`package be.tarsos.dsp.wavelet.lift;/*** * @author Ian Kaplan*/class PolynomialInterpolation { /** number of polynomial interpolation ponts */ private final static int numPts = 4; /** Table for 4-point interpolation coefficients */ private float fourPointTable[][]; /** Table for 2-point interpolation coefficients */ private float twoPointTable[][]; /** * <p> * The polynomial interpolation algorithm assumes that the known points are * located at x-coordinates 0, 1,.. N-1. An interpolated point is calculated * at <b><i>x</i></b>, using N coefficients. The polynomial coefficients for * the point <b><i>x</i></b> can be calculated staticly, using the Lagrange * method. * </p> * * @param x * the x-coordinate of the interpolated point * @param N * the number of polynomial points. * @param c * an array for returning the coefficients */ private void lagrange(float x, int N, float c[]) { float num, denom; for (int i = 0; i < N; i++) { num = 1; denom = 1; for (int k = 0; k < N; k++) { if (i != k) { num = num * (x - k); denom = denom * (i - k); } } // for k c[i] = num / denom; } // for i } // lagrange /** * <p> * For a given N-point polynomial interpolation, fill the coefficient table, * for points 0.5 ... (N-0.5). * </p> */ private void fillTable(int N, float table[][]) { float x; float n = N; int i = 0; for (x = 0.5f; x < n; x = x + 1.0f) { lagrange(x, N, table[i]); i++; } } // fillTable /** * <p> * PolynomialWavelets constructor * </p> * <p> * Build the 4-point and 2-point polynomial coefficient tables. * </p> */ public PolynomialInterpolation() { // Fill in the 4-point polynomial interplation table // for the points 0.5, 1.5, 2.5, 3.5 fourPointTable = new float[numPts][numPts]; fillTable(numPts, fourPointTable); // Fill in the 2-point polynomial interpolation table // for 0.5 and 1.5 twoPointTable = new float[2][2]; fillTable(2, twoPointTable); } // PolynomialWavelets constructor /** * Print an N x N table polynomial coefficient table */ private void printTable(float table[][], int N) { System.out.println(N + "-point interpolation table:"); double x = 0.5; for (int i = 0; i < N; i++) { System.out.print(x + ": "); for (int j = 0; j < N; j++) { System.out.print(table[i][j]); if (j < N - 1) System.out.print(", "); } System.out.println(); x = x + 1.0; } } /** * Print the 4-point and 2-point polynomial coefficient tables. */ public void printTables() { printTable(fourPointTable, numPts); printTable(twoPointTable, 2); } // printTables /** * <p> * For the polynomial interpolation point x-coordinate <b><i>x</i></b>, * return the associated polynomial interpolation coefficients. * </p> * * @param x * the x-coordinate for the interpolated pont * @param n * the number of polynomial interpolation points * @param c * an array to return the polynomial coefficients */ private void getCoef(float x, int n, float c[]) { float table[][] = null; int j = (int) x; if (j < 0 || j >= n) { System.out.println("PolynomialWavelets::getCoef: n = " + n + ", bad x value"); } if (n == numPts) { table = fourPointTable; } else if (n == 2) { table = twoPointTable; c[2] = 0.0f; c[3] = 0.0f; } else { System.out.println("PolynomialWavelets::getCoef: bad value for N"); } if (table != null) { for (int i = 0; i < n; i++) { c[i] = table[j][i]; } } } // getCoef /** * <p> * Given four points at the x,y coordinates {0,d<sub>0</sub>}, * {1,d<sub>1</sub>}, {2,d<sub>2</sub>}, {3,d<sub>3</sub>} return the * y-coordinate value for the polynomial interpolated point at * <b><i>x</i></b>. * </p> * * @param x * the x-coordinate for the point to be interpolated * @param N * the number of interpolation points * @param d * an array containing the y-coordinate values for the known * points (which are located at x-coordinates 0..N-1). * @return the y-coordinate value for the polynomial interpolated point at * <b><i>x</i></b>. */ public float interpPoint(float x, int N, float d[]) { float c[] = new float[numPts]; float point = 0; int n = numPts; if (N < numPts) n = N; getCoef(x, n, c); if (n == numPts) { point = c[0] * d[0] + c[1] * d[1] + c[2] * d[2] + c[3] * d[3]; } else if (n == 2) { point = c[0] * d[0] + c[1] * d[1]; } return point; } // interpPoint} // PolynomialInterpolation`