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Pascal N-Dimensional Arrays

Active · last change 10-22-2026
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README

PaNDA - Pascal N-Dimensional Arrays

PaNDA is a small library that provides classes for working with N-dimensional arrays in Pascal (Delphi). It introduces an INDArray interface that supports slicing syntax similar to Python and Mathematica. Some basic examples are shown below:

Python	PaNDA
`a[0]`	`a[[NDI(0)]]`
`a[1:6:2]`	`a[[NDISpan(1,6,2)]]`
`a[::2]`	`a[[NDISpan(0, -1, 2)]]` or `a[[NDIAll(2)]]`
`a[::2,::2]`	`a[[NDAll(2), NDIAll(2)]]`
`a[[0,2,2]]`	`a[[NDISet([0,2,2])]]` or `a[[NDI([0,2,2])]]`
`a[::,1]`	`a[[NDIAll, NDI(1)]]`

Delphi Compatibility

PaNDA has been tested with Delphi 12 (Athens). Other Delphi versions may work, but have not been fully verified.

Tensor Types

The library also provides tensor types, implemented as records, which wrap ND-arrays and support basic arithmetic operations through operator overloading.

Example:

pascal

var a, b, c: TTensorF32;
begin
  a := TNDAUt.AsArray([1, 2, 3]);
  b := TNDAUt.AsArray([3, 2, 1]);
  c := (a + b)/2;
end;

The library includes common tensor functions such as Dot, Inner, and Outer products. Where available, these functions can use optimized routines from OpenBLAS (described below). PaNDA also includes several optimized assembly implementations that require SSE2/SSE3 instruction sets (assembly can be disabled using the NoASM compiler directive).

Optional OpenBLAS Acceleration

Using OpenBLAS is optional. To enable it, the following conditions must be met:

Define the PANDA_BLAS environment variable
Point it to the directory containing the OpenBLAS binaries.
The directory should include platform-specific subfolders:
pascal
```
  <your-openblas-path>\
    Win32\libopenblas.dll
    Win64\libopenblas.dll
```
Compile the library with the BLAS compiler directive
Add BLAS to your project's conditional defines.

OpenBLAS/CBLAS Interface

PaNDA uses the Delphi port of the CBLAS interface provided by Eric Grange’s LibCBLAS when OpenBLAS acceleration is enabled.

PaNDA4Py

The library includes the TPyNDArray type, which wraps a PaNDA array and exposes the NumPy array interface protocol. This allows sharing arrays between Python and Delphi, using the Python4Delphi framework.

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