You can edit this page using wiki syntax for markup.

Article contents:== Outdated egg! This is an egg for CHICKEN 4, the unsupported old release. You're almost certainly looking for [[/eggref/5/linear-algebra|the CHICKEN 5 version of this egg]], if it exists. If it does not exist, there may be equivalent functionality provided by another egg; have a look at the [[https://wiki.call-cc.org/chicken-projects/egg-index-5.html|egg index]]. Otherwise, please consider porting this egg to the current version of CHICKEN. [[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 <record>(define-structure line-segment p q)</record> <procedure>(p l)</procedure> <procedure>(q l)</procedure> <procedure>(collinear? l1 l2)</procedure> <procedure>(point-on-line-segment? r l)</procedure> <procedure>(intersection-point l1 l2)</procedure> <procedure>(cross? l1 l2)</procedure> <procedure>(intersect? l1 l2)</procedure> <procedure>(line-tangent l)</procedure> <procedure>(normal-2d l)</procedure> <procedure>(line-segment-length l)</procedure> <procedure>(read-line-segments-from-file pathname)</procedure> <procedure>(write-line-segments-to-file line-segments pathname)</procedure> === Vectors <procedure>(x v)</procedure> <procedure>(y v)</procedure> <procedure>(z v)</procedure> <procedure>(dot u v)</procedure> <procedure>(cross-2d u v)</procedure> <procedure>(cross u v)</procedure> <procedure>(v+ u v)</procedure> <procedure>(v- u v)</procedure> <procedure>(k*v k v)</procedure> <procedure>(v*k v k)</procedure> <procedure>(k+v k v)</procedure> <procedure>(v+k v k)</procedure> <procedure>(v/k v k)</procedure> <procedure>(v* u v)</procedure> <procedure>(v/ u v)</procedure> <procedure>(v= u v)</procedure> <procedure>(rotate-90 u)</procedure> <procedure>(rotate-180 u)</procedure> <procedure>(rotate-270 u)</procedure> <procedure>(perpendicular? u v)</procedure> <procedure>(parallel? u v)</procedure> <procedure>(magnitude-squared v)</procedure> <procedure>(magnitude v)</procedure> <procedure>(unit v)</procedure> <procedure>(distance-squared u v)</procedure> <procedure>(distance u v)</procedure> <procedure>(clockwise-angle? u v w)</procedure> <procedure>(clockwise-or-same-angle? u v w)</procedure> <procedure>(append-vector vec1 vec2)</procedure> === Matrices <procedure>(matrix? v)</procedure> <procedure>(list->matrix l)</procedure> <procedure>(make-matrix m n . &rest)</procedure> <procedure>(make-3-by-3-matrix a11 a12 a13 a21 a22 a23 a31 a32 a33)</procedure> <procedure>(matrix-copy m)</procedure> <procedure>(matrix-rows a)</procedure> <procedure>(matrix-columns a)</procedure> <procedure>(matrix-ref a i j)</procedure> <procedure>(matrix-set! a i j x)</procedure> <procedure>(matrix-row-ref a i)</procedure> <procedure>(matrix-column-ref a j)</procedure> <procedure>(matrix-row-set! a i v)</procedure> <procedure>(vector->row-matrix v)</procedure> <procedure>(vector->column-matrix v)</procedure> <procedure>(m+ a b)</procedure> <procedure>(m- a b)</procedure> <procedure>(m+k m k)</procedure> <procedure>(m+k-diagonal m k)</procedure> <procedure>(k+m k m)</procedure> <procedure>(m*v a v)</procedure> <procedure>(matrix-transpose a)</procedure> <procedure>(outer-product f u v)</procedure> <procedure>(self-outer-product f v)</procedure> <procedure>(m* a b)</procedure> <procedure>(m*. a b)</procedure> <procedure>(m/. a b)</procedure> <procedure>(v*m v a)</procedure> <procedure>(k*m k m)</procedure> <procedure>(m*k m k)</procedure> <procedure>(m/k m k)</procedure> <procedure>(v*m*v v m)</procedure> <procedure>(determinant a)</procedure> <procedure>(invert-matrix a)</procedure> <procedure>(simplex a m1 m2 m3)</procedure> <procedure>(jacobi a)</procedure> <procedure>(eigenvalues a)</procedure> <procedure>(eigenvectors a)</procedure> <procedure>(vector->diagonal-matrix v)</procedure> <procedure>(identity-matrix n)</procedure> <procedure>(clip-eigenvalues a v)</procedure> <procedure>(eigenvector-angle1 m)</procedure> <procedure>(eigenvector-angle2 m)</procedure> <procedure>(left-pseudo-inverse m)</procedure> <procedure>(right-pseudo-inverse m)</procedure> <procedure>(ref-1d m a)</procedure> <procedure>(ref-2d m a b)</procedure> <procedure>(ref-3d m a b c)</procedure> <procedure>(ref-4d m a b c d)</procedure> <procedure>(ref-5d m a b c d e)</procedure> <procedure>(map-n-vector-2d f m n)</procedure> <procedure>(map-n-vector-3d f m n p)</procedure> <procedure>(map-n-vector-4d f m n p q)</procedure> <procedure>(map-n-vector-5d f m n p q r)</procedure> <procedure>(matrix-sum f n i)</procedure> <procedure>(matrix-sum-2d f m n i)</procedure> <procedure>(shape-matrix v c)</procedure> <procedure>(unshape-matrix m)</procedure> <procedure>(crop m x y w h)</procedure> <procedure>(submatrix m x-offset y-offset x-size y-size)</procedure> <procedure>(matrix-ref-nd m . is)</procedure> <procedure>(matrix-3d-ref a s i j)</procedure> <procedure>(matrix-set-nd! m v . is)</procedure> <procedure>(matrix-3d-set! a v s i j)</procedure> <procedure>(map-matrix-nd f m n)</procedure> <procedure>(for-each-matrix-nd f m n)</procedure> <procedure>(map-matrix f m)</procedure> <procedure>(for-each-matrix f m)</procedure> <procedure>(map-matrix-3d f m)</procedure> <procedure>(for-each-matrix-3d f m)</procedure> <procedure>(map-n-matrix f i j)</procedure> <procedure>(for-each-n-matrix f i j)</procedure> <procedure>(map-indexed-matrix f m)</procedure> <procedure>(for-each-indexed-matrix f m)</procedure> <procedure>(map-indexed-matrix-3d f p)</procedure> <procedure>(for-each-indexed-matrix-3d f p)</procedure> === Sparse matrices <record>(define-structure sparse-matrix row column blank)</record> <record>(define-structure sparse-matrix-row element i up down)</record> <record>(define-structure sparse-matrix-column element j left right)</record> <record>(define-structure sparse-matrix-element value i up down j left right)</record> <procedure>(create-sparse-matrix blank)</procedure> <procedure>(sparse-matrix-ref sparse-matrix i j)</procedure> === Traversal <procedure>(every-n-2d p v w)</procedure> <procedure>(every-n-3d p v w x)</procedure> <procedure>(every-n-4d p v w x y)</procedure> <procedure>(every-n-5d p v w x y z)</procedure> <procedure>(product-2d f m n)</procedure> <procedure>(sum-2d f m n)</procedure> <procedure>(sum-3d f m n p)</procedure> <procedure>(sum-4d f m n p q)</procedure> <procedure>(sum-pairs f m)</procedure> <procedure>(vector-sum f n i)</procedure> <procedure>(vector-sum-2d f m n i)</procedure> <procedure>(sum-f f l)</procedure> <procedure>(sum-vector v)</procedure> <procedure>(sum-vector-f f v)</procedure> === Statistics <procedure>(list-mean p)</procedure> <procedure>(list-covariance l)</procedure> <procedure>(list-variance s)</procedure> <procedure>(list-skewness l)</procedure> <procedure>(list-kurtosis l)</procedure> <procedure>(list-correlation l1 l2)</procedure> <procedure>(vector-mean v)</procedure> <procedure>(vector-variance v)</procedure> <procedure>(vector-skewness v)</procedure> <procedure>(vector-kurtosis v)</procedure> <procedure>(vector-correlation v1 v2)</procedure> <procedure>(coefficient-of-bimodality v)</procedure> <procedure>(vectors-mean values)</procedure> <procedure>(vectors-variance mu values)</procedure> <procedure>(mahalanobis-distance val mu isigma)</procedure> <procedure>(frequencies l)</procedure> === Misc <parameter>*linear-algebra:epsilon*</parameter> <constant>pi</constant> <constant>half-pi</constant> <constant>two-pi</constant> <constant>minus-pi</constant> <constant>two-pi/360</constant> <constant>three-sixty/two-pi</constant> <procedure>(sqr x)</procedure> <procedure>(quadratic1 a b c)</procedure> <procedure>(quadratic2 a b c)</procedure> === License Copyright 2010-2012 Purdue University. All rights reserved. Contact Andrei Barbu, andrei@0xab.com. 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. Description of your changes:

I would like to authenticate

Spam control

What do you get when you subtract 14 from 19?