convolve

  Signature: (a(m); b(n); indx adims(p); indx bdims(q); [o]c(m))

N-dimensional convolution (Deprecated; use convolveND)

  $new = convolve $x, $kernel

Convolve an array with a kernel, both of which are N-dimensional. This routine does direct convolution (by copying) but uses quasi-periodic boundary conditions: each dim "wraps around" to the next higher row in the next dim.

This routine is kept for backwards compatibility with earlier scripts; for most purposes you want convolveND instead: it runs faster and handles a variety of boundary conditions.

convolve does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

ninterpol()

N-dimensional interpolation routine

 Signature: ninterpol(point(),data(n),[o]value())

      $value = ninterpol($point, $data);

"ninterpol" uses "interpol" to find a linearly interpolated value in N dimensions, assuming the data is spread on a uniform grid. To use an arbitrary grid distribution, need to find the grid-space point from the indexing scheme, then call "ninterpol" -- this is far from trivial (and ill-defined in general).

See also interpND, which includes boundary conditions and allows you to switch the method of interpolation, but which runs somewhat slower.

rebin

  Signature: (a(m); [o]b(n); int ns => n)

N-dimensional rebinning algorithm

  $new = rebin $x, $dim1, $dim2,..;.
  $new = rebin $x, $template;
  $new = rebin $x, $template, {Norm => 1};

Rebin an N-dimensional array to newly specified dimensions. Specifying `Norm' keeps the sum constant, otherwise the intensities are kept constant. If more template dimensions are given than for the input pdl, these dimensions are created; if less, the final dimensions are maintained as they were.

So if $x is a 10 x 10 pdl, then "rebin($x,15)" is a 15 x 10 pdl, while "rebin($x,15,16,17)" is a 15 x 16 x 17 pdl (where the values along the final dimension are all identical).

Expansion is performed by sampling; reduction is performed by averaging. If you want different behavior, use PDL::Transform::map instead. PDL::Transform::map runs slower but is more flexible.

rebin does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.

circ_mean_p

Calculates the circular mean of an n-dim image and returns the projection. Optionally takes the center to be used.

   $cmean=circ_mean_p($im);
   $cmean=circ_mean_p($im,{Center => [10,10]});

circ_mean

Smooths an image by applying circular mean. Optionally takes the center to be used.

   circ_mean($im);
   circ_mean($im,{Center => [10,10]});

kernctr

`centre' a kernel (auxiliary routine to fftconvolve)

        $kernel = kernctr($image,$smallk);
        fftconvolve($image,$kernel);

kernctr centres a small kernel to emulate the behaviour of the direct convolution routines.

convolveND

  Signature: (k0(); SV *k; SV *aa; SV *a)

Speed-optimized convolution with selectable boundary conditions

  $new = convolveND($x, $kernel, [ {options} ]);

Conolve an array with a kernel, both of which are N-dimensional.

If the kernel has fewer dimensions than the array, then the extra array dimensions are broadcasted over. There are options that control the boundary conditions and method used.

The kernel's origin is taken to be at the kernel's center. If your kernel has a dimension of even order then the origin's coordinates get rounded up to the next higher pixel (e.g. (1,2) for a 3x4 kernel). This mimics the behavior of the earlier "convolve" and fftconvolve routines, so convolveND is a drop-in replacement for them.

The kernel may be any size compared to the image, in any dimension.

The kernel and the array are not quite interchangeable (as in mathematical convolution): the code is inplace-aware only for the array itself, and the only allowed boundary condition on the kernel is truncation.

convolveND is inplace-aware: say "convolveND(inplace $x ,$k)" to modify a variable in-place. You don't reduce the working memory that way -- only the final memory.

OPTIONS

Options are parsed by PDL::Options, so unique abbreviations are accepted.

boundary (default: 'truncate')

The boundary condition on the array, which affects any pixel closer to the edge than the half-width of the kernel.

The boundary conditions are the same as those accepted by range, because this option is passed directly into range. Useful options are 'truncate' (the default), 'extend', and 'periodic'. You can select different boundary conditions for different axes -- see range for more detail.

The (default) truncate option marks all the near-boundary pixels as BAD if you have bad values compiled into your PDL and the array's badflag is set.

method (default: 'auto')

The method to use for the convolution. Acceptable alternatives are 'direct', 'fft', or 'auto'. The direct method is an explicit copy-and-multiply operation; the fft method takes the Fourier transform of the input and output kernels. The two methods give the same answer to within double-precision numerical roundoff. The fft method is much faster for large kernels; the direct method is faster for tiny kernels. The tradeoff occurs when the array has about 400x more pixels than the kernel.

The default method is 'auto', which chooses direct or fft convolution based on the size of the input arrays.

NOTES

At the moment there's no way to broadcast over kernels. That could/should be fixed.

The broadcasting over input is cheesy and should probably be fixed: currently the kernel just gets dummy dimensions added to it to match the input dims. That does the right thing tersely but probably runs slower than a dedicated broadcastloop.

The direct copying code uses PP primarily for the generic typing: it includes its own broadcastloops.

convolveND does not process bad values. It will set the bad-value flag of all output ndarrays if the flag is set for any of the input ndarrays.