Implement more vector operations for monzos

src/__tests__/index.spec.ts

@@ -14,6 +14,7 @@ import {
   iteratedEuclid,
   lcm,
   mmod,
+  norm,
   PRIMES,
   valueToCents,
 } from '../index';
@@ -224,3 +225,18 @@ describe('Value clamper', () => {
     expect(clamped).toBe(12800);
   });
 });
+
+describe('Norm', () => {
+  it('calculates an euclidean norm (float32)', () => {
+    const a = new Float32Array([-3, 4]);
+    expect(norm(a)).toBeCloseTo(5);
+  });
+  it('calculates a taxicab norm (int8)', () => {
+    const a = new Int8Array([3, -4]);
+    expect(norm(a, 'taxicab')).toBeCloseTo(7);
+  });
+  it('calculates a max norm (number[])', () => {
+    const a = [-3, -4];
+    expect(norm(a, 'maximum')).toBeCloseTo(4);
+  });
+});

src/index.ts

@@ -540,3 +540,29 @@ export function dot(a: NumberArray, b: NumberArray): number {
   }
   return result;
 }
+
+/**
+ * Calculate the norm (vector length) of an array of real numbers.
+ * @param array The array to measure.
+ * @param type Type of measurement.
+ * @returns The length of the vector.
+ */
+export function norm(
+  array: NumberArray,
+  type: 'euclidean' | 'taxicab' | 'maximum' = 'euclidean'
+) {
+  let result = 0;
+  for (let i = 0; i < array.length; ++i) {
+    if (type === 'taxicab') {
+      result += Math.abs(array[i]);
+    } else if (type === 'maximum') {
+      result = Math.max(result, Math.abs(array[i]));
+    } else {
+      result += array[i] * array[i];
+    }
+  }
+  if (type === 'euclidean') {
+    return Math.sqrt(result);
+  }
+  return result;
+}

src/monzo.ts

@@ -72,6 +72,69 @@ export function sub(a: Monzo, b: Monzo): Monzo {
   return result;
 }
 
+/**
+ * Scale a monzo by a scalar.
+ * @param monzo The monzo to scale.
+ * @param amount The amount to scale by.
+ * @returns The scalar multiple.
+ */
+export function scale(monzo: Monzo, amount: number) {
+  return monzo.map(component => component * amount);
+}
+
+/**
+ * Multiply two monzos component-wise.
+ * @param monzo The first monzo.
+ * @param weights The second monzo. Missing values interpreted as 1 (no change).
+ * @returns The first monzo weighted by the second.
+ */
+export function applyWeights(monzo: Monzo, weights: Monzo) {
+  const result = [...monzo];
+  for (let i = 0; i < Math.min(monzo.length, weights.length); ++i) {
+    result[i] *= weights[i];
+  }
+  return result;
+}
+
+/**
+ * Accumulate a monzo into the first one.
+ * @param target The monzo to accumulate into.
+ * @param source The monzo to add.
+ * @returns The (modified) target monzo.
+ */
+export function accumulate(target: Monzo, source: Monzo) {
+  for (let i = 0; i < Math.min(target.length, source.length); ++i) {
+    target[i] += source[i];
+  }
+  return target;
+}
+
+/**
+ * Decumulate a monzo into the first one.
+ * @param target The monzo to decumulate into.
+ * @param source The monzo to subtract.
+ * @returns The (modified) target monzo.
+ */
+export function decumulate(target: Monzo, source: Monzo) {
+  for (let i = 0; i < Math.min(target.length, source.length); ++i) {
+    target[i] -= source[i];
+  }
+  return target;
+}
+
+/**
+ * Rescale a monzo by a scalar.
+ * @param target The monzo to rescale.
+ * @param amount The amount to scale by.
+ * @returns The (modified) target monzo.
+ */
+export function rescale(target: Monzo, amount: number) {
+  for (let i = 0; i < target.length; ++i) {
+    target[i] *= amount;
+  }
+  return target;
+}
+
 /**
  * Extract the exponents of the prime factors of a rational number.
  * @param n Rational number to convert to a monzo.