how to create an arbitrary size matrix with the elements alonging with specific distribution?

Zfeng,

Something like this:

procedure(CCFbuildMatrix(N mean sigma)
  let((matrix column)
    matrix=makeVector(N)
    for(x 0 N-1
      matrix[x]=column=makeVector(N)
      for(y 0 N-1
        ; convert to integer, clip, do whatever you want here.
        ; in this case I just stretched the normal distribution to the
        ; desired mean and standard deviation
        column[y]=abRandomNormal()*sigma+mean
      )
    )
  matrix
  )
)

This uses the code below to generate random numbers with a gaussian distribution. The return value of this is a matrix - so you can do:

> m=CCFbuildMatrix(100 50 10)
array@0x90ac678
> m[2][4]
53.99555
> m[6][8]
47.73704

For example.

/* abRandomNormal.il

Author     A.D.Beckett
Group      Custom IC (UK), Cadence Design Systems Ltd.
Language   SKILL
Date        
Modified   
By         

Uses Box-Muller method to produce random numbers with
a normal distribution (mean 0, std dev 1).

Call abRandomNormal() multiple times to get such a sequence.

***************************************************

SCCS Info: @(#) abRandomNormal.il 11/30/12.14:22:28 1.1

*/

;------------------------------------------------------------------------
; Store math constants (such as PI) as properties on this symbol
;------------------------------------------------------------------------
(defMathConstants 'abRandomNormal)

/***************************************************************
*                                                              *
*                       (abRandomNormal)                       *
*                                                              *
*  Return a random number with normal distribution using the   *
*                      Box-Muller method                       *
*                                                              *
***************************************************************/
(defun abRandomNormal ()
  (let ((max (rightshift -1 1)) U V)
    (setq U (quotient (float (random max)) max))
    (setq V (quotient (float (random max)) max))
    ;--------------------------------------------------------------------
    ; could generate two independent numbers
    ; the other would use cos instead of sin
    ;--------------------------------------------------------------------
    (times (sqrt (times -2 (log U))) 
           (cos (times 2 (getqq abRandomNormal PI) V)))
    )
  )

/***************************************************************
*                                                              *
*             (abTestRandomNormal numPoints bins)              *
*                                                              *
*   Function for testing - uses ViVA's plotting functions to   *
*  produce a histogram and also compute the mean and std dev   *
*      to ensure that with enough points it looks normal       *
*               (e.g numPoints 100000, bins 100)               *
*                                                              *
***************************************************************/

(defun abTestRandomNormal (numPoints bins)
  (let (x y wave)
    (setq x (drCreateVec 'intlong numPoints))
    (setq y (drCreateVec 'double numPoints))
    (for i 0 numPoints
         (drAddElem x i)
         (drAddElem y (abRandomNormal))
         )
    (setq wave (drCreateWaveform x y))
    (awvPlotWaveform (newWindow) (list (histo wave bins nil nil)))
    (printf "Mean=%g\nStd Dev=%g\n" (average wave) (stddev wave))
    )
  ) 

Andrew.