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Accept vectors in matmul
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Implement matrix add, sub and scale.

ref #41
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@frostburn
frostburn committed Jun 24, 2024
1 parent 7ceadf4 commit 5f5ecee
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3 changes: 3 additions & 0 deletions CHANGELOG.md
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@@ -1,5 +1,8 @@
# Change log

## 0.10.1
* Feature: Accept vectors in `matmul` and `fractionalMatmul` and adjust return types accordingly.
* Feature: `matscale`, `matadd`, `matsub` and fractional variants. [#41](https://github.com/xenharmonic-devs/xen-dev-utils/issues/41)
## 0.10.0
* Feature: New array type `FractionalMonzo` with vector methods `fractionalMonzosEqual`, `fractionalAdd`, `fractionalSub`, `fractionalDot`, `fractionalScale` and `fractionalNorm`.
* Feature: Unnormalized Gram-Schmidt orthogonalization `gram` and `fractionalGram`.
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121 changes: 121 additions & 0 deletions src/__tests__/basis.spec.ts
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Expand Up @@ -7,11 +7,17 @@ import {
fractionalGram,
fractionalInv,
fractionalLenstraLenstraLovasz,
fractionalMatadd,
fractionalMatscale,
fractionalMatsub,
fractionalMatmul,
fractionalTranspose,
gram,
inv,
lenstraLenstraLovasz,
matadd,
matscale,
matsub,
matmul,
minor,
transpose,
Expand Down Expand Up @@ -368,6 +374,33 @@ describe('Matrix multiplication', () => {
]);
});

it('multiplies a matrix with a vector', () => {
const A = [
[1, 2],
[3, 4],
];
const v = [5, 6];
const u = matmul(A, v);
expect(u).toEqual([17, 39]);
});

it('multiplies a vector with a matrix', () => {
const A = [
[1, 2],
[3, 4],
];
const v = [5, 6];
const u = matmul(v, A);
expect(u).toEqual([23, 34]);
});

it('multiplies a vector with a vector', () => {
const u = [1, 2];
const v = [5, 6];
const s = matmul(u, v);
expect(s).toEqual(17);
});

it('multiplies two matrices (fractions)', () => {
const A = [
[1, 0, 1],
Expand All @@ -388,6 +421,33 @@ describe('Matrix multiplication', () => {
['17/3', '9', '6'],
]);
});

it('multiplies a matrix with a vector (fractions)', () => {
const A = [
[1, 2],
[3, 0.5],
];
const v = [5, '1/3'];
const u = fractionalMatmul(A, v);
expect(u.map(f => f.toFraction())).toEqual(['17/3', '91/6']);
});

it('multiplies a vector with a matrix (fractions)', () => {
const A = [
[1, 2],
[3, '1/3'],
];
const v = [5, 0.5];
const u = fractionalMatmul(v, A);
expect(u.map(f => f.toFraction())).toEqual(['13/2', '61/6']);
});

it('multiplies a vector with a vector (fractions)', () => {
const u = [0.5, 2];
const v = [5, '5/7'];
const s = fractionalMatmul(u, v);
expect(s.toFraction()).toBe('55/14');
});
});

describe('Matrix inverse', () => {
Expand Down Expand Up @@ -654,3 +714,64 @@ describe('Transpose', () => {
]);
});
});

describe('Auxiliary matrix methods', () => {
it('scales', () => {
const A = [
[1, 2],
[3, 4],
];
expect(matscale(A, 2)).toEqual([
[2, 4],
[6, 8],
]);
expect(
fractionalMatscale(A, 2).map(row => row.map(f => f.valueOf()))
).toEqual([
[2, 4],
[6, 8],
]);
});

it('adds', () => {
const A = [
[1, 2],
[3, 4],
];
const B = [
[-1, 5],
[6, 7],
];
expect(matadd(A, B)).toEqual([
[0, 7],
[9, 11],
]);
expect(
fractionalMatadd(A, B).map(row => row.map(f => f.valueOf()))
).toEqual([
[0, 7],
[9, 11],
]);
});

it('subtracts', () => {
const A = [
[1, 2],
[3, 4],
];
const B = [
[-1, 5],
[6, 7],
];
expect(matsub(A, B)).toEqual([
[2, -3],
[-3, -3],
]);
expect(
fractionalMatsub(A, B).map(row => row.map(f => f.valueOf()))
).toEqual([
[2, -3],
[-3, -3],
]);
});
});
161 changes: 158 additions & 3 deletions src/basis.ts
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Expand Up @@ -2,6 +2,8 @@ import {Fraction, FractionValue} from './fraction';
import {
FractionalMonzo,
ProtoFractionalMonzo,
add,
fractionalAdd,
fractionalDot,
fractionalScale,
fractionalSub,
Expand Down Expand Up @@ -437,12 +439,35 @@ export function fractionalInv(matrix: ProtoFractionalMonzo[]) {
}

/**
* Compute the matrix product of two arrays of arrays of numbers.
* Compute the matrix product of two matrices or vectors.
* @param A The left operand.
* @param B The right operand.
* @returns The matrix product of the operands.
*/
export function matmul(A: number[][], B: number[][]) {
export function matmul(A: number[], B: number[]): number;
export function matmul(A: number[], B: number[][]): number[];
export function matmul(A: number[][], B: number[]): number[];
export function matmul(A: number[][], B: number[][]): number[][];
export function matmul(A: number[] | number[][], B: number[] | number[][]) {
let numVectors = 0;
if (!Array.isArray(A[0])) {
A = [A as number[]];
numVectors++;
}
if (!Array.isArray(B[0])) {
B = (B as number[]).map(c => [c]);
numVectors++;
}
const result = matmul_(A as number[][], B as number[][]);
if (numVectors === 1) {
return result.flat();
} else if (numVectors === 2) {
return result[0][0];
}
return result;
}

function matmul_(A: number[][], B: number[][]) {
const height = A.length;
let width = 0;
for (const row of B) {
Expand Down Expand Up @@ -471,14 +496,55 @@ export function matmul(A: number[][], B: number[][]) {
}

/**
* Compute the matrix product of two arrays of arrays of fractions.
* Compute the matrix product of two matrices or vectors.
* @param A The left operand.
* @param B The right operand.
* @returns The matrix product of the operands.
*/
export function fractionalMatmul(
A: ProtoFractionalMonzo,
B: ProtoFractionalMonzo
): Fraction;
export function fractionalMatmul(
A: ProtoFractionalMonzo,
B: ProtoFractionalMonzo[]
): FractionalMonzo;
export function fractionalMatmul(
A: ProtoFractionalMonzo[],
B: ProtoFractionalMonzo
): FractionalMonzo;
export function fractionalMatmul(
A: ProtoFractionalMonzo[],
B: ProtoFractionalMonzo[]
): FractionalMonzo[];
export function fractionalMatmul(
A: ProtoFractionalMonzo | ProtoFractionalMonzo[],
B: ProtoFractionalMonzo | ProtoFractionalMonzo[]
) {
let numVectors = 0;
if (!Array.isArray(A[0])) {
A = [A as ProtoFractionalMonzo];
numVectors++;
}
if (!Array.isArray(B[0])) {
B = (B as ProtoFractionalMonzo).map(c => [c]);
numVectors++;
}
const result = fractionalMatmul_(
A as ProtoFractionalMonzo[],
B as ProtoFractionalMonzo[]
);
if (numVectors === 1) {
return result.flat();
} else if (numVectors === 2) {
return result[0][0];
}
return result;
}

export function fractionalMatmul_(
A: ProtoFractionalMonzo[],
B: ProtoFractionalMonzo[]
): FractionalMonzo[] {
const height = A.length;
let width = 0;
Expand Down Expand Up @@ -682,3 +748,92 @@ export function minor(matrix: any[][], i: number, j: number) {
}
return matrix;
}

/**
* Scale a matrix by a scalar.
* @param matrix The matrix to scale.
* @param amount The amount to scale by.
* @returns The scalar multiple.
*/
export function matscale(matrix: number[][], amount: number) {
return matrix.map(row => scale(row, amount));
}

/**
* Add two matrices.
* @param A The first matrix.
* @param B The second matrix.
* @returns The sum.
*/
export function matadd(A: number[][], B: number[][]) {
const result: number[][] = [];
const numRows = Math.max(A.length, B.length);
for (let i = 0; i < numRows; ++i) {
result.push(add(A[i] ?? [], B[i] ?? []));
}
return result;
}

/**
* Subtract two matrices.
* @param A The matrix to subtract from.
* @param B The matrix to subtract by.
* @returns The difference.
*/
export function matsub(A: number[][], B: number[][]) {
const result: number[][] = [];
const numRows = Math.max(A.length, B.length);
for (let i = 0; i < numRows; ++i) {
result.push(sub(A[i] ?? [], B[i] ?? []));
}
return result;
}

/**
* Scale a matrix by a scalar.
* @param matrix The matrix to scale.
* @param amount The amount to scale by.
* @returns The scalar multiple.
*/
export function fractionalMatscale(
matrix: ProtoFractionalMonzo[],
amount: FractionValue
) {
return matrix.map(row => fractionalScale(row, amount));
}

/**
* Add two matrices.
* @param A The first matrix.
* @param B The second matrix.
* @returns The sum.
*/
export function fractionalMatadd(
A: ProtoFractionalMonzo[],
B: ProtoFractionalMonzo[]
) {
const result: FractionalMonzo[] = [];
const numRows = Math.max(A.length, B.length);
for (let i = 0; i < numRows; ++i) {
result.push(fractionalAdd(A[i] ?? [], B[i] ?? []));
}
return result;
}

/**
* Subtract two matrices.
* @param A The matrix to subtract from.
* @param B The matrix to subtract by.
* @returns The difference.
*/
export function fractionalMatsub(
A: ProtoFractionalMonzo[],
B: ProtoFractionalMonzo[]
) {
const result: FractionalMonzo[] = [];
const numRows = Math.max(A.length, B.length);
for (let i = 0; i < numRows; ++i) {
result.push(fractionalSub(A[i] ?? [], B[i] ?? []));
}
return result;
}

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