mathjs/test/unit-tests/function/matrix/expm.test.js

// test expm
import assert from 'assert'

import approx from '../../../../tools/approx.js'
import math from '../../../../src/defaultInstance.js'
const expm = math.expm

describe('expm', function () {
  it('should only accept a square matrix', function () {
    assert.throws(function () { expm(5) }, /Unexpected type/)
    assert.throws(function () { expm([1, 2]) }, /Matrix must be square/)
    assert.throws(function () { expm([[1, 2]]) }, /Matrix must be square/)
    assert.throws(function () { expm([[1, 2, 3], [4, 5, 6]]) }, /Matrix must be square/)
  })

  it('should compute the exponential of a matrix', function () {
    // Trivial example
    approx.deepEqual(expm(
      [[1, 0],
        [0, 1]]
    ),
    math.matrix(
      [[2.718281828, 0],
        [0, 2.718281828]]
    ))

    // Example given in the Moler and Van Loan paper
    approx.deepEqual(expm(
      [[-49, 24],
        [-64, 31]]
    ),
    math.matrix(
      [[-0.735759, 0.551819],
        [-1.471518, 1.103638]]
    ))

    // Another example from the same paper
    approx.deepEqual(expm(
      [[0, 6, 0, 0],
        [0, 0, 6, 0],
        [0, 0, 0, 6],
        [0, 0, 0, 0]]
    ),
    math.matrix(
      [[1, 6, 18, 36],
        [0, 1, 6, 18],
        [0, 0, 1, 6],
        [0, 0, 0, 1]]
    ))

    // And another
    approx.deepEqual(expm(
      [[1, 1],
        [0, 1]]
    ),
    math.matrix(
      [[2.718282, 2.718282],
        [0, 2.718282]]
    ))

    // And another
    approx.deepEqual(expm(
      [[1 + 1e-5, 1],
        [0, 1 - 1e-5]]
    ),
    math.matrix(
      [[2.718309, 2.718282],
        [0, 2.718255]]
    ))
  })

  it('should work on SparseMatrix', function () {
    approx.deepEqual(expm(
      math.sparse(
        [[0, 6, 0, 0],
          [0, 0, 6, 0],
          [0, 0, 0, 6],
          [0, 0, 0, 0]]
      )
    ),
    math.sparse(
      [[1, 6, 18, 36],
        [0, 1, 6, 18],
        [0, 0, 1, 6],
        [0, 0, 0, 1]]
    ))
  })

  it('should LaTeX transpose', function () {
    const expression = math.parse('expm([[1,2],[3,4]])')
    assert.strictEqual(expression.toTex(), '\\exp\\left(\\begin{bmatrix}1&2\\\\3&4\\\\\\end{bmatrix}\\right)')
  })
})