1. linear-algebra
    1. Line segments
    2. Vectors
    3. Matrices
    4. Sparse matrices
    5. Traversal
    6. Statistics
    7. Misc
    8. License

This page is maintained in the package's 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)
[procedure] (p l)
[procedure] (q l)
[procedure] (collinear? l1 l2)
[procedure] (point-on-line-segment? r l)
[procedure] (intersection-point l1 l2)
[procedure] (cross? l1 l2)
[procedure] (intersect? l1 l2)
[procedure] (line-tangent l)
[procedure] (normal-2d l)
[procedure] (line-segment-length l)
[procedure] (read-line-segments-from-file pathname)
[procedure] (write-line-segments-to-file line-segments pathname)

Vectors

[procedure] (x v)
[procedure] (y v)
[procedure] (z v)
[procedure] (dot u v)
[procedure] (cross-2d u v)
[procedure] (cross u v)
[procedure] (v+ u v)
[procedure] (v- u v)
[procedure] (k*v k v)
[procedure] (v*k v k)
[procedure] (k+v k v)
[procedure] (v+k v k)
[procedure] (v/k v k)
[procedure] (v* u v)
[procedure] (v/ u v)
[procedure] (v= u v)
[procedure] (rotate-90 u)
[procedure] (rotate-180 u)
[procedure] (rotate-270 u)
[procedure] (perpendicular? u v)
[procedure] (parallel? u v)
[procedure] (magnitude-squared v)
[procedure] (magnitude v)
[procedure] (unit v)
[procedure] (distance-squared u v)
[procedure] (distance u v)
[procedure] (clockwise-angle? u v w)
[procedure] (clockwise-or-same-angle? u v w)
[procedure] (append-vector vec1 vec2)

Matrices

[procedure] (matrix? v)
[procedure] (list->matrix l)
[procedure] (make-matrix m n . &rest)
[procedure] (make-3-by-3-matrix a11 a12 a13 a21 a22 a23 a31 a32 a33)
[procedure] (matrix-copy m)
[procedure] (matrix-rows a)
[procedure] (matrix-columns a)
[procedure] (matrix-ref a i j)
[procedure] (matrix-set! a i j x)
[procedure] (matrix-row-ref a i)
[procedure] (matrix-column-ref a j)
[procedure] (matrix-row-set! a i v)
[procedure] (vector->row-matrix v)
[procedure] (vector->column-matrix v)
[procedure] (m+ a b)
[procedure] (m- a b)
[procedure] (m+k m k)
[procedure] (m+k-diagonal m k)
[procedure] (k+m k m)
[procedure] (m*v a v)
[procedure] (matrix-transpose a)
[procedure] (outer-product f u v)
[procedure] (self-outer-product f v)
[procedure] (m* a b)
[procedure] (m*. a b)
[procedure] (m/. a b)
[procedure] (v*m v a)
[procedure] (k*m k m)
[procedure] (m*k m k)
[procedure] (m/k m k)
[procedure] (v*m*v v m)
[procedure] (determinant a)
[procedure] (invert-matrix a)
[procedure] (simplex a m1 m2 m3)
[procedure] (jacobi a)
[procedure] (eigenvalues a)
[procedure] (eigenvectors a)
[procedure] (vector->diagonal-matrix v)
[procedure] (identity-matrix n)
[procedure] (clip-eigenvalues a v)
[procedure] (eigenvector-angle1 m)
[procedure] (eigenvector-angle2 m)
[procedure] (left-pseudo-inverse m)
[procedure] (right-pseudo-inverse m)
[procedure] (ref-1d m a)
[procedure] (ref-2d m a b)
[procedure] (ref-3d m a b c)
[procedure] (ref-4d m a b c d)
[procedure] (ref-5d m a b c d e)
[procedure] (map-n-vector-2d f m n)
[procedure] (map-n-vector-3d f m n p)
[procedure] (map-n-vector-4d f m n p q)
[procedure] (map-n-vector-5d f m n p q r)
[procedure] (matrix-sum f n i)
[procedure] (matrix-sum-2d f m n i)
[procedure] (shape-matrix v c)
[procedure] (unshape-matrix m)
[procedure] (crop m x y w h)
[procedure] (submatrix m x-offset y-offset x-size y-size)
[procedure] (matrix-ref-nd m . is)
[procedure] (matrix-3d-ref a s i j)
[procedure] (matrix-set-nd! m v . is)
[procedure] (matrix-3d-set! a v s i j)
[procedure] (map-matrix-nd f m n)
[procedure] (for-each-matrix-nd f m n)
[procedure] (map-matrix f m)
[procedure] (for-each-matrix f m)
[procedure] (map-matrix-3d f m)
[procedure] (for-each-matrix-3d f m)
[procedure] (map-n-matrix f i j)
[procedure] (for-each-n-matrix f i j)
[procedure] (map-indexed-matrix f m)
[procedure] (for-each-indexed-matrix f m)
[procedure] (map-indexed-matrix-3d f p)
[procedure] (for-each-indexed-matrix-3d f p)

Sparse matrices

[record] (define-structure sparse-matrix row column blank)
[record] (define-structure sparse-matrix-row element i up down)
[record] (define-structure sparse-matrix-column element j left right)
[record] (define-structure sparse-matrix-element value i up down j left right)
[procedure] (create-sparse-matrix blank)
[procedure] (sparse-matrix-ref sparse-matrix i j)

Traversal

[procedure] (every-n-2d p v w)
[procedure] (every-n-3d p v w x)
[procedure] (every-n-4d p v w x y)
[procedure] (every-n-5d p v w x y z)
[procedure] (product-2d f m n)
[procedure] (sum-2d f m n)
[procedure] (sum-3d f m n p)
[procedure] (sum-4d f m n p q)
[procedure] (sum-pairs f m)
[procedure] (vector-sum f n i)
[procedure] (vector-sum-2d f m n i)
[procedure] (sum-f f l)
[procedure] (sum-vector v)
[procedure] (sum-vector-f f v)

Statistics

[procedure] (list-mean p)
[procedure] (list-covariance l)
[procedure] (list-variance s)
[procedure] (list-skewness l)
[procedure] (list-kurtosis l)
[procedure] (list-correlation l1 l2)
[procedure] (vector-mean v)
[procedure] (vector-variance v)
[procedure] (vector-skewness v)
[procedure] (vector-kurtosis v)
[procedure] (vector-correlation v1 v2)
[procedure] (coefficient-of-bimodality v)
[procedure] (vectors-mean values)
[procedure] (vectors-variance mu values)
[procedure] (mahalanobis-distance val mu isigma)
[procedure] (frequencies l)

Misc

[parameter] *linear-algebra:epsilon*
[constant] pi
[constant] half-pi
[constant] two-pi
[constant] minus-pi
[constant] two-pi/360
[constant] three-sixty/two-pi
[procedure] (sqr x)
[procedure] (quadratic1 a b c)
[procedure] (quadratic2 a b c)

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.