chickadee » linear-algebra

This page is maintained in the package's github repository.


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


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


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


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


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


sqr xprocedure
quadratic1 a b cprocedure
quadratic2 a b cprocedure


  Copyright 2010-2012 Purdue University. All rights reserved.
  Contact Andrei Barbu,
  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
  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

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