What Is BLAS

The 1979 spec that runs the modern AI stack

Would you rebuild NumPy from scratch just to add two vectors? No. So why hand-roll GPU kernels when BLAS already exists?

BLAS (Basic Linear Algebra Subprograms) is the bedrock API of numerical computing. Conceived in 1979 for Fortran supercomputers, it specifies ~60 routines covering vector ops (Level 1), matrix-vector ops (Level 2), and matrix-matrix ops (Level 3). Almost every scientific library today layers on top of it — directly or indirectly.

Why it matters:

Optimization centralization — vendors pour years of tuning into one tiny set of kernels; everyone inherits the speedups for free.
Portability — a Fortran program from 1982 still compiles and runs on an M3 Ultra in 2025. The interface didn't change.
Composability — NumPy, PyTorch, JAX, MLX, Core ML all call BLAS underneath. They differ in the language above, not the kernels below.

Level	Operand shapes	GPU suitability
1	vector ⊗ vector (AXPY, dot)	Poor — bandwidth-bound
2	matrix ⊗ vector (GEMV)	Meh — still bandwidth-bound
3	matrix ⊗ matrix (GEMM)	Excellent — compute-bound, what GPUs are for

Who ships what?

NVIDIA: cuBLAS (and cuBLASLt for Tensor Core integration).
AMD: rocBLAS / hipBLAS.
Intel / CPU: oneAPI MKL, OpenBLAS.
Apple: Accelerate (CPU) + Metal Performance Shaders' MPSMatrixMultiplication (GPU).

Code

The same call shape, four backends·python

# All of these call vendor BLAS GEMM under the hood.

# NumPy (CPU) — uses OpenBLAS or MKL depending on your wheel
import numpy as np
C = np.matmul(A, B)

# PyTorch CUDA — calls cuBLAS
import torch
C = torch.matmul(A_cuda, B_cuda)

# PyTorch MPS — calls MPSMatrixMultiplication
C = torch.matmul(A_mps, B_mps)

# MLX — calls MPSMatrixMultiplication directly
import mlx.core as mx
C = mx.matmul(A_m, B_m); mx.eval(C)

Exercise

On any environment with NumPy installed, run np.show_config(). Look for 'openblas_info' or 'mkl_info' — that's the actual BLAS library NumPy is linked against on your machine. Compare the build info if you have multiple Python environments. The same NumPy code can be 2-3× faster on MKL-linked builds; that's BLAS choice, not NumPy code.

The 1979 spec that runs the modern AI stack

Who ships what?

Code

External links

Exercise

Progress

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