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/**

* @typedef {number} Cell

* @typedef {Cell[][]|Cell[][][]} Matrix

* @typedef {number[]} Shape

* @typedef {number[]} CellIndices

*/

/**

* Gets the matrix's shape.

*

* @param {Matrix} m

* @returns {Shape}

*/

export const shape = (m) => {

const shapes = [];

let dimension = m;

while (dimension && Array.isArray(dimension)) {

shapes.push(dimension.length);

dimension = (dimension.length && [...dimension][0]) || null;

}

return shapes;

};

/**

* Checks if matrix has a correct type.

*

* @param {Matrix} m

* @throws {Error}

*/

const validateType = (m) => {

if (

!m

|| !Array.isArray(m)

|| !Array.isArray(m[0])

) {

throw new Error('Invalid matrix format');

}

};

/**

* Checks if matrix is two dimensional.

*

* @param {Matrix} m

* @throws {Error}

*/

const validate2D = (m) => {

validateType(m);

const aShape = shape(m);

if (aShape.length !== 2) {

throw new Error('Matrix is not of 2D shape');

}

};

/**

* Validates that matrices are of the same shape.

*

* @param {Matrix} a

* @param {Matrix} b

* @trows {Error}

*/

export const validateSameShape = (a, b) => {

validateType(a);

validateType(b);

const aShape = shape(a);

const bShape = shape(b);

if (aShape.length !== bShape.length) {

throw new Error('Matrices have different dimensions');

}

while (aShape.length && bShape.length) {

if (aShape.pop() !== bShape.pop()) {

throw new Error('Matrices have different shapes');

}

}

};

/**

* Generates the matrix of specific shape with specific values.

*

* @param {Shape} mShape - the shape of the matrix to generate

* @param {function({CellIndex}): Cell} fill - cell values of a generated matrix.

* @returns {Matrix}

*/

export const generate = (mShape, fill) => {

/**

* Generates the matrix recursively.

*

* @param {Shape} recShape - the shape of the matrix to generate

* @param {CellIndices} recIndices

* @returns {Matrix}

*/

const generateRecursively = (recShape, recIndices) => {

if (recShape.length === 1) {

return Array(recShape[0])

.fill(null)

.map((cellValue, cellIndex) => fill([...recIndices, cellIndex]));

}

const m = [];

for (let i = 0; i < recShape[0]; i += 1) {

m.push(generateRecursively(recShape.slice(1), [...recIndices, i]));

}

return m;

};

return generateRecursively(mShape, []);

};

/**

* Generates the matrix of zeros of specified shape.

*

* @param {Shape} mShape - shape of the matrix

* @returns {Matrix}

*/

export const zeros = (mShape) => {

return generate(mShape, () => 0);

};

/**

* @param {Matrix} a

* @param {Matrix} b

* @return Matrix

* @throws {Error}

*/

export const dot = (a, b) => {

// Validate inputs.

validate2D(a);

validate2D(b);

// Check dimensions.

const aShape = shape(a);

const bShape = shape(b);

if (aShape[1] !== bShape[0]) {

throw new Error('Matrices have incompatible shape for multiplication');

}

// Perform matrix multiplication.

const outputShape = [aShape[0], bShape[1]];

const c = zeros(outputShape);

for (let bCol = 0; bCol < b[0].length; bCol += 1) {

for (let aRow = 0; aRow < a.length; aRow += 1) {

let cellSum = 0;

for (let aCol = 0; aCol < a[aRow].length; aCol += 1) {

cellSum += a[aRow][aCol] * b[aCol][bCol];

}

c[aRow][bCol] = cellSum;

}

}

return c;

};

/**

* Transposes the matrix.

*

* @param {Matrix} m

* @returns Matrix

* @throws {Error}

*/

export const t = (m) => {

validate2D(m);

const mShape = shape(m);

const transposed = zeros([mShape[1], mShape[0]]);

for (let row = 0; row < m.length; row += 1) {

for (let col = 0; col < m[0].length; col += 1) {

transposed[col][row] = m[row][col];

}

}

return transposed;

};

/**

* Traverses the matrix.

*

* @param {Matrix} m

* @param {function(indices: CellIndices, c: Cell)} visit

*/

export const walk = (m, visit) => {

/**

* Traverses the matrix recursively.

*

* @param {Matrix} recM

* @param {CellIndices} cellIndices

* @return {Matrix}

*/

const recWalk = (recM, cellIndices) => {

const recMShape = shape(recM);

if (recMShape.length === 1) {

for (let i = 0; i < recM.length; i += 1) {

visit([...cellIndices, i], recM[i]);

}

}

for (let i = 0; i < recM.length; i += 1) {

recWalk(recM[i], [...cellIndices, i]);

}

};

recWalk(m, []);

};

/**

* Gets the matrix cell value at specific index.

*

* @param {Matrix} m - Matrix that contains the cell that needs to be updated

* @param {CellIndices} cellIndices - Array of cell indices

* @return {Cell}

*/

export const getCellAtIndex = (m, cellIndices) => {

// We start from the row at specific index.

let cell = m[cellIndices[0]];

// Going deeper into the next dimensions but not to the last one to preserve

// the pointer to the last dimension array.

for (let dimIdx = 1; dimIdx < cellIndices.length - 1; dimIdx += 1) {

cell = cell[cellIndices[dimIdx]];

}

// At this moment the cell variable points to the array at the last needed dimension.

return cell[cellIndices[cellIndices.length - 1]];

};

/**

* Update the matrix cell at specific index.

*

* @param {Matrix} m - Matrix that contains the cell that needs to be updated

* @param {CellIndices} cellIndices - Array of cell indices

* @param {Cell} cellValue - New cell value

*/

export const updateCellAtIndex = (m, cellIndices, cellValue) => {

// We start from the row at specific index.

let cell = m[cellIndices[0]];

// Going deeper into the next dimensions but not to the last one to preserve

// the pointer to the last dimension array.

for (let dimIdx = 1; dimIdx < cellIndices.length - 1; dimIdx += 1) {

cell = cell[cellIndices[dimIdx]];

}

// At this moment the cell variable points to the array at the last needed dimension.

cell[cellIndices[cellIndices.length - 1]] = cellValue;

};

/**

* Adds two matrices element-wise.

*

* @param {Matrix} a

* @param {Matrix} b

* @return {Matrix}

*/

export const add = (a, b) => {

validateSameShape(a, b);

const result = zeros(shape(a));

walk(a, (cellIndices, cellValue) => {

updateCellAtIndex(result, cellIndices, cellValue);

});

walk(b, (cellIndices, cellValue) => {

const currentCellValue = getCellAtIndex(result, cellIndices);

updateCellAtIndex(result, cellIndices, currentCellValue + cellValue);

});

return result;

};

/**

* Multiplies two matrices element-wise.

*

* @param {Matrix} a

* @param {Matrix} b

* @return {Matrix}

*/

export const mul = (a, b) => {

validateSameShape(a, b);

const result = zeros(shape(a));

walk(a, (cellIndices, cellValue) => {

updateCellAtIndex(result, cellIndices, cellValue);

});

walk(b, (cellIndices, cellValue) => {

const currentCellValue = getCellAtIndex(result, cellIndices);

updateCellAtIndex(result, cellIndices, currentCellValue * cellValue);

});

return result;

};

/**

* Subtract two matrices element-wise.

*

* @param {Matrix} a

* @param {Matrix} b

* @return {Matrix}

*/

export const sub = (a, b) => {

validateSameShape(a, b);

const result = zeros(shape(a));

walk(a, (cellIndices, cellValue) => {

updateCellAtIndex(result, cellIndices, cellValue);

});

walk(b, (cellIndices, cellValue) => {

const currentCellValue = getCellAtIndex(result, cellIndices);

updateCellAtIndex(result, cellIndices, currentCellValue - cellValue);

});

return result;

};