fix: Update types and add tests as requested by review

src/function/matrix/matrixFromFunction.js

@@ -6,8 +6,10 @@ const dependencies = ['typed', 'matrix', 'isZero']
 export const createMatrixFromFunction = /* #__PURE__ */ factory(name, dependencies, ({ typed, matrix, isZero }) => {
   /**
    * Create a matrix by evaluating a generating function at each index.
-   * The simplest overload returns a multi-dimensional array as long as `size` is an array.
-   * Passing `size` as a Matrix or specifying a `format` will result in returning a Matrix.
+   * The simplest overload returns a multi-dimensional array as long as `size`
+   * is an array.
+   * Passing `size` as a Matrix or specifying a `format` will result in
+   * returning a Matrix.
    *
    * Syntax:
    *
@@ -17,6 +19,37 @@ export const createMatrixFromFunction = /* #__PURE__ */ factory(name, dependenci
    *    math.matrixFromFunction(size, format, fn)
    *    math.matrixFromFunction(size, format, datatype, fn)
    *
+   * Where:
+   *
+   *    - `size: (number[] | Matrix)`
+   *      A vector giving the extent of the array to be created in each
+   *      dimension. If size has one entry, a vector is created; if it
+   *      has two, a rectangular array/Matrix is created; if three, a
+   *      three-dimensional array/Matrix is created; and so on.
+   *    - `fn: (index: number[]) => MathType`
+   *      The callback function that will generate the entries of the
+   *      matrix. It is called in turn with the index of each entry of
+   *      the matrix. The index is always an ordinary array of numbers
+   *      with the same length as _size_. So for vectors, you will get
+   *      indices like `[0]` or `[1]`, whereas for matrices, you will
+   *      get indices like `[2, 0]` or `[1,3]`. The return value may
+   *      be any type that can go in an array or Matrix entry, although
+   *      if you supply the _datatype_ argument, you must yourself ensure
+   *      the type of the return value matches. Note that currently,
+   *      your callback _fn_ will receive 0-based indices for the matrix
+   *      entries, regardless of whether matrixFromFunction is invoked
+   *      directly from JavaScript or via the mathjs expression language.
+   *    - `format: 'dense'|'sparse'`
+   *      Specifies the storage format for the resulting Matrix. Note that
+   *      if this argument is given, the return value will always be a
+   *      Matrix (rather than possibly an Array).
+   *    - `datatype: string`
+   *      Specifies the data type of entries of the new matrix. If given,
+   *      it should be the name of a data type that mathjs supports, as
+   *      returned by the math.typeOf function. It is up to the caller
+   *      to make certain that all values returned by _fn_ are consistent
+   *      with this datatype if specified.
+   *
    * Examples:
    *
    *    math.matrixFromFunction([3,3], i => i[0] - i[1]) // an antisymmetric matrix
@@ -25,7 +58,7 @@ export const createMatrixFromFunction = /* #__PURE__ */ factory(name, dependenci
    *
    * See also:
    *
-   *    matrix, zeros
+   *    matrix, typeOf, zeros
    *
    * @param {Array | Matrix} size   The size of the matrix to be created
    * @param {function} fn           Callback function invoked for every entry in the matrix

test/typescript-tests/testTypes.ts

@@ -1268,6 +1268,26 @@ Matrices examples
     const _c = math.multiply(a, b)
     const f: Matrix = math.matrix([1, 0])
     const _d: Matrix = f.subset(math.index(1))
+    const g: number[] =
+      math.matrixFromFunction([3], (i: number[]) => i[0] * i[0])
+    assert.strictEqual(g[2], 4)
+    const h: Matrix = math.matrixFromFunction(
+      [2, 2],
+      (i: number[]) => math.fraction(i[0], i[1] + 1),
+      'dense'
+    )
+    const j: number[][] = math.matrixFromRows(
+      [1, 2, 3],
+      math.matrix([[4], [5], [6]])
+    )
+    assert.strictEqual(j[1][2], 6)
+    const _k: Matrix = math.matrixFromRows(f, math.row(h, 1))
+    const l: number[][] = math.matrixFromColumns(
+      [1, 2, 3],
+      math.matrix([[4], [5], [6]])
+    )
+    assert.strictEqual(l[2][1], 6)
+    const _m: Matrix = math.matrixFromColumns(f, math.row(h, 1))
   }
 
   // get a sub matrix

types/index.d.ts

@@ -23,10 +23,8 @@ export type MathExpression = string | string[] | MathCollection
 
 // add type for Matrix Callback Function and Matrix Storage Format
 export type MatrixStorageFormat = 'dense' | 'sparse'
-
-export interface MatrixFromFunctionCallback<T extends (number | BigNumber)[]> {
-  (value: T): number | BigNumber
-}
+export type MatrixFromFunctionCallback<T extends MathScalarType> =
+    (index: number[]) => T
 
 // eslint-disable-next-line @typescript-eslint/no-explicit-any
 export type FactoryFunction<T> = (scope: any) => T
@@ -759,12 +757,12 @@ export interface MathJsInstance extends MathJsFactory {
    */
   matrix(
     data: MathCollection | string[],
-    format?: 'sparse' | 'dense',
+    format?: MatrixStorageFormat,
     dataType?: string
   ): Matrix
   matrix<T extends MathScalarType>(
     data: MathCollection<T>,
-    format?: 'sparse' | 'dense',
+    format?: MatrixStorageFormat,
     dataType?: string
   ): Matrix<T>
 
@@ -1333,52 +1331,54 @@ export interface MathJsInstance extends MathJsFactory {
    * Create a dense matrix from vectors as individual rows. If you pass column vectors, they will be transposed (but not conjugated!)
    * @param rows - a multi-dimensional number array or matrix
    */
-  matrixFromRows<T extends (number | BigNumber)[] | Matrix>(...rows: T[]): T[]
-  matrixFromRows<T extends (number | BigNumber)[] | Matrix>(rows: T): T[]
+  matrixFromRows(...rows: Matrix[]): Matrix
+  matrixFromRows<T extends MathScalarType>(
+    ...rows: (T[] | [T][] | Matrix)[]
+  ): T[][]
 
   /**
    * Create a dense matrix from vectors as individual columns. If you pass row vectors, they will be transposed (but not conjugated!)
    * @param cols - a multi-dimensional number array or matrix
    */
-  matrixFromColumns<T extends (number | BigNumber)[] | Matrix>(
-    ...cols: T[]
-  ): T[] | Matrix
-  matrixFromColumns<T extends (number | BigNumber)[] | Matrix>(
-    cols: T
-  ): T[] | Matrix
+  matrixFromColumns(...cols: Matrix[]): Matrix
+  matrixFromColumns<T extends MathScalarType>(
+    ...cols: (T[] | [T][] | Matrix)[]
+  ): T[][]
   /**
    * Create a matrix by evaluating a generating function at each index. The simplest overload returns a multi-dimensional array as long as size is an array. Passing size as a Matrix or specifying a format will result in returning a Matrix.
    * @param size - the size of the matrix to be created
    * @param fn - Callback function invoked for every entry in the matrix
    * @param format - The Matrix storage format, either 'dense' or 'sparse'
    * @param datatype - Type of the values
    */
-  matrixFromFunction<T extends (number | BigNumber)[] | Matrix>(
-    size: T,
-    fn: MatrixFromFunctionCallback<(number | BigNumber)[]>
-  ): T[] | Matrix
-  matrixFromFunction<T extends (number | BigNumber)[] | Matrix>(
-    size: T,
-    fn: MatrixFromFunctionCallback<(number | BigNumber)[]>,
-    format: MatrixStorageFormat
-  ): T[] | Matrix
-  matrixFromFunction<T extends (number | BigNumber)[] | Matrix>(
-    size: T,
-    fn: MatrixFromFunctionCallback<(number | BigNumber)[]>,
-    format: MatrixStorageFormat,
-    datatype: string
-  ): T[] | Matrix
-  matrixFromFunction<T extends (number | BigNumber)[] | Matrix>(
-    size: T,
+  matrixFromFunction<T extends MathScalarType>(
+    size: [number],
+    fn: MatrixFromFunctionCallback<T>
+  ): T[]
+  matrixFromFunction<T extends MathScalarType>(
+      size: [number, number],
+    fn: MatrixFromFunctionCallback<T>
+  ): T[][]
+  matrixFromFunction<T extends MathScalarType>(
+    size: number[],
+    fn: MatrixFromFunctionCallback<T>
+  ): MathArray<T>
+  matrixFromFunction(
+    size: Matrix<number>,
+    fn: MatrixFromFunctionCallback<MathScalarType>
+  ): Matrix
+  matrixFromFunction(
+    size: number[] | Matrix<number>,
+    fn: MatrixFromFunctionCallback<MathScalarType>,
     format: MatrixStorageFormat,
-    fn: MatrixFromFunctionCallback<(number | BigNumber)[]>
-  ): T[] | Matrix
-  matrixFromFunction<T extends (number | BigNumber)[] | Matrix>(
-    size: T,
+    datatype?: string
+  ): Matrix
+  matrixFromFunction(
+    size: number[] | Matrix<number>,
     format: MatrixStorageFormat,
-    datatype: string,
-    fn: MatrixFromFunctionCallback<(number | BigNumber)[]>
-  ): T[] | Matrix
+    fn: MatrixFromFunctionCallback<MathScalarType>,
+    datatype?: string
+  ): Matrix
   /**
    * Calculate the least common multiple for two or more values or arrays.
    * lcm is defined as: lcm(a, b) = abs(a * b) / gcd(a, b) For matrices,