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/**

* @brief Computes the inner product of two vectors (dot product).

* @param {Float64Array|Float32Array} a - The first vector.

* @param {Float64Array|Float32Array} b - The second vector.

* @returns {number} The inner product of vectors a and b.

*/

export function inner(a: Float64Array | Float32Array, b: Float64Array | Float32Array): number {

if (a.length !== b.length) {

throw new Error("Vectors must have the same length");

}

let result = 0;

for (let i = 0; i < a.length; i++) {

result += a[i] * b[i];

}

return result;

}

/**

* @brief Computes the dot product of two vectors (same as inner product).

* @param {Float64Array|Float32Array} a - The first vector.

* @param {Float64Array|Float32Array} b - The second vector.

* @returns {number} The dot product of vectors a and b.

*/

export function dot(a: Float64Array | Float32Array, b: Float64Array | Float32Array): number {

return inner(a, b);

}

/**

* @brief Computes the squared Euclidean distance between two vectors.

* @param {Float64Array|Float32Array|Int8Array|Uint8Array} a - The first vector.

* @param {Float64Array|Float32Array|Int8Array|Uint8Array} b - The second vector.

* @returns {number} The squared Euclidean distance between vectors a and b.

*/

export function sqeuclidean(

a: Float64Array | Float32Array | Int8Array | Uint8Array,

b: Float64Array | Float32Array | Int8Array | Uint8Array

): number {

if (a.length !== b.length) {

throw new Error("Vectors must have the same length");

}

let result = 0;

for (let i = 0; i < a.length; i++) {

result += (a[i] - b[i]) * (a[i] - b[i]);

}

return result;

}

/**

* @brief Computes the L2 Euclidean distance between two vectors.

* @param {Float64Array|Float32Array|Int8Array | Uint8Array} a - The first vector.

* @param {Float64Array|Float32Array|Int8Array | Uint8Array} b - The second vector.

* @returns {number} The L2 Euclidean distance between vectors a and b.

*/

export function euclidean(

a: Float64Array | Float32Array | Int8Array | Uint8Array,

b: Float64Array | Float32Array | Int8Array | Uint8Array

): number {

if (a.length !== b.length) {

throw new Error("Vectors must have the same length");

}

let result = 0;

for (let i = 0; i < a.length; i++) {

result += (a[i] - b[i]) * (a[i] - b[i]);

}

return Math.sqrt(result);

}

/**

* @brief Computes the cosine distance between two vectors.

* @param {Float64Array|Float32Array|Int8Array} a - The first vector.

* @param {Float64Array|Float32Array|Int8Array} b - The second vector.

* @returns {number} The cosine distance between vectors a and b.

*/

export function cosine(

a: Float64Array | Float32Array | Int8Array,

b: Float64Array | Float32Array | Int8Array

): number {

if (a.length !== b.length) {

throw new Error("Vectors must have the same length");

}

let dotProduct = 0;

let magnitudeA = 0;

let magnitudeB = 0;

for (let i = 0; i < a.length; i++) {

dotProduct += a[i] * b[i];

magnitudeA += a[i] * a[i];

magnitudeB += b[i] * b[i];

}

magnitudeA = Math.sqrt(magnitudeA);

magnitudeB = Math.sqrt(magnitudeB);

if (magnitudeA === 0 && magnitudeB === 0) return 0; // distance when both zero

if (magnitudeA === 0 || magnitudeB === 0) return 1; // distance when one is zero

return 1 - dotProduct / (magnitudeA * magnitudeB);

}

/**

* @brief Computes the bitwise Hamming distance between two vectors.

* @param {Uint8Array} a - The first vector.

* @param {Uint8Array} b - The second vector.

* @returns {number} The Hamming distance between vectors a and b.

*/

export const hamming = (a: Uint8Array, b: Uint8Array): number => {

if (a.length !== b.length) {

throw new Error("Arrays must be of the same length");

}

let distance = 0;

for (let i = 0; i < a.length; i++) {

let xor = a[i] ^ b[i]; // XOR operation to find differing bits

// Count the number of set bits (differing bits)

while (xor > 0) {

distance += xor & 1;

xor >>= 1;

}

}

return distance;

};

/**

* @brief Computes the bitwise Jaccard distance between two vectors.

* @param {Uint8Array} a - The first vector.

* @param {Uint8Array} b - The second vector.

* @returns {number} The Jaccard distance between vectors a and b.

*/

export const jaccard = (a: Uint8Array, b: Uint8Array): number => {

if (a.length !== b.length) {

throw new Error("Arrays must be of the same length");

}

let intersection = 0;

let union = 0;

for (let i = 0; i < a.length; i++) {

let ai = a[i];

let bi = b[i];

// Count the number of set bits in a AND b for intersection

let and = ai & bi;

while (and > 0) {

intersection += and & 1;

and >>= 1;

}

// Count the number of set bits in a OR b for union

let or = ai | bi;

while (or > 0) {

union += or & 1;

or >>= 1;

}

}

if (union === 0) return 0; // Avoid division by zero

return 1 - intersection / union;

};

/**

* @brief Computes the Kullback-Leibler divergence between two probability distributions.

* @param {Float64Array|Float32Array} a - The first vector.

* @param {Float64Array|Float32Array} b - The second vector.

* @returns {number} The Kullback-Leibler divergence between vectors a and b.

*/

export const kullbackleibler = (a: Float64Array | Float32Array, b: Float64Array | Float32Array): number => {

if (a.length !== b.length) {

throw new Error("Arrays must be of the same length");

}

let divergence = 0.0;

for (let i = 0; i < a.length; i++) {

if (a[i] < 0 || b[i] < 0) {

throw new Error("Negative values are not allowed in probability distributions");

}

if (b[i] === 0) {

throw new Error(

"Division by zero encountered in KL divergence calculation"

);

}

divergence += a[i] * Math.log(a[i] / b[i]);

}

return divergence;

};

/**

* @brief Computes the Jensen-Shannon distance between two probability distributions.

* @param {Float64Array|Float32Array} a - The first probability distribution.

* @param {Float64Array|Float32Array} b - The second probability distribution.

* @returns {number} The Jensen-Shannon distance between distributions a and b.

*/

export const jensenshannon = (a: Float64Array | Float32Array, b: Float64Array | Float32Array): number => {

if (a.length !== b.length) {

throw new Error("Arrays must be of the same length");

}

let divergence = 0;

for (let i = 0; i < a.length; i++) {

if (a[i] < 0 || b[i] < 0) {

throw new Error("Negative values are not allowed in probability distributions");

}

const m = (a[i] + b[i]) / 2;

if (m > 0) {

if (a[i] > 0) divergence += a[i] * Math.log(a[i] / m);

if (b[i] > 0) divergence += b[i] * Math.log(b[i] / m);

}

}

divergence /= 2;

return Math.sqrt(divergence);

};

export default {

sqeuclidean,

euclidean,

cosine,

inner,

hamming,

jaccard,

kullbackleibler,

jensenshannon,

};