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Math library which provides non-sparse, rank-N tensor math

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Weyl is a single-header library for doing math with dense tensors of any finite rank and dimension. It's named after this guy.

Usage

Examples: Tensor Convolutions

Example 1

The sum across the only index of two single-index tensors, if the indexes are 3-dimensional, is the same as the dot product of two 3-dimensional vectors.

[ a b c ] * [ d e f ] = (a * d) + (b * e) + (c * f)

or

weyl::tensor<float, 3> abc({ a, b, c});
weyl::tensor<float, 3> def({ d, e, f});
float product = weyl::sum<0, 0>(abc, def);

The sum function template will expand to the following.

value = 0.0f;
value += abc[0] * def[0];
value += abc[1] * def[1];
value += abc[2] * def[2];
return value;

Example 2

The sum across the second index of a 3x3 tensor with the first index of another 3x3 tensor is essentially a matrix product.

[ a b c ]   [ j k l ]   [ (a*j)+(b*m)+(c*p)  (a*k)+(b*n)+(c*q)  (a*l)+(b*o)+(c*r) ]
[ d e f ] * [ m n o ] = [ (d*j)+(e*m)+(f*p)  (d*k)+(e*n)+(f*q)  (d*l)+(e*o)+(f*r) ]
[ g h i ]   [ p q r ]   [ (g*j)+(h*m)+(i*p)  (g*k)+(h*n)+(i*q)  (g*l)+(h*o)+(i*r) ]

or

weyl::tensor<float, 3, 3> a({ { ... }, { ... }, { ... } });
weyl::tensor<float, 3, 3> b({ { ... }, { ... }, { ... } });
weyl::tensor<float, 3, 3> product = weyl::sum<1, 0>(a, b);

In this case, sum will expand to something equivalent to the following, but with unrolled loops.

weyl::tensor<float, 3, 3> value(0.0f);
for (size_t n = 0; n < 3; ++n) // 1st dimension of a (2nd skipped - it is in the sum)
for (size_t m = 0; m < 3; ++m) // 2nd dimension of b (1st skipped - it is in the sum)
for (size_t i = 0; i < 3; ++i) // index for the 2nd and 1st dimensions of a and b respectively
    value[n][m] += a[n][i] * b[i][m];

Testing

The library has been tested on Windows with MinGW using the following command from the repository root.

g++ -std=c++17 tests/*.cpp -Iinclude. && .\a.exe && rm a.exe

Documentation

To compile html documentation, run doxygen in the repository root directory.

Notes

Despite the ideal of high-ranking generalizations, for convenience Weyl includes a number of special functions for tensors of particular rank and dimensionality. For example magnitude will return the length of a first-rank tensor (vector). These functions remain because they are useful, but they may be removed in future versions of the library. For this reason, they are in the experimental namespace.

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Math library which provides non-sparse, rank-N tensor math

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