Documentation

Learn JMax.

The math-native language: write the math, see the result, measure the energy. Everything here is also writable right now in the playground.

start here

Quickstart

Write your first JMax program and run it in the browser — execution, the computation graph, and a timing reading, in about a minute. No install, no account.

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reference

Built-in Functions

Every built-in, by domain: linear algebra, statistics, signal processing, ML, symbolic math, optimization, ODEs, dataframes, units, and plotting.

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the cli

The jmax Command Line

One binary across the whole scientific-computing surface — eval, run, plot, grad, minimize, ode, fit, verify, and emit to ONNX / StableHLO / WGSL / MLIR.

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examples

Examples

Runnable programs across linear algebra, statistics, FFT, ML, finance, and bioinformatics — each one opens directly in the playground.

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the language

Why JMax

Matrices are values. Plots are statements. Every computation is measured in joules and compiled to native speed. Read the language thesis.

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source

GitHub

The compiler, the standard library, the visualization stack, and the WebAssembly playground that runs this page — all in the open.

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Linear Algebra

A * B

Matrix multiply. Use * operator on matrices.

A \ b

Solve linear system Ax = b. NxN via LU decomposition.

eig(A)

Eigenvalues of a symmetric matrix via QR algorithm.

svd(A)

Singular values via eigendecomposition of A'A.

qr(A)

QR decomposition via Gram-Schmidt.

cholesky(A)

Cholesky decomposition. A must be symmetric positive definite.

inv(A)

Matrix inverse via Gauss-Jordan elimination.

det(A)

Determinant via LU decomposition.

trace(A)

Sum of diagonal elements.

rank(A)

Matrix rank via SVD.

A'

Matrix transpose. Use postfix apostrophe.

eye(n)

Identity matrix.

zeros(m, n)

Zero matrix.

ones(m, n)

All-ones matrix.

linspace(start, end, n)

N evenly spaced values.

Statistics

mean(data)

Arithmetic mean.

std(data)

Standard deviation (sample).

var(data)

Variance (sample).

median(data)

Median value.

percentile(data, p)

P-th percentile (0-1).

correlation(x, y)

Pearson correlation coefficient.

covariance(x, y)

Sample covariance.

t_test(a, b)

Welch's two-sample t-test. Returns p-value.

chi_squared(observed, expected)

Chi-squared test statistic.

linear_regression(x, y)

OLS. Returns [intercept, slope, r_squared].

normal_cdf(x)

Standard normal CDF.

normal_pdf(x)

Standard normal PDF.

Signal Processing

fft(signal)

Fast Fourier Transform (Cooley-Tukey). Returns magnitude spectrum.

ifft(spectrum)

Inverse FFT.

convolve(a, b)

Linear convolution.

fir_filter(signal, coeffs)

FIR filter.

spectrogram(signal, win, hop)

STFT magnitude spectrogram.

hann(n)

Hann window of length n.

hamming(n)

Hamming window of length n.

blackman(n)

Blackman window of length n.

Machine Learning

relu(x)

Rectified linear unit. max(0, x).

sigmoid(x)

1 / (1 + exp(-x)).

tanh_act(x)

Hyperbolic tangent activation.

gelu(x)

Gaussian error linear unit.

swish(x)

x * sigmoid(x).

softmax(logits)

Softmax over a vector. Numerically stable.

cross_entropy(pred, target)

Cross-entropy loss.

mse_loss(pred, target)

Mean squared error loss.

accuracy(pred, target)

Classification accuracy.

Symbolic Math

sin(x)

Sine.

cos(x)

Cosine.

tan(x)

Tangent.

asin(x)

Arcsine.

acos(x)

Arccosine.

exp(x)

e^x.

log(x)

Natural logarithm.

log2(x)

Base-2 logarithm.

log10(x)

Base-10 logarithm.

sqrt(x)

Square root.

abs(x)

Absolute value.

floor(x)

Floor.

ceil(x)

Ceiling.

round(x)

Round to nearest integer.

Finance

black_scholes_call(S, K)

Black-Scholes call option price. T=1yr, r=5%, sigma=20%.

black_scholes_put(S, K)

Black-Scholes put option price.

sma(data, window)

Simple moving average.

ema(data, span)

Exponential moving average.

sharpe(returns, risk_free)

Sharpe ratio.

max_drawdown(prices)

Maximum drawdown.

npv(rate, cash_flows)

Net present value.

irr(cash_flows)

Internal rate of return.

Bioinformatics

smith_waterman(seq1, seq2)

Local alignment score.

needleman_wunsch(seq1, seq2)

Global alignment score.

gc_content(seq)

GC content ratio (0-1).

reverse_complement(seq)

DNA reverse complement.

translate_dna(seq)

Translate DNA to protein.

Data Analysis

sort(data)

Sort a vector ascending.

unique(data)

Remove duplicates.

cumsum(data)

Cumulative sum.

diff(data)

First differences.

len(data)

Length of a vector or array.

Visualization

plot line data

Line chart.

plot scatter data

Scatter plot.

plot bar data

Bar chart.

plot histogram data

Histogram with automatic binning.

plot heatmap matrix

Heatmap with Viridis colormap.

plot surface matrix

3D surface plot.

plot contour matrix

Contour plot with marching squares.

plot boxplot data

Box-and-whisker plot.

plot violin data

Violin plot with KDE.

plot radar data

Radar/spider chart.

Calculus & Autodiff

d/dx(f)

Exact symbolic differentiation.

integrate(f, x)

Rule-based symbolic integration (linearity, power rule, standard functions).

expand(e)

Distribute products and expand integer powers of sums.

simplify(e)

Canonical simplification via equality-saturation (e-graph).

solve(expr, x)

Solve polynomial equations exactly (linear, quadratic).

grad(f, point)

Gradient by reverse-mode automatic differentiation.

hessian(f, point)

Full Hessian by second-order AD.

Optimization

minimize(f, x0)

Unconstrained minimization — gradient descent or Newton (AD Hessian).

root(f, x0)

Find a root by Newton's method (AD derivative).

fit(model, data)

Levenberg-Marquardt nonlinear least-squares curve fitting.

lp(c, A, b)

Linear program by two-phase simplex (Bland anti-cycling).

qp(G, a, C, d)

Quadratic program — equality (KKT) or inequality (active-set).

Differential Equations

ode("dy/dt", y0)

Adaptive Dormand-Prince RK45 integrator.

ode(…, --stiff)

Implicit backward-Euler for stiff systems; Jacobian via AD.

Hypothesis Tests

anova(g1, g2, …)

One-way ANOVA F-test for equal group means.

wilcoxon(a, b)

Wilcoxon signed-rank test (paired, nonparametric).

mann_whitney(a, b)

Mann-Whitney U test (independent samples).

levene(g1, g2, …)

Levene/Brown-Forsythe test for equal variances.

friedman(blocks)

Friedman repeated-measures test.

ks_two_sample(a, b)

Two-sample Kolmogorov-Smirnov test.

Dataframes

df file.csv

Typed columnar dataframe from CSV (with type inference).

groupby(key, value, op)

Group-by aggregation: sum, mean, count, min, max.

pivot(index, cols, value)

Pivot table.

join(other, on)

Inner, left, or outer join.

--to-parquet out

Write real Parquet (validated against Apache Arrow).

Units

convert(v, from, to)

Dimensional unit conversion with compound units and metric prefixes.

Quantity{value, dim}

Dimension-tracked arithmetic (SI base dimensions).