Standard Library

boxcar

DOCUMENT boxcar(a, n)

  returns array A smoothed by a boxcar of 2*N+1 pixels.
  If A is multi-dimensional, N may be a vector with as many
  components as A has dimensions, specifying how many pixels
  to smooth in that dimension.  N may be shorter than the number
  of dimensions of A; unspecified dimensions are unsmoothed
  (as if N were 0).  If A is multi-dimensional and N is scalar,
  that N is applied to all dimensions.

  Each pixel of the result is averaged with the N pixels to
  its left and N pixels to its right (so N=0 means no averaging).
  For pixels less than N from the left edge, the averaging includes
  fewer pixels on the left, but still N on the right, and similarly
  for pixels less than N from the right edge.  Hence, the effective
  smoothing is reduced and the centering is skewed, near the edges
  of the array.

SEE ALSO: convoln, gaussm

convol

DOCUMENT convol(a,b)

  returns convolution of vector a with vector b, a vector
  of length na+nb-1 where na=numberof(a), nb=numberof(b).

  In detail, for i=[1 to na+nb-1]
    result(i) = sum j=[max(1,1+i-nb) to min(na,i)] (a(j)*b(1+i-j))

  The n0= and n1= keywords can be used to control the section of
  the full array that is actually returned, 1<=n0
  
SEE ALSO: fft_good, fft, convoln, gaussm, boxcar

convoln

DOCUMENT convoln(a, b)

  returns convolution of array A with array B.  This is naturally
  of length na+nb-1 where na=length of A, nb=length of B.  However,
  convoln returns a result the same size as A, which is extracted
  from the center of this full array.  Typically, B will be a much
  smaller array than A, which you are using to smooth A.  If the
  dimensions of B are odd, then the elements of the returned array
  will be centered as you would expect.

  In detail, for i=[1 to na+nb-1]
    result(i) = sum j=[max(1,1+i-nb) to min(na,i)] (A(j)*B(1+i-j))
  with this operation repeated along each dimension of A and B.

  The n0= and n1= keywords can be used to control the section of
  the full array that is actually returned, 1<=n0
  
SEE ALSO: convol, gaussm, boxcar

fft_good

DOCUMENT fft_good(n)

  returns the smallest number of the form 2^x*3^y*5^z greater
  than or equal to n.  An fft of this length will be much faster
  than a number with larger prime factors; the speed difference
  can be an order of magnitude or more.

  For n>100, the worst cases result in a little over a 11% increase
  in n; for n>1000, the worst are a bit over 6%; still larger n are
  better yet.  The median increase for n<=10000 is about 1.5%.

SEE ALSO: fft, fft_setup, convol

gaussm

DOCUMENT gaussm(a, n)

  returns array A smoothed by a Gaussian with a sigma of N pixels.
  If A is multi-dimensional, N may be a vector with as many
  components as A has dimensions, specifying how many pixels
  to smooth in that dimension.  N may be shorter than the number
  of dimensions of A; unspecified dimensions are unsmoothed
  (as if N were 0.0).  If A is multi-dimensional and N is scalar,
  that N is applied to all dimensions.

  With the fwhm=1 keyword, N is the full width at half maximum
  of the Guassian.  The fwhm= keyword may also be a vector of
  the same length as N, 1 where N is to be interpreted as a FWHM
  and 0 where N is to be interpreted as a sigma.

SEE ALSO: convoln, boxcar