chickadee » linear-algebra

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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 qrecord

p lprocedure

q lprocedure

collinear? l1 l2procedure

point-on-line-segment? r lprocedure

intersection-point l1 l2procedure

cross? l1 l2procedure

intersect? l1 l2procedure

line-tangent lprocedure

normal-2d lprocedure

line-segment-length lprocedure

read-line-segments-from-file pathnameprocedure

write-line-segments-to-file line-segments pathnameprocedure

Vectors

x vprocedure

y vprocedure

z vprocedure

dot u vprocedure

cross-2d u vprocedure

cross u vprocedure

v+ u vprocedure

v- u vprocedure

k*v k vprocedure

v*k v kprocedure

k+v k vprocedure

v+k v kprocedure

v/k v kprocedure

v* u vprocedure

v/ u vprocedure

v= u vprocedure

rotate-90 uprocedure

rotate-180 uprocedure

rotate-270 uprocedure

perpendicular? u vprocedure

parallel? u vprocedure

magnitude-squared vprocedure

magnitude vprocedure

unit vprocedure

distance-squared u vprocedure

distance u vprocedure

clockwise-angle? u v wprocedure

clockwise-or-same-angle? u v wprocedure

append-vector vec1 vec2procedure

Matrices

matrix? vprocedure

list->matrix lprocedure

make-matrix m n #!rest &restprocedure

make-3-by-3-matrix a11 a12 a13 a21 a22 a23 a31 a32 a33procedure

matrix-copy mprocedure

matrix-rows aprocedure

matrix-columns aprocedure

matrix-ref a i jprocedure

matrix-set! a i j xprocedure

matrix-row-ref a iprocedure

matrix-column-ref a jprocedure

matrix-row-set! a i vprocedure

vector->row-matrix vprocedure

vector->column-matrix vprocedure

m+ a bprocedure

m- a bprocedure

m+k m kprocedure

m+k-diagonal m kprocedure

k+m k mprocedure

m*v a vprocedure

matrix-transpose aprocedure

outer-product f u vprocedure

self-outer-product f vprocedure

m* a bprocedure

m*. a bprocedure

m/. a bprocedure

v*m v aprocedure

k*m k mprocedure

m*k m kprocedure

m/k m kprocedure

v*m*v v mprocedure

determinant aprocedure

invert-matrix aprocedure

simplex a m1 m2 m3procedure

jacobi aprocedure

eigenvalues aprocedure

eigenvectors aprocedure

vector->diagonal-matrix vprocedure

identity-matrix nprocedure

clip-eigenvalues a vprocedure

eigenvector-angle1 mprocedure

eigenvector-angle2 mprocedure

left-pseudo-inverse mprocedure

right-pseudo-inverse mprocedure

ref-1d m aprocedure

ref-2d m a bprocedure

ref-3d m a b cprocedure

ref-4d m a b c dprocedure

ref-5d m a b c d eprocedure

map-n-vector-2d f m nprocedure

map-n-vector-3d f m n pprocedure

map-n-vector-4d f m n p qprocedure

map-n-vector-5d f m n p q rprocedure

matrix-sum f n iprocedure

matrix-sum-2d f m n iprocedure

shape-matrix v cprocedure

unshape-matrix mprocedure

crop m x y w hprocedure

submatrix m x-offset y-offset x-size y-sizeprocedure

matrix-ref-nd m #!rest isprocedure

matrix-3d-ref a s i jprocedure

matrix-set-nd! m v #!rest isprocedure

matrix-3d-set! a v s i jprocedure

map-matrix-nd f m nprocedure

for-each-matrix-nd f m nprocedure

map-matrix f mprocedure

for-each-matrix f mprocedure

map-matrix-3d f mprocedure

for-each-matrix-3d f mprocedure

map-n-matrix f i jprocedure

for-each-n-matrix f i jprocedure

map-indexed-matrix f mprocedure

for-each-indexed-matrix f mprocedure

map-indexed-matrix-3d f pprocedure

for-each-indexed-matrix-3d f pprocedure

Sparse matrices

define-structure sparse-matrix row column blankrecord

define-structure sparse-matrix-row element i up downrecord

define-structure sparse-matrix-column element j left rightrecord

define-structure sparse-matrix-element value i up down j left rightrecord

create-sparse-matrix blankprocedure

sparse-matrix-ref sparse-matrix i jprocedure

Traversal

every-n-2d p v wprocedure

every-n-3d p v w xprocedure

every-n-4d p v w x yprocedure

every-n-5d p v w x y zprocedure

product-2d f m nprocedure

sum-2d f m nprocedure

sum-3d f m n pprocedure

sum-4d f m n p qprocedure

sum-pairs f mprocedure

vector-sum f n iprocedure

vector-sum-2d f m n iprocedure

sum-f f lprocedure

sum-vector vprocedure

sum-vector-f f vprocedure

Statistics

list-mean pprocedure

list-covariance lprocedure

list-variance sprocedure

list-skewness lprocedure

list-kurtosis lprocedure

list-correlation l1 l2procedure

vector-mean vprocedure

vector-variance vprocedure

vector-skewness vprocedure

vector-kurtosis vprocedure

vector-correlation v1 v2procedure

coefficient-of-bimodality vprocedure

vectors-mean valuesprocedure

vectors-variance mu valuesprocedure

mahalanobis-distance val mu isigmaprocedure

frequencies lprocedure

Misc

*linear-algebra:epsilon*parameter

piconstant

half-piconstant

two-piconstant

minus-piconstant

two-pi/360constant

three-sixty/two-piconstant

sqr xprocedure

quadratic1 a b cprocedure

quadratic2 a b cprocedure

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.