59 lines
1.6 KiB
Scheme
59 lines
1.6 KiB
Scheme
;; The Great Computer Language Shootout
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;; http://shootout.alioth.debian.org/
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;; Translated directly from the C# version, which was:
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;; contributed by Isaac Gouy
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#lang scheme/base
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(require scheme/cmdline)
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(define (Approximate n)
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(let ([u (make-vector n 1.0)]
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[v (make-vector n 0.0)])
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;; 20 steps of the power method
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(for ([i (in-range 10)])
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(MultiplyAtAv n u v)
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(MultiplyAtAv n v u))
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;; B=AtA A multiplied by A transposed
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;; v.Bv /(v.v) eigenvalue of v
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(let loop ([i 0][vBv 0][vv 0])
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(if (= i n)
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(sqrt (/ vBv vv))
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(let ([vi (vector-ref v i)])
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(loop (add1 i)
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(+ vBv (* (vector-ref u i) vi))
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(+ vv (* vi vi))))))))
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;; return element i,j of infinite matrix A
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(define (A i j)
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(/ 1.0 (+ (* (+ i j) (/ (+ i j 1) 2)) i 1)))
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;; multiply vector v by matrix A
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(define (MultiplyAv n v Av)
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(for ([i (in-range n)])
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(vector-set! Av i
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(for/fold ([r 0])
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([j (in-range n)])
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(+ r (* (A i j) (vector-ref v j)))))))
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;; multiply vector v by matrix A transposed
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(define (MultiplyAtv n v Atv)
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(for ([i (in-range n)])
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(vector-set! Atv i
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(for/fold ([r 0])
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([j (in-range n)])
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(+ r (* (A j i) (vector-ref v j)))))))
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;; multiply vector v by matrix A and then by matrix A transposed
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(define (MultiplyAtAv n v AtAv)
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(let ([u (make-vector n 0.0)])
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(MultiplyAv n v u)
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(MultiplyAtv n u AtAv)))
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(printf "~a\n"
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(real->decimal-string
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(Approximate (command-line #:args (n) (string->number n)))
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9))
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