* nearlyEqual with absolute and relative tolerances
* Format
* nearlyEqual for bigNumber
* Added skip for NaN
* Reduce diff a bit
* Issue with examples in jsdcos
* Updated all calls for nearlyEqual
* Fixed failing tests
* Changed epsilon to relTol, absTol
* Changed references to epsilon in docs and tests
* Added warning for config.epsilon
* Fix warning in zeta.test
* Added config test
* Added sinon to test console.warn
---------
Co-authored-by: Jos de Jong <wjosdejong@gmail.com>
* feat: Add option to eigs() to turn off eigenvector computation
For large matrices, the eigenvector computation can be noticeably expensive
and so it's worthwhile to have a way to turn it off if the eigenvectors
will not be used.
Resolves#2180.
* fix: Add test for precision in options arg of eigs
And also a fix for a small bug that the new test uncovered.
* test: check eigs with matrix and options
* refactor: remove dead code from complexEigs.js
* fix: add new signatures of eigs to typescript
* test: ensure eigenvectors property not present with eigenvectors: false option
* fix: correct balancing code in complexEigs
* fix: Find eigenvectors of defective matrices
Previously, attempting to take the `eigs` of any defective matrix
was doomed to fail in an attempt to solve a singular linear system.
This PR detects the situation (as best as it can given the
inherent numerical instability of the current methods used) and
handles it. Note that in such cases, it's not possible to return
a square matrix whose columns are the eigenvectors corresponding to
the returned eigenvalues. In light of that fact and issue #3014, this
PR also changes the return value of `eigs` so that the eigenvectors
are passed back in a property `eigenvectors` which is an array of
plain objects `{value: e, vector: v}`.
Note that this PR makes the ancillary changes of correcting the
spelling of the filename which was "realSymetric.js," and replacing
the now-unnecessary auxiliary function "createArray" therein with
`Array(size).fill(element)`. The rationale for performing these
changes not strictly related to the issues at hand is that this
file is rarely touched and with the level of maintenance hours we have
at hand, it's more efficient to do these small refactorings in parallel
with the actual bugfixes, which are orthogonal and so will not be
obfuscated by this refactor. Note `git diff` does properly track the
file name change.
However, it also makes a potentially more pervasive change: in order for
the numerically-sensitive algorithm to work, it changes the condition
on when two very close (double) numbers are "nearlyEqual" from differing by
less than DBL_EPSILON to differing by less than or equal to DBL_EPSILON.
Although this may change other behaviors than the ones primarily being
addressed, I believe it is an acceptable change because
(a) It preserves all tests.
(b) DBL_EPSILON is well below the standard config.epsilon anyway
(c) I believe there are extant issues noting the odd/inconsistent
behavior of nearlyEqual near 0 anyway, so I believe this will
be overhauled in the future in any case. If so, the eigenvector
computation will make a good test that a future nearlyEqual
algorithm is working well.
To be clear, the direct motivation for the change is that there are
multiple cases in the eigenvector computation in which a coefficient
that is "supposed" to be zero comes out to precisely DBL_EPSILON, which
is fairly unsurprising given that these coefficients are produced by
subtracting an eigenvalue from a diagonal entry of a matrix, which is
likely to be essentially equal to that eigenvalue.
As many tests of defective matrices as I could readily find by web
searching have been added as unit tests (and one more in the typescript
type testing). An additional case I found still fails, but in the
_eigenvalue_ computation rather than the _eigenvector_ search, so that
was deemed beyond the scope of this PR and has been filed as issue #3036.
Resolves#2879.
Resolves#2927.
Resolves#3014.
* refactor: remove comma that lint now doesn't like
* test: add a test for eigs with a precision argument
* feat: Use simple shifts in QR eigenvalue iterations that improve convergence
Although we might want to use better shifts in the future, we might just
use a library instead. But for now I think this:
Resolves#2178.
Also responds to the review feedback provided in PR #3037.
* setup linting with eslint-config-standard, prettier
* [autofix] npm run lint -- --fix with new setup
* [manual] fix types/ directory errors
* [manual] fix linting errors in test/ directory
* [manual] fix single linting error in src/
* revert ts-expect-error comment change
* error on .only in mocha tests
* fix test description typo
* move some short objects to single line
* add and gitignore eslintcache
* individually suppress ts any
* set --max-warnings to 0
* extract matrices to constants
* update ts-expect-error comments
Also adds the test case that revealed the problem and corrects the other test
case that could have found it except the tolerance had been cranked up very
high.
Resolves#2478.
This change fixes a typing problem in complexEigs.js in which
real-valued norms were inadvertently being typed as complex numbers.
Resolves#2439
Co-authored-by: Jos de Jong <wjosdejong@gmail.com>
* split the eigs function into multiple algorithms
* moved checks and coersions to eigs.js, made them more robust
* fix little bugs, make im and re more robust
* Implemented matrix balancing algorithm
* fix typos
* a draft of reduction to Hessenberg matrix
* finished implementation of reduction to Hessenberg
* fix Hessenberg elimination for complex numbers
* implemented non-shifted explicit QR algorithm for real matrices
* implemented vector computation, won't work untill usolve is fixed
* refactored to match yarn lint
* some minor changes
* solve merge conflicts
* refactored and re-fixed #1789
* some old uncommited changes
* fix small problems introduced by merging
* done some polishing
* improved jsdoc description of eigs
* little changes in jsdoc
Co-authored-by: Jos de Jong <wjosdejong@gmail.com>
* Add `.js` extension to source file imports
* Specify package `exports` in `package.json`
Specify package type as `commonjs` (It's good to be specific)
* Move all compiled scripts into `lib` directory
Remove ./number.js (You can use the compiled ones in `./lib/*`)
Tell node that the `esm` directory is type `module` and enable tree shaking.
Remove unused files from packages `files` property
* Allow importing of package.json
* Make library ESM first
* - Fix merge conflicts
- Refactor `bundleAny` into `defaultInstance.js` and `browserBundle.cjs`
- Refactor unit tests to be able to run with plain nodejs (no transpiling)
- Fix browser examples
* Fix browser and browserstack tests
* Fix running unit tests on Node 10 (which has no support for modules)
* Fix node.js examples (those are still commonjs)
* Remove the need for `browserBundle.cjs`
* Generate minified bundle only
* [Security] Bump node-fetch from 2.6.0 to 2.6.1 (#1963)
Bumps [node-fetch](https://github.com/bitinn/node-fetch) from 2.6.0 to 2.6.1. **This update includes a security fix.**
- [Release notes](https://github.com/bitinn/node-fetch/releases)
- [Changelog](https://github.com/node-fetch/node-fetch/blob/master/docs/CHANGELOG.md)
- [Commits](https://github.com/bitinn/node-fetch/compare/v2.6.0...v2.6.1)
Signed-off-by: dependabot-preview[bot] <support@dependabot.com>
Co-authored-by: dependabot-preview[bot] <27856297+dependabot-preview[bot]@users.noreply.github.com>
* Cleanup console.log
* Add integration tests to test the entry points (commonjs/esm, full/number only)
* Create backward compatibility error messages in the files moved/removed since v8
* Describe breaking changes in HISTORY.md
* Bump karma from 5.2.1 to 5.2.2 (#1965)
Bumps [karma](https://github.com/karma-runner/karma) from 5.2.1 to 5.2.2.
- [Release notes](https://github.com/karma-runner/karma/releases)
- [Changelog](https://github.com/karma-runner/karma/blob/master/CHANGELOG.md)
- [Commits](https://github.com/karma-runner/karma/compare/v5.2.1...v5.2.2)
Signed-off-by: dependabot-preview[bot] <support@dependabot.com>
Co-authored-by: dependabot-preview[bot] <27856297+dependabot-preview[bot]@users.noreply.github.com>
Co-authored-by: Lee Langley-Rees <lee@greenimp.co.uk>
Co-authored-by: dependabot-preview[bot] <27856297+dependabot-preview[bot]@users.noreply.github.com>
* eigs test file initialize
* file for function for diagonalization of a real symmetrix matrix
* eigs typed function written according to mathjs requirements
* some linting issues addressed
* more linting issues in eigs
* linting passed for eigs (blank template function)
* making eigs fail
* eigs added to factory any
* initial check of input in eigs
* linting issues fix in eigs
* added rotation and theta matrix
* diagonalization loop added
* diagonalization result return
* diagonalization returns eigenvalue and eigenvectors
* function for updating Sij
* function for updating matrix
* a small bug fix
* some linting fixed in eigs
* lint and bug fix at eigs
* linting passed in eigs
* tests for input in eigs
* tests for trivial eigenvalue problem (sanity check)
* 2x2 check for non-diagonal matrix
* sorting added to eigs
* sorting function lint fix in eigs
* example for eigs updated
* 3x3 diagonalization by eigs passed
* bug in eigenvector
* eigenvalues seem to work
* cloning array so that original matrix do not get transformed in eigs
* eigenvector check
* eigenvector deep check and eigs description modified
* embedding dos for eigs
* doc for eigs fix
* slight change in example
* adding checkInput type
* type error for bad matrix elements
* type error for every element
* name change for typecheck function
* check matrix type of array input
* type error message update in eigs
* type error message grammer in eigs
* eigs bug fix
* eigs bug fix in check function
* eigs typecheck test
* some lint fix in eigs and corresponding tests
* before adding bingNumber implementation in eigs
* support for fractions
* obtain angle for bigNumber type
* theta for bignumbers
* update overlap for bigNumber
* jacobi rotation of input matrix for BigNumbers
* largest element for bigNumbers
* diagonalization for bigNumbers
* adding dependedncies
* diagonization for bigNumber
* diag for bigNumber is tested
* linting fix for eig and eigs test
* problem for bigNumber fix
* error message modification for eigs
* more coverage for eigs function
* eigs test bug fix
* simplify test
* is Symmetric function
* use matrix instead in eigs
* slight cleanup
* is symmetric bug fix
* no need to return in isSymmetrix
* small bug fix for fractions
* using scalar function when possible
* small lint correction
* return object in eigs
* bug fix in array eigs
* test object implementation
* description update
Co-authored-by: Jos de Jong <wjosdejong@gmail.com>
