193 lines
4.1 KiB
Markdown
193 lines
4.1 KiB
Markdown
# sylvester
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Modern and expanded implementation of James Coglan's "Sylvester" matrix math library. The original project can be found at http://sylvester.jcoglan.com/
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# Documentation
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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}[http://www.chrisumbel.com/article/sylvester_node_js_matrix_vector_math]. We're looking for someone to help get the documentation situation under control.
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# Installation
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npm install sylvester
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# Usage
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## New Stuff
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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.
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Note that the decompositions are all available in pure JavaScript, but if the [lapack](https://github.com/NaturalNode/node-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.
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### Vector
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require('sylvester');
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var a = $V([1, 2, 3]);
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element-wise log:
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console.log(a.log());
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norm computation:
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console.log(a.norm());
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element-wise multiplication:
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a.elementMultiply(vector);
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element-wise division:
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a.elementDivide(vector);
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remove first n nodes:
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a.chomp(n);
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return vector with first n nodes:
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a.top(n);
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add all elements into a single scalar:
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a.sum()
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multiply all elements into a single scalar:
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a.product()
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return a vector with the elements parameter on the bottom:
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a.augment(elements)
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### Matrix
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var A = $M([[1, 2, 3], [4, 5, 6]]);
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return subset of rows, columns:
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// startRow, endRow, startCol, endCol
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A.slice(2, 3, 2, 3);
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divide matricies:
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A.div($M([[0.5, 1], [1, 2], [2, 3]]));
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scalar addition/subtraction
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A.add(1);
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A.subtract(1);
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element-wise log:
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console.log(A.log());
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element-wise multiplication:
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A.elementMultiply(vector)
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add all elements into a single scalar:
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A.sum()
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returns a vector of the indexes of maximum values ([3 3]):
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$M([[1, 2, 3], [5, 4, 6]]).maxColumnIndexes()
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returns a vector of minimum column indexes ([1 2]):
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$M([[1, 2, 3], [5, 4, 6]]).minColumnIndexes();
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returns a vector of max values ([3 6]):
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$M([[1, 2, 3], [5, 4, 6]]).maxColumns()
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returns a vector of minimum values ([1 4]):
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$M([[1, 2, 3], [5, 4, 6]]).minColumns()
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create a 2x3 matrix of ones:
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var Ones = Matrix.One(2, 3);
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LU decomposition (with partial pivoting)
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var lu = A.lu();
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console.log(lu.L);
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console.log(lu.U);
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console.log(lu.P);
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QR decomposition (feature still inefficient and experimental, but uses pure javascript):
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var qr = A.qr();
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console.log(qr.Q);
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console.log(qr.R);
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SVD decomposition (feature still inefficient and experimental, but uses pure javascript):
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var svd = A.svd();
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console.log(svd.U);
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console.log(svd.S);
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console.log(svd.V);
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PCA
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var A = $M([[1, 2], [5, 7]]).pcaProject(1).eql($M([
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[-2.2120098720461616],
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[-8.601913944732665]
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]);
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var pca = A.pcaProject(1);
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var Z = pca.Z;
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var A = Z.pcaRecover(pca.U);
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Solving systems of equations
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// sovle Ax = b for x
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var A = $M([[2, 4], [2, 1]]);
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var b = $V([1, 0]);
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console.log(A.solve(b));
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== Old Stuff
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Below is a basic illustration of standard matrix/vector math using the standard
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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.
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### Vectors
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require('sylvester');
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create two vectors:
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var a = $V([1, 2, 3]);
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var b = $V([2, 3, 4]);
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compute the dot product:
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var r = a.dot(b);
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add two vectors:
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var c = a.add(b);
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multiply by scalar:
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var d = a.x(2);
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### Matrices
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require('sylvester');
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create two matrices:
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var A = $M([[1, 2], [3, 4]]);
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var B = $M([[1, 2, 3], [4, 5, 6]]);
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multiply the matrices:
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var C = A.x(B);
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transpose a matrix:
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var B_T = B.transpose();
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// B is 2x3, B_T is 3x2
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