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https://github.com/abarbu/linear-algebra

Chicken egg for linear algebra
https://github.com/abarbu/linear-algebra

Last synced: 25 days ago
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Chicken egg for linear algebra

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README 

        
[[tags: egg math]]

[[toc:]]



This page is maintained in the package's

[[https://github.com/abarbu/linear-algebra|github repository]].



== linear-algebra



This implements various linear algebra and other math operations. Much

of this code is originally from Jeff Siskind's QobiScheme.



=== Line segments



(define-structure line-segment p q)

(p l)

(q l)

(collinear? l1 l2)

(point-on-line-segment? r l)

(intersection-point l1 l2)

(cross? l1 l2)

(intersect? l1 l2)

(line-tangent l)

(normal-2d l)

(line-segment-length l)

(read-line-segments-from-file pathname)

(write-line-segments-to-file line-segments pathname)



=== Vectors



(x v)

(y v)

(z v)

(dot u v)

(cross-2d u v)

(cross u v)

(v+ u v)

(v- u v)

(k*v k v)

(v*k v k)

(k+v k v)

(v+k v k)

(v/k v k)

(v* u v)

(v/ u v)

(v= u v)

(rotate-90 u)

(rotate-180 u)

(rotate-270 u)

(perpendicular? u v)

(parallel? u v)

(magnitude-squared v)

(magnitude v)

(unit v)

(distance-squared u v)

(distance u v)

(clockwise-angle? u v w)

(clockwise-or-same-angle? u v w)

(append-vector vec1 vec2)



=== Matrices



(matrix? v)

(list->matrix l)

(make-matrix m n . &rest)

(make-3-by-3-matrix a11 a12 a13 a21 a22 a23 a31 a32 a33)

(matrix-copy m)

(matrix-rows a)

(matrix-columns a)

(matrix-ref a i j)

(matrix-set! a i j x)

(matrix-row-ref a i)

(matrix-column-ref a j)

(matrix-row-set! a i v)

(vector->row-matrix v)

(vector->column-matrix v)

(m+ a b)

(m- a b)

(m+k m k)

(m+k-diagonal m k)

(k+m k m)

(m*v a v)

(matrix-transpose a)

(outer-product f u v)

(self-outer-product f v)

(m* a b)

(m*. a b)

(m/. a b)

(v*m v a)

(k*m k m)

(m*k m k)

(m/k m k)

(v*m*v v m)

(determinant a)

(invert-matrix a)

(simplex a m1 m2 m3)

(jacobi a)

(eigenvalues a)

(eigenvectors a)

(vector->diagonal-matrix v)

(identity-matrix n)

(clip-eigenvalues a v)

(eigenvector-angle1 m)

(eigenvector-angle2 m)

(left-pseudo-inverse m)

(right-pseudo-inverse m)

(ref-1d m a)

(ref-2d m a b)

(ref-3d m a b c)

(ref-4d m a b c d)

(ref-5d m a b c d e)

(map-n-vector-2d f m n)

(map-n-vector-3d f m n p)

(map-n-vector-4d f m n p q)

(map-n-vector-5d f m n p q r)

(matrix-sum f n i)

(matrix-sum-2d f m n i)

(shape-matrix v c)

(unshape-matrix m)

(crop m x y w h)

(submatrix m x-offset y-offset x-size y-size)

(matrix-ref-nd m . is)

(matrix-3d-ref a s i j)

(matrix-set-nd! m v . is)

(matrix-3d-set! a v s i j)

(map-matrix-nd f m n)

(for-each-matrix-nd f m n)

(map-matrix f m)

(for-each-matrix f m)

(map-matrix-3d f m)

(for-each-matrix-3d f m)

(map-n-matrix f i j)

(for-each-n-matrix f i j)

(map-indexed-matrix f m)

(for-each-indexed-matrix f m)

(map-indexed-matrix-3d f p)

(for-each-indexed-matrix-3d f p)



=== Sparse matrices



(define-structure sparse-matrix row column blank)

(define-structure sparse-matrix-row element i up down)

(define-structure sparse-matrix-column element j left right)

(define-structure sparse-matrix-element value i up down j left right)

(create-sparse-matrix blank)

(sparse-matrix-ref sparse-matrix i j)



=== Traversal



(every-n-2d p v w)

(every-n-3d p v w x)

(every-n-4d p v w x y)

(every-n-5d p v w x y z)

(product-2d f m n)

(sum-2d f m n)

(sum-3d f m n p)

(sum-4d f m n p q)

(sum-pairs f m)

(vector-sum f n i)

(vector-sum-2d f m n i)

(sum-f f l)

(sum-vector v)

(sum-vector-f f v)



=== Statistics



(list-mean p)

(list-covariance l)

(list-variance s)

(list-skewness l)

(list-kurtosis l)

(list-correlation l1 l2)

(vector-mean v)

(vector-variance v)

(vector-skewness v)

(vector-kurtosis v)

(vector-correlation v1 v2)

(coefficient-of-bimodality v)

(vectors-mean values)

(vectors-variance mu values)

(mahalanobis-distance val mu isigma)

(frequencies l)



=== Misc



*linear-algebra:epsilon*

pi

half-pi

two-pi

minus-pi

two-pi/360

three-sixty/two-pi

(sqr x)

(quadratic1 a b c)

(quadratic2 a b c)



=== License



   Copyright 2010-2012 Purdue University. All rights reserved.



   Contact Andrei Barbu, [email protected].



   This program is free software: you can redistribute it and/or modify

   it under the terms of the GNU Lesser General Public License as published by

   the Free Software Foundation, either version 3 of the License, or

   (at your option) any later version.

   This program is distributed in the hope that it will be useful,

   but WITHOUT ANY WARRANTY; without even the implied warranty of

   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the

   GNU Lesser General Public License for more details.

   You should have received a copy of the GNU Lesser General Public License

   along with this program.  If not, see http://www.gnu.org/licenses.