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# NaturalNode/node-sylvester

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# node-sylvester

node.js implementation of James Coglan's “Sylvester” matrix math library. The original project can be found at sylvester.jcoglan.com/

This project is maintained by Chris Umbel & Rob Ellis

# Documentation

The original documentation for “Sylvester” should help you through basic operations. An intro that contains node-specific features can also be found on Chris Umbel’s blog. We're looking for someone to help get the documentation situation under control.

# Installation

npm install sylvester

# Usage

## New Stuff

First I'd like to show some examples of features that aren't in the standard (non-node) Sylvester. I'll likely attempt to commit these back to Sylvester at some point soon.

Note that the decompositions are all available in pure JavaScript, but if the lapack NPM is installed with LAPACK built as a shared library then efficient native code will be used. The LAPACK integration is still highly experimental.

### Vector

require('sylvester');
var a = \$V([1, 2, 3]);

element-wise log:

console.log(a.log());

norm computation:

console.log(a.norm());

element-wise multiplication:

a.elementMultiply(vector);

element-wise division:

a.elementDivide(vector);

remove first n nodes:

a.chomp(n);

return vector with first n nodes:

a.top(n);

add all elements into a single scalar:

a.sum()

multiply all elements into a single scalar:

a.product()

return a vector with the elements parameter on the bottom:

a.augment(elements)

### Matrix

var A = \$M([[1, 2, 3], [4, 5, 6]]);

return subset of rows, columns:

// startRow, endRow, startCol, endCol
A.slice(2, 3, 2, 3);

divide matricies:

A.div(\$M([[0.5, 1], [1, 2], [2, 3]]));

scalar addition/subtraction

A.add(1);
A.subtract(1);

element-wise log:

console.log(A.log());

element-wise multiplication:

A.elementMultiply(vector)

add all elements into a single scalar:

A.sum()

returns a vector of the indexes of maximum values ([3 3]):

\$M([[1, 2, 3], [5, 4, 6]]).maxColumnIndexes()

returns a vector of minimum column indexes ([1 2]):

\$M([[1, 2, 3], [5, 4, 6]]).minColumnIndexes();

returns a vector of max values ([3 6]):

\$M([[1, 2, 3], [5, 4, 6]]).maxColumns()

returns a vector of minimum values ([1 4]):

\$M([[1, 2, 3], [5, 4, 6]]).minColumns()

create a 2x3 matrix of ones:

var Ones = Matrix.One(2, 3);

LU decomposition (with partial pivoting)

var lu = A.lu();
console.log(lu.L);
console.log(lu.U);
console.log(lu.P);

QR decomposition (feature still inefficient and experimental, but uses pure javascript):

var qr = A.qr();
console.log(qr.Q);
console.log(qr.R);

SVD decomposition (feature still inefficient and experimental, but uses pure javascript):

var svd = A.svd();
console.log(svd.U);
console.log(svd.S);
console.log(svd.V);

PCA

var A = \$M([[1, 2], [5, 7]]).pcaProject(1).eql(\$M([
[-2.2120098720461616],
[-8.601913944732665]
]);
var pca = A.pcaProject(1);
var Z = pca.Z;
var A = Z.pcaRecover(pca.U);

Solving systems of equations

// sovle Ax = b for x
var A = \$M([[2, 4], [2, 1]]);
var b = \$V([1, 0]);
console.log(A.solve(b));

## Old Stuff

Below is a basic illustration of standard matrix/vector math using the standard Sylvester API. This documentation is rather incomplete and for further details please consult the official sylvester API documentation at sylvester.jcoglan.com/docs.

### Vectors

require('sylvester');

create two vectors:

var a = \$V([1, 2, 3]);
var b = \$V([2, 3, 4]);

compute the dot product:

var r = a.dot(b);

add two vectors:

var c = a.add(b);

multiply by scalar:

var d = a.x(2);

### Matrices

require('sylvester');

create two matrices:

var A = \$M([[1, 2], [3, 4]]);
var B = \$M([[1, 2, 3], [4, 5, 6]]);

multiply the matrices:

var C = A.x(B);

transpose a matrix:

var B_T = B.transpose();
// B is 2x3, B_T is 3x2

# License

This project is released under The MIT License

Copyright © 2011, Chris Umbel, Rob Ellis, James Coglan

Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the “Software”), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED “AS IS”, WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.

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