Choose an operation

Start with the problem you want to solve, then select an available interface. The Python wheel includes the native library. Domain namespaces expose the original Haskell algorithms through Python and C; the tables below point to function-level contracts.

Python, C, and Wave

Task	Python	C	Wave
Add scalars	add(a, b)	hmath_scalar_add	scalar_add
Construct a matrix	Tensor.matrix	hmath_matrix_copy	matrix_copy
Sum all elements	tensor.sum()	hmath_tensor_sum	tensor_sum
Sum corresponding products	a.dot(b)	hmath_tensor_dot	tensor_dot
Add corresponding elements	a + b	hmath_tensor_add	tensor_add
Multiply two matrices	a @ b	hmath_tensor_matmul	tensor_matmul
Exchange NumPy arrays	Tensor.from_numpy, tensor.numpy	Storage/DLPack ABI	Use the C ABI
Reinterpret a contiguous shape	tensor.reshape	hmath_tensor_reshape	Use the C ABI

dot reduces every corresponding product to a scalar at any rank. Matrix multiplication requires rank two and matching inner dimensions. Elementwise addition requires identical shapes. Broadcasting and batched matrix products are not supported by these wrappers.

Read the Python, C, or Wave reference for complete contracts. The matrix calculation guide demonstrates the three operations on the same inputs.

Domain algorithms in Python and C

Task	Python namespace	C reference
Factor matrices, solve systems and compute eigenpairs	matrix, decomposition, iterative, sparse	Linear algebra
Differentiate, integrate and solve ODE/PDE systems	calculus, root, ode, pde	Numerical solvers
Build expressions and compute gradients	expression, symbolic, autodiff	Expressions, autodiff
Optimize objectives or update parameters	optimization	Optimizers
Process tensors and neural layers	tensor, deeplearning_core, deeplearning_layers	Tensors, deep learning
Fit models and preprocess datasets	machinelearning	Machine learning
Work with distributions, generators and forecasts	probability, random, timeseries	Probability/random, time series
Transform and filter signals	fourier, signal, interpolation	Spectral functions
Exchange arrays and stream files	interchange	Interchange

See the Python namespace index for other domains and structured values for shared C ownership and callback rules. Wave can call the public C ABI; its convenience wrapper retains the smaller tensor interface listed above.

Haskell numerical algorithms

Task	Start with	Guide / reference
Solve a square linear system	HMath.Matrix.LU.solve	Linear algebra API
Fit an overdetermined linear model	HMath.Matrix.QR.leastSquares	Least squares
Regularize a linear fit	HMath.Matrix.QR.ridgeSolve	QR contracts
Estimate a derivative	HMath.Calculus.derivative	Calculus
Integrate a smooth finite-interval function	HMath.Calculus.integrateComposite	Calculus
Request adaptive integration	HMath.Calculus.adaptiveIntegrate	Calculus
Compute descriptive statistics	HMath.Statistics	Summarize data
Explore optimization, probability, graphs, or transforms	Select a numerical area	Haskell module index

These functions require Haskell imports; they are not additional Python functions. Check numerical conventions before selecting tolerances or interpreting convergence.