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 performance measurements

Each table row shows performance measurements for this Racket program with a particular command-line input value N.

 N  CPU secs Elapsed secs Memory KB Code B ≈ CPU Load
5000.450.4518,008446  2% 2% 16% 100%
3,00012.0412.0419,616446  0% 0% 1% 100%
5,50040.1740.1819,868446  0% 0% 1% 100%

Read the ↓ make, command line, and program output logs to see how this program was run.

Read spectral-norm benchmark to see what this program should do.

 notes

Welcome to Racket v6.0.

 spectral-norm Racket program source code

#lang racket/base

;;; The Computer Language Benchmarks Game
;;; http://benchmarksgame.alioth.debian.org/

;;; Translated directly from the C# version by Isaac Gouy
;;; contributed by Matthew Flatt

(require racket/cmdline
         racket/flonum)

(define (Approximate n)
  (let ([u (make-flvector n 1.0)]
        [v (make-flvector n 0.0)])
    ;; 20 steps of the power method
    (for ([i (in-range 10)])
      (MultiplyAtAv n u v)
      (MultiplyAtAv n v u))
    
    ;; B=AtA         A multiplied by A transposed
    ;; v.Bv /(v.v)   eigenvalue of v
    (let loop ([i 0][vBv 0.0][vv 0.0])
      (if (= i n)
          (flsqrt (fl/ vBv vv))
          (let ([vi (flvector-ref v i)])
            (loop (add1 i)
                  (fl+ vBv (fl* (flvector-ref u i) vi))
                  (fl+ vv (fl* vi vi))))))))

;; return element i,j of infinite matrix A
(define (A i j)
  (fl/ 1.0 (fl+ (fl* (->fl (+ i j))
                     (fl/ (->fl (+ i (+ j 1))) 2.0)) 
                (->fl (+ i 1)))))

;; multiply vector v by matrix A
(define (MultiplyAv n v Av)
  (for ([i (in-range n)])
    (flvector-set! Av i 
                   (for/fold ([r 0.0])
                       ([j (in-range n)])
                     (fl+ r (fl* (A i j) (flvector-ref v j)))))))

;; multiply vector v by matrix A transposed
(define (MultiplyAtv n v Atv)
  (for ([i (in-range n)])
    (flvector-set! Atv i
                   (for/fold ([r 0.0])
                       ([j (in-range n)])
                     (fl+ r (fl* (A j i) (flvector-ref v j)))))))

;; multiply vector v by matrix A and then by matrix A transposed 
(define (MultiplyAtAv n v AtAv)
  (let ([u (make-flvector n 0.0)])
    (MultiplyAv n v u)
    (MultiplyAtv n u AtAv)))

(printf "~a\n"
        (real->decimal-string
         (Approximate (command-line #:args (n) (string->number n)))
         9))

 make, command-line, and program output logs

Fri, 28 Feb 2014 10:50:17 GMT

COMMAND LINE:
/usr/local/src/racket-6.0/bin/racket  spectralnorm.racket 5500

PROGRAM OUTPUT:
1.274224153

Revised BSD license

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