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;; timing test for generalized ref/set!
(define invert-matrix
(let ((+documentation+ "(invert-matrix matrix b (zero 1.0e-7)) inverts 'matrix'"))
(lambda* (matrix b (zero 1.0e-7))
;; translated from Numerical Recipes (gaussj)
(call-with-exit
(lambda (return)
(let ((n (vector-dimension matrix 0)))
(let ((cols (make-int-vector n))
(rows (make-int-vector n))
(pivots (make-int-vector n)))
(do ((i 0 (+ i 1))
(col 0 0)
(row 0 0))
((= i n))
(do ((biggest 0.0)
(j 0 (+ j 1)))
((= j n)
(if (< biggest zero)
(return #f)))
(if (not (= (pivots j) 1))
(do ((k 0 (+ k 1)))
((= k n))
(if (= (pivots k) 0)
(let ((val (abs (matrix j k))))
(when (> val biggest)
(set! col k)
(set! row j)
(set! biggest val)))
(if (> (pivots k) 1)
(return #f))))))
(set! (pivots col) (+ (pivots col) 1))
(if (not (= row col))
(let ((temp (if (sequence? b) (b row) 0.0)))
(when (sequence? b)
(set! (b row) (b col))
(set! (b col) temp))
(do ((k 0 (+ k 1)))
((= k n))
(set! temp (matrix row k))
(set! (matrix row k) (matrix col k))
(set! (matrix col k) temp))))
(set! (cols i) col)
(set! (rows i) row)
;; round-off troubles here
(if (< (abs (matrix col col)) zero)
(return #f))
(let ((inverse-pivot (/ 1.0 (matrix col col))))
(set! (matrix col col) 1.0)
(do ((k 0 (+ k 1)))
((= k n))
(set! (matrix col k) (* inverse-pivot (matrix col k))))
(if b (set! (b col) (* inverse-pivot (b col)))))
(do ((k 0 (+ k 1)))
((= k n))
(if (not (= k col))
(let ((scl (matrix k col)))
(set! (matrix k col) 0.0)
(do ((m 0 (+ 1 m)))
((= m n))
(set! (matrix k m) (- (matrix k m) (* scl (matrix col m)))))
(if b (set! (b k) (- (b k) (* scl (b col)))))))))
(do ((i (- n 1) (- i 1)))
((< i 0))
(if (not (= (rows i) (cols i)))
(do ((k 0 (+ k 1)))
((= k n))
(let ((temp (matrix k (rows i))))
(set! (matrix k (rows i)) (matrix k (cols i)))
(set! (matrix k (cols i)) temp)))))
(list matrix b))))))))
(define (matrix-multiply A B)
(let ((size (vector-dimension A 0)))
(do ((C (make-float-vector (list size size)))
(i 0 (+ i 1)))
((= i size) C)
(do ((j 0 (+ j 1)))
((= j size))
(do ((sum 0.0)
(k 0 (+ k 1)))
((= k size)
(set! (C i j) sum))
(set! sum (+ sum (* (A i k) (B k j)))))))))
;;; Rosetta scheme code + changes
(define (square-matrix mat)
(matrix-multiply mat mat))
(define (matrix-exp mat pow)
(cond ((= pow 0)
(let ((m (copy mat)))
(fill! m 0.0)
(let ((size (car (vector-dimensions mat))))
(do ((i 0 (+ i 1)))
((= i size) m)
(set! (m i i) 1.0)))))
((= pow 1)
mat)
((negative? pow)
(let ((im (invert-matrix (matrix-exp mat (abs pow)))))
(and (pair? im)
(car im))))
((even? pow)
(square-matrix (matrix-exp mat (ash pow -1))))
(else
(matrix-multiply mat (matrix-exp mat (- pow 1))))))
(define (testm)
(do ((i 0 (+ i 1)))
((= i 10000))
(let ((v (make-float-vector '(4 4)))
(pow (+ 1 (random 10))))
(do ((k 0 (+ k 1)))
((= k 4))
(do ((n 0 (+ n 1)))
((= n 4))
(set! (v k n) (- (random 50.0) 100.0))))
(let ((mn (matrix-exp (copy v) (- pow))))
(if mn
(let* ((m1 (matrix-multiply mn (matrix-exp (copy v) pow)))
(mx1 (m1 0 0))
(mx0 0.0))
(do ((k 1 (+ k 1)))
((= k 4))
(if (> (abs (- (m1 k k) 1.0)) (abs (- mx1 1.0)))
(set! mx1 (m1 k k))))
(do ((k 0 (+ k 1)))
((= k 4))
(do ((n 0 (+ n 1)))
((= n 4))
(unless (= k n)
(set! mx0 (max mx0 (abs (m1 k n)))))))))))))
(testm)
;;; --------------------------------------------------------------------------------
(define flarray #r2d((0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20)
(0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20)
(0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20)
(0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20)
(0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20)
(0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20)
(0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20)))
(define tfl #r2d((0 0 0 0 0 0 0) (1 1 1 1 1 1 1) (2 2 2 2 2 2 2) (3 3 3 3 3 3 3)
(4 4 4 4 4 4 4) (5 5 5 5 5 5 5) (6 6 6 6 6 6 6) (7 7 7 7 7 7 7)
(8 8 8 8 8 8 8) (9 9 9 9 9 9 9) (10 10 10 10 10 10 10) (11 11 11 11 11 11 11)
(12 12 12 12 12 12 12) (13 13 13 13 13 13 13) (14 14 14 14 14 14 14) (15 15 15 15 15 15 15)
(16 16 16 16 16 16 16) (17 17 17 17 17 17 17) (18 18 18 18 18 18 18) (19 19 19 19 19 19 19) (20 20 20 20 20 20 20)))
(define narray #2d((0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20)
(0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20)
(0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20)
(0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20)
(0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20)
(0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20)
(0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20)))
(define tna #2d((0 0 0 0 0 0 0) (1 1 1 1 1 1 1) (2 2 2 2 2 2 2) (3 3 3 3 3 3 3)
(4 4 4 4 4 4 4) (5 5 5 5 5 5 5) (6 6 6 6 6 6 6) (7 7 7 7 7 7 7)
(8 8 8 8 8 8 8) (9 9 9 9 9 9 9) (10 10 10 10 10 10 10) (11 11 11 11 11 11 11)
(12 12 12 12 12 12 12) (13 13 13 13 13 13 13) (14 14 14 14 14 14 14) (15 15 15 15 15 15 15)
(16 16 16 16 16 16 16) (17 17 17 17 17 17 17) (18 18 18 18 18 18 18) (19 19 19 19 19 19 19) (20 20 20 20 20 20 20)))
(define tries 10000)
(set! (*s7* 'print-length) 123123)
(define (matrix-transpose mat)
(let* ((dims (vector-dimensions mat))
(new-mat (make-vector (reverse dims)))
(end1 (car dims))
(end2 (cadr dims)))
(do ((i 0 (+ i 1)))
((= i end1) new-mat)
(do ((j 0 (+ j 1)))
((= j end2))
(set! (new-mat j i) (mat i j))))))
(unless (equal? (matrix-transpose narray) tna)
(format *stderr* "tna: ~S~%" (matrix-transpose narray)))
(define (test-transpose)
(do ((i 0 (+ i 1)))
((= i tries))
(matrix-transpose narray)))
(test-transpose)
(define (matrix-transpose1 mat)
(let* ((dims (vector-dimensions mat))
(new-mat (make-vector (reverse dims)))
(end1 (car dims))
(end2 (cadr dims)))
(do ((i 0 (+ i 1)))
((= i end1) new-mat)
(do ((j 0 (+ j 1)))
((= j end2))
(vector-set! new-mat j i (vector-ref mat i j))))))
(unless (equal? (matrix-transpose1 narray) tna)
(format *stderr* "tna1: ~S~%" (matrix-transpose1 narray)))
(define (test-transpose1)
(do ((i 0 (+ i 1)))
((= i tries))
(matrix-transpose1 narray)))
(test-transpose1)
(define (float-matrix-transpose mat)
(let* ((dims (vector-dimensions mat))
(new-mat (make-float-vector (reverse dims)))
(end1 (car dims))
(end2 (cadr dims)))
(do ((i 0 (+ i 1)))
((= i end1) new-mat)
(do ((j 0 (+ j 1)))
((= j end2))
(set! (new-mat j i) (mat i j))))))
(unless (equal? (float-matrix-transpose flarray) tfl)
(format *stderr* "tfl: ~S~%" (float-matrix-transpose flarray)))
(define (test-float-transpose)
(do ((i 0 (+ i 1)))
((= i tries))
(float-matrix-transpose flarray)))
(test-float-transpose)
(define (float-matrix-transpose1 mat)
(let* ((dims (vector-dimensions mat))
(new-mat (make-float-vector (reverse dims)))
(end1 (car dims))
(end2 (cadr dims)))
(do ((i 0 (+ i 1)))
((= i end1) new-mat)
(do ((j 0 (+ j 1)))
((= j end2))
(float-vector-set! new-mat j i (float-vector-ref mat i j))))))
(unless (equal? (float-matrix-transpose1 flarray) tfl)
(format *stderr* "tfl1: ~S~%" (float-matrix-transpose1 flarray)))
(define (test-float-transpose1)
(do ((i 0 (+ i 1)))
((= i tries))
(float-matrix-transpose1 flarray)))
(test-float-transpose1)
(when (> (*s7* 'profile) 0)
(show-profile 200))
(exit)
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