Published
Edited
Apr 11, 2021
Importers
9 stars
// Clenshaw's method.
evaluate = function evaluate(coeffs, x) {
const x2 = 2 * x;
let d = coeffs.length - 1, b2 = 0, b1 = (d % 2) ? coeffs[d--] : 0;
for (let i = d; i >= 2; i -= 2) {
b2 = coeffs[i] + x2 * b1 - b2;
b1 = coeffs[i-1] + x2 * b2 - b1;
}
return coeffs[0] + x * b1 - b2;
}
// definite integral from -1 to 1
sum = function sum(coeffs) {
let s = 0, i = coeffs.length;
i = i + i % 2;
while ((i -= 2) >= 0) s += 2 * coeffs[i] / (1 - i*i);
return s;
}
// indefinite integral
cumsum = function cumsum(coeffs) {
let c = coeffs.slice(), i = c.push(0, 0) - 1, k = 0, newcoeffs = [];
c[0] *= 2;
while (--i) k = (newcoeffs[i] = (c[i-1] - c[i+1]) / (2*i)) - k;
newcoeffs[0] = (1 - 2 * coeffs.length % 2) * k;
return newcoeffs;
}
// derivative
diff = function diff(coeffs) {
let newcoeffs = [], i = coeffs.length;
newcoeffs[i--] = newcoeffs[i] = 0;
while (i--) newcoeffs[i] = newcoeffs[i+2] + 2*(i+1)*coeffs[i+1];
newcoeffs[0] *= .5;
newcoeffs.splice(-2);
return newcoeffs;
}
// Chebyshev nodes of the 2nd kind in [-1, 1]
chebpts = function chebpts (n) {
let pts = [], scale = Math.PI * .5 / (n - 1);
for (let i = n - 1; i >= 0; i--) {
pts[i] = Math.sin((1 - n + 2*i) * scale);
}
return pts;
}
coeffs2vals = function coeffs2vals (coeffs) {
// for now, only deal with real-valued coefficients.
coeffs = coeffs.slice();
const n = coeffs.length - 1;
if (n <= 0) return coeffs;
for (let i = 1; i < n; i++) {
coeffs[2*n - i] = coeffs[i] *= .5;
}
let imag = []; imag.length = 2*n; imag.fill(0);
fft_in_place(coeffs, imag);
let values = [];
for (let i = n; i >=0; i--) {
values[i] = coeffs[n-i];
}
return values;
}
vals2coeffs = function vals2coeffs (vals) {
const n = vals.length - 1;
if (n <= 0) return vals.slice();
let coeffs = [];
for (let i = n - 1; i >= 1; i--) {
coeffs[n + i] = coeffs[n - i] = vals[i];
}
coeffs[0] = vals[n]; coeffs[n] = vals[0];
let imag = []; imag.length = 2*n; imag.fill(0);
fft_in_place(imag, coeffs);
const scale = 1/n;
for (let i = 1; i <= n; i++) {
coeffs[i] *= scale;
}
coeffs[0] *= scale * .5; coeffs[n] *= scale * .5;
coeffs.splice(n+1);
return coeffs;
}
// Either truncate the array or pad it with zeros to match the desired length.
fixlength = function fixlength(array, n) {
const k = array.length;
if (k < n) { array.length = n; array.fill(0, k); }
else { array.splice(n); }
return array
}
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