Tutorial: Matrix and vectors operations

The following linear algebra operations are supported for tensors of rank 1 (vectors) and 2 (matrices):

• dot product (Vector to Vector) using dot
• addition and substraction (any rank) using + and -
• in-place addition and substraction (any-rank) using += and -=
• multiplication or division by a scalar using * and /
• matrix-matrix multiplication using *
• matrix-vector multiplication using *
• element-wise multiplication (Hadamard product) using *.

Note: Matrix operations for floats are accelerated using BLAS (Intel MKL, OpenBLAS, Apple Accelerate …). Unfortunately there is no acceleration routine for integers. Integer matrix-matrix and matrix-vector multiplications are implemented via semi-optimized routines, see the benchmarks section.

echo foo_float * foo_float # Accelerated Matrix-Matrix multiplication (needs float)
# Tensor[float] of shape "[5, 5]" on backend "Cpu"
# |15.0         55.0      225.0       979.0       4425.0|
# |258.0      1146.0     5274.0     24810.0     118458.0|
# |1641.0     7653.0    36363.0    174945.0     849171.0|
# |6372.0    30340.0   146244.0    710980.0    3478212.0|
# |18555.0   89355.0   434205.0   2123655.0   10436805.0|