Fisher Matrix Analysis Pipeline

The Fisher matrix analysis pipeline provides a complete framework for power spectrum parameter forecasting from partial-sky observations of spin-0 and spin-2 fields. This script orchestrates the full computation workflow from input validation through results output.

Overview

The main_fisher.py script implements a comprehensive Fisher information matrix computation pipeline optimized for cosmological parameter forecasting. It handles:

  • Multi-field CMB analysis (temperature and polarization)

  • MPI parallelization for large-scale computations

  • Flexible input/output file management

  • Robust error handling and validation

  • Integration with the broader CosmoForge analysis framework

Mathematical Foundation

The pipeline computes the Fisher information matrix:

\[F_{ij} = \frac{1}{2} \text{Tr}\left[ \mathbf{C}^{-1} \frac{\partial \mathbf{C}}{\partial \theta_i} \mathbf{C}^{-1} \frac{\partial \mathbf{C}}{\partial \theta_j} \right]\]

This quantifies the information content of observations about cosmological parameters \(\theta_i\), providing the foundation for parameter constraint forecasts and optimal survey design.

Usage

Command Line Interface

# Single-process execution
python main_fisher.py

# MPI parallel execution
mpirun -n 8 python main_fisher.py

# With custom configuration
python main_fisher.py --config custom_config.yaml

Script Workflow

The execution pipeline follows these stages:

  1. Environment Setup: Initialize MPI communicator and process management

  2. Configuration Loading: Parse YAML configuration with validation

  3. Input Verification: Check file existence and format compatibility

  4. Fisher Initialization: Create Fisher analysis object with validated parameters

  5. Computation Execution: Run distributed Fisher matrix calculation

  6. Results Collection: Gather and synchronize results across processes

  7. Output Generation: Save Fisher matrix and derived quantities

  8. Cleanup: Release resources and finalize MPI environment

Configuration Requirements

The script expects a YAML configuration file with the following structure:

# Analysis configuration for Fisher matrix computation

# HEALPix parameters
nside: 512
lmin: 2
lmax: 3000

# Field specification
nfields: 3
physical_labels: ["T", "Q", "U"]

# Analysis mode
do_cross: false  # Auto-correlation analysis

# Input files (relative to script directory)
covmatfile1: "inputs/noise_covariance.bin"
clfile: "inputs/fiducial_spectra.txt"
beamfile: "inputs/beam_transfer.fits"
maskfile: "inputs/analysis_mask.fits"

# Output files
outfilefisher: "outputs/fisher_matrix.dat"
outinvcovmatfile1: "outputs/inverse_covariance.bin"
outgeometryfile: "outputs/analysis_geometry.dat"

Implementation Details

Key Components

The script integrates several critical components:

  • MPI Management: Distributed computation with proper process synchronization

  • File I/O: Robust handling of binary covariance matrices and FITS files

  • Memory Management: Efficient allocation for large covariance matrices

  • Error Recovery: Graceful handling of computational failures

  • Progress Monitoring: Status reporting for long-running computations

Performance Optimization

The pipeline includes several optimization strategies:

  • Lazy Loading: Input files loaded only when needed

  • Memory Pooling: Reuse of large array allocations

  • Process Distribution: Optimal work distribution across MPI ranks

  • I/O Optimization: Parallel file operations where possible

Error Handling

Comprehensive error handling covers:

  • Configuration Validation: Parameter range and type checking

  • File System Errors: Missing files, permission issues, corrupted data

  • Memory Errors: Insufficient memory for large matrices

  • MPI Errors: Process failures, communication timeouts

  • Numerical Errors: Matrix singularities, convergence failures

Output Products

Standard Outputs

The pipeline generates several output files:

  1. Fisher Matrix (fisher_matrix.dat):

    • Text format with parameter labels

    • Full Fisher information matrix F_ij

    • Parameter error estimates (diagonal of F^-1)

  2. Inverse Covariance (inverse_covariance.bin):

    • Binary format for computational efficiency

    • Useful for subsequent QML analysis

    • Includes proper conditioning and regularization

  3. Geometry Information (analysis_geometry.dat):

    • Pixel selection and indexing

    • Multipole binning specification

    • Analysis mask and beam information

Diagnostic Outputs

Additional diagnostic information includes:

  • Computation Log: Timing, memory usage, convergence metrics

  • Parameter Summary: Input configuration and derived quantities

  • Quality Metrics: Matrix condition numbers, eigenvalue analysis

Examples

Basic Fisher Analysis

"""
Example: Standard Fisher matrix computation for CMB forecasting
"""
import subprocess
import yaml

# Create configuration
config = {
    'nside': 256,
    'lmin': 2,
    'lmax': 2000,
    'nfields': 3,
    'physical_labels': ['T', 'Q', 'U'],
    'do_cross': False,
    'covmatfile1': 'inputs/planck_noise.bin',
    'clfile': 'inputs/planck2018_spectra.txt',
    'beamfile': 'inputs/planck_beam.fits',
    'outfilefisher': 'outputs/planck_fisher.dat'
}

# Save configuration
with open('fisher_config.yaml', 'w') as f:
    yaml.dump(config, f)

# Run Fisher analysis
subprocess.run(['python', 'main_fisher.py', '--config', 'fisher_config.yaml'])

Cross-Survey Analysis

# Compare different survey configurations

# Current generation (Planck-like)
python main_fisher.py --config configs/current_survey.yaml

# Next generation (LiteBIRD/CMB-S4)
mpirun -n 16 python main_fisher.py --config configs/future_survey.yaml

# Ultimate precision (post-CMB-S4)
mpirun -n 32 python main_fisher.py --config configs/ultimate_survey.yaml

Systematic Studies

"""
Example: Systematic error impact on Fisher forecasts
"""

# Test different analysis choices
systematics = {
    'lmax_test': [1500, 2000, 2500, 3000],
    'beam_uncertainty': [0.0, 0.5, 1.0, 2.0],  # arcmin FWHM
    'noise_scaling': [0.8, 1.0, 1.2, 1.5]
}

for lmax in systematics['lmax_test']:
    config['lmax'] = lmax
    config['outfilefisher'] = f'outputs/fisher_lmax{lmax}.dat'

    with open(f'config_lmax{lmax}.yaml', 'w') as f:
        yaml.dump(config, f)

    subprocess.run(['mpirun', '-n', '8', 'python', 'main_fisher.py',
                   '--config', f'config_lmax{lmax}.yaml'])

Performance Guidelines

Resource Requirements

Typical resource needs for different analysis scales:

Analysis Scale

Active Pixels

Memory (GB)

Compute Time

Recommended Cores

Quick test

~10k

~1

~10 min

1-4

Standard analysis

~200k

~16

~4 hours

8-16

High resolution

~800k

~128

~24 hours

16-32

Ultimate precision

~3M

~1000

~1 week

32-64

Optimization Tips

For optimal performance:

  1. Memory: Ensure sufficient RAM for covariance matrices (8×N_pix² bytes)

  2. Storage: Use fast I/O for large binary files (covariance matrices)

  3. Network: High-bandwidth interconnect for MPI communication

  4. CPU: Prefer many cores over high clock speeds

  5. Scheduling: Request appropriate walltime for job completion

Troubleshooting

Common Issues

Memory Errors:

  • Reduce nside or lmax parameters

  • Use more MPI processes to distribute memory load

  • Enable swap space (not recommended for production)

Convergence Problems:

  • Check covariance matrix conditioning

  • Verify input file formats and units

  • Examine numerical precision requirements

MPI Communication Failures:

  • Verify MPI installation and configuration

  • Check network connectivity between nodes

  • Monitor for process failures or timeouts

File I/O Errors:

  • Confirm file paths and permissions

  • Verify sufficient disk space for outputs

  • Check file system compatibility (NFS issues)

See Also