ferrolearn-decomp 0.5.0

Dimensionality reduction and decomposition for the ferrolearn ML framework
Documentation
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//! Incremental Principal Component Analysis (IncrementalPCA).
//!
//! [`IncrementalPCA`] performs PCA incrementally by processing data in batches.
//! This is useful for datasets that are too large to fit in memory, or when
//! data arrives as a stream.
//!
//! # Algorithm
//!
//! Mirrors scikit-learn's `IncrementalPCA.partial_fit`. Maintains a running
//! per-feature mean and variance (Youngs-Cramer / Chan update) and performs an
//! incremental SVD update. For each batch `X_batch` (with `n` samples already
//! seen):
//! 1. Update the running `(mean, var, n_samples_seen)` via the numerically
//!    stable incremental mean-and-variance combination.
//! 2. If this is the first batch, centre by the column mean: `M = X_centred`.
//!    Otherwise centre the batch by its **own batch mean** and stack three
//!    blocks: `M = vstack([singular_values * components, X_batch_centred,
//!    mean_correction])`, where `mean_correction = sqrt((n / n_total) * n_batch)
//!    * (running_mean - batch_mean)`.
//! 3. Compute a thin SVD of `M` and apply `svd_flip` (per component row, the
//!    max-abs entry is made positive) for a deterministic sign.
//! 4. Extract updated `components` (rows of `V^T`), `singular_values`,
//!    `explained_variance = S^2 / (n_total - 1)`, and
//!    `explained_variance_ratio = S^2 / sum(var * n_total)` (fraction of total
//!    feature variance).
//!
//! The [`Fit::fit`] method processes the dataset in `batch_size` chunks
//! internally. Use [`IncrementalPCA::partial_fit`] to update the model with
//! one batch at a time (for streaming use cases).
//!
//! # Examples
//!
//! ```
//! use ferrolearn_decomp::IncrementalPCA;
//! use ferrolearn_core::traits::{Fit, Transform};
//! use ndarray::array;
//!
//! let ipca = IncrementalPCA::<f64>::new(1);
//! let x = array![[1.0, 2.0], [3.0, 4.0], [5.0, 6.0], [7.0, 8.0]];
//! let fitted = ipca.fit(&x, &()).unwrap();
//! let projected = fitted.transform(&x).unwrap();
//! assert_eq!(projected.ncols(), 1);
//! ```
//!
//! ## REQ status
//!
//! Design: `.design/decomp/incremental_pca.md`. Tracking: #1584. Each REQ is
//! BINARY — SHIPPED (impl + non-test consumer + tests + green verification) or
//! NOT-STARTED (concrete open blocker). Non-test consumers: crate re-export
//! (`lib.rs:88`) + the PyO3 `_RsIncrementalPCA` binding
//! (`ferrolearn-python/src/extras.rs:1094`, registered `lib.rs:72`). Oracle = live
//! sklearn 1.5.2 (`_incremental_pca.py`), run from `/tmp` (R-CHAR-3). `partial_fit`
//! is DETERMINISTIC and now ports sklearn faithfully — full value parity (single +
//! multi-batch).
//!
//! | REQ | Scope | Status | Evidence / Blocker |
//! |---|---|---|---|
//! | REQ-1 | `svd_flip` sign + `components_`/`transform` value parity | SHIPPED | per-Vt-row max-abs-positive after `thin_svd` (= `_incremental_pca.py:357`); matches sklearn incl. sign (single 2.2e-16, multi 6.3e-15). Was #1585, fixed. Test `divergence_svd_flip_sign` |
//! | REQ-2 | Multi-batch `mean_correction` + batch-mean centering (3-block SVD stack) | SHIPPED | `partial_fit_batch` ports `_incremental_pca.py:342-354`; multi-batch components/EV/SV match sklearn ≤2.8e-14. Was #1586, fixed. Test `divergence_multibatch_mean_correction` |
//! | REQ-3 | `explained_variance_ratio_` = `S²/Σ(var·n_total)` (total feature variance) + running `var_` | SHIPPED | `= _incremental_pca.py:359`; running variance via Youngs-Cramer port (`extmath.py:1057-1180`); ratio + `var_` match sklearn (var_ exact). Was #1587, fixed. Test `divergence_explained_variance_ratio_denominator` |
//! | REQ-4 | Running mean (incremental) | SHIPPED | matches sklearn `mean_` element-wise (1e-9, multi-batch); `test_mean_is_correct`, `test_batch_size_*` |
//! | REQ-5 | `components_` shape `(n_components, n_features)` | SHIPPED | `test_fit_output_shape`/`_two_components`; matches sklearn element-wise (REQ-1) |
//! | REQ-6 | `explained_variance_` = `S²/(n_total−1)` | SHIPPED | matches sklearn (single 1.8e-15); `test_explained_variance_positive` |
//! | REQ-7 | `singular_values_` | SHIPPED | matches sklearn (single 1.3e-15) |
//! | REQ-8 | `components_` rows unit-norm | SHIPPED | `test_components_approx_unit_length` |
//! | REQ-9 | Error/parameter contracts (incl. NON-FINITE rejection) | SHIPPED (scoped) | `fit`/`partial_fit`/`transform` guards. NON-FINITE: `partial_fit_batch` (the fit/partial_fit core) + `transform` call `reject_non_finite` (`incremental_pca.rs` symbol `reject_non_finite`) BEFORE the incremental-SVD/projection math, returning the CLEAN finiteness `InvalidParameter{name:"X", reason:"Input X contains NaN or infinity."}` = sklearn `_validate_data(force_all_finite=True)` (`_incremental_pca.py:227`,`:281`,`utils/validation.py:147-154`). `tests/divergence_nonfinite_spillover.rs::divergence_incremental_pca_fit_nan`/`_transform_nan` match the live sklearn 1.5.2 oracle (#2290). FLAG: ferrolearn rejects `n_components>=n_features`; sklearn allows `n_components==n_features ≤ min(n,p)` (REQ-14 #1590) |
//! | REQ-10 | `n_samples_seen` accumulation + `partial_fit` chaining + batch chunking | SHIPPED | `test_partial_fit_chaining`, `test_n_samples_seen`, `test_batch_size_*` |
//! | REQ-12 | f32/f64 generic | SHIPPED | `test_f32_support` |
//! | REQ-15 | running `var_` fitted attr + accessor | SHIPPED | `var_` field + `var()` accessor; matches sklearn `var_` exactly (was #1591, retired into REQ-3) |
//! | REQ-11 | `PipelineTransformer` integration | NOT-STARTED | no impl (cf. `pca.rs:565`) — blocker #1588 |
//! | REQ-13 | `batch_size` auto-default = `5*n_features` | NOT-STARTED | ferrolearn defaults to full-data — blocker #1589 |
//! | REQ-14 | `n_components=None` + `n_components==n_features` acceptance | NOT-STARTED | sklearn `_incremental_pca.py:294-308` — blocker #1590 |
//! | REQ-16 | `noise_variance_` attr | NOT-STARTED | sklearn `_incremental_pca.py:369-372` — blocker #1592 |
//! | REQ-17 | `whiten` + `copy` ctor params | NOT-STARTED | sklearn `_incremental_pca.py:194-198` — blocker #1593 |
//! | REQ-18 | `n_features_in_` attr | NOT-STARTED | blocker #1594 |
//! | REQ-19 | ferray substrate | NOT-STARTED | `ndarray` + hand-rolled Jacobi — blocker #1595 |
//!
//! Count: **12 SHIPPED (REQ-1..10,12,15) / 7 NOT-STARTED (REQ-11,13,14,16,17,18,19)**.

use ferrolearn_core::error::FerroError;
use ferrolearn_core::traits::{Fit, Transform};
use ndarray::{Array1, Array2};
use num_traits::Float;
use std::any::TypeId;

/// Reject non-finite input the way sklearn's `_validate_data` does.
///
/// sklearn runs `check_array` with the default `force_all_finite=True` at the
/// top of `IncrementalPCA.fit`/`partial_fit`/`transform`
/// (`sklearn/decomposition/_incremental_pca.py:227`,`:281`), raising
/// `ValueError("Input X contains NaN.")` / `"... contains infinity ..."`
/// (`sklearn/utils/validation.py:147-154`) BEFORE any SVD math. NaN AND
/// infinity are both rejected. The message names "NaN" and "infinity" to mirror
/// sklearn's `ValueError`. Never panics (R-CODE-2).
fn reject_non_finite<F: Float>(x: &Array2<F>) -> Result<(), FerroError> {
    if x.iter().any(|v| !v.is_finite()) {
        return Err(FerroError::InvalidParameter {
            name: "X".into(),
            reason: "Input X contains NaN or infinity.".into(),
        });
    }
    Ok(())
}

// ---------------------------------------------------------------------------
// IncrementalPCA (unfitted)
// ---------------------------------------------------------------------------

/// Incremental PCA configuration.
///
/// Holds `n_components` and an optional `batch_size`. Calling [`Fit::fit`]
/// processes the data in batches and returns a [`FittedIncrementalPCA`].
///
/// # Type Parameters
///
/// - `F`: The floating-point type (`f32` or `f64`).
#[derive(Debug, Clone)]
pub struct IncrementalPCA<F> {
    /// Number of principal components to retain.
    n_components: usize,
    /// Number of samples per batch. If `None`, the whole dataset is processed
    /// in a single batch (equivalent to standard PCA on the full data).
    batch_size: Option<usize>,
    _marker: std::marker::PhantomData<F>,
}

impl<F: Float + Send + Sync + 'static> IncrementalPCA<F> {
    /// Create a new `IncrementalPCA` that retains `n_components` components.
    ///
    /// If `batch_size` is not set, the whole dataset is processed at once.
    #[must_use]
    pub fn new(n_components: usize) -> Self {
        Self {
            n_components,
            batch_size: None,
            _marker: std::marker::PhantomData,
        }
    }

    /// Set the batch size.
    ///
    /// Each call to the internal loop will process this many samples.
    #[must_use]
    pub fn with_batch_size(mut self, batch_size: usize) -> Self {
        self.batch_size = Some(batch_size);
        self
    }

    /// Return the number of components.
    #[must_use]
    pub fn n_components(&self) -> usize {
        self.n_components
    }

    /// Return the configured batch size, if any.
    #[must_use]
    pub fn batch_size(&self) -> Option<usize> {
        self.batch_size
    }
}

// ---------------------------------------------------------------------------
// FittedIncrementalPCA
// ---------------------------------------------------------------------------

/// A fitted Incremental PCA model.
///
/// Created either by calling [`Fit::fit`] on an [`IncrementalPCA`] or by
/// calling [`IncrementalPCA::partial_fit`] one batch at a time.
///
/// Implements [`Transform<Array2<F>>`] to project new data onto the
/// learned principal components.
#[derive(Debug, Clone)]
pub struct FittedIncrementalPCA<F> {
    /// Principal component directions, shape `(n_components, n_features)`.
    components_: Array2<F>,
    /// Variance explained by each component (singular_value^2 / n_samples_seen).
    explained_variance_: Array1<F>,
    /// Ratio of variance explained by each component to total variance.
    explained_variance_ratio_: Array1<F>,
    /// Per-feature running mean.
    mean_: Array1<F>,
    /// Per-feature running population variance (ddof=0), tracked via the
    /// Youngs-Cramer / Chan parallel-variance update (sklearn
    /// `_incremental_mean_and_var`). Used as the denominator of
    /// `explained_variance_ratio_`.
    var_: Array1<F>,
    /// Number of samples seen so far.
    n_samples_seen_: usize,
    /// Singular values of the current incremental SVD.
    singular_values_: Array1<F>,
}

impl<F: Float + Send + Sync + 'static> FittedIncrementalPCA<F> {
    /// Principal components, shape `(n_components, n_features)`.
    #[must_use]
    pub fn components(&self) -> &Array2<F> {
        &self.components_
    }

    /// Explained variance per component.
    #[must_use]
    pub fn explained_variance(&self) -> &Array1<F> {
        &self.explained_variance_
    }

    /// Explained variance ratio per component.
    #[must_use]
    pub fn explained_variance_ratio(&self) -> &Array1<F> {
        &self.explained_variance_ratio_
    }

    /// Running per-feature mean.
    #[must_use]
    pub fn mean(&self) -> &Array1<F> {
        &self.mean_
    }

    /// Running per-feature population variance (ddof=0), as tracked by the
    /// incremental Youngs-Cramer update. Mirrors sklearn `IncrementalPCA.var_`.
    #[must_use]
    pub fn var(&self) -> &Array1<F> {
        &self.var_
    }

    /// Number of samples seen during fitting.
    #[must_use]
    pub fn n_samples_seen(&self) -> usize {
        self.n_samples_seen_
    }

    /// Singular values of the incremental SVD.
    #[must_use]
    pub fn singular_values(&self) -> &Array1<F> {
        &self.singular_values_
    }

    /// Map reduced data back to the original feature space. Mirrors
    /// sklearn `IncrementalPCA.inverse_transform`. Returns shape
    /// `(n_samples, n_features)` via `X_reduced @ components + mean`.
    ///
    /// # Errors
    ///
    /// Returns [`FerroError::ShapeMismatch`] if `x_reduced.ncols()` does
    /// not equal the number of components.
    pub fn inverse_transform(&self, x_reduced: &Array2<F>) -> Result<Array2<F>, FerroError> {
        let n_components = self.components_.nrows();
        if x_reduced.ncols() != n_components {
            return Err(FerroError::ShapeMismatch {
                expected: vec![x_reduced.nrows(), n_components],
                actual: vec![x_reduced.nrows(), x_reduced.ncols()],
                context: "FittedIncrementalPCA::inverse_transform".into(),
            });
        }
        let mut result = x_reduced.dot(&self.components_);
        for mut row in result.rows_mut() {
            for (v, &m) in row.iter_mut().zip(self.mean_.iter()) {
                *v = *v + m;
            }
        }
        Ok(result)
    }

    /// Process one additional batch, updating the model in-place.
    ///
    /// This is the core of the incremental algorithm. See the module-level
    /// documentation for the algorithm details.
    ///
    /// # Errors
    ///
    /// - [`FerroError::InsufficientSamples`] if the batch is empty.
    /// - [`FerroError::ShapeMismatch`] if the batch has the wrong number of
    ///   features (after the first batch has been seen).
    /// - [`FerroError::NumericalInstability`] if a numerical failure occurs.
    pub fn partial_fit_batch(&mut self, x_batch: &Array2<F>) -> Result<(), FerroError> {
        let (batch_n, n_features) = x_batch.dim();

        if batch_n == 0 {
            return Err(FerroError::InsufficientSamples {
                required: 1,
                actual: 0,
                context: "IncrementalPCA::partial_fit_batch requires non-empty batch".into(),
            });
        }

        // Check feature consistency if we have already seen samples.
        if self.n_samples_seen_ > 0 && n_features != self.mean_.len() {
            return Err(FerroError::ShapeMismatch {
                expected: vec![self.mean_.len()],
                actual: vec![n_features],
                context: "IncrementalPCA::partial_fit_batch: feature dimension mismatch".into(),
            });
        }

        // Reject NaN/Inf BEFORE any incremental-SVD math (sklearn
        // `_validate_data(force_all_finite=True)` at `_incremental_pca.py:227`
        // (fit) / `:281` (partial_fit), `utils/validation.py:147-154`).
        reject_non_finite(x_batch)?;

        let n_components = self.components_.nrows();
        let last_count = self.n_samples_seen_;
        let new_n = last_count + batch_n;
        let new_n_f = F::from(new_n).unwrap_or_else(F::one);

        // ----------------------------------------------------------------
        // Update running per-feature mean and (population) variance via the
        // Youngs-Cramer / Chan parallel-variance formula, porting sklearn
        // `_incremental_mean_and_var` (`sklearn/utils/extmath.py:1057-1180`).
        // `last_sample_count` is the scalar `n_samples_seen_` broadcast over
        // all features (`_incremental_pca.py:329-334`), so the per-feature
        // counts are equal and we can use scalars.
        // ----------------------------------------------------------------
        let last_count_f = F::from(last_count).unwrap_or_else(F::zero);
        let new_count_f = F::from(batch_n).unwrap_or_else(F::one);

        // new_sum = X.sum(axis=0); batch_mean = new_sum / new_count.
        let mut new_sum = Array1::<F>::zeros(n_features);
        for row in x_batch.rows() {
            for (s, &v) in new_sum.iter_mut().zip(row.iter()) {
                *s = *s + v;
            }
        }
        let mut col_batch_mean = Array1::<F>::zeros(n_features);
        for j in 0..n_features {
            col_batch_mean[j] = new_sum[j] / new_count_f;
        }

        // last_sum = last_mean * last_count (per feature).
        // updated_mean = (last_sum + new_sum) / updated_count.
        let mut col_mean = Array1::<F>::zeros(n_features);
        for j in 0..n_features {
            let last_sum = self.mean_[j] * last_count_f;
            col_mean[j] = (last_sum + new_sum[j]) / new_n_f;
        }

        // new_unnormalized_variance = sum((X - T)^2) - correction^2 / new_count
        // where T = batch_mean and correction = sum(X - T) (the corrected
        // 2-pass term, `extmath.py:1142-1162`).
        let mut new_unnorm_var = Array1::<F>::zeros(n_features);
        {
            let mut correction = Array1::<F>::zeros(n_features);
            for row in x_batch.rows() {
                for j in 0..n_features {
                    let temp = row[j] - col_batch_mean[j];
                    correction[j] = correction[j] + temp;
                    new_unnorm_var[j] = new_unnorm_var[j] + temp * temp;
                }
            }
            for j in 0..n_features {
                new_unnorm_var[j] = new_unnorm_var[j] - correction[j] * correction[j] / new_count_f;
            }
        }

        // Combine with the prior unnormalized variance (Chan update). When
        // last_count == 0 the combined value is just the batch's.
        let mut col_var = Array1::<F>::zeros(n_features);
        for j in 0..n_features {
            let updated_unnorm_var = if last_count == 0 {
                new_unnorm_var[j]
            } else {
                let last_sum = self.mean_[j] * last_count_f;
                let last_unnorm_var = self.var_[j] * last_count_f;
                let last_over_new_count = last_count_f / new_count_f;
                let diff = last_sum / last_over_new_count - new_sum[j];
                last_unnorm_var + new_unnorm_var[j] + last_over_new_count / new_n_f * diff * diff
            };
            col_var[j] = updated_unnorm_var / new_n_f;
        }

        // ----------------------------------------------------------------
        // Whitening + build the stacked matrix M (`_incremental_pca.py:337-354`).
        // First step: centre by `col_mean`, M = X_centred. Otherwise centre by
        // the BATCH mean and stack THREE blocks:
        //   [ singular_values * components ; X_batch_centred ; mean_correction ]
        // with mean_correction a single length-`n_features` row
        //   sqrt((n_samples_seen / n_total) * n_batch) * (mean_ - col_batch_mean).
        // ----------------------------------------------------------------
        let m_mat: Array2<F> = if last_count == 0 || n_components == 0 {
            let mut x_centred = x_batch.to_owned();
            for mut row in x_centred.rows_mut() {
                for (v, &m) in row.iter_mut().zip(col_mean.iter()) {
                    *v = *v - m;
                }
            }
            x_centred
        } else {
            // Batch-mean-centred data.
            let mut x_centred = x_batch.to_owned();
            for mut row in x_centred.rows_mut() {
                for (v, &m) in row.iter_mut().zip(col_batch_mean.iter()) {
                    *v = *v - m;
                }
            }

            // Block 1: singular_values[:,None] * components_.
            let mut weighted = Array2::zeros((n_components, n_features));
            for k in 0..n_components {
                let sv = self.singular_values_[k];
                for j in 0..n_features {
                    weighted[[k, j]] = sv * self.components_[[k, j]];
                }
            }

            // Block 3: mean_correction row.
            let scale = (last_count_f / new_n_f * new_count_f).sqrt();
            let mut mean_correction = Array2::zeros((1, n_features));
            for j in 0..n_features {
                mean_correction[[0, j]] = scale * (self.mean_[j] - col_batch_mean[j]);
            }

            // Stack: [weighted ; x_centred ; mean_correction].
            let top = stack_vertical(&weighted, &x_centred);
            stack_vertical(&top, &mean_correction)
        };

        // ----------------------------------------------------------------
        // Thin SVD of M.
        // ----------------------------------------------------------------
        let max_rank = m_mat.nrows().min(m_mat.ncols()).min(n_components);
        if max_rank == 0 {
            self.mean_ = col_mean;
            self.var_ = col_var;
            self.n_samples_seen_ = new_n;
            return Ok(());
        }

        let (_, sigma, vt) = thin_svd(&m_mat, max_rank)?;

        // ----------------------------------------------------------------
        // Update components and singular values, applying
        // `svd_flip(u_based_decision=False)` (`_incremental_pca.py:357`,
        // `extmath.py:897-905`): for each Vt row find the column index of the
        // max ABS value (numpy `argmax` → FIRST on ties, via strict `>`); if
        // that entry is negative, negate the WHOLE row so its max-abs entry is
        // positive. Same convention as `pca.rs`.
        // ----------------------------------------------------------------
        for k in 0..n_components.min(max_rank) {
            for j in 0..n_features {
                self.components_[[k, j]] = vt[[k, j]];
            }
            self.singular_values_[k] = if k < sigma.len() { sigma[k] } else { F::zero() };

            let mut j_max = 0usize;
            let mut max_abs = self.components_[[k, 0]].abs();
            for j in 1..n_features {
                let abs_j = self.components_[[k, j]].abs();
                if abs_j > max_abs {
                    max_abs = abs_j;
                    j_max = j;
                }
            }
            if self.components_[[k, j_max]] < F::zero() {
                for j in 0..n_features {
                    self.components_[[k, j]] = -self.components_[[k, j]];
                }
            }
        }
        // Zero out any components beyond max_rank if n_components > max_rank.
        for k in max_rank..n_components {
            for j in 0..n_features {
                self.components_[[k, j]] = F::zero();
            }
            self.singular_values_[k] = F::zero();
        }

        // ----------------------------------------------------------------
        // Explained variance / ratio (`_incremental_pca.py:358-359`):
        //   explained_variance      = S^2 / (n_total - 1)
        //   explained_variance_ratio = S^2 / sum(col_var * n_total)
        // The ratio denominator is the TOTAL feature variance, NOT the sum of
        // the retained explained variances.
        // ----------------------------------------------------------------
        let denom = F::from(new_n.saturating_sub(1).max(1)).unwrap_or_else(F::one);
        for k in 0..n_components {
            let sv = self.singular_values_[k];
            self.explained_variance_[k] = sv * sv / denom;
        }

        let mut total_feature_var = F::zero();
        for j in 0..n_features {
            total_feature_var = total_feature_var + col_var[j] * new_n_f;
        }
        if total_feature_var > F::zero() {
            for k in 0..n_components {
                let sv = self.singular_values_[k];
                self.explained_variance_ratio_[k] = sv * sv / total_feature_var;
            }
        } else {
            for k in 0..n_components {
                self.explained_variance_ratio_[k] = F::zero();
            }
        }

        // Update state.
        self.mean_ = col_mean;
        self.var_ = col_var;
        self.n_samples_seen_ = new_n;

        Ok(())
    }
}

// ---------------------------------------------------------------------------
// IncrementalPCA: partial_fit (public streaming API)
// ---------------------------------------------------------------------------

impl<F: Float + Send + Sync + 'static> IncrementalPCA<F> {
    /// Process a single batch and return the updated fitted model.
    ///
    /// Calling `partial_fit` repeatedly on successive batches gives the same
    /// result as calling `fit` on the concatenation of all batches (up to
    /// floating-point rounding).
    ///
    /// The first call initialises the model; subsequent calls update it.
    ///
    /// # Errors
    ///
    /// - [`FerroError::InvalidParameter`] if `n_components == 0` or
    ///   `n_components >= n_features`.
    /// - [`FerroError::InsufficientSamples`] if the batch is empty.
    /// - [`FerroError::ShapeMismatch`] if the batch has the wrong number of
    ///   features after the first batch.
    pub fn partial_fit(
        &self,
        x_batch: &Array2<F>,
        state: Option<FittedIncrementalPCA<F>>,
    ) -> Result<FittedIncrementalPCA<F>, FerroError> {
        let n_features = x_batch.ncols();

        if self.n_components == 0 {
            return Err(FerroError::InvalidParameter {
                name: "n_components".into(),
                reason: "must be at least 1".into(),
            });
        }
        if n_features == 0 {
            return Err(FerroError::InvalidParameter {
                name: "n_features".into(),
                reason: "must be at least 1".into(),
            });
        }
        if self.n_components >= n_features {
            return Err(FerroError::InvalidParameter {
                name: "n_components".into(),
                reason: format!(
                    "n_components ({}) must be < n_features ({})",
                    self.n_components, n_features
                ),
            });
        }

        let mut fitted = state.unwrap_or_else(|| FittedIncrementalPCA {
            components_: Array2::zeros((self.n_components, n_features)),
            explained_variance_: Array1::zeros(self.n_components),
            explained_variance_ratio_: Array1::zeros(self.n_components),
            mean_: Array1::zeros(n_features),
            var_: Array1::zeros(n_features),
            n_samples_seen_: 0,
            singular_values_: Array1::zeros(self.n_components),
        });

        fitted.partial_fit_batch(x_batch)?;
        Ok(fitted)
    }
}

// ---------------------------------------------------------------------------
// Fit trait
// ---------------------------------------------------------------------------

impl<F: Float + Send + Sync + 'static> Fit<Array2<F>, ()> for IncrementalPCA<F> {
    type Fitted = FittedIncrementalPCA<F>;
    type Error = FerroError;

    /// Fit the model by processing the data in mini-batches.
    ///
    /// If `batch_size` is `None`, the entire dataset is processed in one batch.
    ///
    /// # Errors
    ///
    /// - [`FerroError::InvalidParameter`] if `n_components == 0`,
    ///   `n_components >= n_features`, or `batch_size == 0`.
    /// - [`FerroError::InsufficientSamples`] if there are fewer than 2 samples.
    fn fit(&self, x: &Array2<F>, _y: &()) -> Result<FittedIncrementalPCA<F>, FerroError> {
        let (n_samples, n_features) = x.dim();

        if self.n_components == 0 {
            return Err(FerroError::InvalidParameter {
                name: "n_components".into(),
                reason: "must be at least 1".into(),
            });
        }
        if n_features == 0 {
            return Err(FerroError::InvalidParameter {
                name: "n_features".into(),
                reason: "must be at least 1".into(),
            });
        }
        if self.n_components >= n_features {
            return Err(FerroError::InvalidParameter {
                name: "n_components".into(),
                reason: format!(
                    "n_components ({}) must be < n_features ({})",
                    self.n_components, n_features
                ),
            });
        }
        if n_samples < 2 {
            return Err(FerroError::InsufficientSamples {
                required: 2,
                actual: n_samples,
                context: "IncrementalPCA::fit requires at least 2 samples".into(),
            });
        }

        let batch_size = match self.batch_size {
            Some(bs) => {
                if bs == 0 {
                    return Err(FerroError::InvalidParameter {
                        name: "batch_size".into(),
                        reason: "must be at least 1 when specified".into(),
                    });
                }
                bs
            }
            // sklearn: `batch_size_ = 5 * n_features` when `batch_size is None`
            // (`sklearn/decomposition/_incremental_pca.py:236-237`), to balance
            // approximation accuracy and memory. `5*n_features` may exceed
            // `n_samples` (→ a single batch, handled by the gen_batches loop
            // below — no panic, R-CODE-2).
            None => 5 * n_features,
        };

        // Slice into batches exactly like sklearn's
        // `gen_batches(n_samples, batch_size_, min_batch_size=self.n_components or 0)`
        // (`sklearn/decomposition/_incremental_pca.py:241-243`,
        // `sklearn/utils/_chunking.py:67-75`). The `min_batch_size = n_components`
        // term MERGES a trailing remainder smaller than `n_components` into the
        // previous full batch (e.g. 20 rows, batch_size 6, n_components 3 →
        // batches 6+6+8, NOT 6+6+6+2), so the incremental merge sequence — and
        // hence `components_`/`singular_values_`/`explained_variance_` — matches
        // sklearn (#2386).
        let min_batch_size = self.n_components;
        let mut state: Option<FittedIncrementalPCA<F>> = None;
        let mut start = 0;
        for _ in 0..(n_samples / batch_size) {
            let end = start + batch_size;
            // Skip this full batch when the remainder after it would be a
            // too-small trailing batch (`end + min_batch_size > n`): leave
            // `start` unchanged so the trailing rows fold into the final slice.
            if end + min_batch_size > n_samples {
                continue;
            }
            let batch = x.slice(ndarray::s![start..end, ..]).to_owned();
            state = Some(self.partial_fit(&batch, state)?);
            start = end;
        }
        if start < n_samples {
            let batch = x.slice(ndarray::s![start..n_samples, ..]).to_owned();
            state = Some(self.partial_fit(&batch, state)?);
        }

        state.ok_or_else(|| FerroError::InsufficientSamples {
            required: 1,
            actual: 0,
            context: "IncrementalPCA::fit: no batches processed".into(),
        })
    }
}

// ---------------------------------------------------------------------------
// Transform trait
// ---------------------------------------------------------------------------

impl<F: Float + Send + Sync + 'static> Transform<Array2<F>> for FittedIncrementalPCA<F> {
    type Output = Array2<F>;
    type Error = FerroError;

    /// Project data onto the principal components: `(X - mean) @ components^T`.
    ///
    /// # Errors
    ///
    /// Returns [`FerroError::ShapeMismatch`] if the number of columns does not
    /// match the number of features seen during fitting.
    fn transform(&self, x: &Array2<F>) -> Result<Array2<F>, FerroError> {
        let n_features = self.mean_.len();
        if x.ncols() != n_features {
            return Err(FerroError::ShapeMismatch {
                expected: vec![x.nrows(), n_features],
                actual: vec![x.nrows(), x.ncols()],
                context: "FittedIncrementalPCA::transform".into(),
            });
        }

        // Reject NaN/Inf BEFORE the projection (sklearn re-validates with
        // `_validate_data(reset=False, force_all_finite=True)` at
        // `_incremental_pca.py:281`, `utils/validation.py:147-154`).
        reject_non_finite(x)?;

        let mut x_centred = x.to_owned();
        for mut row in x_centred.rows_mut() {
            for (v, &m) in row.iter_mut().zip(self.mean_.iter()) {
                *v = *v - m;
            }
        }

        // Project: X_centred @ components^T
        Ok(x_centred.dot(&self.components_.t()))
    }
}

// ---------------------------------------------------------------------------
// Internal linear algebra helpers (no external SVD library needed)
// ---------------------------------------------------------------------------

/// Stack two matrices vertically: `[a; b]`.
fn stack_vertical<F: Float>(a: &Array2<F>, b: &Array2<F>) -> Array2<F> {
    let na = a.nrows();
    let nb = b.nrows();
    let p = a.ncols();
    let mut out = Array2::zeros((na + nb, p));
    for i in 0..na {
        for j in 0..p {
            out[[i, j]] = a[[i, j]];
        }
    }
    for i in 0..nb {
        for j in 0..p {
            out[[na + i, j]] = b[[i, j]];
        }
    }
    out
}

/// `(U, sigma, Vt)` triple returned by [`thin_svd`].
type SvdTriple<F> = (Array2<F>, Array1<F>, Array2<F>);

/// Thin SVD of the merge matrix `m` via `ferray::linalg::svd_lapack` (LAPACK
/// `gesdd`) for f64/f32, with a Jacobi-eigendecomposition fallback for exotic
/// float types.
///
/// This routes the incremental-PCA merge SVD through the SAME LAPACK `gesdd`
/// driver `scipy.linalg.svd(X, full_matrices=False)` calls in sklearn's
/// `IncrementalPCA.partial_fit` (`sklearn/decomposition/_incremental_pca.py:356`),
/// exactly as `pca.rs` does for `PCA`'s `full` solver. The hand-rolled Jacobi
/// `thin_svd` failed to reproduce LAPACK's SVD of the recursively-stacked merge
/// matrix to working precision (single-batch ~1e-15; 4-batch ~1e-2 — far past
/// the R-DEV-1 ~1e-6 bar, #2386); LAPACK `gesdd` is bit-identical to scipy
/// (ferray #2116), so the multi-batch spectrum now matches sklearn.
///
/// Returns `(U, sigma, Vt)` where:
/// - `sigma` has length `max_rank`, sorted descending (non-increasing, the
///   LAPACK `gesdd` contract).
/// - `Vt` has shape `(max_rank, n_features)`, row `k` = `k`-th right singular
///   vector — exactly sklearn's `Vt[:n_components_]` (`_incremental_pca.py:362`).
/// - `U` is unused by the caller (sklearn's `svd_flip(U, Vt,
///   u_based_decision=False)` only needs `Vt`), so an empty `(nr, 0)` matrix is
///   returned to keep the SVD engine from doing wasted work.
///
/// Never panics (R-CODE-2): a `svd_lapack`/conversion failure propagates as
/// [`FerroError::NumericalInstability`].
fn thin_svd<F: Float + Send + Sync + 'static>(
    m: &Array2<F>,
    max_rank: usize,
) -> Result<SvdTriple<F>, FerroError> {
    let (nr, nc) = m.dim();
    if nr == 0 || nc == 0 || max_rank == 0 {
        return Ok((
            Array2::zeros((nr, 0)),
            Array1::zeros(0),
            Array2::zeros((0, nc)),
        ));
    }

    let rank = max_rank.min(nr).min(nc);

    // Full thin SVD (`min(nr, nc)` singular values / Vt rows). LAPACK `gesdd`
    // for f64/f32; Jacobi fallback for exotic F. `s_full`/`vt_full` come back
    // descending, then we truncate to `rank` (sklearn truncates `Vt`/`S` to
    // `n_components_`, `_incremental_pca.py:362-363`).
    let (s_full, vt_full) = thin_svd_full(m)?;

    let mut sigma = Array1::zeros(rank);
    let mut vt = Array2::zeros((rank, nc));
    for k in 0..rank {
        sigma[k] = if k < s_full.len() {
            s_full[k]
        } else {
            F::zero()
        };
        if k < vt_full.nrows() {
            for j in 0..nc {
                vt[[k, j]] = vt_full[[k, j]];
            }
        }
    }

    // `U` is unused at the call site (svd_flip with `u_based_decision=False`
    // operates only on `Vt`); return an empty matrix.
    Ok((Array2::zeros((nr, 0)), sigma, vt))
}

/// `(S, Vt)` full thin-SVD of `m`: `S` are the `min(nr, nc)` singular values in
/// non-increasing order, `Vt` is `(min(nr, nc), nc)`. f64/f32 dispatch to
/// `ferray::linalg::svd_lapack` (LAPACK `gesdd`); other float types use the
/// Jacobi eigendecomposition of the Gram matrix as a fallback.
fn thin_svd_full<F: Float + Send + Sync + 'static>(
    m: &Array2<F>,
) -> Result<(Array1<F>, Array2<F>), FerroError> {
    // SAFETY: each branch checks `TypeId` at runtime and only reinterprets the
    // ndarray buffers when the concrete type matches (`F == f64` / `F == f32`),
    // so every transmute is between identical types. Same pattern as
    // `pca.rs::svd_dispatch`. `forget` prevents a double free of the moved-out
    // f64/f32 arrays.
    if TypeId::of::<F>() == TypeId::of::<f64>() {
        let m_f64: &Array2<f64> = unsafe { &*(std::ptr::from_ref(m).cast::<Array2<f64>>()) };
        let (s, vt) = ferray_svd_lapack_f64(m_f64)?;
        let s_f: Array1<F> = unsafe { std::mem::transmute_copy::<Array1<f64>, Array1<F>>(&s) };
        let vt_f: Array2<F> = unsafe { std::mem::transmute_copy::<Array2<f64>, Array2<F>>(&vt) };
        std::mem::forget(s);
        std::mem::forget(vt);
        Ok((s_f, vt_f))
    } else if TypeId::of::<F>() == TypeId::of::<f32>() {
        let m_f32: &Array2<f32> = unsafe { &*(std::ptr::from_ref(m).cast::<Array2<f32>>()) };
        let (s, vt) = ferray_svd_lapack_f32(m_f32)?;
        let s_f: Array1<F> = unsafe { std::mem::transmute_copy::<Array1<f32>, Array1<F>>(&s) };
        let vt_f: Array2<F> = unsafe { std::mem::transmute_copy::<Array2<f32>, Array2<F>>(&vt) };
        std::mem::forget(s);
        std::mem::forget(vt);
        Ok((s_f, vt_f))
    } else {
        // Exotic-F fallback: eigendecompose the Gram matrix C = MᵀM
        // (nc × nc). Its eigenvectors are the right singular vectors V;
        // singular values are sqrt(max(eigval, 0)), sorted descending.
        let nc = m.ncols();
        let mtm = m.t().dot(m);
        let max_iter = nc * nc * 100 + 1000;
        let (eigenvalues, eigenvectors) = jacobi_eigen_symmetric(&mtm, max_iter)?;
        let mut indices: Vec<usize> = (0..nc).collect();
        indices.sort_by(|&a, &b| {
            eigenvalues[b]
                .partial_cmp(&eigenvalues[a])
                .unwrap_or(std::cmp::Ordering::Equal)
        });
        let size = m.nrows().min(nc);
        let mut s = Array1::<F>::zeros(size);
        let mut vt = Array2::<F>::zeros((size, nc));
        for (k, &idx) in indices.iter().take(size).enumerate() {
            let ev = eigenvalues[idx];
            s[k] = if ev > F::zero() { ev.sqrt() } else { F::zero() };
            for j in 0..nc {
                vt[[k, j]] = eigenvectors[[j, idx]];
            }
        }
        Ok((s, vt))
    }
}

/// Thin SVD of an f64 matrix via `ferray::linalg::svd_lapack` (LAPACK `gesdd`),
/// mirroring `scipy.linalg.svd(X, full_matrices=False)` of sklearn's
/// `IncrementalPCA.partial_fit` (`sklearn/decomposition/_incremental_pca.py:356`).
/// Returns `(s, vt)`: `s` the `min(m, n)` singular values descending, `vt` the
/// `(min(m, n), n)` right singular vectors. `U` is not needed (svd_flip uses
/// only `Vt`). Copies the `pca.rs::ferray_svd_lapack_f64` bridge (R-SUBSTRATE-4).
fn ferray_svd_lapack_f64(a: &Array2<f64>) -> Result<(Array1<f64>, Array2<f64>), FerroError> {
    let (m, n) = a.dim();
    let data: Vec<f64> = a.iter().copied().collect();
    let fa = ferray::Array::<f64, ferray::Ix2>::from_vec(ferray::Ix2::new([m, n]), data).map_err(
        |e| FerroError::NumericalInstability {
            message: format!("ferray array construction failed: {e}"),
        },
    )?;
    let (_u, s, vt) =
        ferray::linalg::svd_lapack(&fa, false).map_err(|e| FerroError::NumericalInstability {
            message: format!("ferray svd_lapack (gesdd) failed: {e}"),
        })?;
    let s_nd: Array1<f64> = s.into_ndarray();
    let vt_nd: Array2<f64> = vt.into_ndarray();
    Ok((s_nd, vt_nd))
}

/// Thin SVD of an f32 matrix via `ferray::linalg::svd_lapack` (LAPACK `gesdd`).
/// See [`ferray_svd_lapack_f64`].
fn ferray_svd_lapack_f32(a: &Array2<f32>) -> Result<(Array1<f32>, Array2<f32>), FerroError> {
    let (m, n) = a.dim();
    let data: Vec<f32> = a.iter().copied().collect();
    let fa = ferray::Array::<f32, ferray::Ix2>::from_vec(ferray::Ix2::new([m, n]), data).map_err(
        |e| FerroError::NumericalInstability {
            message: format!("ferray array construction failed: {e}"),
        },
    )?;
    let (_u, s, vt) =
        ferray::linalg::svd_lapack(&fa, false).map_err(|e| FerroError::NumericalInstability {
            message: format!("ferray svd_lapack (gesdd) failed: {e}"),
        })?;
    let s_nd: Array1<f32> = s.into_ndarray();
    let vt_nd: Array2<f32> = vt.into_ndarray();
    Ok((s_nd, vt_nd))
}

/// Jacobi eigendecomposition for symmetric matrices.
///
/// Returns `(eigenvalues, eigenvectors)` where column `i` of `eigenvectors`
/// corresponds to `eigenvalues[i]`. The output is **not** sorted.
fn jacobi_eigen_symmetric<F: Float + Send + Sync + 'static>(
    a: &Array2<F>,
    max_iter: usize,
) -> Result<(Array1<F>, Array2<F>), FerroError> {
    let n = a.nrows();
    if n == 0 {
        return Ok((Array1::zeros(0), Array2::zeros((0, 0))));
    }
    if n == 1 {
        return Ok((
            Array1::from_vec(vec![a[[0, 0]]]),
            Array2::from_shape_vec((1, 1), vec![F::one()]).unwrap(),
        ));
    }

    let mut mat = a.to_owned();
    let mut v = Array2::<F>::zeros((n, n));
    for i in 0..n {
        v[[i, i]] = F::one();
    }

    let tol = F::from(1e-12).unwrap_or_else(F::epsilon);

    for _iteration in 0..max_iter {
        // Find the off-diagonal element with the largest absolute value.
        let mut max_off = F::zero();
        let mut p = 0;
        let mut q = 1;
        for i in 0..n {
            for j in (i + 1)..n {
                let val = mat[[i, j]].abs();
                if val > max_off {
                    max_off = val;
                    p = i;
                    q = j;
                }
            }
        }

        if max_off < tol {
            let eigenvalues = Array1::from_shape_fn(n, |i| mat[[i, i]]);
            return Ok((eigenvalues, v));
        }

        let app = mat[[p, p]];
        let aqq = mat[[q, q]];
        let apq = mat[[p, q]];

        let theta = if (app - aqq).abs() < tol {
            F::from(std::f64::consts::FRAC_PI_4).unwrap_or_else(F::one)
        } else {
            let tau = (aqq - app) / (F::from(2.0).unwrap() * apq);
            let t = if tau >= F::zero() {
                F::one() / (tau.abs() + (F::one() + tau * tau).sqrt())
            } else {
                -F::one() / (tau.abs() + (F::one() + tau * tau).sqrt())
            };
            t.atan()
        };

        let c = theta.cos();
        let s = theta.sin();

        let mut new_mat = mat.clone();
        for i in 0..n {
            if i != p && i != q {
                let mip = mat[[i, p]];
                let miq = mat[[i, q]];
                new_mat[[i, p]] = c * mip - s * miq;
                new_mat[[p, i]] = new_mat[[i, p]];
                new_mat[[i, q]] = s * mip + c * miq;
                new_mat[[q, i]] = new_mat[[i, q]];
            }
        }

        new_mat[[p, p]] = c * c * app - F::from(2.0).unwrap() * s * c * apq + s * s * aqq;
        new_mat[[q, q]] = s * s * app + F::from(2.0).unwrap() * s * c * apq + c * c * aqq;
        new_mat[[p, q]] = F::zero();
        new_mat[[q, p]] = F::zero();
        mat = new_mat;

        for i in 0..n {
            let vip = v[[i, p]];
            let viq = v[[i, q]];
            v[[i, p]] = c * vip - s * viq;
            v[[i, q]] = s * vip + c * viq;
        }
    }

    Err(FerroError::ConvergenceFailure {
        iterations: max_iter,
        message: "Jacobi eigendecomposition did not converge in IncrementalPCA".into(),
    })
}

// ---------------------------------------------------------------------------
// Tests
// ---------------------------------------------------------------------------

#[cfg(test)]
mod tests {
    use super::*;
    use approx::assert_abs_diff_eq;
    use ndarray::array;

    // -----------------------------------------------------------------------
    // Basic shape and structure tests
    // -----------------------------------------------------------------------

    #[test]
    fn test_fit_output_shape() {
        let ipca = IncrementalPCA::<f64>::new(1);
        let x = array![[1.0, 2.0], [3.0, 4.0], [5.0, 6.0], [7.0, 8.0]];
        let fitted = ipca.fit(&x, &()).unwrap();
        assert_eq!(fitted.components().dim(), (1, 2));
        assert_eq!(fitted.explained_variance().len(), 1);
        assert_eq!(fitted.explained_variance_ratio().len(), 1);
        assert_eq!(fitted.mean().len(), 2);
        assert_eq!(fitted.n_samples_seen(), 4);
    }

    #[test]
    fn test_transform_output_shape() {
        let ipca = IncrementalPCA::<f64>::new(1);
        let x = array![[1.0, 2.0], [3.0, 4.0], [5.0, 6.0], [7.0, 8.0]];
        let fitted = ipca.fit(&x, &()).unwrap();
        let projected = fitted.transform(&x).unwrap();
        assert_eq!(projected.dim(), (4, 1));
    }

    #[test]
    fn test_fit_two_components() {
        let ipca = IncrementalPCA::<f64>::new(2);
        let x = array![
            [1.0, 2.0, 3.0],
            [4.0, 5.0, 6.0],
            [7.0, 8.0, 9.0],
            [10.0, 11.0, 12.0],
        ];
        let fitted = ipca.fit(&x, &()).unwrap();
        assert_eq!(fitted.components().dim(), (2, 3));

        let projected = fitted.transform(&x).unwrap();
        assert_eq!(projected.dim(), (4, 2));
    }

    #[test]
    fn test_mean_is_correct() {
        // Column means for [[0,0],[2,4]] should be [1, 2].
        let ipca = IncrementalPCA::<f64>::new(1);
        let x = array![[0.0, 0.0], [2.0, 4.0]];
        let fitted = ipca.fit(&x, &()).unwrap();
        assert_abs_diff_eq!(fitted.mean()[0], 1.0, epsilon = 1e-10);
        assert_abs_diff_eq!(fitted.mean()[1], 2.0, epsilon = 1e-10);
    }

    #[test]
    fn test_explained_variance_positive() {
        let ipca = IncrementalPCA::<f64>::new(1);
        let x = array![[1.0, 2.0], [3.0, 4.0], [5.0, 6.0], [7.0, 8.0]];
        let fitted = ipca.fit(&x, &()).unwrap();
        for &v in fitted.explained_variance() {
            assert!(v >= 0.0, "explained variance should be non-negative: {v}");
        }
    }

    #[test]
    fn test_explained_variance_ratio_in_unit_interval() {
        let ipca = IncrementalPCA::<f64>::new(1);
        let x = array![[1.0, 2.0], [3.0, 4.0], [5.0, 6.0], [7.0, 8.0]];
        let fitted = ipca.fit(&x, &()).unwrap();
        let ratio_sum: f64 = fitted.explained_variance_ratio().iter().sum();
        assert!(
            (0.0..=1.0 + 1e-10).contains(&ratio_sum),
            "ratio sum {ratio_sum} not in [0,1]"
        );
    }

    #[test]
    fn test_batch_size_single_batch() {
        // batch_size == n_samples should give the same result as no batch_size.
        let ipca_no_bs = IncrementalPCA::<f64>::new(1);
        let ipca_bs = IncrementalPCA::<f64>::new(1).with_batch_size(4);
        let x = array![[1.0, 2.0], [3.0, 4.0], [5.0, 6.0], [7.0, 8.0]];

        let fitted_no_bs = ipca_no_bs.fit(&x, &()).unwrap();
        let fitted_bs = ipca_bs.fit(&x, &()).unwrap();

        // Means should be identical.
        for (a, b) in fitted_no_bs.mean().iter().zip(fitted_bs.mean().iter()) {
            assert_abs_diff_eq!(a, b, epsilon = 1e-10);
        }
        assert_eq!(fitted_no_bs.n_samples_seen(), fitted_bs.n_samples_seen());
    }

    #[test]
    fn test_batch_size_two_batches() {
        let ipca = IncrementalPCA::<f64>::new(1).with_batch_size(2);
        let x = array![[1.0, 2.0], [3.0, 4.0], [5.0, 6.0], [7.0, 8.0]];
        let fitted = ipca.fit(&x, &()).unwrap();
        assert_eq!(fitted.n_samples_seen(), 4);
        assert_eq!(fitted.components().dim(), (1, 2));
    }

    #[test]
    fn test_partial_fit_chaining() {
        // Fit in two batches using partial_fit.
        let ipca = IncrementalPCA::<f64>::new(1);
        let b1 = array![[1.0, 2.0], [3.0, 4.0]];
        let b2 = array![[5.0, 6.0], [7.0, 8.0]];

        let state1 = ipca.partial_fit(&b1, None).unwrap();
        assert_eq!(state1.n_samples_seen(), 2);

        let state2 = ipca.partial_fit(&b2, Some(state1)).unwrap();
        assert_eq!(state2.n_samples_seen(), 4);
    }

    #[test]
    fn test_transform_shape_mismatch_error() {
        let ipca = IncrementalPCA::<f64>::new(1);
        let x = array![[1.0, 2.0], [3.0, 4.0], [5.0, 6.0], [7.0, 8.0]];
        let fitted = ipca.fit(&x, &()).unwrap();
        let x_bad = array![[1.0, 2.0, 3.0]];
        assert!(fitted.transform(&x_bad).is_err());
    }

    #[test]
    fn test_invalid_n_components_zero_error() {
        let ipca = IncrementalPCA::<f64>::new(0);
        let x = array![[1.0, 2.0], [3.0, 4.0], [5.0, 6.0]];
        assert!(ipca.fit(&x, &()).is_err());
    }

    #[test]
    fn test_invalid_n_components_ge_n_features_error() {
        let ipca = IncrementalPCA::<f64>::new(2);
        let x = array![[1.0, 2.0], [3.0, 4.0], [5.0, 6.0]];
        assert!(ipca.fit(&x, &()).is_err());
    }

    #[test]
    fn test_insufficient_samples_error() {
        let ipca = IncrementalPCA::<f64>::new(1);
        let x = array![[1.0, 2.0]]; // only 1 sample
        assert!(ipca.fit(&x, &()).is_err());
    }

    #[test]
    fn test_zero_batch_size_error() {
        let ipca = IncrementalPCA::<f64>::new(1).with_batch_size(0);
        let x = array![[1.0, 2.0], [3.0, 4.0], [5.0, 6.0]];
        assert!(ipca.fit(&x, &()).is_err());
    }

    #[test]
    fn test_f32_support() {
        let ipca = IncrementalPCA::<f32>::new(1);
        let x: Array2<f32> = array![[1.0f32, 2.0], [3.0, 4.0], [5.0, 6.0], [7.0, 8.0]];
        let fitted = ipca.fit(&x, &()).unwrap();
        let projected = fitted.transform(&x).unwrap();
        assert_eq!(projected.ncols(), 1);
    }

    #[test]
    fn test_components_approx_unit_length() {
        let ipca = IncrementalPCA::<f64>::new(1);
        let x = array![[2.5, 2.4], [0.5, 0.7], [2.2, 2.9], [1.9, 2.2], [3.1, 3.0],];
        let fitted = ipca.fit(&x, &()).unwrap();
        let c = fitted.components();
        for i in 0..c.nrows() {
            let norm: f64 = c.row(i).iter().map(|v| v * v).sum::<f64>().sqrt();
            assert_abs_diff_eq!(norm, 1.0, epsilon = 1e-6);
        }
    }

    #[test]
    fn test_n_samples_seen() {
        let ipca = IncrementalPCA::<f64>::new(1).with_batch_size(3);
        let x = array![[1.0, 2.0], [3.0, 4.0], [5.0, 6.0], [7.0, 8.0], [9.0, 10.0]];
        let fitted = ipca.fit(&x, &()).unwrap();
        assert_eq!(fitted.n_samples_seen(), 5);
    }

    #[test]
    fn test_getters() {
        let ipca = IncrementalPCA::<f64>::new(2).with_batch_size(50);
        assert_eq!(ipca.n_components(), 2);
        assert_eq!(ipca.batch_size(), Some(50));

        let ipca2 = IncrementalPCA::<f64>::new(1);
        assert!(ipca2.batch_size().is_none());
    }
}