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chez-matrices.sls
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chez-matrices.sls
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;; -*- mode: scheme; coding: utf-8 -*-
;; Copyright (c) 2021 Liam Packer
;; SPDX-License-Identifier: MIT
#!r6rs
(library (chez-matrices)
(export make-matrix matrix-ref matrix-set! matrix-shape matrix-rank
matrix-num-vals matrix-num-rows matrix-num-cols matrix? matrix-copy
matrix-flatten vec->row-matrix matrix-ref-row matrix-set-row!
matrix-set-diagonal! matrix-identity
matrix-max matrix-min matrix-contract matrix-ref-col matrix-set-col!
matrix-map mul T matrix-fold tr euclidean-norm cross-product
theta phi linsolve matrix-inverse matrix= do-matrix matrix-fold
matrix-generate matrix-slice matrix-slice-view)
(import (rnrs (6))
(only (srfi :133 vectors) vector-fold))
(define (matrix-shape tensor)
(let tensor-dims-rec ([tensor tensor] [dim-list (list)])
(if (not (vector? (vector-ref tensor 0)))
(reverse (cons (vector-length tensor) dim-list))
(tensor-dims-rec (vector-ref tensor 0) (cons (vector-length tensor) dim-list)))))
(define (matrix-rank tensor)
(length (matrix-shape tensor)))
(define-syntax do-matrix
(syntax-rules ()
[(_ m () rest ...) (begin rest ...)]
[(_ m (() j ...) rest ...)
(do ([i 0 (+ 1 i)])
((>= i 1))
(do-matrix (matrix-ref m 0) (j ...) rest ...))]
[(_ m (i j ...) rest ...)
(do ([i 0 (+ 1 i)])
((>= i (car (matrix-shape m))))
(do-matrix (matrix-ref m 0) (j ...) rest ...))]
[(_ m ((i Upper) j ...) rest ...)
(do ([i 0 (+ 1 i)])
((>= i Upper))
(do-matrix (matrix-ref m 0) (j ...) rest ...))]
[(_ m ((i Lower Upper) j ...) rest ...)
(do ([i Lower (+ 1 i)])
((>= i Upper))
(do-matrix (matrix-ref m 0) (j ...) rest ...))]
[(_ m ret (i j ...) rest ...)
(do ([i 0 (+ 1 i)])
((>= i (car (matrix-shape m))) ret)
(do-matrix (matrix-ref m 0) (j ...) rest ...))]))
;; TODO: not tail-recursive :(
(define make-matrix
(lambda ids
(cond
[(= 1 (length ids)) (make-vector (car ids))]
[(= 2 (length ids))
(do ([m (make-vector (car ids))]
[k 0 (+ k 1)])
((= k (car ids)) m)
(vector-set! m k (make-vector (cadr ids))))]
[(> 2 (length ids))
(make-vector (car ids) (apply make-matrix (cdr ids)))])))
(define (matrix-ref m . ids)
(if (= 1 (length ids))
(vector-ref m (car ids))
(apply matrix-ref (cons (vector-ref m (car ids)) (cdr ids)))))
(define (%matrix-set! m val . ids)
(if (= 1 (length ids))
(vector-set! m (car ids) val)
(apply %matrix-set!
(cons (vector-ref m (car ids))
(cons val (cdr ids))))))
(define-syntax matrix-set!
(syntax-rules ()
[(_ m i j ... val) (%matrix-set! m val i j ...)]))
(define (matrix-num-vals m) (map * (matrix-shape m)))
(define (matrix-num-rows a) (vector-length a))
(define (matrix-num-cols a)
(if (vector? (matrix-ref a 0))
(vector-length (matrix-ref a 0))
1))
(define matrix?
(lambda (x)
(and (vector? x)
(> (vector-length x) 0)
(vector? (vector-ref x 0)))))
;; row matrix
(define (vec->row-matrix v)
(let ([w (make-vector 1)])
(vector-set! w 0 v)
w))
(define (matrix-flatten m)
(let* ([v (make-vector (* (matrix-num-cols m) (matrix-num-rows m)))])
(do-matrix m v (i j)
(vector-set! v (+ j (* i (matrix-num-cols m)))
(matrix-ref m i j)))))
(define (%matrix-slicer m ret . ids)
(when (not (null? ids))
(let ([upperLower (car ids)])
(do ([i (cadr upperLower) (+ 1 i)])
((>= i (car upperLower)))
(if (= 1 (length ids))
(matrix-set! ret (- i (cadr upperLower))
(matrix-ref m i))
(apply %matrix-slicer
;; idk a better way to make (list m ret ids)
(cons (matrix-ref m i)
(cons (matrix-ref ret (- i (cadr upperLower)))
(cdr ids)))))))))
(define (matrix-slice-view m . lst)
(let ([ret (apply make-matrix (map (lambda (x) (- (car x) (cadr x))) lst))])
(apply %matrix-slicer (cons m (cons ret lst)))
ret))
(define (matrix-slice m . lst)
(let ([ret (apply make-matrix (map (lambda (x) (- (car x) (cadr x))) lst))])
(apply %matrix-slicer (cons (matrix-copy m) (cons ret lst)))
ret))
(define (matrix-ref-row m i) (matrix-ref m i))
(define (matrix-set-row! m i v) (matrix-set! m i v))
;; verry inefficient but clean!
(define (matrix-ref-col m i)
(matrix-ref-row (T m) i))
(define (matrix-set-col! m i v)
(do-matrix m (row ()) (matrix-set! m row i (vector-ref v row))))
;; assert len(v) = min(dimensions(m))
(define (matrix-set-diagonal! m v)
(let ([new-m (matrix-copy m)])
(do ([i 0 (+ 1 i)])
((>= i (vector-length v)) m)
(matrix-set! m i i (vector-ref v i)))))
(define (matrix-identity dim)
(let ([m (make-matrix dim dim)])
(matrix-set-diagonal! m (make-vector dim 1))
m))
(define (matrix-contract m1 m2 i k)
(do ([j 0 (+ 1 j)]
[accum 0 (+ accum (* (matrix-ref m1 i j)
(matrix-ref m2 j k)))])
((>= j (matrix-num-cols m1)) accum)))
(define matrix-map
(lambda (f . As)
(if (> (matrix-rank (car As)) 2)
(apply vector-map (cons (lambda r (apply matrix-map (cons f r))) As))
(apply vector-map (cons (lambda r (apply vector-map (cons f r))) As)))))
(define (%matrix-fold1 f init m)
(if (> (matrix-rank m) 1)
(vector-fold f init (vector-map (lambda (x) (%matrix-fold1 f init x)) m))
(vector-fold f init m)))
(define (matrix-fold f init . ms)
(fold-left f init (map (lambda (m) (%matrix-fold1 f init m)) ms)))
(define-syntax matrix-generate
(syntax-rules ()
[(_ (lambda (i j ...) rest ...) n m ...)
(let ([a (make-matrix n m ...)])
(do-matrix a (i j ...)
(matrix-set! a i j ... ((lambda (i j ...) rest ...) i j ...)))
a)]))
;; assert proper dims
(define (matrix-copy a)
(matrix-map (lambda (x) x) a))
(define (matrix-copy! a b)
(do-matrix a (i j) (matrix-set! a i j (matrix-ref b i j))))
;; throw error if dims of a1 and a2 are bad
;; case on a1/a2 being a constant or not
(define (mul a1 a2)
(cond
[(and (matrix? a1) (matrix? a2))
(let* ([m (make-matrix (matrix-num-rows a1) (matrix-num-cols a2))])
(do-matrix m m (i k) (matrix-set! m i k (matrix-contract a1 a2 i k))))]
[(and (matrix? a2) (number? a1))
(matrix-map (lambda (x) (* a1 x)) a2)]
[(and (matrix? a1) (number? a2))
(matrix-map (lambda (x) (* a2 x)) a1)]))
(define (tr m)
(do ([i 0 (+ 1 i)]
[accum 0 (+ accum (matrix-ref m i i))])
((>= i (min (matrix-num-cols m) (matrix-num-rows m))) accum)))
(define (T a1)
(let ([m (make-matrix (matrix-num-cols a1) (matrix-num-rows a1))])
(do-matrix m m (i j)
(matrix-set! m j i (matrix-ref a1 i j)))))
;; assert len(v) = len(w) and both vectors and all that
(define (dot v w)
(matrix-ref (mul (T v) w) 0))
(define matrix=
(lambda (A B)
(matrix-fold
(lambda (x y) (and x y))
#t
(matrix-map = A B))))
;; Norms
(define (matrix-max m)
(matrix-fold max -inf.0 m))
(define (matrix-min m)
(matrix-fold min +inf.0 m))
(define (frobenius-norm m)
(matrix-fold
+
0 (matrix-map (lambda (x) (expt x 2)) m)))
(define (euclidean-norm M)
(cond
[(matrix? M)
(let ([ret 0])
(matrix-map (lambda (x) (set! ret (+ ret (expt x 2)))) M))]
[(vector? M)
(do ([i 0 (+ 1 i)]
[accum 0 (+ accum (expt (vector-ref M i) 2))])
((>= i (vector-length M)) (sqrt accum)))]))
;; Solve linear equation
(define (linsolve input-A input-B)
(when (and (matrix? input-A) (matrix? input-B))
(let* ([A (matrix-copy input-A)]
[B (matrix-copy input-B)]
[nrows (matrix-num-rows A)]
[ncols (matrix-num-cols A)])
(let ([leading
(lambda (col-idx)
(call/cc (lambda (break)
(do ([i col-idx (+ 1 i)])
((or (>= col-idx nrows) (>= i ncols)) #f)
(when (not (zero? (matrix-ref A i col-idx)))
(break i))))))]
[normalize-row
(lambda (row col)
(let ([norm-val (matrix-ref A row col)])
(matrix-set-row! A row
(vector-map (lambda (x) (/ x norm-val))
(matrix-ref-row A row)))
(matrix-set! B row 0
(/ (matrix-ref B row 0) norm-val))))]
[swap-rows
(lambda (row-idx1 row-idx2)
(unless (= row-idx1 row-idx2)
(let ([tmp-row (matrix-ref-row A row-idx1)]
[tmp-b (matrix-ref B row-idx1 0)])
(matrix-set-row! A row-idx1 (matrix-ref-row A row-idx2))
(matrix-set-row! A row-idx2 tmp-row)
(matrix-set! B row-idx1 0 (matrix-ref B row-idx2 0))
(matrix-set! B row-idx2 0 tmp-b))))]
[eliminate-row
(lambda (row-idx col-idx basis-idx)
(let ([ratio (matrix-ref A row-idx col-idx)])
(do ([i col-idx (+ 1 i)])
((>= i ncols))
(matrix-set! A row-idx i
(- (matrix-ref A row-idx i)
(* ratio (matrix-ref A basis-idx i)))))
(matrix-set! B row-idx 0
(- (matrix-ref B row-idx 0)
(* ratio (matrix-ref B basis-idx 0))))))])
(call/cc
(lambda (break)
(do ([j 0 (+ 1 j)])
((>= j ncols) B)
(let ([lead (leading j)])
(when (not lead)
(break #f))
(normalize-row lead j)
(do ([i 0 (+ 1 i)])
((>= i nrows))
(unless (= i lead)
(eliminate-row i j lead)))
(swap-rows j lead)))))))))
(define (matrix-inverse input-A)
(when (and (= (matrix-num-cols input-A) (matrix-num-rows input-A)) (matrix? input-A))
(let* ([A (matrix-copy input-A)]
[nrows (matrix-num-rows A)]
[ncols (matrix-num-cols A)]
[inv-A (matrix-identity nrows)])
(let ([leading
(lambda (col-idx)
(call/cc
(lambda (break)
(do ([i col-idx (+ 1 i)])
((or (>= col-idx nrows) (>= i ncols)) #f)
(when (not (zero? (matrix-ref A i col-idx)))
(break i))))))]
[normalize-row
(lambda (row col)
(let ([norm-val (matrix-ref A row col)])
(matrix-set-row! A row
(vector-map (lambda (x) (/ x norm-val))
(matrix-ref-row A row)))
(matrix-set-row! inv-A row
(vector-map (lambda (x) (/ x norm-val))
(matrix-ref-row inv-A row)))))]
[swap-rows
(lambda (row-idx1 row-idx2)
(unless (= row-idx1 row-idx2)
(let ([tmp-row (matrix-ref-row A row-idx1)]
[tmp-row-inv (matrix-ref-row inv-A row-idx1)])
(matrix-set-row! A row-idx1 (matrix-ref-row A row-idx2))
(matrix-set-row! A row-idx2 tmp-row)
(matrix-set-row! inv-A row-idx1 (matrix-ref-row inv-A row-idx2))
(matrix-set-row! inv-A row-idx2 tmp-row-inv))))]
[eliminate-row
(lambda (row-idx col-idx basis-idx)
(let ([ratio (matrix-ref A row-idx col-idx)])
(do ([i 0 (+ 1 i)])
((>= i ncols))
(matrix-set! A row-idx i
(- (matrix-ref A row-idx i)
(* ratio (matrix-ref A basis-idx i))))
(matrix-set! inv-A row-idx i
(- (matrix-ref inv-A row-idx i)
(* ratio (matrix-ref inv-A basis-idx i)))))))])
(call/cc
(lambda (break)
(do ([j 0 (+ 1 j)])
((>= j ncols) inv-A)
(let ([lead (leading j)])
(when (not lead)
(break #f))
(normalize-row lead j)
(do ([i 0 (+ 1 i)])
((>= i nrows))
(unless (= i lead)
(eliminate-row i j lead)))
(swap-rows j lead)))
))))))
;; Using the physics notation of the azimuthal 2\pi angle being phi
(define (phi v)
(atan (vector-ref v 1)
(vector-ref v 0)))
(define (theta v)
(acos (/ (vector-ref v 2)
(euclidean-norm v))))
;; assert dim 3
(define (cross-product v w)
(let ([cross-vw (make-vector 3)])
(apply
(lambda (ax ay az bx by bz)
(vector-set! cross-vw 0 (- (* ay bz)
(* by az)))
(vector-set! cross-vw 1 (- (- (* ax bz)
(* bx az))))
(vector-set! cross-vw 2 (- (* ax by)
(* bx ay))))
(append (vector->list v) (vector->list w)))
cross-vw)))