Examples of org.apache.commons.math3.fraction.BigFraction

Package org.apache.commons.math3.fraction

Examples of org.apache.commons.math3.fraction.BigFraction

org.apache.commons.math3.fraction.BigFraction
Representation of a rational number without any overflow. This class is immutable. @since 2.0

        final int k = (int) FastMath.ceil(n * d);


        final FieldMatrix<BigFraction> H = this.createH(d);
        final FieldMatrix<BigFraction> Hpower = H.power(n);


        BigFraction pFrac = Hpower.getEntry(k - 1, k - 1);


        for (int i = 1; i <= n; ++i) {
            pFrac = pFrac.multiply(i).divide(n);
        }


        /*
         * BigFraction.doubleValue converts numerator to double and the
         * denominator to double and divides afterwards. That gives NaN quite
         * easy. This does not (scale is the number of digits):
         */
        return pFrac.bigDecimalValue(20, BigDecimal.ROUND_HALF_UP).doubleValue();
    }

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        if (hDouble >= 1) {
            throw new NumberIsTooLargeException(hDouble, 1.0, false);
        }


        BigFraction h = null;


        try {
            h = new BigFraction(hDouble, 1.0e-20, 10000);
        } catch (FractionConversionException e1) {
            try {
                h = new BigFraction(hDouble, 1.0e-10, 10000);
            } catch (FractionConversionException e2) {
                h = new BigFraction(hDouble, 1.0e-5, 10000);
            }
        }


        final BigFraction[][] Hdata = new BigFraction[m][m];


        /*
         * Start by filling everything with either 0 or 1.
         */
        for (int i = 0; i < m; ++i) {
            for (int j = 0; j < m; ++j) {
                if (i - j + 1 < 0) {
                    Hdata[i][j] = BigFraction.ZERO;
                } else {
                    Hdata[i][j] = BigFraction.ONE;
                }
            }
        }


        /*
         * Setting up power-array to avoid calculating the same value twice:
         * hPowers[0] = h^1 ... hPowers[m-1] = h^m
         */
        final BigFraction[] hPowers = new BigFraction[m];
        hPowers[0] = h;
        for (int i = 1; i < m; ++i) {
            hPowers[i] = h.multiply(hPowers[i - 1]);
        }


        /*
         * First column and last row has special values (each other reversed).
         */
        for (int i = 0; i < m; ++i) {
            Hdata[i][0] = Hdata[i][0].subtract(hPowers[i]);
            Hdata[m - 1][i] = Hdata[m - 1][i].subtract(hPowers[m - i - 1]);
        }


        /*
         * [1] states: "For 1/2 < h < 1 the bottom left element of the matrix
         * should be (1 - 2*h^m + (2h - 1)^m )/m!" Since 0 <= h < 1, then if h >
         * 1/2 is sufficient to check:
         */
        if (h.compareTo(BigFraction.ONE_HALF) == 1) {
            Hdata[m - 1][0] = Hdata[m - 1][0].add(h.multiply(2).subtract(1).pow(m));
        }


        /*
         * Aside from the first column and last row, the (i, j)-th element is
         * 1/(i - j + 1)! if i - j + 1 >= 0, else 0. 1's and 0's are already

View Full Code Here

                        //      y_0 = -m_13 / (2 m_11)
                        //      z_0 = +m_14 / (2 m_11)
                        // Note that the minors m_11, m_12, m_13 and m_14 all have the last column
                        // filled with 1.0, hence simplifying the computation
                        final BigFraction[] c2 = new BigFraction[] {
                            new BigFraction(vA.getX()), new BigFraction(vB.getX()),
                            new BigFraction(vC.getX()), new BigFraction(vD.getX())
                        };
                        final BigFraction[] c3 = new BigFraction[] {
                            new BigFraction(vA.getY()), new BigFraction(vB.getY()),
                            new BigFraction(vC.getY()), new BigFraction(vD.getY())
                        };
                        final BigFraction[] c4 = new BigFraction[] {
                            new BigFraction(vA.getZ()), new BigFraction(vB.getZ()),
                            new BigFraction(vC.getZ()), new BigFraction(vD.getZ())
                        };
                        final BigFraction[] c1 = new BigFraction[] {
                            c2[0].multiply(c2[0]).add(c3[0].multiply(c3[0])).add(c4[0].multiply(c4[0])),
                            c2[1].multiply(c2[1]).add(c3[1].multiply(c3[1])).add(c4[1].multiply(c4[1])),
                            c2[2].multiply(c2[2]).add(c3[2].multiply(c3[2])).add(c4[2].multiply(c4[2])),
                            c2[3].multiply(c2[3]).add(c3[3].multiply(c3[3])).add(c4[3].multiply(c4[3]))
                        };
                        final BigFraction twoM11  = minor(c2, c3, c4).multiply(2);
                        final BigFraction m12     = minor(c1, c3, c4);
                        final BigFraction m13     = minor(c1, c2, c4);
                        final BigFraction m14     = minor(c1, c2, c3);
                        final BigFraction centerX = m12.divide(twoM11);
                        final BigFraction centerY = m13.divide(twoM11).negate();
                        final BigFraction centerZ = m14.divide(twoM11);
                        final BigFraction dx      = c2[0].subtract(centerX);
                        final BigFraction dy      = c3[0].subtract(centerY);
                        final BigFraction dz      = c4[0].subtract(centerZ);
                        final BigFraction r2      = dx.multiply(dx).add(dy.multiply(dy)).add(dz.multiply(dz));
                        return new EnclosingBall<Euclidean3D, Vector3D>(new Vector3D(centerX.doubleValue(),
                                                                                     centerY.doubleValue(),
                                                                                     centerZ.doubleValue()),
                                                                        FastMath.sqrt(r2.doubleValue()),
                                                                        vA, vB, vC, vD);
                    }
                }
            }
        }

View Full Code Here

        final int k = (int) Math.ceil(n * d);


        final FieldMatrix<BigFraction> H = this.createExactH(d, n);
        final FieldMatrix<BigFraction> Hpower = H.power(n);


        BigFraction pFrac = Hpower.getEntry(k - 1, k - 1);


        for (int i = 1; i <= n; ++i) {
            pFrac = pFrac.multiply(i).divide(n);
        }


        /*
         * BigFraction.doubleValue converts numerator to double and the denominator to double and
         * divides afterwards. That gives NaN quite easy. This does not (scale is the number of
         * digits):
         */
        return pFrac.bigDecimalValue(20, BigDecimal.ROUND_HALF_UP).doubleValue();
    }

View Full Code Here

        final int m = 2 * k - 1;
        final double hDouble = k - n * d;
        if (hDouble >= 1) {
            throw new NumberIsTooLargeException(hDouble, 1.0, false);
        }
        BigFraction h = null;
        try {
            h = new BigFraction(hDouble, 1.0e-20, 10000);
        } catch (final FractionConversionException e1) {
            try {
                h = new BigFraction(hDouble, 1.0e-10, 10000);
            } catch (final FractionConversionException e2) {
                h = new BigFraction(hDouble, 1.0e-5, 10000);
            }
        }
        final BigFraction[][] Hdata = new BigFraction[m][m];


        /*
         * Start by filling everything with either 0 or 1.
         */
        for (int i = 0; i < m; ++i) {
            for (int j = 0; j < m; ++j) {
                if (i - j + 1 < 0) {
                    Hdata[i][j] = BigFraction.ZERO;
                } else {
                    Hdata[i][j] = BigFraction.ONE;
                }
            }
        }


        /*
         * Setting up power-array to avoid calculating the same value twice: hPowers[0] = h^1 ...
         * hPowers[m-1] = h^m
         */
        final BigFraction[] hPowers = new BigFraction[m];
        hPowers[0] = h;
        for (int i = 1; i < m; ++i) {
            hPowers[i] = h.multiply(hPowers[i - 1]);
        }


        /*
         * First column and last row has special values (each other reversed).
         */
        for (int i = 0; i < m; ++i) {
            Hdata[i][0] = Hdata[i][0].subtract(hPowers[i]);
            Hdata[m - 1][i] = Hdata[m - 1][i].subtract(hPowers[m - i - 1]);
        }


        /*
         * [1] states: "For 1/2 < h < 1 the bottom left element of the matrix should be (1 - 2*h^m +
         * (2h - 1)^m )/m!" Since 0 <= h < 1, then if h > 1/2 is sufficient to check:
         */
        if (h.compareTo(BigFraction.ONE_HALF) == 1) {
            Hdata[m - 1][0] = Hdata[m - 1][0].add(h.multiply(2).subtract(1).pow(m));
        }


        /*
         * Aside from the first column and last row, the (i, j)-th element is 1/(i - j + 1)! if i -
         * j + 1 >= 0, else 0. 1's and 0's are already put, so only division with (i - j + 1)! is

View Full Code Here

    }


    @Test
    public void testBigFractionConverter() {
        BigFraction[][] bfData = {
                { new BigFraction(1), new BigFraction(2), new BigFraction(3) },
                { new BigFraction(2), new BigFraction(5), new BigFraction(3) },
                { new BigFraction(1), new BigFraction(0), new BigFraction(8) }
        };
        FieldMatrix<BigFraction> m = new Array2DRowFieldMatrix<BigFraction>(bfData, false);
        RealMatrix converted = MatrixUtils.bigFractionMatrixToRealMatrix(m);
        RealMatrix reference = new Array2DRowRealMatrix(testData, false);
        Assert.assertEquals(0.0, converted.subtract(reference).getNorm(), 0.0);

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            /** {@inheritDoc} */
            public BigFraction[] generate(int k) {
                return new BigFraction[] {
                        BigFraction.ZERO,
                        BigFraction.TWO,
                        new BigFraction(2 * k)};
            }
        });
    }

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                new RecurrenceCoefficientsGenerator() {
            /** {@inheritDoc} */
            public BigFraction[] generate(int k) {
                final int kP1 = k + 1;
                return new BigFraction[] {
                        new BigFraction(2 * k + 1, kP1),
                        new BigFraction(-1, kP1),
                        new BigFraction(k, kP1)};
            }
        });
    }

View Full Code Here

            /** {@inheritDoc} */
            public BigFraction[] generate(int k) {
                final int kP1 = k + 1;
                return new BigFraction[] {
                        BigFraction.ZERO,
                        new BigFraction(k + kP1, kP1),
                        new BigFraction(k, kP1)};
            }
        });
    }

View Full Code Here


            // Pv,w,0(x) = 1;
            list.add(BigFraction.ONE);


            // P1(x) = (v - w) / 2 + (2 + v + w) * X / 2
            list.add(new BigFraction(v - w, 2));
            list.add(new BigFraction(2 + v + w, 2));


        }


        return buildPolynomial(degree, JACOBI_COEFFICIENTS.get(key),
                               new RecurrenceCoefficientsGenerator() {
            /** {@inheritDoc} */
            public BigFraction[] generate(int k) {
                k++;
                final int kvw      = k + v + w;
                final int twoKvw   = kvw + k;
                final int twoKvwM1 = twoKvw - 1;
                final int twoKvwM2 = twoKvw - 2;
                final int den      = 2 * k *  kvw * twoKvwM2;


                return new BigFraction[] {
                    new BigFraction(twoKvwM1 * (v * v - w * w), den),
                    new BigFraction(twoKvwM1 * twoKvw * twoKvwM2, den),
                    new BigFraction(2 * (k + v - 1) * (k + w - 1) * twoKvw, den)
                };
            }
        });


    }

View Full Code Here

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