoeffsForCubicZeros(a, b, c, &p, &q, &r);
  ASSERT_EQ(3, SolveCubicPolynomial(p, q, r, &aa, &bb, &cc));
  EXPECT_NEAR(a, aa, 1e-10);
  EXPECT_NEAR(b, bb, 1e-10);
  EXPECT_NEAR(c, cc, 1e-10);
 
  a = 28;
  b = 28;
  c = 105;
  CoeffsForCubicZeros(a, b, c, &p, &q, &r);
  ASSERT_EQ(3, SolveCubicPolynomial(p, q, r, &aa, &bb, &cc));
  EXPECT_NEAR(a, aa, 1e-10);
  EXPECT_NEAR(b, bb, 1e-10);
  EXPECT_NEAR(c, cc, 1e-10);
}
}  // namespace