June 2018 Update
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Ingy döt Net
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5278 changed files with 84726 additions and 14379 deletions
47
Task/Polynomial-regression/D/polynomial-regression.d
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47
Task/Polynomial-regression/D/polynomial-regression.d
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import std.algorithm;
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import std.range;
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import std.stdio;
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auto average(R)(R r) {
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auto t = r.fold!("a+b", "a+1")(0, 0);
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return cast(double) t[0] / t[1];
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}
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void polyRegression(int[] x, int[] y) {
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auto n = x.length;
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auto r = iota(0, n).array;
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auto xm = x.average();
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auto ym = y.average();
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auto x2m = r.map!"a*a".average();
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auto x3m = r.map!"a*a*a".average();
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auto x4m = r.map!"a*a*a*a".average();
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auto xym = x.zip(y).map!"a[0]*a[1]".average();
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auto x2ym = x.zip(y).map!"a[0]*a[0]*a[1]".average();
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auto sxx = x2m - xm * xm;
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auto sxy = xym - xm * ym;
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auto sxx2 = x3m - xm * x2m;
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auto sx2x2 = x4m - x2m * x2m;
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auto sx2y = x2ym - x2m * ym;
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auto b = (sxy * sx2x2 - sx2y * sxx2) / (sxx * sx2x2 - sxx2 * sxx2);
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auto c = (sx2y * sxx - sxy * sxx2) / (sxx * sx2x2 - sxx2 * sxx2);
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auto a = ym - b * xm - c * x2m;
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real abc(int xx) {
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return a + b * xx + c * xx * xx;
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}
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writeln("y = ", a, " + ", b, "x + ", c, "x^2");
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writeln(" Input Approximation");
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writeln(" x y y1");
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foreach (i; 0..n) {
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writefln("%2d %3d %5.1f", x[i], y[i], abc(x[i]));
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}
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}
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void main() {
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auto x = iota(0, 11).array;
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auto y = [1, 6, 17, 34, 57, 86, 121, 162, 209, 262, 321];
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polyRegression(x, y);
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}
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50
Task/Polynomial-regression/Java/polynomial-regression.java
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50
Task/Polynomial-regression/Java/polynomial-regression.java
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import java.util.Arrays;
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import java.util.function.IntToDoubleFunction;
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import java.util.stream.IntStream;
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public class PolynomialRegression {
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private static void polyRegression(int[] x, int[] y) {
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int n = x.length;
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int[] r = IntStream.range(0, n).toArray();
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double xm = Arrays.stream(x).average().orElse(Double.NaN);
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double ym = Arrays.stream(y).average().orElse(Double.NaN);
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double x2m = Arrays.stream(r).map(a -> a * a).average().orElse(Double.NaN);
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double x3m = Arrays.stream(r).map(a -> a * a * a).average().orElse(Double.NaN);
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double x4m = Arrays.stream(r).map(a -> a * a * a * a).average().orElse(Double.NaN);
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double xym = 0.0;
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for (int i = 0; i < x.length && i < y.length; ++i) {
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xym += x[i] * y[i];
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}
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xym /= Math.min(x.length, y.length);
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double x2ym = 0.0;
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for (int i = 0; i < x.length && i < y.length; ++i) {
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x2ym += x[i] * x[i] * y[i];
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}
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x2ym /= Math.min(x.length, y.length);
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double sxx = x2m - xm * xm;
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double sxy = xym - xm * ym;
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double sxx2 = x3m - xm * x2m;
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double sx2x2 = x4m - x2m * x2m;
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double sx2y = x2ym - x2m * ym;
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double b = (sxy * sx2x2 - sx2y * sxx2) / (sxx * sx2x2 - sxx2 * sxx2);
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double c = (sx2y * sxx - sxy * sxx2) / (sxx * sx2x2 - sxx2 * sxx2);
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double a = ym - b * xm - c * x2m;
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IntToDoubleFunction abc = (int xx) -> a + b * xx + c * xx * xx;
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System.out.println("y = " + a + " + " + b + "x + " + c + "x^2");
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System.out.println(" Input Approximation");
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System.out.println(" x y y1");
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for (int i = 0; i < n; ++i) {
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System.out.printf("%2d %3d %5.1f\n", x[i], y[i], abc.applyAsDouble(x[i]));
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}
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}
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public static void main(String[] args) {
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int[] x = IntStream.range(0, 11).toArray();
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int[] y = new int[]{1, 6, 17, 34, 57, 86, 121, 162, 209, 262, 321};
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polyRegression(x, y);
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}
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}
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@ -1,4 +1,5 @@
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function polyfit(x, y, n)
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A = [ float(x[i])^p for i = 1:length(x), p = 0:n ]
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A \ y
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end
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polyfit(x::Vector, y::Vector, deg::Int) = collect(v ^ p for v in x, p in 0:deg) \ y
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x = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
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y = [1, 6, 17, 34, 57, 86, 121, 162, 209, 262, 321]
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@show polyfit(x, y, 2)
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// version 1.1.51
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fun polyRegression(x: IntArray, y: IntArray) {
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val n = x.size
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val r = 0 until n
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val xm = x.average()
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val ym = y.average()
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val x2m = r.map { it * it }.average()
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val x3m = r.map { it * it * it }.average()
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val x4m = r.map { it * it * it * it }.average()
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val xym = x.zip(y).map { it.first * it.second }.average()
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val x2ym = x.zip(y).map { it.first * it.first * it.second }.average()
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val sxx = x2m - xm * xm
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val sxy = xym - xm * ym
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val sxx2 = x3m - xm * x2m
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val sx2x2 = x4m - x2m * x2m
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val sx2y = x2ym - x2m * ym
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val b = (sxy * sx2x2 - sx2y * sxx2) / (sxx * sx2x2 - sxx2 * sxx2)
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val c = (sx2y * sxx - sxy * sxx2) / (sxx * sx2x2 - sxx2 * sxx2)
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val a = ym - b * xm - c * x2m
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fun abc(xx: Int) = a + b * xx + c * xx * xx
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println("y = $a + ${b}x + ${c}x^2\n")
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println(" Input Approximation")
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println(" x y y1")
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for (i in 0 until n) {
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System.out.printf("%2d %3d %5.1f\n", x[i], y[i], abc(x[i]))
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}
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}
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fun main(args: Array<String>) {
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val x = IntArray(11) { it }
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val y = intArrayOf(1, 6, 17, 34, 57, 86, 121, 162, 209, 262, 321)
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polyRegression(x, y)
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}
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@ -0,0 +1,87 @@
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MODULE PolynomialRegression;
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FROM FormatString IMPORT FormatString;
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FROM RealStr IMPORT RealToStr;
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FROM Terminal IMPORT WriteString,WriteLn,ReadChar;
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PROCEDURE Eval(a,b,c,x : REAL) : REAL;
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BEGIN
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RETURN a + b*x + c*x*x;
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END Eval;
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PROCEDURE Regression(x,y : ARRAY OF INTEGER);
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VAR
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n,i : INTEGER;
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xm,x2m,x3m,x4m : REAL;
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ym : REAL;
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xym,x2ym : REAL;
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sxx,sxy,sxx2,sx2x2,sx2y : REAL;
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a,b,c : REAL;
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buf : ARRAY[0..63] OF CHAR;
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BEGIN
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n := SIZE(x)/SIZE(INTEGER);
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xm := 0.0;
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ym := 0.0;
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x2m := 0.0;
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x3m := 0.0;
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x4m := 0.0;
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xym := 0.0;
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x2ym := 0.0;
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FOR i:=0 TO n-1 DO
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xm := xm + FLOAT(x[i]);
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ym := ym + FLOAT(y[i]);
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x2m := x2m + FLOAT(x[i]) * FLOAT(x[i]);
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x3m := x3m + FLOAT(x[i]) * FLOAT(x[i]) * FLOAT(x[i]);
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x4m := x4m + FLOAT(x[i]) * FLOAT(x[i]) * FLOAT(x[i]) * FLOAT(x[i]);
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xym := xym + FLOAT(x[i]) * FLOAT(y[i]);
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x2ym := x2ym + FLOAT(x[i]) * FLOAT(x[i]) * FLOAT(y[i]);
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END;
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xm := xm / FLOAT(n);
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ym := ym / FLOAT(n);
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x2m := x2m / FLOAT(n);
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x3m := x3m / FLOAT(n);
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x4m := x4m / FLOAT(n);
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xym := xym / FLOAT(n);
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x2ym := x2ym / FLOAT(n);
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sxx := x2m - xm * xm;
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sxy := xym - xm * ym;
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sxx2 := x3m - xm * x2m;
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sx2x2 := x4m - x2m * x2m;
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sx2y := x2ym - x2m * ym;
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b := (sxy * sx2x2 - sx2y * sxx2) / (sxx * sx2x2 - sxx2 * sxx2);
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c := (sx2y * sxx - sxy * sxx2) / (sxx * sx2x2 - sxx2 * sxx2);
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a := ym - b * xm - c * x2m;
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WriteString("y = ");
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RealToStr(a, buf);
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WriteString(buf);
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WriteString(" + ");
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RealToStr(b, buf);
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WriteString(buf);
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WriteString("x + ");
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RealToStr(c, buf);
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WriteString(buf);
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WriteString("x^2");
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WriteLn;
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FOR i:=0 TO n-1 DO
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FormatString("%2i %3i ", buf, x[i], y[i]);
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WriteString(buf);
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RealToStr(Eval(a,b,c,FLOAT(x[i])), buf);
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WriteString(buf);
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WriteLn;
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END;
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END Regression;
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TYPE R = ARRAY[0..10] OF INTEGER;
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VAR
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x,y : R;
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BEGIN
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x := R{0,1,2,3,4,5,6,7,8,9,10};
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y := R{1,6,17,34,57,86,121,162,209,262,321};
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Regression(x,y);
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ReadChar;
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END PolynomialRegression.
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@ -1,10 +1,10 @@
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require 'matrix'
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def regress x, y, degree
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x_data = x.map { |xi| (0..degree).map { |pow| (xi**pow).to_f } }
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x_data = x.map { |xi| (0..degree).map { |pow| (xi**pow).to_r } }
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mx = Matrix[*x_data]
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my = Matrix.column_vector(y)
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((mx.t * mx).inv * mx.t * my).transpose.to_a[0]
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((mx.t * mx).inv * mx.t * my).transpose.to_a[0].map(&:to_f)
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end
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@ -1,5 +1,3 @@
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betas = regress [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10],
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[1, 6, 17, 34, 57, 86, 121, 162, 209, 262, 321],
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2
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p betas
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p regress([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10],
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[1, 6, 17, 34, 57, 86, 121, 162, 209, 262, 321],
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2)
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