Replace 1D apply_interpolation with np.interp (#168)

* refactor: get residual matrix without a helper

* perf: remove unused derivatives from apply_interpolation

* chore: remove old residual matrix and reference to derivatives

* refactor: replace remaining apply_interpolation with np.interp

* style: remove references to old variable names

---------

Co-authored-by: John Halloran <jhalloran@oxy.edu>

Author: john-halloran

src/diffpy/snmf/snmf_class.py

@@ -303,18 +303,48 @@ def outer_loop(self):
             )
 
     def get_residual_matrix(self, components=None, weights=None, stretch=None):
-        # Initialize residual matrix as negative of source_matrix
+        """
+        Return the residuals (difference) between the source matrix and its reconstruction
+        from the given components, weights, and stretch factors.
+
+        Each component profile is stretched, interpolated to fractional positions,
+        weighted per signal, and summed to form the reconstruction. The residuals
+        are the source matrix minus this reconstruction.
+
+        Parameters
+        ----------
+        components : (signal_len, n_components) array, optional
+        weights    : (n_components, n_signals) array, optional
+        stretch    : (n_components, n_signals) array, optional
+
+        Returns
+        -------
+        residuals : (signal_len, n_signals) array
+        """
+
         if components is None:
             components = self.components
         if weights is None:
             weights = self.weights
         if stretch is None:
             stretch = self.stretch
+
         residuals = -self.source_matrix.copy()
-        # Compute transformed components for all (k, m) pairs
-        for k in range(weights.shape[0]):  # K
-            stretched_components, _, _ = apply_interpolation(stretch[k, :], components[:, k])  # Only use Ax
-            residuals += weights[k, :] * stretched_components  # Element-wise scaling and sum
+        sample_indices = np.arange(components.shape[0])  # (signal_len,)
+
+        for comp in range(components.shape[1]):  # loop over components
+            residuals += (
+                np.interp(
+                    sample_indices[:, None]
+                    / stretch[comp][None, :],  # fractional positions (signal_len, n_signals)
+                    sample_indices,  # (signal_len,)
+                    components[:, comp],  # component profile (signal_len,)
+                    left=components[0, comp],
+                    right=components[-1, comp],
+                )
+                * weights[comp][None, :]  # broadcast (n_signals,) over rows
+            )
+
         return residuals
 
     def get_objective_function(self, residuals=None, stretch=None):
@@ -579,42 +609,47 @@ def update_components(self):
 
     def update_weights(self):
         """
-        Updates weights using matrix operations, solving a quadratic program to do so.
+        Updates weights by building the stretched component matrix `stretched_comps` with np.interp
+        and solving a quadratic program for each signal.
         """
 
-        signal_length = self.signal_length
-        n_signals = self.n_signals
-
-        for m in range(n_signals):
-            t = np.zeros((signal_length, self.n_components))
-
-            # Populate t using apply_interpolation
-            for k in range(self.n_components):
-                t[:, k] = apply_interpolation(self.stretch[k, m], self.components[:, k])[0].squeeze()
-
-            # Solve quadratic problem for y
-            y = self.solve_quadratic_program(t=t, m=m)
+        sample_indices = np.arange(self.signal_length)
+        for signal in range(self.n_signals):
+            # Stretch factors for this signal across components:
+            this_stretch = self.stretch[:, signal]
+            # Build stretched_comps[:, k] by interpolating component at frac. pos. index / this_stretch[comp]
+            stretched_comps = np.empty((self.signal_length, self.n_components), dtype=self.components.dtype)
+            for comp in range(self.n_components):
+                pos = sample_indices / this_stretch[comp]
+                stretched_comps[:, comp] = np.interp(
+                    pos,
+                    sample_indices,
+                    self.components[:, comp],
+                    left=self.components[0, comp],
+                    right=self.components[-1, comp],
+                )
 
-            # Update Y
-            self.weights[:, m] = y
+            # Solve quadratic problem for a given signal and update its weight
+            new_weight = self.solve_quadratic_program(t=stretched_comps, m=signal)
+            self.weights[:, signal] = new_weight
 
     def regularize_function(self, stretch=None):
         if stretch is None:
             stretch = self.stretch
 
-        K = self.n_components
-        M = self.n_signals
-        N = self.signal_length
-
         stretched_components, d_stretch_comps, dd_stretch_comps = self.apply_interpolation_matrix(stretch=stretch)
-        intermediate = stretched_components.flatten(order="F").reshape((N * M, K), order="F")
-        residuals = intermediate.sum(axis=1).reshape((N, M), order="F") - self.source_matrix
+        intermediate = stretched_components.flatten(order="F").reshape(
+            (self.signal_length * self.n_signals, self.n_components), order="F"
+        )
+        residuals = (
+            intermediate.sum(axis=1).reshape((self.signal_length, self.n_signals), order="F") - self.source_matrix
+        )
 
         fun = self.get_objective_function(residuals, stretch)
 
-        tiled_res = np.tile(residuals, (1, K))
+        tiled_res = np.tile(residuals, (1, self.n_components))
         grad_flat = np.sum(d_stretch_comps * tiled_res, axis=0)
-        gra = grad_flat.reshape((M, K), order="F").T
+        gra = grad_flat.reshape((self.n_signals, self.n_components), order="F").T
         gra += self.rho * stretch @ (self._spline_smooth_operator.T @ self._spline_smooth_operator)
 
         # Hessian would go here
@@ -623,10 +658,10 @@ def regularize_function(self, stretch=None):
 
     def update_stretch(self):
         """
-        Updates matrix A using constrained optimization (equivalent to fmincon in MATLAB).
+        Updates stretching matrix using constrained optimization (equivalent to fmincon in MATLAB).
         """
 
-        # Flatten A for compatibility with the optimizer (since SciPy expects 1D inputs)
+        # Flatten stretch for compatibility with the optimizer (since SciPy expects 1D input)
         stretch_flat_initial = self.stretch.flatten()
 
         # Define the optimization function
@@ -648,7 +683,7 @@ def objective(stretch_vec):
             bounds=bounds,
         )
 
-        # Update A with the optimized values
+        # Update stretch with the optimized values
         self.stretch = result.x.reshape(self.stretch.shape)
 
 
@@ -683,48 +718,3 @@ def cubic_largest_real_root(p, q):
     y = np.max(real_roots, axis=0) * (delta < 0)  # Keep only real roots when delta < 0
 
     return y
-
-
-def apply_interpolation(a, x):
-    """
-    Applies an interpolation-based transformation to `x` based on scaling `a`.
-    Also computes first (`d_intr_x`) and second (`dd_intr_x`) derivatives.
-    """
-    x_len = len(x)
-
-    # Ensure `a` is an array and reshape for broadcasting
-    a = np.atleast_1d(np.asarray(a))  # Ensures a is at least 1D
-
-    # Compute fractional indices, broadcasting over `a`
-    fractional_indices = np.arange(x_len)[:, None] / a  # Shape (N, M)
-
-    integer_indices = np.floor(fractional_indices).astype(int)  # Integer part (still (N, M))
-    valid_mask = integer_indices < (x_len - 1)  # Ensure indices are within bounds
-
-    # Apply valid_mask to keep correct indices
-    idx_int = np.where(valid_mask, integer_indices, x_len - 2)  # Prevent out-of-bounds indexing (previously "I")
-    idx_frac = np.where(valid_mask, fractional_indices, integer_indices)  # Keep aligned (previously "i")
-
-    # Ensure x is a 1D array
-    x = np.asarray(x).ravel()
-
-    # Compute interpolated_x (linear interpolation)
-    interpolated_x = x[idx_int] * (1 - idx_frac + idx_int) + x[np.minimum(idx_int + 1, x_len - 1)] * (
-        idx_frac - idx_int
-    )
-
-    # Fill the tail with the last valid value
-    intr_x_tail = np.full((x_len - len(idx_int), interpolated_x.shape[1]), interpolated_x[-1, :])
-    interpolated_x = np.vstack([interpolated_x, intr_x_tail])
-
-    # Compute first derivative (d_intr_x)
-    di = -idx_frac / a
-    d_intr_x = x[idx_int] * (-di) + x[np.minimum(idx_int + 1, x_len - 1)] * di
-    d_intr_x = np.vstack([d_intr_x, np.zeros((x_len - len(idx_int), d_intr_x.shape[1]))])
-
-    # Compute second derivative (dd_intr_x)
-    ddi = -di / a + idx_frac * a**-2
-    dd_intr_x = x[idx_int] * (-ddi) + x[np.minimum(idx_int + 1, x_len - 1)] * ddi
-    dd_intr_x = np.vstack([dd_intr_x, np.zeros((x_len - len(idx_int), dd_intr_x.shape[1]))])
-
-    return interpolated_x, d_intr_x, dd_intr_x