dsp-collection/math/PolyReal.js

A collection of JavaScript modules for digital signal processing (written in TypeScript)

import MutableComplex from "./MutableComplex.js";
export function evaluateReal(a, x) {
    if (a.length == 0) {
        throw new Error("Zero length array.");
    }
    const n = a.length - 1;
    let r = a[n];
    for (let i = n - 1; i >= 0; i--) {
        r *= x;
        r += a[i];
    }
    return r;
}
export function evaluateComplex(a, x) {
    if (a.length == 0) {
        throw new Error("Zero length array.");
    }
    const n = a.length - 1;
    const r = new MutableComplex(a[n]);
    for (let i = n - 1; i >= 0; i--) {
        r.mulBy(x);
        r.addRealTo(a[i]);
    }
    return r;
}
export function expand(zeros) {
    const n = zeros.length;
    if (n == 0) {
        return Float64Array.of(1);
    }
    let a = Float64Array.of(-zeros[0], 1);
    for (let i = 1; i < n; i++) {
        const a2 = Float64Array.of(-zeros[i], 1);
        a = multiply(a, a2);
    }
    return a;
}
export function compareEqual(a1, a2, eps = 0) {
    const n1 = a1.length - 1;
    const n2 = a2.length - 1;
    const n = Math.max(n1, n2);
    for (let i = 0; i <= n; i++) {
        const v1 = (i <= n1) ? a1[i] : 0;
        const v2 = (i <= n2) ? a2[i] : 0;
        if (Math.abs(v1 - v2) > eps) {
            return false;
        }
    }
    return true;
}
export function add(a1, a2, eps = 0) {
    const n1 = a1.length - 1;
    const n2 = a2.length - 1;
    const n3 = Math.max(n1, n2);
    const a3 = new Float64Array(n3 + 1);
    for (let i = 0; i <= n3; i++) {
        const v1 = (i <= n1) ? a1[i] : 0;
        const v2 = (i <= n2) ? a2[i] : 0;
        a3[i] = v1 + v2;
    }
    return trim(a3, eps);
}
export function multiply(a1, a2, eps = 0) {
    if (a1.length == 0 || a2.length == 0) {
        throw new Error("Zero length arrays.");
    }
    if (a1.length == 1 && a1[0] == 0 || a2.length == 1 && a2[0] == 0) {
        return Float64Array.of(0);
    }
    const n1 = a1.length - 1;
    const n2 = a2.length - 1;
    const n3 = n1 + n2;
    const a3 = new Float64Array(n3 + 1);
    for (let i = 0; i <= n3; i++) {
        let t = 0;
        const p1 = Math.max(0, i - n2);
        const p2 = Math.min(n1, i);
        for (let j = p1; j <= p2; j++) {
            t += a1[j] * a2[i - j];
        }
        a3[i] = t;
    }
    return trim(a3, eps);
}
export function divide(a1r, a2r, eps = 0) {
    if (a1r.length == 0 || a2r.length == 0) {
        throw new Error("Zero length arrays.");
    }
    const a1 = trim(a1r, eps);
    const a2 = trim(a2r, eps);
    if (a2.length == 1) {
        if (a2[0] == 0) {
            throw new Error("Polynomial division by zero.");
        }
        if (a2[0] == 1) {
            return [Float64Array.from(a1), Float64Array.of(0)];
        }
        return [divByReal(a1, a2[0]), Float64Array.of(0)];
    }
    const n1 = a1.length - 1;
    const n2 = a2.length - 1;
    if (n1 < n2) {
        return [Float64Array.of(0), Float64Array.from(a1)];
    }
    const a = Float64Array.from(a1);
    const lc2 = a2[n2];
    for (let i = n1 - n2; i >= 0; i--) {
        const r = a[n2 + i] / lc2;
        a[n2 + i] = r;
        for (let j = 0; j < n2; ++j) {
            a[i + j] -= r * a2[j];
        }
    }
    const quotient = trim(a.subarray(n2), eps);
    const remainder = trim(a.subarray(0, n2), eps);
    return [quotient, remainder];
}
export function gcd(a1, a2, eps = 0) {
    let r1 = trim(a1, eps);
    let r2 = trim(a2, eps);
    makeMonic(r1);
    makeMonic(r2);
    if (r1.length < r2.length) {
        [r1, r2] = [r2, r1];
    }
    while (true) {
        if (r2.length < 2) {
            return Float64Array.of(1);
        }
        const r = divide(r1, r2, eps)[1];
        if (r.length == 1 && r[0] == 0) {
            return r2;
        }
        makeMonic(r);
        r1 = r2;
        r2 = r;
    }
}
function trim(a, eps = 0) {
    if (a.length == 0) {
        throw new Error("Zero length array.");
    }
    if (Math.abs(a[a.length - 1]) > eps) {
        return Float64Array.from(a);
    }
    let len = a.length - 1;
    while (len > 0 && Math.abs(a[len - 1]) <= eps) {
        len--;
    }
    if (len == 0) {
        return Float64Array.of(0);
    }
    const a2 = new Float64Array(len);
    for (let i = 0; i < len; i++) {
        a2[i] = a[i];
    }
    return a2;
}
function makeMonic(a) {
    const len = a.length;
    if (len == 0) {
        throw new Error("Zero length array.");
    }
    const lc = a[len - 1];
    if (lc == 1) {
        return;
    }
    if (lc == 0) {
        throw new Error("Leading coefficient is zero.");
    }
    a[len - 1] = 1;
    for (let i = 0; i < len - 1; i++) {
        a[i] /= lc;
    }
}
function divByReal(a, b) {
    const a2 = new Float64Array(a.length);
    for (let i = 0; i < a.length; i++) {
        a2[i] = a[i] / b;
    }
    return a2;
}
function divByRealInPlace(a, b) {
    for (let i = 0; i < a.length; i++) {
        a[i] /= b;
    }
}
export function evaluateFractionComplex(f, x) {
    const v1 = evaluateComplex(f[0], x);
    const v2 = evaluateComplex(f[1], x);
    return v1.div(v2);
}
export function addFractions(f1, f2, eps = 0) {
    if (compareEqual(f1[1], f2[1], eps)) {
        return [add(f1[0], f2[0], eps), Float64Array.from(f1[1])];
    }
    const g = gcd(f1[1], f2[1], eps);
    if (g.length == 1 && g[0] == 1) {
        const top = add(multiply(f1[0], f2[1], eps), multiply(f2[0], f1[1], eps));
        const bottom = multiply(f1[1], f2[1], eps);
        return [top, bottom];
    }
    const q1 = divide(f1[1], g, eps);
    const q2 = divide(f2[1], g, eps);
    const m1 = q1[0];
    const m2 = q2[0];
    const top = add(multiply(f1[0], m2, eps), multiply(f2[0], m1, eps));
    const bottom = multiply(f1[1], m2, eps);
    return [top, bottom];
}
export function multiplyFractions(f1, f2, eps = 0) {
    const top = multiply(f1[0], f2[0], eps);
    const bottom = multiply(f1[1], f2[1], eps);
    return [top, bottom];
}
export function normalizeFraction(f, eps = 0) {
    const top = trim(f[0], eps);
    const bottom = trim(f[1], eps);
    const lc = bottom[bottom.length - 1];
    if (lc == 0) {
        throw new Error("Fraction denominator is zero.");
    }
    divByRealInPlace(top, lc);
    divByRealInPlace(bottom, lc);
    return [top, bottom];
}
//# sourceMappingURL=PolyReal.js.map