jamma 4.4.2

High-performance Multi-method Mixed-Model Association for large-scale GWAS

JAMMA (High-performance Multi-method Mixed-Model Association) — a modern Python and C reimplementation of GEMMA for large-scale GWAS.

• GEMMA-compatible: Drop-in replacement with identical CLI flags and output formats
• Numerical equivalence: Validated against GEMMA — 100% significance agreement, 100% effect direction agreement
• Fast: Up to 17x faster than GEMMA 0.98.5
• Memory-safe: Pre-flight memory checks prevent OOM crashes before allocation
• Cross-platform: Runs on Linux, macOS, and Windows — NumPy backend works everywhere, JAX adds batch acceleration on Linux and ARM Mac
• Optimized for Intel: Best performance on Intel CPUs with MKL BLAS. Runs well on Apple Silicon (Accelerate BLAS). Other architectures (AMD, ARM Linux) work correctly but with less BLAS optimization
• Pure Python + jlinalg + optional C extensions: NumPy + optional JAX stack; jlinalg C layer for vendor BLAS dispatch (DSYEVD/DSYEVR eigendecomposition, DSYRK, DGEMM) and OpenMP-parallel Wald tests, JAX for batch MLE optimization
• Large-scale ready: Optional numpy-mkl ILP64 wheels (numpy 2.4.2) for >46k sample eigendecomposition

Installation

macOS (Intel or ARM)

pip install jamma          # NumPy backend
pip install 'jamma[jax]'   # + JAX acceleration (ARM Mac only)

That's it. macOS Accelerate BLAS handles large matrices natively.

Linux / Windows / Intel Mac

For small datasets (<46k samples), the standard install works:

pip install jamma          # NumPy backend
pip install 'jamma[jax]'   # + JAX acceleration

For large-scale GWAS (>46k samples) on x86_64 (Linux or Intel Mac), install numpy-mkl first — standard numpy uses 32-bit BLAS integers which overflow at ~46k samples. MKL is x86_64-only; Windows users are limited to <46k samples (ARM Mac uses Accelerate-ILP64 natively). Pre-built ILP64 wheels are available for Python 3.11–3.14:

NumPy backend only:

pip install numpy \
  --extra-index-url https://michael-denyer.github.io/numpy-mkl \
  --force-reinstall --upgrade
pip install jamma --no-deps
pip install psutil loguru threadpoolctl click progressbar2 bed-reader

With JAX acceleration:

pip install numpy \
  --extra-index-url https://michael-denyer.github.io/numpy-mkl \
  --force-reinstall --upgrade
pip install 'jamma[jax]' --no-deps
pip install psutil loguru threadpoolctl click progressbar2 bed-reader \
  jax jaxlib jaxtyping

From Git (latest development version):

pip install numpy \
  --extra-index-url https://michael-denyer.github.io/numpy-mkl \
  --force-reinstall --upgrade
pip install git+https://github.com/michael-denyer/jamma.git --no-deps
pip install psutil loguru threadpoolctl click progressbar2 bed-reader

Why --no-deps? JAMMA depends on numpy>=2.0.0, so a normal pip install jamma will pull in standard numpy and overwrite the ILP64 build. --no-deps prevents this; you install the runtime dependencies manually instead.

See the User Guide for ILP64 verification steps.

Platform Support

Platform	pip install jamma	pip install jamma[jax]	BLAS	Notes
Linux x86_64 (Intel)	JAX (auto-included)	—	MKL (optimal)	Best performance; ILP64 for >46k samples
Linux x86_64 (AMD)	JAX (auto-included)	—	OpenBLAS	Works well; MKL also works on AMD but less optimized
ARM Mac (M1+)	JAX (auto-included)	—	Accelerate	Excellent performance; ILP64 via Accelerate for >46k samples
ARM Linux	NumPy only	JAX manual install	OpenBLAS	Works correctly; less BLAS optimization
Intel Mac	NumPy only	Not available	MKL / Accelerate	JAX dropped Intel Mac; ILP64 for >46k samples
Windows	NumPy only	Not available	OpenBLAS	JAX dropped Windows support; limited to <46k samples

JAMMA's heavy computation (eigendecomposition, matrix multiplication, REML optimization) is BLAS-bound. Intel MKL delivers the best throughput, particularly at scale. Apple Accelerate is a close second on Apple Silicon. OpenBLAS works correctly everywhere but is less tuned for these workloads.

JAX is auto-included on Linux and ARM Mac via platform markers. Force a specific backend with --backend numpy or --backend jax.

Quick Start

# Compute kinship matrix (centered relatedness)
jamma -gk 1 -bfile data/my_study -o output
# Output: output/output.cXX.npy (binary, fast)
# Add --legacy-text for GEMMA-compatible text format

# Run LMM association (Wald test)
jamma -lmm 1 -bfile data/my_study -k output/output.cXX.npy -o results

# Multiple phenotypes (eigendecomp computed once, reused)
jamma -lmm 1 -bfile data/my_study -k output/output.cXX.npy -n "1 2 3" -o results

Output files:

• output.cXX.npy — Kinship matrix (binary NumPy format; .cXX.txt with --legacy-text)
• results.assoc.txt — Association results (chr, rs, ps, n_miss, allele1, allele0, af, beta, se, logl_H1, l_remle, p_wald)
• results.log.txt — Run log

The reader auto-detects format, so existing .cXX.txt files still work as -k input.

Python API

One-call GWAS (recommended)

The gwas() function is the recommended way to run JAMMA from Python. It handles the full pipeline — data loading, kinship computation, eigendecomposition, and LMM association — in a single call. You don't need to compute a kinship matrix separately unless you want to reuse it across runs.

from jamma import gwas

# Simplest usage: computes kinship internally, no separate kinship step needed
result = gwas("data/my_study")
print(f"Tested {result.n_snps_tested} SNPs in {result.timing['total_s']:.1f}s")

# Or supply a pre-computed kinship matrix to skip recomputation
result = gwas("data/my_study", kinship_file="data/kinship.cXX.npy")

# Compute kinship from scratch and save it for reuse
result = gwas("data/my_study", save_kinship=True, output_dir="output")

# With covariates and LRT test
result = gwas("data/my_study", kinship_file="k.txt", covariate_file="covars.txt", lmm_mode=2)

# LOCO analysis (leave-one-chromosome-out)
result = gwas("data/my_study", loco=True)

# LOCO with eigen caching (skip eigendecomp on subsequent runs)
result = gwas("data/my_study", loco=True, write_eigen=True, eigen_dir="output/eigen")
result = gwas("data/my_study", loco=True, eigen_dir="output/eigen")  # reuses cache

# Multi-phenotype with eigendecomp reuse (Python API)
result = gwas("data/my_study", write_eigen=True, phenotype_column=1)
result = gwas("data/my_study", eigenvalue_file="output/result.eigenD.npy",
              eigenvector_file="output/result.eigenU.npy", phenotype_column=2)
# Or use the CLI for automatic multi-phenotype: jamma -lmm 1 ... -n "1 2 3"

# SNP filtering
result = gwas("data/my_study", kinship_file="k.txt", snps_file="snps.txt", hwe=0.001)

Low-level API (JAX backend)

import numpy as np

from jamma.io import load_plink_binary
from jamma.kinship import compute_centered_kinship
from jamma.lmm import run_lmm_association_streaming
from jamma.lmm.eigen import eigendecompose_kinship

# Load PLINK data and phenotypes
data = load_plink_binary("data/my_study")
phenotypes = np.loadtxt("data/my_study.pheno")  # loaded separately from .fam or phenotype file

# Compute kinship and eigendecompose (treat kinship as consumed after this)
kinship = compute_centered_kinship(data.genotypes)
eigenvalues, eigenvectors = eigendecompose_kinship(kinship)

# Run association (streaming from disk)
results, n_tested = run_lmm_association_streaming(
    bed_path="data/my_study",
    phenotypes=phenotypes,
    eigenvalues=eigenvalues,
    eigenvectors=eigenvectors,
    chunk_size=5000,
)

Low-level API (NumPy backend)

import numpy as np

from jamma.io import load_plink_binary
from jamma.kinship import compute_centered_kinship
from jamma.lmm import run_lmm_association_numpy
from jamma.lmm.eigen import eigendecompose_kinship

data = load_plink_binary("data/my_study")
phenotypes = np.loadtxt("data/my_study.pheno")
kinship = compute_centered_kinship(data.genotypes)
eigenvalues, eigenvectors = eigendecompose_kinship(kinship)

snp_info = [
    {"chr": str(data.chromosome[i]), "rs": data.sid[i],
     "pos": int(data.bp_position[i]), "a1": data.allele_1[i], "a0": data.allele_2[i]}
    for i in range(data.n_snps)
]

# Returns LmmRunResult — .associations for list[AssocResult], .pve for heritability, .pve_se for SE
run_result = run_lmm_association_numpy(
    genotypes=data.genotypes,
    phenotypes=phenotypes,
    kinship=None,  # Not needed when eigenvalues/eigenvectors provided
    snp_info=snp_info,
    eigenvalues=eigenvalues,
    eigenvectors=eigenvectors,
    lmm_mode=1,
)
results = run_result.associations

Memory Safety

Unlike GEMMA, JAMMA includes pre-flight memory checks that prevent out-of-memory crashes:

from jamma.core.memory import estimate_workflow_memory

# Check memory requirements BEFORE loading data
estimate = estimate_workflow_memory(n_samples=125_000, n_snps=95_000)
print(f"Peak memory: {estimate.total_gb:.1f}GB")
print(f"Available: {estimate.available_gb:.1f}GB")
print(f"Sufficient: {estimate.sufficient}")

Key features:

• Pre-flight checks before large allocations (eigendecomposition, genotype loading)
• RSS memory logging at workflow boundaries
• Incremental result writing (no memory accumulation)
• Safe chunk size defaults with hard caps

GEMMA will silently OOM and get killed by the OS. JAMMA fails fast with clear error messages.

Performance

Benchmark on mouse_hs1940 (1,940 samples × 12,226 SNPs), Apple M2, GEMMA 0.98.5. Best-of runs, end-to-end wall clock:

Operation	GEMMA (OpenBLAS)	GEMMA (Accelerate)	JAMMA NumPy	JAMMA NumPy+C	JAMMA NumPy+C (stream)	JAMMA JAX (batch)	JAMMA JAX (streaming)	C speedup	vs GEMMA (OB)	vs GEMMA (Accel)
Kinship (-gk 1)	2.1s	1.7s	262ms	262ms	—	—	—	1.0x	8.0x	6.5x
LMM Wald (-lmm 1)	11.0s	7.6s	4.1s	879ms	1.1s	2.0s	2.5s	4.7x	12.5x	8.7x
LMM All (-lmm 4)	20.5s	13.9s	6.0s	1.3s	1.4s	2.8s	4.1s	4.7x	16.0x	10.9x
LMM Wald+4cov (-lmm 1 -c)	40.8s	18.8s	9.1s	2.4s	2.6s	4.1s	5.1s	3.8x	17.0x	7.8x

GEMMA (Accelerate) is GEMMA 0.98.5 compiled against Apple's Accelerate framework instead of Homebrew OpenBLAS — 1.3–2.2x faster due to AMX-accelerated BLAS, with identical numerical results. NumPy+C uses a C extension with OpenMP for Wald (-lmm 1) — REML optimization is compute-bound and parallelizes well across SNPs. The C speedup grows with covariates because the Pab table recursion is more expensive. NumPy+C is the fastest backend at all modes including all-tests (-lmm 4) at mouse scale. NumPy+C (stream) reads genotypes from disk in chunks — slightly slower than batch but the production code path for large datasets that don't fit in memory. JAX (batch) uses jax.vmap batching for MLE optimization. JAX (streaming) is the JAX equivalent of disk-streaming. Kinship is always pure NumPy/BLAS regardless of backend.

LOCO (Leave-One-Chromosome-Out)

Backend	LOCO Wald	vs GEMMA
GEMMA 0.98.5	3m31s	1.0x
JAMMA NumPy+C	7.3s	28.8x
JAMMA JAX	11.6s	18.1x

The large speedup has two sources: (1) JAMMA computes per-chromosome LOCO kinship via streaming and tests only that chromosome's SNPs, while GEMMA -loco tests all SNPs against each LOCO kinship (19× redundant work on 19 chromosomes); (2) JAMMA runs all chromosomes in a single process, avoiding 19 cold-start overheads. On this dataset, NumPy+C is faster than JAX because the JIT compilation overhead per chromosome outweighs XLA's compute benefit at 1,940 samples.

Supported Features

Current

• Kinship matrix computation — centered (-gk 1) and standardized (-gk 2)
• Univariate LMM Wald test (-lmm 1)
• Likelihood ratio test (-lmm 2)
• Score test (-lmm 3)
• All tests mode (-lmm 4)
• LOCO kinship — leave-one-chromosome-out analysis (-loco)
• Binary .npy I/O — default for kinship and eigen files; --legacy-text for GEMMA text format
• Multi-phenotype support — -n "1 2 3" with single eigendecomposition reuse
• Eigendecomposition reuse — manual via -d/-u/-eigen, automatic in multi-phenotype mode
• LOCO eigen caching — --eigen-dir saves/loads per-chromosome eigen files across runs
• Phenotype column selection (-n)
• SNP subset selection for association and kinship (-snps/-ksnps)
• HWE QC filtering (-hwe)
• Pre-computed kinship input (-k)
• Covariate support (-c)
• PLINK binary format (.bed/.bim/.fam) with input dimension validation
• Large-scale streaming I/O (>100k samples via numpy-mkl ILP64 — numpy 2.4.2)
• JAX acceleration (CPU) with automatic device sharding
• XLA profiling traces (--profile-dir) for TensorBoard/Perfetto
• Lambda optimization bounds (-lmin/-lmax)
• Individual weights for kinship (-widv)
• Categorical covariates with one-hot encoding (-cat)
• Pre-flight memory checks (fail-fast before OOM)
• RSS memory logging at workflow boundaries
• Incremental result writing
• In-place mean imputation for missing genotypes (per-chunk, zero-copy)
• Early sample filtering — kinship accumulated at filtered size when phenotype missingness is present
• jlinalg C layer: vendor BLAS dispatch for eigendecomposition (DSYEVD default, DSYEVR O(n) workspace fallback under memory pressure), DSYRK, DGEMM, plus jlinalg D&C fallback when no vendor LAPACK available
• Optional C extension: OpenMP-parallel Wald tests (auto-fallback to pure Python)

Planned

• Multivariate LMM (mvLMM)

Architecture

JAMMA uses NumPy for data loading and kinship. Eigendecomposition uses jlinalg.eigh which dispatches to vendor DSYEVD (default) or DSYEVR (O(n) workspace, under memory pressure) via the jlinalg C layer, with a jlinalg D&C fallback when no vendor LAPACK is available. At LMM it splits into a JAX backend (JIT, vmap, sharding; batch or streaming) or a NumPy backend with an optional C extension for OpenMP-parallel Wald tests (batch or two-pass disk streaming). Mode is auto-selected based on available memory.

flowchart TD
    CLI["CLI / gwas()"] --> PIPE["PipelineRunner"]
    PIPE --> LOAD["Load PLINK + Phenotypes<br>(NumPy)"]
    LOAD --> KIN["Kinship<br>(NumPy matmul)"]
    KIN --> EIG["Eigendecomposition<br>(jlinalg.eigh · vendor DSYEVD/DSYEVR dispatch)"]
    EIG --> DET{"detect_backend()"}
    DET -->|"jax"| JAXM{"memory?"}
    JAXM -->|"fits"| JAXB["JAX Batch Runner<br>JIT + vmap"]
    JAXM -->|"large"| JAXS["JAX Streaming Runner<br>JIT + vmap + sharding"]
    DET -->|"numpy"| NPM{"memory?"}
    NPM -->|"fits"| NP["NumPy Batch Runner"]
    NPM -->|"large"| NPS["NumPy Streaming Runner<br>two-pass disk streaming"]
    NP --> CEXT{"C extension?"}
    NPS --> CEXT
    CEXT -->|yes| C["C Extension<br>OpenMP + SIMD"]
    CEXT -->|no| PY["Pure Python<br>fallback"]
    JAXB --> RES["AssocResult"]
    JAXS --> RES
    C --> RES
    PY --> RES

Both backends share the same core algorithms (likelihood.py, prepare_common.py) and produce identical results. Backend-specific files follow a naming convention: *_jax.py / *_numpy.py.

jlinalg: Controlled C Compute Layer

JAMMA includes jlinalg, a controlled C compute layer that provides the specific BLAS and LAPACK operations needed for GWAS (dgemm, dsyrk, eigh, QR, SVD). jlinalg dispatches to vendor BLAS (MKL-ILP64, Accelerate-ILP64) when available and falls back to its own C implementations with AVX2/NEON microkernels. This eliminates numpy BLAS compatibility issues (LP64 integer overflow at >46k samples, scipy ILP64 incompatibility).

graph TD
    A["jamma CLI / Python API"] --> B["LMM Pipeline"]
    B --> C["jlinalg Python API"]
    C --> D{"C Extension"}
    D -->|Loaded| E["Vendor Dispatch<br/>MKL-ILP64 / Accelerate-ILP64"]
    D -->|Loaded| F["jlinalg Own<br/>AVX2 / NEON kernels"]
    D -->|Not loaded| G["NumPy Fallback"]
    B --> H["_lmm_accel.c<br/>Wald/Score/LRT"]

jlinalg provides symmetric BLAS specialization (dsyrk tile-skipping for ~50% fewer tile iterations than dgemm) and vendor LAPACK dispatch (DSYEVD/DSYEVR) for eigendecomposition. See the jlinalg Architecture doc for layer diagrams, microkernel details, and the contributing guide.

See Code Map for the full architecture diagram with source links.

Documentation

• Why JAMMA? — Key differentiators from GEMMA
• User Guide — Installation, usage examples, CLI reference
• Code Map — Architecture diagrams and source navigation
• Equivalence Proof — Mathematical proofs and empirical validation against GEMMA
• GEMMA Divergences — Known differences from GEMMA
• Performance — Bottleneck analysis, scale validation, configuration guide
• jlinalg Architecture — C compute layer design, vendor dispatch, microkernel tutorial
• jlinalg Algorithms — Cache blocking, D&C eigendecomposition, SVD
• Contributing — Development setup, testing, and PR guidelines
• Changelog — Version history

Requirements

• Python 3.11+
• NumPy 2.0+
• JAX 0.5.0+ (auto-included on Linux/ARM Mac; explicit extra on other platforms: pip install 'jamma[jax]')

License

GPL-3.0 (same as GEMMA)