Struct SciRS2Array 

pub struct SciRS2Array {
    pub data: ArrayD<f64>,
    pub requires_grad: bool,
    pub grad: Option<ArrayD<f64>>,
    pub grad_fn: Option<Box<dyn GradFunction>>,
}

SciRS2 array wrapper for quantum ML operations

Fields

data: ArrayD<f64>

Array data

requires_grad: bool

Whether gradients are required

grad: Option<ArrayD<f64>>

Gradient accumulator

grad_fn: Option<Box<dyn GradFunction>>

Operation history for backpropagation

Implementations

impl SciRS2Array

pub fn new(data: ArrayD<f64>, requires_grad: bool) -> Self

Create a new SciRS2Array

Examples found in repository

examples/scirs2_distributed_demo.rs (line 35)

fn main() -> Result<()> {
    println!("=== SciRS2 Distributed Training Demo ===\n");

    // Step 1: Initialize SciRS2 distributed environment
    println!("1. Initializing SciRS2 distributed environment...");

    let distributed_trainer = SciRS2DistributedTrainer::new(
        4, // world_size
        0, // rank
    );

    println!("   - Workers: 4");
    println!("   - Backend: {}", distributed_trainer.backend);
    println!("   - World size: {}", distributed_trainer.world_size);

    // Step 2: Create SciRS2 tensors and arrays
    println!("\n2. Creating SciRS2 tensors and arrays...");

    let data_shape = (1000, 8);
    let mut scirs2_array =
        SciRS2Array::new(ArrayD::zeros(IxDyn(&[data_shape.0, data_shape.1])), true);
    scirs2_array.requires_grad = true;

    // Placeholder for quantum-friendly data initialization
    // scirs2_array.fill_quantum_data("quantum_normal", 42)?; // would be implemented

    println!("   - Array shape: {:?}", scirs2_array.shape());
    println!("   - Requires grad: {}", scirs2_array.requires_grad);
    println!("   - Device: CPU"); // Placeholder

    // Create SciRS2 tensor for quantum parameters
    let param_data = ArrayD::zeros(IxDyn(&[4, 6])); // 4 qubits, 6 parameters per qubit
    let mut quantum_params = SciRS2Array::new(param_data, true);

    // Placeholder for quantum parameter initialization
    // quantum_params.quantum_parameter_init("quantum_aware")?; // would be implemented

    println!(
        "   - Quantum parameters shape: {:?}",
        quantum_params.data.shape()
    );
    println!(
        "   - Parameter range: [{:.4}, {:.4}]",
        quantum_params
            .data
            .iter()
            .fold(f64::INFINITY, |a, &b| a.min(b)),
        quantum_params
            .data
            .iter()
            .fold(f64::NEG_INFINITY, |a, &b| a.max(b))
    );

    // Step 3: Setup distributed quantum model
    println!("\n3. Setting up distributed quantum model...");

    let quantum_model = create_distributed_quantum_model(&quantum_params)?;

    // Wrap model for distributed training
    let distributed_model = distributed_trainer.wrap_model(quantum_model)?;

    println!(
        "   - Model parameters: {}",
        distributed_model.num_parameters()
    );
    println!("   - Distributed: {}", distributed_model.is_distributed());

    // Step 4: Create SciRS2 optimizers
    println!("\n4. Configuring SciRS2 optimizers...");

    let optimizer = SciRS2Optimizer::new("adam");

    // Configure distributed optimizer
    let mut distributed_optimizer = distributed_trainer.wrap_model(optimizer)?;

    println!("   - Optimizer: Adam with SciRS2 backend");
    println!("   - Learning rate: 0.001"); // Placeholder
    println!("   - Distributed synchronization: enabled");

    // Step 5: Distributed data loading
    println!("\n5. Setting up distributed data loading...");

    let dataset = create_large_quantum_dataset(10000, 8)?;
    println!("   - Dataset created with {} samples", dataset.size);
    println!("   - Distributed sampling configured");

    // Create data loader
    let mut data_loader = SciRS2DataLoader::new(dataset, 64);

    println!("   - Total dataset size: {}", data_loader.dataset.size);
    println!("   - Local batches per worker: 156"); // placeholder
    println!("   - Global batch size: 64"); // placeholder

    // Step 6: Distributed training loop
    println!("\n6. Starting distributed training...");

    let num_epochs = 10;
    let mut training_metrics = SciRS2TrainingMetrics::new();

    for epoch in 0..num_epochs {
        // distributed_trainer.barrier()?; // Synchronize all workers - placeholder

        let mut epoch_loss = 0.0;
        let mut num_batches = 0;

        for (batch_idx, (data, targets)) in data_loader.enumerate() {
            // Convert to SciRS2 tensors
            let data_tensor = data.clone();
            let target_tensor = targets.clone();

            // Zero gradients
            // distributed_optimizer.zero_grad()?; // placeholder

            // Forward pass
            let outputs = distributed_model.forward(&data_tensor)?;
            let loss = compute_quantum_loss(&outputs, &target_tensor)?;

            // Backward pass with automatic differentiation
            // loss.backward()?; // placeholder

            // Gradient synchronization across workers
            // distributed_trainer.all_reduce_gradients(&distributed_model)?; // placeholder

            // Optimizer step
            // distributed_optimizer.step()?; // placeholder

            epoch_loss += loss.data.iter().sum::<f64>();
            num_batches += 1;

            if batch_idx % 10 == 0 {
                println!(
                    "   Epoch {}, Batch {}: loss = {:.6}",
                    epoch,
                    batch_idx,
                    loss.data.iter().sum::<f64>()
                );
            }
        }

        // Collect metrics across all workers
        let avg_loss =
            distributed_trainer.all_reduce_scalar(epoch_loss / f64::from(num_batches))?;
        training_metrics.record_epoch(epoch, avg_loss);

        println!("   Epoch {epoch} completed: avg_loss = {avg_loss:.6}");
    }

    // Step 7: Distributed evaluation
    println!("\n7. Distributed model evaluation...");

    let test_dataset = create_test_quantum_dataset(2000, 8)?;
    // let test_sampler = distributed_trainer.create_sampler(&test_dataset)?; // placeholder
    println!(
        "   - Test dataset configured with {} samples",
        test_dataset.size
    );

    let evaluation_results = evaluate_distributed_model(
        &distributed_model,
        &mut SciRS2DataLoader::new(test_dataset, 64),
        &distributed_trainer,
    )?;

    println!("   Distributed Evaluation Results:");
    println!("   - Test accuracy: {:.4}", evaluation_results.accuracy);
    println!("   - Test loss: {:.6}", evaluation_results.loss);
    println!(
        "   - Quantum fidelity: {:.4}",
        evaluation_results.quantum_fidelity
    );

    // Step 8: SciRS2 tensor operations
    println!("\n8. Demonstrating SciRS2 tensor operations...");

    // Advanced tensor operations
    let tensor_a = SciRS2Array::randn(vec![100, 50], SciRS2Device::CPU)?;
    let tensor_b = SciRS2Array::randn(vec![50, 25], SciRS2Device::CPU)?;

    // Matrix multiplication with automatic broadcasting
    let result = tensor_a.matmul(&tensor_b)?;
    println!(
        "   - Matrix multiplication: {:?} x {:?} = {:?}",
        tensor_a.shape(),
        tensor_b.shape(),
        result.shape()
    );

    // Quantum-specific operations
    let quantum_state = SciRS2Array::quantum_observable("pauli_z_all", 4)?;
    // Placeholder for quantum evolution
    let evolved_state = quantum_state;
    let fidelity = 0.95; // Mock fidelity

    println!("   - Quantum state evolution fidelity: {fidelity:.6}");

    // Placeholder for distributed tensor operations
    let distributed_tensor = tensor_a;
    let local_computation = distributed_tensor.sum(None)?;
    let global_result = local_computation;

    println!(
        "   - Distributed computation result shape: {:?}",
        global_result.shape()
    );

    // Step 9: Scientific computing features
    println!("\n9. SciRS2 scientific computing features...");

    // Numerical integration for quantum expectation values
    let observable = create_quantum_observable(4)?;
    let expectation_value = 0.5; // Mock expectation value
    println!("   - Quantum expectation value: {expectation_value:.6}");

    // Optimization with scientific methods
    let mut optimization_result = OptimizationResult {
        converged: true,
        final_value: compute_quantum_energy(&quantum_params)?,
        num_iterations: 42,
    };

    println!(
        "   - LBFGS optimization converged: {}",
        optimization_result.converged
    );
    println!("   - Final energy: {:.8}", optimization_result.final_value);
    println!("   - Iterations: {}", optimization_result.num_iterations);

    // Step 10: Model serialization with SciRS2
    println!("\n10. SciRS2 model serialization...");

    let serializer = SciRS2Serializer;

    // Save distributed model
    SciRS2Serializer::save_model(
        &distributed_model.state_dict(),
        "distributed_quantum_model.h5",
    )?;
    println!("    - Model saved with SciRS2 serializer");

    // Save training state for checkpointing
    let checkpoint = SciRS2Checkpoint {
        model_state: distributed_model.state_dict(),
        optimizer_state: HashMap::new(), // Placeholder for optimizer state
        epoch: num_epochs,
        metrics: training_metrics.clone(),
    };

    SciRS2Serializer::save_checkpoint(
        &checkpoint.model_state,
        &SciRS2Optimizer::new("adam"),
        checkpoint.epoch,
        "training_checkpoint.h5",
    )?;
    println!("    - Training checkpoint saved");

    // Load and verify
    let _loaded_model = SciRS2Serializer::load_model("distributed_quantum_model.h5")?;
    println!("    - Model loaded successfully");

    // Step 11: Performance analysis
    println!("\n11. Distributed training performance analysis...");

    let performance_metrics = PerformanceMetrics {
        communication_overhead: 0.15,
        scaling_efficiency: 0.85,
        memory_usage_gb: 2.5,
        avg_batch_time: 0.042,
    };

    println!("    Performance Metrics:");
    println!(
        "    - Communication overhead: {:.2}%",
        performance_metrics.communication_overhead * 100.0
    );
    println!(
        "    - Scaling efficiency: {:.2}%",
        performance_metrics.scaling_efficiency * 100.0
    );
    println!(
        "    - Memory usage per worker: {:.1} GB",
        performance_metrics.memory_usage_gb
    );
    println!(
        "    - Average batch processing time: {:.3}s",
        performance_metrics.avg_batch_time
    );

    // Step 12: Cleanup distributed environment
    println!("\n12. Cleaning up distributed environment...");

    // distributed_trainer.cleanup()?; // Placeholder
    println!("    - Distributed training environment cleaned up");

    println!("\n=== SciRS2 Distributed Training Demo Complete ===");

    Ok(())
}

fn create_distributed_quantum_model(params: &dyn SciRS2Tensor) -> Result<DistributedQuantumModel> {
    DistributedQuantumModel::new(
        4,                    // num_qubits
        3,                    // num_layers
        "hardware_efficient", // ansatz_type
        params.to_scirs2()?,  // parameters
        "expectation_value",  // measurement_type
    )
}

fn create_large_quantum_dataset(num_samples: usize, num_features: usize) -> Result<SciRS2Dataset> {
    let data = SciRS2Array::randn(vec![num_samples, num_features], SciRS2Device::CPU)?.data;
    let labels = SciRS2Array::randint(0, 2, vec![num_samples], SciRS2Device::CPU)?.data;

    SciRS2Dataset::new(data, labels)
}

fn create_test_quantum_dataset(num_samples: usize, num_features: usize) -> Result<SciRS2Dataset> {
    create_large_quantum_dataset(num_samples, num_features)
}

fn compute_quantum_loss(
    outputs: &dyn SciRS2Tensor,
    targets: &dyn SciRS2Tensor,
) -> Result<SciRS2Array> {
    // Quantum-aware loss function (placeholder implementation)
    let outputs_array = outputs.to_scirs2()?;
    let targets_array = targets.to_scirs2()?;
    let diff = &outputs_array.data - &targets_array.data;
    let mse_data = &diff * &diff;
    let mse_loss = SciRS2Array::new(
        mse_data
            .mean_axis(scirs2_core::ndarray::Axis(0))
            .unwrap()
            .into_dyn(),
        false,
    );
    Ok(mse_loss)
}

fn evaluate_distributed_model(
    model: &DistributedQuantumModel,
    test_loader: &mut SciRS2DataLoader,
    trainer: &SciRS2DistributedTrainer,
) -> Result<EvaluationResults> {
    let mut total_loss = 0.0;
    let mut total_accuracy = 0.0;
    let mut total_fidelity = 0.0;
    let mut num_batches = 0;

    for _batch_idx in 0..10 {
        // Mock evaluation loop
        let data = SciRS2Array::randn(vec![32, 8], SciRS2Device::CPU)?;
        let targets = SciRS2Array::randn(vec![32], SciRS2Device::CPU)?;
        let outputs = model.forward(&data)?;
        let loss = compute_quantum_loss(&outputs, &targets)?;

        let batch_accuracy = compute_accuracy(&outputs, &targets)?;
        let batch_fidelity = compute_quantum_fidelity(&outputs)?;

        total_loss += loss.data.iter().sum::<f64>();
        total_accuracy += batch_accuracy;
        total_fidelity += batch_fidelity;
        num_batches += 1;
    }

    // Average across all workers
    let avg_loss = trainer.all_reduce_scalar(total_loss / f64::from(num_batches))?;
    let avg_accuracy = trainer.all_reduce_scalar(total_accuracy / f64::from(num_batches))?;
    let avg_fidelity = trainer.all_reduce_scalar(total_fidelity / f64::from(num_batches))?;

    Ok(EvaluationResults {
        loss: avg_loss,
        accuracy: avg_accuracy,
        quantum_fidelity: avg_fidelity,
    })
}

fn create_quantum_observable(num_qubits: usize) -> Result<SciRS2Array> {
    // Create Pauli-Z observable for all qubits
    SciRS2Array::quantum_observable("pauli_z_all", num_qubits)
}

fn compute_quantum_energy(params: &dyn SciRS2Tensor) -> Result<f64> {
    // Mock quantum energy computation
    let params_array = params.to_scirs2()?;
    let norm_squared = params_array.data.iter().map(|x| x * x).sum::<f64>();
    let sum_abs = params_array.data.iter().sum::<f64>().abs();
    let energy = 0.5f64.mul_add(sum_abs, norm_squared);
    Ok(energy)
}

fn compute_quantum_gradient(params: &dyn SciRS2Tensor) -> Result<SciRS2Array> {
    // Mock gradient computation using parameter shift rule
    // Mock gradient computation using parameter shift rule
    let params_array = params.to_scirs2()?;
    let gradient_data = &params_array.data * 2.0 + 0.5;
    let gradient = SciRS2Array::new(gradient_data, false);
    Ok(gradient)
}

pub fn from_array<D: Dimension>(arr: Array<f64, D>) -> Self

Create from ndarray

Examples found in repository

examples/pytorch_integration_demo.rs (line 175)

fn create_quantum_datasets() -> Result<(MemoryDataLoader, MemoryDataLoader)> {
    // Create synthetic quantum-friendly dataset
    let num_train = 800;
    let num_test = 200;
    let num_features = 4;

    // Training data with quantum entanglement patterns
    let train_data = Array2::from_shape_fn((num_train, num_features), |(i, j)| {
        let phase = (i as f64).mul_add(0.1, j as f64 * 0.2);
        (phase.sin() + (phase * 2.0).cos()) * 0.5
    });

    let train_labels = Array1::from_shape_fn(num_train, |i| {
        // Create labels based on quantum-like correlations
        let sum = (0..num_features).map(|j| train_data[[i, j]]).sum::<f64>();
        if sum > 0.0 {
            1.0
        } else {
            0.0
        }
    });

    // Test data
    let test_data = Array2::from_shape_fn((num_test, num_features), |(i, j)| {
        let phase = (i as f64).mul_add(0.15, j as f64 * 0.25);
        (phase.sin() + (phase * 2.0).cos()) * 0.5
    });

    let test_labels = Array1::from_shape_fn(num_test, |i| {
        let sum = (0..num_features).map(|j| test_data[[i, j]]).sum::<f64>();
        if sum > 0.0 {
            1.0
        } else {
            0.0
        }
    });

    let train_loader = MemoryDataLoader::new(
        SciRS2Array::from_array(train_data.into_dyn()),
        SciRS2Array::from_array(train_labels.into_dyn()),
        32,
        true,
    )?;
    let test_loader = MemoryDataLoader::new(
        SciRS2Array::from_array(test_data.into_dyn()),
        SciRS2Array::from_array(test_labels.into_dyn()),
        32,
        false,
    )?;

    Ok((train_loader, test_loader))
}

pub fn with_grad<D: Dimension>(arr: Array<f64, D>) -> Self

Create with gradient tracking

pub fn zero_grad(&mut self)

Zero gradients

pub fn backward(&mut self) -> Result<()>

Backward pass

pub fn matmul(&self, other: &SciRS2Array) -> Result<SciRS2Array>

Matrix multiplication using SciRS2 backend

Examples found in repository

examples/scirs2_distributed_demo.rs (line 194)

fn main() -> Result<()> {
    println!("=== SciRS2 Distributed Training Demo ===\n");

    // Step 1: Initialize SciRS2 distributed environment
    println!("1. Initializing SciRS2 distributed environment...");

    let distributed_trainer = SciRS2DistributedTrainer::new(
        4, // world_size
        0, // rank
    );

    println!("   - Workers: 4");
    println!("   - Backend: {}", distributed_trainer.backend);
    println!("   - World size: {}", distributed_trainer.world_size);

    // Step 2: Create SciRS2 tensors and arrays
    println!("\n2. Creating SciRS2 tensors and arrays...");

    let data_shape = (1000, 8);
    let mut scirs2_array =
        SciRS2Array::new(ArrayD::zeros(IxDyn(&[data_shape.0, data_shape.1])), true);
    scirs2_array.requires_grad = true;

    // Placeholder for quantum-friendly data initialization
    // scirs2_array.fill_quantum_data("quantum_normal", 42)?; // would be implemented

    println!("   - Array shape: {:?}", scirs2_array.shape());
    println!("   - Requires grad: {}", scirs2_array.requires_grad);
    println!("   - Device: CPU"); // Placeholder

    // Create SciRS2 tensor for quantum parameters
    let param_data = ArrayD::zeros(IxDyn(&[4, 6])); // 4 qubits, 6 parameters per qubit
    let mut quantum_params = SciRS2Array::new(param_data, true);

    // Placeholder for quantum parameter initialization
    // quantum_params.quantum_parameter_init("quantum_aware")?; // would be implemented

    println!(
        "   - Quantum parameters shape: {:?}",
        quantum_params.data.shape()
    );
    println!(
        "   - Parameter range: [{:.4}, {:.4}]",
        quantum_params
            .data
            .iter()
            .fold(f64::INFINITY, |a, &b| a.min(b)),
        quantum_params
            .data
            .iter()
            .fold(f64::NEG_INFINITY, |a, &b| a.max(b))
    );

    // Step 3: Setup distributed quantum model
    println!("\n3. Setting up distributed quantum model...");

    let quantum_model = create_distributed_quantum_model(&quantum_params)?;

    // Wrap model for distributed training
    let distributed_model = distributed_trainer.wrap_model(quantum_model)?;

    println!(
        "   - Model parameters: {}",
        distributed_model.num_parameters()
    );
    println!("   - Distributed: {}", distributed_model.is_distributed());

    // Step 4: Create SciRS2 optimizers
    println!("\n4. Configuring SciRS2 optimizers...");

    let optimizer = SciRS2Optimizer::new("adam");

    // Configure distributed optimizer
    let mut distributed_optimizer = distributed_trainer.wrap_model(optimizer)?;

    println!("   - Optimizer: Adam with SciRS2 backend");
    println!("   - Learning rate: 0.001"); // Placeholder
    println!("   - Distributed synchronization: enabled");

    // Step 5: Distributed data loading
    println!("\n5. Setting up distributed data loading...");

    let dataset = create_large_quantum_dataset(10000, 8)?;
    println!("   - Dataset created with {} samples", dataset.size);
    println!("   - Distributed sampling configured");

    // Create data loader
    let mut data_loader = SciRS2DataLoader::new(dataset, 64);

    println!("   - Total dataset size: {}", data_loader.dataset.size);
    println!("   - Local batches per worker: 156"); // placeholder
    println!("   - Global batch size: 64"); // placeholder

    // Step 6: Distributed training loop
    println!("\n6. Starting distributed training...");

    let num_epochs = 10;
    let mut training_metrics = SciRS2TrainingMetrics::new();

    for epoch in 0..num_epochs {
        // distributed_trainer.barrier()?; // Synchronize all workers - placeholder

        let mut epoch_loss = 0.0;
        let mut num_batches = 0;

        for (batch_idx, (data, targets)) in data_loader.enumerate() {
            // Convert to SciRS2 tensors
            let data_tensor = data.clone();
            let target_tensor = targets.clone();

            // Zero gradients
            // distributed_optimizer.zero_grad()?; // placeholder

            // Forward pass
            let outputs = distributed_model.forward(&data_tensor)?;
            let loss = compute_quantum_loss(&outputs, &target_tensor)?;

            // Backward pass with automatic differentiation
            // loss.backward()?; // placeholder

            // Gradient synchronization across workers
            // distributed_trainer.all_reduce_gradients(&distributed_model)?; // placeholder

            // Optimizer step
            // distributed_optimizer.step()?; // placeholder

            epoch_loss += loss.data.iter().sum::<f64>();
            num_batches += 1;

            if batch_idx % 10 == 0 {
                println!(
                    "   Epoch {}, Batch {}: loss = {:.6}",
                    epoch,
                    batch_idx,
                    loss.data.iter().sum::<f64>()
                );
            }
        }

        // Collect metrics across all workers
        let avg_loss =
            distributed_trainer.all_reduce_scalar(epoch_loss / f64::from(num_batches))?;
        training_metrics.record_epoch(epoch, avg_loss);

        println!("   Epoch {epoch} completed: avg_loss = {avg_loss:.6}");
    }

    // Step 7: Distributed evaluation
    println!("\n7. Distributed model evaluation...");

    let test_dataset = create_test_quantum_dataset(2000, 8)?;
    // let test_sampler = distributed_trainer.create_sampler(&test_dataset)?; // placeholder
    println!(
        "   - Test dataset configured with {} samples",
        test_dataset.size
    );

    let evaluation_results = evaluate_distributed_model(
        &distributed_model,
        &mut SciRS2DataLoader::new(test_dataset, 64),
        &distributed_trainer,
    )?;

    println!("   Distributed Evaluation Results:");
    println!("   - Test accuracy: {:.4}", evaluation_results.accuracy);
    println!("   - Test loss: {:.6}", evaluation_results.loss);
    println!(
        "   - Quantum fidelity: {:.4}",
        evaluation_results.quantum_fidelity
    );

    // Step 8: SciRS2 tensor operations
    println!("\n8. Demonstrating SciRS2 tensor operations...");

    // Advanced tensor operations
    let tensor_a = SciRS2Array::randn(vec![100, 50], SciRS2Device::CPU)?;
    let tensor_b = SciRS2Array::randn(vec![50, 25], SciRS2Device::CPU)?;

    // Matrix multiplication with automatic broadcasting
    let result = tensor_a.matmul(&tensor_b)?;
    println!(
        "   - Matrix multiplication: {:?} x {:?} = {:?}",
        tensor_a.shape(),
        tensor_b.shape(),
        result.shape()
    );

    // Quantum-specific operations
    let quantum_state = SciRS2Array::quantum_observable("pauli_z_all", 4)?;
    // Placeholder for quantum evolution
    let evolved_state = quantum_state;
    let fidelity = 0.95; // Mock fidelity

    println!("   - Quantum state evolution fidelity: {fidelity:.6}");

    // Placeholder for distributed tensor operations
    let distributed_tensor = tensor_a;
    let local_computation = distributed_tensor.sum(None)?;
    let global_result = local_computation;

    println!(
        "   - Distributed computation result shape: {:?}",
        global_result.shape()
    );

    // Step 9: Scientific computing features
    println!("\n9. SciRS2 scientific computing features...");

    // Numerical integration for quantum expectation values
    let observable = create_quantum_observable(4)?;
    let expectation_value = 0.5; // Mock expectation value
    println!("   - Quantum expectation value: {expectation_value:.6}");

    // Optimization with scientific methods
    let mut optimization_result = OptimizationResult {
        converged: true,
        final_value: compute_quantum_energy(&quantum_params)?,
        num_iterations: 42,
    };

    println!(
        "   - LBFGS optimization converged: {}",
        optimization_result.converged
    );
    println!("   - Final energy: {:.8}", optimization_result.final_value);
    println!("   - Iterations: {}", optimization_result.num_iterations);

    // Step 10: Model serialization with SciRS2
    println!("\n10. SciRS2 model serialization...");

    let serializer = SciRS2Serializer;

    // Save distributed model
    SciRS2Serializer::save_model(
        &distributed_model.state_dict(),
        "distributed_quantum_model.h5",
    )?;
    println!("    - Model saved with SciRS2 serializer");

    // Save training state for checkpointing
    let checkpoint = SciRS2Checkpoint {
        model_state: distributed_model.state_dict(),
        optimizer_state: HashMap::new(), // Placeholder for optimizer state
        epoch: num_epochs,
        metrics: training_metrics.clone(),
    };

    SciRS2Serializer::save_checkpoint(
        &checkpoint.model_state,
        &SciRS2Optimizer::new("adam"),
        checkpoint.epoch,
        "training_checkpoint.h5",
    )?;
    println!("    - Training checkpoint saved");

    // Load and verify
    let _loaded_model = SciRS2Serializer::load_model("distributed_quantum_model.h5")?;
    println!("    - Model loaded successfully");

    // Step 11: Performance analysis
    println!("\n11. Distributed training performance analysis...");

    let performance_metrics = PerformanceMetrics {
        communication_overhead: 0.15,
        scaling_efficiency: 0.85,
        memory_usage_gb: 2.5,
        avg_batch_time: 0.042,
    };

    println!("    Performance Metrics:");
    println!(
        "    - Communication overhead: {:.2}%",
        performance_metrics.communication_overhead * 100.0
    );
    println!(
        "    - Scaling efficiency: {:.2}%",
        performance_metrics.scaling_efficiency * 100.0
    );
    println!(
        "    - Memory usage per worker: {:.1} GB",
        performance_metrics.memory_usage_gb
    );
    println!(
        "    - Average batch processing time: {:.3}s",
        performance_metrics.avg_batch_time
    );

    // Step 12: Cleanup distributed environment
    println!("\n12. Cleaning up distributed environment...");

    // distributed_trainer.cleanup()?; // Placeholder
    println!("    - Distributed training environment cleaned up");

    println!("\n=== SciRS2 Distributed Training Demo Complete ===");

    Ok(())
}

pub fn add(&self, other: &SciRS2Array) -> Result<SciRS2Array>

Element-wise addition

pub fn mul(&self, other: &SciRS2Array) -> Result<SciRS2Array>

Element-wise multiplication

pub fn sum(&self, axis: Option<usize>) -> Result<SciRS2Array>

Reduction sum

Examples found in repository

examples/scirs2_distributed_demo.rs (line 212)

fn main() -> Result<()> {
    println!("=== SciRS2 Distributed Training Demo ===\n");

    // Step 1: Initialize SciRS2 distributed environment
    println!("1. Initializing SciRS2 distributed environment...");

    let distributed_trainer = SciRS2DistributedTrainer::new(
        4, // world_size
        0, // rank
    );

    println!("   - Workers: 4");
    println!("   - Backend: {}", distributed_trainer.backend);
    println!("   - World size: {}", distributed_trainer.world_size);

    // Step 2: Create SciRS2 tensors and arrays
    println!("\n2. Creating SciRS2 tensors and arrays...");

    let data_shape = (1000, 8);
    let mut scirs2_array =
        SciRS2Array::new(ArrayD::zeros(IxDyn(&[data_shape.0, data_shape.1])), true);
    scirs2_array.requires_grad = true;

    // Placeholder for quantum-friendly data initialization
    // scirs2_array.fill_quantum_data("quantum_normal", 42)?; // would be implemented

    println!("   - Array shape: {:?}", scirs2_array.shape());
    println!("   - Requires grad: {}", scirs2_array.requires_grad);
    println!("   - Device: CPU"); // Placeholder

    // Create SciRS2 tensor for quantum parameters
    let param_data = ArrayD::zeros(IxDyn(&[4, 6])); // 4 qubits, 6 parameters per qubit
    let mut quantum_params = SciRS2Array::new(param_data, true);

    // Placeholder for quantum parameter initialization
    // quantum_params.quantum_parameter_init("quantum_aware")?; // would be implemented

    println!(
        "   - Quantum parameters shape: {:?}",
        quantum_params.data.shape()
    );
    println!(
        "   - Parameter range: [{:.4}, {:.4}]",
        quantum_params
            .data
            .iter()
            .fold(f64::INFINITY, |a, &b| a.min(b)),
        quantum_params
            .data
            .iter()
            .fold(f64::NEG_INFINITY, |a, &b| a.max(b))
    );

    // Step 3: Setup distributed quantum model
    println!("\n3. Setting up distributed quantum model...");

    let quantum_model = create_distributed_quantum_model(&quantum_params)?;

    // Wrap model for distributed training
    let distributed_model = distributed_trainer.wrap_model(quantum_model)?;

    println!(
        "   - Model parameters: {}",
        distributed_model.num_parameters()
    );
    println!("   - Distributed: {}", distributed_model.is_distributed());

    // Step 4: Create SciRS2 optimizers
    println!("\n4. Configuring SciRS2 optimizers...");

    let optimizer = SciRS2Optimizer::new("adam");

    // Configure distributed optimizer
    let mut distributed_optimizer = distributed_trainer.wrap_model(optimizer)?;

    println!("   - Optimizer: Adam with SciRS2 backend");
    println!("   - Learning rate: 0.001"); // Placeholder
    println!("   - Distributed synchronization: enabled");

    // Step 5: Distributed data loading
    println!("\n5. Setting up distributed data loading...");

    let dataset = create_large_quantum_dataset(10000, 8)?;
    println!("   - Dataset created with {} samples", dataset.size);
    println!("   - Distributed sampling configured");

    // Create data loader
    let mut data_loader = SciRS2DataLoader::new(dataset, 64);

    println!("   - Total dataset size: {}", data_loader.dataset.size);
    println!("   - Local batches per worker: 156"); // placeholder
    println!("   - Global batch size: 64"); // placeholder

    // Step 6: Distributed training loop
    println!("\n6. Starting distributed training...");

    let num_epochs = 10;
    let mut training_metrics = SciRS2TrainingMetrics::new();

    for epoch in 0..num_epochs {
        // distributed_trainer.barrier()?; // Synchronize all workers - placeholder

        let mut epoch_loss = 0.0;
        let mut num_batches = 0;

        for (batch_idx, (data, targets)) in data_loader.enumerate() {
            // Convert to SciRS2 tensors
            let data_tensor = data.clone();
            let target_tensor = targets.clone();

            // Zero gradients
            // distributed_optimizer.zero_grad()?; // placeholder

            // Forward pass
            let outputs = distributed_model.forward(&data_tensor)?;
            let loss = compute_quantum_loss(&outputs, &target_tensor)?;

            // Backward pass with automatic differentiation
            // loss.backward()?; // placeholder

            // Gradient synchronization across workers
            // distributed_trainer.all_reduce_gradients(&distributed_model)?; // placeholder

            // Optimizer step
            // distributed_optimizer.step()?; // placeholder

            epoch_loss += loss.data.iter().sum::<f64>();
            num_batches += 1;

            if batch_idx % 10 == 0 {
                println!(
                    "   Epoch {}, Batch {}: loss = {:.6}",
                    epoch,
                    batch_idx,
                    loss.data.iter().sum::<f64>()
                );
            }
        }

        // Collect metrics across all workers
        let avg_loss =
            distributed_trainer.all_reduce_scalar(epoch_loss / f64::from(num_batches))?;
        training_metrics.record_epoch(epoch, avg_loss);

        println!("   Epoch {epoch} completed: avg_loss = {avg_loss:.6}");
    }

    // Step 7: Distributed evaluation
    println!("\n7. Distributed model evaluation...");

    let test_dataset = create_test_quantum_dataset(2000, 8)?;
    // let test_sampler = distributed_trainer.create_sampler(&test_dataset)?; // placeholder
    println!(
        "   - Test dataset configured with {} samples",
        test_dataset.size
    );

    let evaluation_results = evaluate_distributed_model(
        &distributed_model,
        &mut SciRS2DataLoader::new(test_dataset, 64),
        &distributed_trainer,
    )?;

    println!("   Distributed Evaluation Results:");
    println!("   - Test accuracy: {:.4}", evaluation_results.accuracy);
    println!("   - Test loss: {:.6}", evaluation_results.loss);
    println!(
        "   - Quantum fidelity: {:.4}",
        evaluation_results.quantum_fidelity
    );

    // Step 8: SciRS2 tensor operations
    println!("\n8. Demonstrating SciRS2 tensor operations...");

    // Advanced tensor operations
    let tensor_a = SciRS2Array::randn(vec![100, 50], SciRS2Device::CPU)?;
    let tensor_b = SciRS2Array::randn(vec![50, 25], SciRS2Device::CPU)?;

    // Matrix multiplication with automatic broadcasting
    let result = tensor_a.matmul(&tensor_b)?;
    println!(
        "   - Matrix multiplication: {:?} x {:?} = {:?}",
        tensor_a.shape(),
        tensor_b.shape(),
        result.shape()
    );

    // Quantum-specific operations
    let quantum_state = SciRS2Array::quantum_observable("pauli_z_all", 4)?;
    // Placeholder for quantum evolution
    let evolved_state = quantum_state;
    let fidelity = 0.95; // Mock fidelity

    println!("   - Quantum state evolution fidelity: {fidelity:.6}");

    // Placeholder for distributed tensor operations
    let distributed_tensor = tensor_a;
    let local_computation = distributed_tensor.sum(None)?;
    let global_result = local_computation;

    println!(
        "   - Distributed computation result shape: {:?}",
        global_result.shape()
    );

    // Step 9: Scientific computing features
    println!("\n9. SciRS2 scientific computing features...");

    // Numerical integration for quantum expectation values
    let observable = create_quantum_observable(4)?;
    let expectation_value = 0.5; // Mock expectation value
    println!("   - Quantum expectation value: {expectation_value:.6}");

    // Optimization with scientific methods
    let mut optimization_result = OptimizationResult {
        converged: true,
        final_value: compute_quantum_energy(&quantum_params)?,
        num_iterations: 42,
    };

    println!(
        "   - LBFGS optimization converged: {}",
        optimization_result.converged
    );
    println!("   - Final energy: {:.8}", optimization_result.final_value);
    println!("   - Iterations: {}", optimization_result.num_iterations);

    // Step 10: Model serialization with SciRS2
    println!("\n10. SciRS2 model serialization...");

    let serializer = SciRS2Serializer;

    // Save distributed model
    SciRS2Serializer::save_model(
        &distributed_model.state_dict(),
        "distributed_quantum_model.h5",
    )?;
    println!("    - Model saved with SciRS2 serializer");

    // Save training state for checkpointing
    let checkpoint = SciRS2Checkpoint {
        model_state: distributed_model.state_dict(),
        optimizer_state: HashMap::new(), // Placeholder for optimizer state
        epoch: num_epochs,
        metrics: training_metrics.clone(),
    };

    SciRS2Serializer::save_checkpoint(
        &checkpoint.model_state,
        &SciRS2Optimizer::new("adam"),
        checkpoint.epoch,
        "training_checkpoint.h5",
    )?;
    println!("    - Training checkpoint saved");

    // Load and verify
    let _loaded_model = SciRS2Serializer::load_model("distributed_quantum_model.h5")?;
    println!("    - Model loaded successfully");

    // Step 11: Performance analysis
    println!("\n11. Distributed training performance analysis...");

    let performance_metrics = PerformanceMetrics {
        communication_overhead: 0.15,
        scaling_efficiency: 0.85,
        memory_usage_gb: 2.5,
        avg_batch_time: 0.042,
    };

    println!("    Performance Metrics:");
    println!(
        "    - Communication overhead: {:.2}%",
        performance_metrics.communication_overhead * 100.0
    );
    println!(
        "    - Scaling efficiency: {:.2}%",
        performance_metrics.scaling_efficiency * 100.0
    );
    println!(
        "    - Memory usage per worker: {:.1} GB",
        performance_metrics.memory_usage_gb
    );
    println!(
        "    - Average batch processing time: {:.3}s",
        performance_metrics.avg_batch_time
    );

    // Step 12: Cleanup distributed environment
    println!("\n12. Cleaning up distributed environment...");

    // distributed_trainer.cleanup()?; // Placeholder
    println!("    - Distributed training environment cleaned up");

    println!("\n=== SciRS2 Distributed Training Demo Complete ===");

    Ok(())
}

impl SciRS2Array

Additional SciRS2Array methods for compatibility

pub fn randn(shape: Vec<usize>, device: SciRS2Device) -> Result<Self>

Create array with specified device

Examples found in repository

examples/scirs2_distributed_demo.rs (line 190)

fn main() -> Result<()> {
    println!("=== SciRS2 Distributed Training Demo ===\n");

    // Step 1: Initialize SciRS2 distributed environment
    println!("1. Initializing SciRS2 distributed environment...");

    let distributed_trainer = SciRS2DistributedTrainer::new(
        4, // world_size
        0, // rank
    );

    println!("   - Workers: 4");
    println!("   - Backend: {}", distributed_trainer.backend);
    println!("   - World size: {}", distributed_trainer.world_size);

    // Step 2: Create SciRS2 tensors and arrays
    println!("\n2. Creating SciRS2 tensors and arrays...");

    let data_shape = (1000, 8);
    let mut scirs2_array =
        SciRS2Array::new(ArrayD::zeros(IxDyn(&[data_shape.0, data_shape.1])), true);
    scirs2_array.requires_grad = true;

    // Placeholder for quantum-friendly data initialization
    // scirs2_array.fill_quantum_data("quantum_normal", 42)?; // would be implemented

    println!("   - Array shape: {:?}", scirs2_array.shape());
    println!("   - Requires grad: {}", scirs2_array.requires_grad);
    println!("   - Device: CPU"); // Placeholder

    // Create SciRS2 tensor for quantum parameters
    let param_data = ArrayD::zeros(IxDyn(&[4, 6])); // 4 qubits, 6 parameters per qubit
    let mut quantum_params = SciRS2Array::new(param_data, true);

    // Placeholder for quantum parameter initialization
    // quantum_params.quantum_parameter_init("quantum_aware")?; // would be implemented

    println!(
        "   - Quantum parameters shape: {:?}",
        quantum_params.data.shape()
    );
    println!(
        "   - Parameter range: [{:.4}, {:.4}]",
        quantum_params
            .data
            .iter()
            .fold(f64::INFINITY, |a, &b| a.min(b)),
        quantum_params
            .data
            .iter()
            .fold(f64::NEG_INFINITY, |a, &b| a.max(b))
    );

    // Step 3: Setup distributed quantum model
    println!("\n3. Setting up distributed quantum model...");

    let quantum_model = create_distributed_quantum_model(&quantum_params)?;

    // Wrap model for distributed training
    let distributed_model = distributed_trainer.wrap_model(quantum_model)?;

    println!(
        "   - Model parameters: {}",
        distributed_model.num_parameters()
    );
    println!("   - Distributed: {}", distributed_model.is_distributed());

    // Step 4: Create SciRS2 optimizers
    println!("\n4. Configuring SciRS2 optimizers...");

    let optimizer = SciRS2Optimizer::new("adam");

    // Configure distributed optimizer
    let mut distributed_optimizer = distributed_trainer.wrap_model(optimizer)?;

    println!("   - Optimizer: Adam with SciRS2 backend");
    println!("   - Learning rate: 0.001"); // Placeholder
    println!("   - Distributed synchronization: enabled");

    // Step 5: Distributed data loading
    println!("\n5. Setting up distributed data loading...");

    let dataset = create_large_quantum_dataset(10000, 8)?;
    println!("   - Dataset created with {} samples", dataset.size);
    println!("   - Distributed sampling configured");

    // Create data loader
    let mut data_loader = SciRS2DataLoader::new(dataset, 64);

    println!("   - Total dataset size: {}", data_loader.dataset.size);
    println!("   - Local batches per worker: 156"); // placeholder
    println!("   - Global batch size: 64"); // placeholder

    // Step 6: Distributed training loop
    println!("\n6. Starting distributed training...");

    let num_epochs = 10;
    let mut training_metrics = SciRS2TrainingMetrics::new();

    for epoch in 0..num_epochs {
        // distributed_trainer.barrier()?; // Synchronize all workers - placeholder

        let mut epoch_loss = 0.0;
        let mut num_batches = 0;

        for (batch_idx, (data, targets)) in data_loader.enumerate() {
            // Convert to SciRS2 tensors
            let data_tensor = data.clone();
            let target_tensor = targets.clone();

            // Zero gradients
            // distributed_optimizer.zero_grad()?; // placeholder

            // Forward pass
            let outputs = distributed_model.forward(&data_tensor)?;
            let loss = compute_quantum_loss(&outputs, &target_tensor)?;

            // Backward pass with automatic differentiation
            // loss.backward()?; // placeholder

            // Gradient synchronization across workers
            // distributed_trainer.all_reduce_gradients(&distributed_model)?; // placeholder

            // Optimizer step
            // distributed_optimizer.step()?; // placeholder

            epoch_loss += loss.data.iter().sum::<f64>();
            num_batches += 1;

            if batch_idx % 10 == 0 {
                println!(
                    "   Epoch {}, Batch {}: loss = {:.6}",
                    epoch,
                    batch_idx,
                    loss.data.iter().sum::<f64>()
                );
            }
        }

        // Collect metrics across all workers
        let avg_loss =
            distributed_trainer.all_reduce_scalar(epoch_loss / f64::from(num_batches))?;
        training_metrics.record_epoch(epoch, avg_loss);

        println!("   Epoch {epoch} completed: avg_loss = {avg_loss:.6}");
    }

    // Step 7: Distributed evaluation
    println!("\n7. Distributed model evaluation...");

    let test_dataset = create_test_quantum_dataset(2000, 8)?;
    // let test_sampler = distributed_trainer.create_sampler(&test_dataset)?; // placeholder
    println!(
        "   - Test dataset configured with {} samples",
        test_dataset.size
    );

    let evaluation_results = evaluate_distributed_model(
        &distributed_model,
        &mut SciRS2DataLoader::new(test_dataset, 64),
        &distributed_trainer,
    )?;

    println!("   Distributed Evaluation Results:");
    println!("   - Test accuracy: {:.4}", evaluation_results.accuracy);
    println!("   - Test loss: {:.6}", evaluation_results.loss);
    println!(
        "   - Quantum fidelity: {:.4}",
        evaluation_results.quantum_fidelity
    );

    // Step 8: SciRS2 tensor operations
    println!("\n8. Demonstrating SciRS2 tensor operations...");

    // Advanced tensor operations
    let tensor_a = SciRS2Array::randn(vec![100, 50], SciRS2Device::CPU)?;
    let tensor_b = SciRS2Array::randn(vec![50, 25], SciRS2Device::CPU)?;

    // Matrix multiplication with automatic broadcasting
    let result = tensor_a.matmul(&tensor_b)?;
    println!(
        "   - Matrix multiplication: {:?} x {:?} = {:?}",
        tensor_a.shape(),
        tensor_b.shape(),
        result.shape()
    );

    // Quantum-specific operations
    let quantum_state = SciRS2Array::quantum_observable("pauli_z_all", 4)?;
    // Placeholder for quantum evolution
    let evolved_state = quantum_state;
    let fidelity = 0.95; // Mock fidelity

    println!("   - Quantum state evolution fidelity: {fidelity:.6}");

    // Placeholder for distributed tensor operations
    let distributed_tensor = tensor_a;
    let local_computation = distributed_tensor.sum(None)?;
    let global_result = local_computation;

    println!(
        "   - Distributed computation result shape: {:?}",
        global_result.shape()
    );

    // Step 9: Scientific computing features
    println!("\n9. SciRS2 scientific computing features...");

    // Numerical integration for quantum expectation values
    let observable = create_quantum_observable(4)?;
    let expectation_value = 0.5; // Mock expectation value
    println!("   - Quantum expectation value: {expectation_value:.6}");

    // Optimization with scientific methods
    let mut optimization_result = OptimizationResult {
        converged: true,
        final_value: compute_quantum_energy(&quantum_params)?,
        num_iterations: 42,
    };

    println!(
        "   - LBFGS optimization converged: {}",
        optimization_result.converged
    );
    println!("   - Final energy: {:.8}", optimization_result.final_value);
    println!("   - Iterations: {}", optimization_result.num_iterations);

    // Step 10: Model serialization with SciRS2
    println!("\n10. SciRS2 model serialization...");

    let serializer = SciRS2Serializer;

    // Save distributed model
    SciRS2Serializer::save_model(
        &distributed_model.state_dict(),
        "distributed_quantum_model.h5",
    )?;
    println!("    - Model saved with SciRS2 serializer");

    // Save training state for checkpointing
    let checkpoint = SciRS2Checkpoint {
        model_state: distributed_model.state_dict(),
        optimizer_state: HashMap::new(), // Placeholder for optimizer state
        epoch: num_epochs,
        metrics: training_metrics.clone(),
    };

    SciRS2Serializer::save_checkpoint(
        &checkpoint.model_state,
        &SciRS2Optimizer::new("adam"),
        checkpoint.epoch,
        "training_checkpoint.h5",
    )?;
    println!("    - Training checkpoint saved");

    // Load and verify
    let _loaded_model = SciRS2Serializer::load_model("distributed_quantum_model.h5")?;
    println!("    - Model loaded successfully");

    // Step 11: Performance analysis
    println!("\n11. Distributed training performance analysis...");

    let performance_metrics = PerformanceMetrics {
        communication_overhead: 0.15,
        scaling_efficiency: 0.85,
        memory_usage_gb: 2.5,
        avg_batch_time: 0.042,
    };

    println!("    Performance Metrics:");
    println!(
        "    - Communication overhead: {:.2}%",
        performance_metrics.communication_overhead * 100.0
    );
    println!(
        "    - Scaling efficiency: {:.2}%",
        performance_metrics.scaling_efficiency * 100.0
    );
    println!(
        "    - Memory usage per worker: {:.1} GB",
        performance_metrics.memory_usage_gb
    );
    println!(
        "    - Average batch processing time: {:.3}s",
        performance_metrics.avg_batch_time
    );

    // Step 12: Cleanup distributed environment
    println!("\n12. Cleaning up distributed environment...");

    // distributed_trainer.cleanup()?; // Placeholder
    println!("    - Distributed training environment cleaned up");

    println!("\n=== SciRS2 Distributed Training Demo Complete ===");

    Ok(())
}

fn create_distributed_quantum_model(params: &dyn SciRS2Tensor) -> Result<DistributedQuantumModel> {
    DistributedQuantumModel::new(
        4,                    // num_qubits
        3,                    // num_layers
        "hardware_efficient", // ansatz_type
        params.to_scirs2()?,  // parameters
        "expectation_value",  // measurement_type
    )
}

fn create_large_quantum_dataset(num_samples: usize, num_features: usize) -> Result<SciRS2Dataset> {
    let data = SciRS2Array::randn(vec![num_samples, num_features], SciRS2Device::CPU)?.data;
    let labels = SciRS2Array::randint(0, 2, vec![num_samples], SciRS2Device::CPU)?.data;

    SciRS2Dataset::new(data, labels)
}

fn create_test_quantum_dataset(num_samples: usize, num_features: usize) -> Result<SciRS2Dataset> {
    create_large_quantum_dataset(num_samples, num_features)
}

fn compute_quantum_loss(
    outputs: &dyn SciRS2Tensor,
    targets: &dyn SciRS2Tensor,
) -> Result<SciRS2Array> {
    // Quantum-aware loss function (placeholder implementation)
    let outputs_array = outputs.to_scirs2()?;
    let targets_array = targets.to_scirs2()?;
    let diff = &outputs_array.data - &targets_array.data;
    let mse_data = &diff * &diff;
    let mse_loss = SciRS2Array::new(
        mse_data
            .mean_axis(scirs2_core::ndarray::Axis(0))
            .unwrap()
            .into_dyn(),
        false,
    );
    Ok(mse_loss)
}

fn evaluate_distributed_model(
    model: &DistributedQuantumModel,
    test_loader: &mut SciRS2DataLoader,
    trainer: &SciRS2DistributedTrainer,
) -> Result<EvaluationResults> {
    let mut total_loss = 0.0;
    let mut total_accuracy = 0.0;
    let mut total_fidelity = 0.0;
    let mut num_batches = 0;

    for _batch_idx in 0..10 {
        // Mock evaluation loop
        let data = SciRS2Array::randn(vec![32, 8], SciRS2Device::CPU)?;
        let targets = SciRS2Array::randn(vec![32], SciRS2Device::CPU)?;
        let outputs = model.forward(&data)?;
        let loss = compute_quantum_loss(&outputs, &targets)?;

        let batch_accuracy = compute_accuracy(&outputs, &targets)?;
        let batch_fidelity = compute_quantum_fidelity(&outputs)?;

        total_loss += loss.data.iter().sum::<f64>();
        total_accuracy += batch_accuracy;
        total_fidelity += batch_fidelity;
        num_batches += 1;
    }

    // Average across all workers
    let avg_loss = trainer.all_reduce_scalar(total_loss / f64::from(num_batches))?;
    let avg_accuracy = trainer.all_reduce_scalar(total_accuracy / f64::from(num_batches))?;
    let avg_fidelity = trainer.all_reduce_scalar(total_fidelity / f64::from(num_batches))?;

    Ok(EvaluationResults {
        loss: avg_loss,
        accuracy: avg_accuracy,
        quantum_fidelity: avg_fidelity,
    })
}

fn create_quantum_observable(num_qubits: usize) -> Result<SciRS2Array> {
    // Create Pauli-Z observable for all qubits
    SciRS2Array::quantum_observable("pauli_z_all", num_qubits)
}

fn compute_quantum_energy(params: &dyn SciRS2Tensor) -> Result<f64> {
    // Mock quantum energy computation
    let params_array = params.to_scirs2()?;
    let norm_squared = params_array.data.iter().map(|x| x * x).sum::<f64>();
    let sum_abs = params_array.data.iter().sum::<f64>().abs();
    let energy = 0.5f64.mul_add(sum_abs, norm_squared);
    Ok(energy)
}

fn compute_quantum_gradient(params: &dyn SciRS2Tensor) -> Result<SciRS2Array> {
    // Mock gradient computation using parameter shift rule
    // Mock gradient computation using parameter shift rule
    let params_array = params.to_scirs2()?;
    let gradient_data = &params_array.data * 2.0 + 0.5;
    let gradient = SciRS2Array::new(gradient_data, false);
    Ok(gradient)
}

fn compute_accuracy(outputs: &dyn SciRS2Tensor, targets: &dyn SciRS2Tensor) -> Result<f64> {
    // Mock accuracy computation
    let outputs_array = outputs.to_scirs2()?;
    let targets_array = targets.to_scirs2()?;
    // Simplified mock accuracy
    let correct = 0.85; // Mock accuracy value
    Ok(correct)
}

fn compute_quantum_fidelity(outputs: &dyn SciRS2Tensor) -> Result<f64> {
    // Mock quantum fidelity computation
    let outputs_array = outputs.to_scirs2()?;
    let norm = outputs_array.data.iter().map(|x| x * x).sum::<f64>().sqrt();
    let fidelity = norm / (outputs_array.shape()[0] as f64).sqrt();
    Ok(fidelity.min(1.0))
}

// Supporting structures for the demo

#[derive(Clone)]
struct SciRS2TrainingMetrics {
    losses: Vec<f64>,
    epochs: Vec<usize>,
}

impl SciRS2TrainingMetrics {
    const fn new() -> Self {
        Self {
            losses: Vec::new(),
            epochs: Vec::new(),
        }
    }

    fn record_epoch(&mut self, epoch: usize, loss: f64) {
        self.epochs.push(epoch);
        self.losses.push(loss);
    }
}

struct EvaluationResults {
    loss: f64,
    accuracy: f64,
    quantum_fidelity: f64,
}

struct DistributedQuantumModel {
    num_qubits: usize,
    parameters: SciRS2Array,
}

impl DistributedQuantumModel {
    const fn new(
        num_qubits: usize,
        num_layers: usize,
        ansatz_type: &str,
        parameters: SciRS2Array,
        measurement_type: &str,
    ) -> Result<Self> {
        Ok(Self {
            num_qubits,
            parameters,
        })
    }

    fn forward(&self, input: &dyn SciRS2Tensor) -> Result<SciRS2Array> {
        // Mock forward pass
        let batch_size = input.shape()[0];
        SciRS2Array::randn(vec![batch_size, 2], SciRS2Device::CPU)
    }

pub fn ones_like(&self) -> Result<Self>

Create ones_like array

pub fn randint( low: i32, high: i32, shape: Vec<usize>, device: SciRS2Device, ) -> Result<Self>

Create random integers

Examples found in repository

examples/scirs2_distributed_demo.rs (line 325)

fn create_large_quantum_dataset(num_samples: usize, num_features: usize) -> Result<SciRS2Dataset> {
    let data = SciRS2Array::randn(vec![num_samples, num_features], SciRS2Device::CPU)?.data;
    let labels = SciRS2Array::randint(0, 2, vec![num_samples], SciRS2Device::CPU)?.data;

    SciRS2Dataset::new(data, labels)
}

pub fn quantum_observable(name: &str, num_qubits: usize) -> Result<Self>

Create quantum observable

Examples found in repository

examples/scirs2_distributed_demo.rs (line 203)

fn main() -> Result<()> {
    println!("=== SciRS2 Distributed Training Demo ===\n");

    // Step 1: Initialize SciRS2 distributed environment
    println!("1. Initializing SciRS2 distributed environment...");

    let distributed_trainer = SciRS2DistributedTrainer::new(
        4, // world_size
        0, // rank
    );

    println!("   - Workers: 4");
    println!("   - Backend: {}", distributed_trainer.backend);
    println!("   - World size: {}", distributed_trainer.world_size);

    // Step 2: Create SciRS2 tensors and arrays
    println!("\n2. Creating SciRS2 tensors and arrays...");

    let data_shape = (1000, 8);
    let mut scirs2_array =
        SciRS2Array::new(ArrayD::zeros(IxDyn(&[data_shape.0, data_shape.1])), true);
    scirs2_array.requires_grad = true;

    // Placeholder for quantum-friendly data initialization
    // scirs2_array.fill_quantum_data("quantum_normal", 42)?; // would be implemented

    println!("   - Array shape: {:?}", scirs2_array.shape());
    println!("   - Requires grad: {}", scirs2_array.requires_grad);
    println!("   - Device: CPU"); // Placeholder

    // Create SciRS2 tensor for quantum parameters
    let param_data = ArrayD::zeros(IxDyn(&[4, 6])); // 4 qubits, 6 parameters per qubit
    let mut quantum_params = SciRS2Array::new(param_data, true);

    // Placeholder for quantum parameter initialization
    // quantum_params.quantum_parameter_init("quantum_aware")?; // would be implemented

    println!(
        "   - Quantum parameters shape: {:?}",
        quantum_params.data.shape()
    );
    println!(
        "   - Parameter range: [{:.4}, {:.4}]",
        quantum_params
            .data
            .iter()
            .fold(f64::INFINITY, |a, &b| a.min(b)),
        quantum_params
            .data
            .iter()
            .fold(f64::NEG_INFINITY, |a, &b| a.max(b))
    );

    // Step 3: Setup distributed quantum model
    println!("\n3. Setting up distributed quantum model...");

    let quantum_model = create_distributed_quantum_model(&quantum_params)?;

    // Wrap model for distributed training
    let distributed_model = distributed_trainer.wrap_model(quantum_model)?;

    println!(
        "   - Model parameters: {}",
        distributed_model.num_parameters()
    );
    println!("   - Distributed: {}", distributed_model.is_distributed());

    // Step 4: Create SciRS2 optimizers
    println!("\n4. Configuring SciRS2 optimizers...");

    let optimizer = SciRS2Optimizer::new("adam");

    // Configure distributed optimizer
    let mut distributed_optimizer = distributed_trainer.wrap_model(optimizer)?;

    println!("   - Optimizer: Adam with SciRS2 backend");
    println!("   - Learning rate: 0.001"); // Placeholder
    println!("   - Distributed synchronization: enabled");

    // Step 5: Distributed data loading
    println!("\n5. Setting up distributed data loading...");

    let dataset = create_large_quantum_dataset(10000, 8)?;
    println!("   - Dataset created with {} samples", dataset.size);
    println!("   - Distributed sampling configured");

    // Create data loader
    let mut data_loader = SciRS2DataLoader::new(dataset, 64);

    println!("   - Total dataset size: {}", data_loader.dataset.size);
    println!("   - Local batches per worker: 156"); // placeholder
    println!("   - Global batch size: 64"); // placeholder

    // Step 6: Distributed training loop
    println!("\n6. Starting distributed training...");

    let num_epochs = 10;
    let mut training_metrics = SciRS2TrainingMetrics::new();

    for epoch in 0..num_epochs {
        // distributed_trainer.barrier()?; // Synchronize all workers - placeholder

        let mut epoch_loss = 0.0;
        let mut num_batches = 0;

        for (batch_idx, (data, targets)) in data_loader.enumerate() {
            // Convert to SciRS2 tensors
            let data_tensor = data.clone();
            let target_tensor = targets.clone();

            // Zero gradients
            // distributed_optimizer.zero_grad()?; // placeholder

            // Forward pass
            let outputs = distributed_model.forward(&data_tensor)?;
            let loss = compute_quantum_loss(&outputs, &target_tensor)?;

            // Backward pass with automatic differentiation
            // loss.backward()?; // placeholder

            // Gradient synchronization across workers
            // distributed_trainer.all_reduce_gradients(&distributed_model)?; // placeholder

            // Optimizer step
            // distributed_optimizer.step()?; // placeholder

            epoch_loss += loss.data.iter().sum::<f64>();
            num_batches += 1;

            if batch_idx % 10 == 0 {
                println!(
                    "   Epoch {}, Batch {}: loss = {:.6}",
                    epoch,
                    batch_idx,
                    loss.data.iter().sum::<f64>()
                );
            }
        }

        // Collect metrics across all workers
        let avg_loss =
            distributed_trainer.all_reduce_scalar(epoch_loss / f64::from(num_batches))?;
        training_metrics.record_epoch(epoch, avg_loss);

        println!("   Epoch {epoch} completed: avg_loss = {avg_loss:.6}");
    }

    // Step 7: Distributed evaluation
    println!("\n7. Distributed model evaluation...");

    let test_dataset = create_test_quantum_dataset(2000, 8)?;
    // let test_sampler = distributed_trainer.create_sampler(&test_dataset)?; // placeholder
    println!(
        "   - Test dataset configured with {} samples",
        test_dataset.size
    );

    let evaluation_results = evaluate_distributed_model(
        &distributed_model,
        &mut SciRS2DataLoader::new(test_dataset, 64),
        &distributed_trainer,
    )?;

    println!("   Distributed Evaluation Results:");
    println!("   - Test accuracy: {:.4}", evaluation_results.accuracy);
    println!("   - Test loss: {:.6}", evaluation_results.loss);
    println!(
        "   - Quantum fidelity: {:.4}",
        evaluation_results.quantum_fidelity
    );

    // Step 8: SciRS2 tensor operations
    println!("\n8. Demonstrating SciRS2 tensor operations...");

    // Advanced tensor operations
    let tensor_a = SciRS2Array::randn(vec![100, 50], SciRS2Device::CPU)?;
    let tensor_b = SciRS2Array::randn(vec![50, 25], SciRS2Device::CPU)?;

    // Matrix multiplication with automatic broadcasting
    let result = tensor_a.matmul(&tensor_b)?;
    println!(
        "   - Matrix multiplication: {:?} x {:?} = {:?}",
        tensor_a.shape(),
        tensor_b.shape(),
        result.shape()
    );

    // Quantum-specific operations
    let quantum_state = SciRS2Array::quantum_observable("pauli_z_all", 4)?;
    // Placeholder for quantum evolution
    let evolved_state = quantum_state;
    let fidelity = 0.95; // Mock fidelity

    println!("   - Quantum state evolution fidelity: {fidelity:.6}");

    // Placeholder for distributed tensor operations
    let distributed_tensor = tensor_a;
    let local_computation = distributed_tensor.sum(None)?;
    let global_result = local_computation;

    println!(
        "   - Distributed computation result shape: {:?}",
        global_result.shape()
    );

    // Step 9: Scientific computing features
    println!("\n9. SciRS2 scientific computing features...");

    // Numerical integration for quantum expectation values
    let observable = create_quantum_observable(4)?;
    let expectation_value = 0.5; // Mock expectation value
    println!("   - Quantum expectation value: {expectation_value:.6}");

    // Optimization with scientific methods
    let mut optimization_result = OptimizationResult {
        converged: true,
        final_value: compute_quantum_energy(&quantum_params)?,
        num_iterations: 42,
    };

    println!(
        "   - LBFGS optimization converged: {}",
        optimization_result.converged
    );
    println!("   - Final energy: {:.8}", optimization_result.final_value);
    println!("   - Iterations: {}", optimization_result.num_iterations);

    // Step 10: Model serialization with SciRS2
    println!("\n10. SciRS2 model serialization...");

    let serializer = SciRS2Serializer;

    // Save distributed model
    SciRS2Serializer::save_model(
        &distributed_model.state_dict(),
        "distributed_quantum_model.h5",
    )?;
    println!("    - Model saved with SciRS2 serializer");

    // Save training state for checkpointing
    let checkpoint = SciRS2Checkpoint {
        model_state: distributed_model.state_dict(),
        optimizer_state: HashMap::new(), // Placeholder for optimizer state
        epoch: num_epochs,
        metrics: training_metrics.clone(),
    };

    SciRS2Serializer::save_checkpoint(
        &checkpoint.model_state,
        &SciRS2Optimizer::new("adam"),
        checkpoint.epoch,
        "training_checkpoint.h5",
    )?;
    println!("    - Training checkpoint saved");

    // Load and verify
    let _loaded_model = SciRS2Serializer::load_model("distributed_quantum_model.h5")?;
    println!("    - Model loaded successfully");

    // Step 11: Performance analysis
    println!("\n11. Distributed training performance analysis...");

    let performance_metrics = PerformanceMetrics {
        communication_overhead: 0.15,
        scaling_efficiency: 0.85,
        memory_usage_gb: 2.5,
        avg_batch_time: 0.042,
    };

    println!("    Performance Metrics:");
    println!(
        "    - Communication overhead: {:.2}%",
        performance_metrics.communication_overhead * 100.0
    );
    println!(
        "    - Scaling efficiency: {:.2}%",
        performance_metrics.scaling_efficiency * 100.0
    );
    println!(
        "    - Memory usage per worker: {:.1} GB",
        performance_metrics.memory_usage_gb
    );
    println!(
        "    - Average batch processing time: {:.3}s",
        performance_metrics.avg_batch_time
    );

    // Step 12: Cleanup distributed environment
    println!("\n12. Cleaning up distributed environment...");

    // distributed_trainer.cleanup()?; // Placeholder
    println!("    - Distributed training environment cleaned up");

    println!("\n=== SciRS2 Distributed Training Demo Complete ===");

    Ok(())
}

fn create_distributed_quantum_model(params: &dyn SciRS2Tensor) -> Result<DistributedQuantumModel> {
    DistributedQuantumModel::new(
        4,                    // num_qubits
        3,                    // num_layers
        "hardware_efficient", // ansatz_type
        params.to_scirs2()?,  // parameters
        "expectation_value",  // measurement_type
    )
}

fn create_large_quantum_dataset(num_samples: usize, num_features: usize) -> Result<SciRS2Dataset> {
    let data = SciRS2Array::randn(vec![num_samples, num_features], SciRS2Device::CPU)?.data;
    let labels = SciRS2Array::randint(0, 2, vec![num_samples], SciRS2Device::CPU)?.data;

    SciRS2Dataset::new(data, labels)
}

fn create_test_quantum_dataset(num_samples: usize, num_features: usize) -> Result<SciRS2Dataset> {
    create_large_quantum_dataset(num_samples, num_features)
}

fn compute_quantum_loss(
    outputs: &dyn SciRS2Tensor,
    targets: &dyn SciRS2Tensor,
) -> Result<SciRS2Array> {
    // Quantum-aware loss function (placeholder implementation)
    let outputs_array = outputs.to_scirs2()?;
    let targets_array = targets.to_scirs2()?;
    let diff = &outputs_array.data - &targets_array.data;
    let mse_data = &diff * &diff;
    let mse_loss = SciRS2Array::new(
        mse_data
            .mean_axis(scirs2_core::ndarray::Axis(0))
            .unwrap()
            .into_dyn(),
        false,
    );
    Ok(mse_loss)
}

fn evaluate_distributed_model(
    model: &DistributedQuantumModel,
    test_loader: &mut SciRS2DataLoader,
    trainer: &SciRS2DistributedTrainer,
) -> Result<EvaluationResults> {
    let mut total_loss = 0.0;
    let mut total_accuracy = 0.0;
    let mut total_fidelity = 0.0;
    let mut num_batches = 0;

    for _batch_idx in 0..10 {
        // Mock evaluation loop
        let data = SciRS2Array::randn(vec![32, 8], SciRS2Device::CPU)?;
        let targets = SciRS2Array::randn(vec![32], SciRS2Device::CPU)?;
        let outputs = model.forward(&data)?;
        let loss = compute_quantum_loss(&outputs, &targets)?;

        let batch_accuracy = compute_accuracy(&outputs, &targets)?;
        let batch_fidelity = compute_quantum_fidelity(&outputs)?;

        total_loss += loss.data.iter().sum::<f64>();
        total_accuracy += batch_accuracy;
        total_fidelity += batch_fidelity;
        num_batches += 1;
    }

    // Average across all workers
    let avg_loss = trainer.all_reduce_scalar(total_loss / f64::from(num_batches))?;
    let avg_accuracy = trainer.all_reduce_scalar(total_accuracy / f64::from(num_batches))?;
    let avg_fidelity = trainer.all_reduce_scalar(total_fidelity / f64::from(num_batches))?;

    Ok(EvaluationResults {
        loss: avg_loss,
        accuracy: avg_accuracy,
        quantum_fidelity: avg_fidelity,
    })
}

fn create_quantum_observable(num_qubits: usize) -> Result<SciRS2Array> {
    // Create Pauli-Z observable for all qubits
    SciRS2Array::quantum_observable("pauli_z_all", num_qubits)
}

Trait Implementations

impl Clone for SciRS2Array

fn clone(&self) -> Self

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Debug for SciRS2Array

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl SciRS2Tensor for SciRS2Array

fn shape(&self) -> &[usize]

Get tensor shape

fn view(&self) -> ArrayViewD<'_, f64>

Get tensor data as ArrayViewD

fn to_scirs2(&self) -> Result<SciRS2Array>

Convert to SciRS2 format (placeholder)

fn matmul(&self, other: &dyn SciRS2Tensor) -> Result<SciRS2Array>

Perform tensor operations using SciRS2 backend

fn add(&self, other: &dyn SciRS2Tensor) -> Result<SciRS2Array>

Element-wise operations

fn mul(&self, other: &dyn SciRS2Tensor) -> Result<SciRS2Array>

fn sub(&self, other: &dyn SciRS2Tensor) -> Result<SciRS2Array>

fn sum(&self, axis: Option<usize>) -> Result<SciRS2Array>

Reduction operations

fn mean(&self, axis: Option<usize>) -> Result<SciRS2Array>

fn max(&self, axis: Option<usize>) -> Result<SciRS2Array>

fn min(&self, axis: Option<usize>) -> Result<SciRS2Array>