`eigs` throws TypeError for some BigNumber matrices

[pro7onmatrix]

The eigs function throws a TypeError for some (but not all) matrices using BigNumber.

This example from eigs.test.js works as expected:

var A = [
    [-4.78, -1.0, -2.59, -3.26, 4.24, 4.14],
    [-1.0, -2.45, -0.92, -2.33, -4.68, 4.27],
    [-2.59, -0.92, -2.45, 4.17, -3.33, 3.05],
    [-3.26, -2.33, 4.17, 2.51, 1.67, 2.24],
    [4.24, -4.68, -3.33, 1.67, 2.80, 2.73],
    [4.14, 4.27, 3.05, 2.24, 2.73, -4.47]
];
A = math.bignumber(A);
const ans = math.eigs(A);

However, the following example produces a TypeError:

var B = [
    [0.0, 1.0, 0.0, 0.0, 0.0, 1.0],
    [1.0, 0.0, 1.0, 0.0, 0.0, 0.0],
    [0.0, 1.0, 0.0, 1.0, 0.0, 0.0],
    [0.0, 0.0, 1.0, 0.0, 1.0, 0.0],
    [0.0, 0.0, 0.0, 1.0, 0.0, 1.0],
    [1.0, 0.0, 0.0, 0.0, 1.0, 0.0]
];
B = math.bignumber(B);
const ans2 = math.eigs(B);

TypeError: Cannot implicitly convert a number with >15 significant digits to BigNumber (value: 0.7071067811865476). Use function bignumber(x) to convert to BigNumber.
    at convert (/home/professorchaos/Dokumente/javascript/node_modules/mathjs/lib/core/function/typed.js:208:15)
    at Array.convertArg (/home/professorchaos/Dokumente/javascript/node_modules/typed-function/typed-function.js:819:22)
    at convertArgs (/home/professorchaos/Dokumente/javascript/node_modules/typed-function/typed-function.js:766:45)
    at generic (/home/professorchaos/Dokumente/javascript/node_modules/typed-function/typed-function.js:1073:27)
    at multiplyScalar (/home/professorchaos/Dokumente/javascript/node_modules/typed-function/typed-function.js:1092:24)
    at Sij1Big (/home/professorchaos/Dokumente/javascript/node_modules/mathjs/lib/function/matrix/eigs.js:274:25)
    at diagBig (/home/professorchaos/Dokumente/javascript/node_modules/mathjs/lib/function/matrix/eigs.js:202:13)
    at checkAndSubmit (/home/professorchaos/Dokumente/javascript/node_modules/mathjs/lib/function/matrix/eigs.js:143:14)
    at Array (/home/professorchaos/Dokumente/javascript/node_modules/mathjs/lib/function/matrix/eigs.js:73:17)
    at Object.eigs (/home/professorchaos/Dokumente/javascript/node_modules/typed-function/typed-function.js:1085:85)

I'm using math.js v6.6.1, the problem occurs both in node and in the browser using math.min.js. Let me know if you need any additional info.

[josdejong]

Thanks for reporting. It turned out the BigNumber implementation of eigs was calculated using a mix of numbers and BigNumbers, causing the output to have number precision only in some cases like your example.

Fix created, not yet published.

[josdejong]

Fixed now in v6.6.2

[pro7onmatrix]

Thanks very much for the quick fix! On an unrelated note, seeing as you already have a precision parameter in the diag and diagBig functions in eigs.js, would it be possible to pass the precision from eigs? Should I open a new issue for this?

[josdejong]

That's a very good point @professorchaos97 . I've addressed this in this commit: 7e8d128, so the function eigs consistently uses config.epsilon (not yet published).

Does that address your concern?

[pro7onmatrix]

Yes, it does. Thanks again!

[josdejong]

👍