7fife-backend/node_modules/sylvester/README.rdoc

= node-sylvester

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

This project is maintained by {Chris Umbel}[http://www.chrisumbel.com] & Rob Ellis

= 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.

=== 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);

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);

== 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}[http://sylvester.jcoglan.com/docs] at http://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 (c) 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.