335 lines
10 KiB
JavaScript
335 lines
10 KiB
JavaScript
"use strict";
|
||
|
||
var _interopRequireDefault = require("@babel/runtime/helpers/interopRequireDefault");
|
||
Object.defineProperty(exports, "__esModule", {
|
||
value: true
|
||
});
|
||
exports.createEigs = void 0;
|
||
var _extends2 = _interopRequireDefault(require("@babel/runtime/helpers/extends"));
|
||
var _factory = require("../../utils/factory.js");
|
||
var _string = require("../../utils/string.js");
|
||
var _complexEigs = require("./eigs/complexEigs.js");
|
||
var _realSymmetric = require("./eigs/realSymmetric.js");
|
||
var _is = require("../../utils/is.js");
|
||
const name = 'eigs';
|
||
|
||
// The absolute state of math.js's dependency system:
|
||
const dependencies = ['config', 'typed', 'matrix', 'addScalar', 'equal', 'subtract', 'abs', 'atan', 'cos', 'sin', 'multiplyScalar', 'divideScalar', 'inv', 'bignumber', 'multiply', 'add', 'larger', 'column', 'flatten', 'number', 'complex', 'sqrt', 'diag', 'size', 'reshape', 'qr', 'usolve', 'usolveAll', 'im', 're', 'smaller', 'matrixFromColumns', 'dot'];
|
||
const createEigs = exports.createEigs = /* #__PURE__ */(0, _factory.factory)(name, dependencies, _ref => {
|
||
let {
|
||
config,
|
||
typed,
|
||
matrix,
|
||
addScalar,
|
||
subtract,
|
||
equal,
|
||
abs,
|
||
atan,
|
||
cos,
|
||
sin,
|
||
multiplyScalar,
|
||
divideScalar,
|
||
inv,
|
||
bignumber,
|
||
multiply,
|
||
add,
|
||
larger,
|
||
column,
|
||
flatten,
|
||
number,
|
||
complex,
|
||
sqrt,
|
||
diag,
|
||
size,
|
||
reshape,
|
||
qr,
|
||
usolve,
|
||
usolveAll,
|
||
im,
|
||
re,
|
||
smaller,
|
||
matrixFromColumns,
|
||
dot
|
||
} = _ref;
|
||
const doRealSymmetric = (0, _realSymmetric.createRealSymmetric)({
|
||
config,
|
||
addScalar,
|
||
subtract,
|
||
column,
|
||
flatten,
|
||
equal,
|
||
abs,
|
||
atan,
|
||
cos,
|
||
sin,
|
||
multiplyScalar,
|
||
inv,
|
||
bignumber,
|
||
complex,
|
||
multiply,
|
||
add
|
||
});
|
||
const doComplexEigs = (0, _complexEigs.createComplexEigs)({
|
||
config,
|
||
addScalar,
|
||
subtract,
|
||
multiply,
|
||
multiplyScalar,
|
||
flatten,
|
||
divideScalar,
|
||
sqrt,
|
||
abs,
|
||
bignumber,
|
||
diag,
|
||
size,
|
||
reshape,
|
||
qr,
|
||
inv,
|
||
usolve,
|
||
usolveAll,
|
||
equal,
|
||
complex,
|
||
larger,
|
||
smaller,
|
||
matrixFromColumns,
|
||
dot
|
||
});
|
||
|
||
/**
|
||
* Compute eigenvalues and optionally eigenvectors of a square matrix.
|
||
* The eigenvalues are sorted by their absolute value, ascending, and
|
||
* returned as a vector in the `values` property of the returned project.
|
||
* An eigenvalue with algebraic multiplicity k will be listed k times, so
|
||
* that the returned `values` vector always has length equal to the size
|
||
* of the input matrix.
|
||
*
|
||
* The `eigenvectors` property of the return value provides the eigenvectors.
|
||
* It is an array of plain objects: the `value` property of each gives the
|
||
* associated eigenvalue, and the `vector` property gives the eigenvector
|
||
* itself. Note that the same `value` property will occur as many times in
|
||
* the list provided by `eigenvectors` as the geometric multiplicity of
|
||
* that value.
|
||
*
|
||
* If the algorithm fails to converge, it will throw an error –
|
||
* in that case, however, you may still find useful information
|
||
* in `err.values` and `err.vectors`.
|
||
*
|
||
* Note that the 'precision' option does not directly specify the _accuracy_
|
||
* of the returned eigenvalues. Rather, it determines how small an entry
|
||
* of the iterative approximations to an upper triangular matrix must be
|
||
* in order to be considered zero. The actual accuracy of the returned
|
||
* eigenvalues may be greater or less than the precision, depending on the
|
||
* conditioning of the matrix and how far apart or close the actual
|
||
* eigenvalues are. Note that currently, relatively simple, "traditional"
|
||
* methods of eigenvalue computation are being used; this is not a modern,
|
||
* high-precision eigenvalue computation. That said, it should typically
|
||
* produce fairly reasonable results.
|
||
*
|
||
* Syntax:
|
||
*
|
||
* math.eigs(x, [prec])
|
||
* math.eigs(x, {options})
|
||
*
|
||
* Examples:
|
||
*
|
||
* const { eigs, multiply, column, transpose, matrixFromColumns } = math
|
||
* const H = [[5, 2.3], [2.3, 1]]
|
||
* const ans = eigs(H) // returns {values: [E1,E2...sorted], eigenvectors: [{value: E1, vector: v2}, {value: e, vector: v2}, ...]
|
||
* const E = ans.values
|
||
* const V = ans.eigenvectors
|
||
* multiply(H, V[0].vector)) // returns multiply(E[0], V[0].vector))
|
||
* const U = matrixFromColumns(...V.map(obj => obj.vector))
|
||
* const UTxHxU = multiply(transpose(U), H, U) // diagonalizes H if possible
|
||
* E[0] == UTxHxU[0][0] // returns true always
|
||
*
|
||
* // Compute only approximate eigenvalues:
|
||
* const {values} = eigs(H, {eigenvectors: false, precision: 1e-6})
|
||
*
|
||
* See also:
|
||
*
|
||
* inv
|
||
*
|
||
* @param {Array | Matrix} x Matrix to be diagonalized
|
||
*
|
||
* @param {number | BigNumber | OptsObject} [opts] Object with keys `precision`, defaulting to config.relTol, and `eigenvectors`, defaulting to true and specifying whether to compute eigenvectors. If just a number, specifies precision.
|
||
* @return {{values: Array|Matrix, eigenvectors?: Array<EVobj>}} Object containing an array of eigenvalues and an array of {value: number|BigNumber, vector: Array|Matrix} objects. The eigenvectors property is undefined if eigenvectors were not requested.
|
||
*
|
||
*/
|
||
return typed('eigs', {
|
||
// The conversion to matrix in the first two implementations,
|
||
// just to convert back to an array right away in
|
||
// computeValuesAndVectors, is unfortunate, and should perhaps be
|
||
// streamlined. It is done because the Matrix object carries some
|
||
// type information about its entries, and so constructing the matrix
|
||
// is a roundabout way of doing type detection.
|
||
Array: function (x) {
|
||
return doEigs(matrix(x));
|
||
},
|
||
'Array, number|BigNumber': function (x, prec) {
|
||
return doEigs(matrix(x), {
|
||
precision: prec
|
||
});
|
||
},
|
||
'Array, Object'(x, opts) {
|
||
return doEigs(matrix(x), opts);
|
||
},
|
||
Matrix: function (mat) {
|
||
return doEigs(mat, {
|
||
matricize: true
|
||
});
|
||
},
|
||
'Matrix, number|BigNumber': function (mat, prec) {
|
||
return doEigs(mat, {
|
||
precision: prec,
|
||
matricize: true
|
||
});
|
||
},
|
||
'Matrix, Object': function (mat, opts) {
|
||
const useOpts = {
|
||
matricize: true
|
||
};
|
||
(0, _extends2.default)(useOpts, opts);
|
||
return doEigs(mat, useOpts);
|
||
}
|
||
});
|
||
function doEigs(mat) {
|
||
var _opts$precision;
|
||
let opts = arguments.length > 1 && arguments[1] !== undefined ? arguments[1] : {};
|
||
const computeVectors = 'eigenvectors' in opts ? opts.eigenvectors : true;
|
||
const prec = (_opts$precision = opts.precision) !== null && _opts$precision !== void 0 ? _opts$precision : config.relTol;
|
||
const result = computeValuesAndVectors(mat, prec, computeVectors);
|
||
if (opts.matricize) {
|
||
result.values = matrix(result.values);
|
||
if (computeVectors) {
|
||
result.eigenvectors = result.eigenvectors.map(_ref2 => {
|
||
let {
|
||
value,
|
||
vector
|
||
} = _ref2;
|
||
return {
|
||
value,
|
||
vector: matrix(vector)
|
||
};
|
||
});
|
||
}
|
||
}
|
||
if (computeVectors) {
|
||
Object.defineProperty(result, 'vectors', {
|
||
enumerable: false,
|
||
// to make sure that the eigenvectors can still be
|
||
// converted to string.
|
||
get: () => {
|
||
throw new Error('eigs(M).vectors replaced with eigs(M).eigenvectors');
|
||
}
|
||
});
|
||
}
|
||
return result;
|
||
}
|
||
function computeValuesAndVectors(mat, prec, computeVectors) {
|
||
const arr = mat.toArray(); // NOTE: arr is guaranteed to be unaliased
|
||
// and so safe to modify in place
|
||
const asize = mat.size();
|
||
if (asize.length !== 2 || asize[0] !== asize[1]) {
|
||
throw new RangeError(`Matrix must be square (size: ${(0, _string.format)(asize)})`);
|
||
}
|
||
const N = asize[0];
|
||
if (isReal(arr, N, prec)) {
|
||
coerceReal(arr, N); // modifies arr by side effect
|
||
|
||
if (isSymmetric(arr, N, prec)) {
|
||
const type = coerceTypes(mat, arr, N); // modifies arr by side effect
|
||
return doRealSymmetric(arr, N, prec, type, computeVectors);
|
||
}
|
||
}
|
||
const type = coerceTypes(mat, arr, N); // modifies arr by side effect
|
||
return doComplexEigs(arr, N, prec, type, computeVectors);
|
||
}
|
||
|
||
/** @return {boolean} */
|
||
function isSymmetric(arr, N, prec) {
|
||
for (let i = 0; i < N; i++) {
|
||
for (let j = i; j < N; j++) {
|
||
// TODO proper comparison of bignum and frac
|
||
if (larger(bignumber(abs(subtract(arr[i][j], arr[j][i]))), prec)) {
|
||
return false;
|
||
}
|
||
}
|
||
}
|
||
return true;
|
||
}
|
||
|
||
/** @return {boolean} */
|
||
function isReal(arr, N, prec) {
|
||
for (let i = 0; i < N; i++) {
|
||
for (let j = 0; j < N; j++) {
|
||
// TODO proper comparison of bignum and frac
|
||
if (larger(bignumber(abs(im(arr[i][j]))), prec)) {
|
||
return false;
|
||
}
|
||
}
|
||
}
|
||
return true;
|
||
}
|
||
function coerceReal(arr, N) {
|
||
for (let i = 0; i < N; i++) {
|
||
for (let j = 0; j < N; j++) {
|
||
arr[i][j] = re(arr[i][j]);
|
||
}
|
||
}
|
||
}
|
||
|
||
/** @return {'number' | 'BigNumber' | 'Complex'} */
|
||
function coerceTypes(mat, arr, N) {
|
||
/** @type {string} */
|
||
const type = mat.datatype();
|
||
if (type === 'number' || type === 'BigNumber' || type === 'Complex') {
|
||
return type;
|
||
}
|
||
let hasNumber = false;
|
||
let hasBig = false;
|
||
let hasComplex = false;
|
||
for (let i = 0; i < N; i++) {
|
||
for (let j = 0; j < N; j++) {
|
||
const el = arr[i][j];
|
||
if ((0, _is.isNumber)(el) || (0, _is.isFraction)(el)) {
|
||
hasNumber = true;
|
||
} else if ((0, _is.isBigNumber)(el)) {
|
||
hasBig = true;
|
||
} else if ((0, _is.isComplex)(el)) {
|
||
hasComplex = true;
|
||
} else {
|
||
throw TypeError('Unsupported type in Matrix: ' + (0, _is.typeOf)(el));
|
||
}
|
||
}
|
||
}
|
||
if (hasBig && hasComplex) {
|
||
console.warn('Complex BigNumbers not supported, this operation will lose precission.');
|
||
}
|
||
if (hasComplex) {
|
||
for (let i = 0; i < N; i++) {
|
||
for (let j = 0; j < N; j++) {
|
||
arr[i][j] = complex(arr[i][j]);
|
||
}
|
||
}
|
||
return 'Complex';
|
||
}
|
||
if (hasBig) {
|
||
for (let i = 0; i < N; i++) {
|
||
for (let j = 0; j < N; j++) {
|
||
arr[i][j] = bignumber(arr[i][j]);
|
||
}
|
||
}
|
||
return 'BigNumber';
|
||
}
|
||
if (hasNumber) {
|
||
for (let i = 0; i < N; i++) {
|
||
for (let j = 0; j < N; j++) {
|
||
arr[i][j] = number(arr[i][j]);
|
||
}
|
||
}
|
||
return 'number';
|
||
} else {
|
||
throw TypeError('Matrix contains unsupported types only.');
|
||
}
|
||
}
|
||
}); |