Initial commit of pivoted cholesky algorith from GPyTorch

Author: kunalghosh

pymc/gp/pivoted_cholesky.py

@@ -0,0 +1,63 @@
+import numpy as np
+import torch
+
+from gpytorch.utils.permutation import apply_permutation
+
+pp = lambda x: np.array2string(x, precision=4, floatmode="fixed")
+
+
+def pivoted_cholesky_np_gpt(mat: np.matrix, error_tol=1e-6, max_iter=np.Infinity):
+    """
+    mat: numpy matrix of N x N
+
+    This is to replicate what is done in GPyTorch verbatim.
+    """
+    n = mat.shape[-1]
+    max_iter = min(int(max_iter), n)
+
+    d = np.array(np.diag(mat))
+    orig_error = np.max(d)
+    error = np.linalg.norm(d, 1) / orig_error
+    pi = np.arange(n)
+
+    L = np.zeros((max_iter, n))
+
+    m = 0
+    while m < max_iter and error > error_tol:
+        permuted_d = d[pi]
+        max_diag_idx = np.argmax(permuted_d[m:])
+        max_diag_idx = max_diag_idx + m
+        max_diag_val = permuted_d[max_diag_idx]
+        i = max_diag_idx
+
+        # swap pi_m and pi_i
+        pi[m], pi[i] = pi[i], pi[m]
+        pim = pi[m]
+
+        L[m, pim] = np.sqrt(max_diag_val)
+
+        if m + 1 < n:
+            row = apply_permutation(
+                torch.from_numpy(mat), torch.tensor(pim), right_permutation=None
+            )  # left permutation just swaps row
+            row = row.numpy().flatten()
+            pi_i = pi[m + 1 :]
+            L_m_new = row[pi_i]  # length = 9
+
+            if m > 0:
+                L_prev = L[:m, pi_i]
+                update = L[:m, pim]
+                prod = update @ L_prev
+                L_m_new = L_m_new - prod  # np.sum(prod, axis=-1)
+
+            L_m = L[m, :]
+            L_m_new = L_m_new / L_m[pim]
+            L_m[pi_i] = L_m_new
+
+            matrix_diag_current = d[pi_i]
+            d[pi_i] = matrix_diag_current - L_m_new**2
+
+            L[m, :] = L_m
+            error = np.linalg.norm(d[pi_i], 1) / orig_error
+        m = m + 1
+    return L, pi

scripts/run_mypy.py

@@ -43,6 +43,7 @@
 pymc/gp/gp.py
 pymc/gp/mean.py
 pymc/gp/util.py
+pymc/gp/pivoted_cholesky.py
 pymc/math.py
 pymc/ode/__init__.py
 pymc/ode/ode.py