Hosvd (#67)

* HOSVD: Preliminary outline of core functionality

* HOSVD: Fix numeric bug
* Was slicing incorrectly
* Update test to check convergence

* HOSVD: Finish output and test coverage

* TENSOR: Prune numbers real
* Real and mypy don't play nice python/mypy#3186
* This allows partial typing support of HOSVD

Author: ntjohnson1

pyttb/__init__.py

@@ -9,6 +9,7 @@
 from pyttb.cp_als import cp_als
 from pyttb.cp_apr import *
 from pyttb.export_data import export_data
+from pyttb.hosvd import hosvd
 from pyttb.import_data import import_data
 from pyttb.khatrirao import khatrirao
 from pyttb.ktensor import ktensor

pyttb/hosvd.py

@@ -0,0 +1,138 @@
+"""Higher Order SVD Implementation"""
+import warnings
+from typing import List, Optional
+
+import numpy as np
+import scipy
+
+import pyttb as ttb
+
+
+def hosvd(
+    tensor,
+    tol: float,
+    verbosity: float = 1,
+    dimorder: Optional[List[int]] = None,
+    sequential: bool = True,
+    ranks: Optional[List[int]] = None,
+):
+    """Compute sequentially-truncated higher-order SVD (Tucker).
+
+    Computes a Tucker decomposition with relative error
+    specified by tol, i.e., it computes a ttensor T such that
+    ||X-T||/||X|| <= tol.
+
+    Parameters
+    ----------
+    tensor: Tensor to factor
+    tol: Relative error to stop at
+    verbosity: Print level
+    dimorder: Order to loop through dimensions
+    sequential: Use sequentially-truncated version
+    ranks: Specify ranks to consider rather than computing
+
+    Example
+    -------
+    >>> data = np.array([[29, 39.], [63., 85.]])
+    >>> tol = 1e-4
+    >>> disable_printing = -1
+    >>> tensorInstance = ttb.tensor().from_data(data)
+    >>> result = hosvd(tensorInstance, tol, verbosity=disable_printing)
+    >>> ((result.full() - tensorInstance).norm() / tensorInstance.norm()) < tol
+    True
+    """
+    # In tucker als this is N
+    d = tensor.ndims
+
+    if ranks is not None:
+        if len(ranks) != d:
+            raise ValueError(
+                f"Ranks must be a list of length tensor ndims. Ndims: {d} but got "
+                f"ranks: {ranks}."
+            )
+    else:
+        ranks = [0] * d
+
+    # Set up dimorder if not specified (this is copy past from tucker_als
+    if not dimorder:
+        dimorder = list(range(d))
+    else:
+        if not isinstance(dimorder, list):
+            raise ValueError("Dimorder must be a list")
+        elif tuple(range(d)) != tuple(sorted(dimorder)):
+            raise ValueError(
+                "Dimorder must be a list or permutation of range(tensor.ndims)"
+            )
+
+    # TODO should unify printing throughout. Probably easier to use python logging levels
+    if verbosity > 0:
+        print("Computing HOSVD...\n")
+
+    normxsqr = (tensor**2).collapse()
+    eigsumthresh = ((tol**2) * normxsqr) / d
+
+    if verbosity > 2:
+        print(
+            f"||X||^2 = {normxsqr: g}\n"
+            f"tol = {tol: g}\n"
+            f"eigenvalue sum threshold = tol^2 ||X||^2 / d = {eigsumthresh: g}"
+        )
+
+    # Main Loop
+    factor_matrices = [np.empty(1)] * d
+    # Copy input tensor, shrinks every step for sequential
+    Y = ttb.tensor.from_tensor_type(tensor)
+
+    for k in dimorder:
+        # Compute Gram matrix
+        Yk = ttb.tenmat.from_tensor_type(Y, np.array([k])).double()
+        Z = np.dot(Yk, Yk.transpose())
+
+        # Compute eigenvalue decomposition
+        D, V = scipy.linalg.eigh(Z)
+        pi = np.argsort(-D, kind="quicksort")
+        eigvec = D[pi]
+
+        # If rank not provided compute it.
+        if ranks[k] == 0:
+            eigsum = np.cumsum(eigvec[::-1])
+            eigsum = eigsum[::-1]
+            ranks[k] = np.where(eigsum > eigsumthresh)[0][-1]
+
+            if verbosity > 5:
+                print(f"Reverse cummulative sum of evals of Gram matrix:")
+                for i in range(len(eigsum)):
+                    print_msg = f"{i: d}: {eigsum[i]: 6.4f}"
+                    if i == ranks[k]:
+                        print_msg += " <-- Cutoff"
+                    print(print_msg)
+
+        # Extract factor matrix b picking leading eigenvectors of V
+        # NOTE: Plus 1 in pi slice for inclusive range to match MATLAB
+        factor_matrices[k] = V[:, pi[0 : ranks[k] + 1]]
+
+        # Shrink!
+        if sequential:
+            Y = Y.ttm(factor_matrices[k].transpose(), k)
+    # Extract final core
+    if sequential:
+        G = Y
+    else:
+        G = Y.ttm(factor_matrices, transpose=True)
+
+    result = ttb.ttensor.from_data(G, factor_matrices)
+
+    if verbosity > 0:
+        diffnormsqr = ((tensor - result.full()) ** 2).collapse()
+        relnorm = np.sqrt(diffnormsqr / normxsqr)
+        print(f" Size of core: {G.shape}")
+        if relnorm <= tol:
+            print(f"||X-T||/||X|| = {relnorm: g} <=" f"{tol: f} (tol)")
+        else:
+            print(
+                "Tolerance not satisfied!! "
+                f"||X-T||/||X|| = {relnorm: g} >="
+                f"{tol: f} (tol)"
+            )
+            warnings.warn("Specified tolerance was not achieved")
+    return result

pyttb/tensor.py

@@ -7,7 +7,6 @@
 import warnings
 from itertools import permutations
 from math import factorial
-from numbers import Real
 from typing import Any, Callable, List, Literal, Optional, Tuple, Union
 
 import numpy as np
@@ -181,9 +180,9 @@ def collapse(
         self,
         dims: Optional[np.ndarray] = None,
         fun: Union[
-            Literal["sum"], Callable[[np.ndarray], Union[Real, np.ndarray]]
+            Literal["sum"], Callable[[np.ndarray], Union[float, np.ndarray]]
         ] = "sum",
-    ) -> Union[Real, np.ndarray, tensor]:
+    ) -> Union[float, np.ndarray, tensor]:
         """
         Collapse tensor along specified dimensions.
 
@@ -389,7 +388,7 @@ def full(self) -> tensor:
         """
         return ttb.tensor.from_data(self.data)
 
-    def innerprod(self, other: Union[tensor, ttb.sptensor, ttb.ktensor]) -> Real:
+    def innerprod(self, other: Union[tensor, ttb.sptensor, ttb.ktensor]) -> float:
         """
         Efficient inner product with a tensor
 
@@ -542,7 +541,7 @@ def issymmetric(
                 return bool((all_diffs == 0).all())
             return bool((all_diffs == 0).all()), all_diffs, all_perms
 
-    def logical_and(self, B: Union[Real, tensor]) -> tensor:
+    def logical_and(self, B: Union[float, tensor]) -> tensor:
         """
         Logical and for tensors
 
@@ -578,7 +577,7 @@ def logical_not(self) -> tensor:
         """
         return ttb.tensor.from_data(np.logical_not(self.data))
 
-    def logical_or(self, other: Union[Real, tensor]) -> tensor:
+    def logical_or(self, other: Union[float, tensor]) -> tensor:
         """
         Logical or for tensors
 
@@ -598,7 +597,7 @@ def tensor_or(x, y):
 
         return ttb.tt_tenfun(tensor_or, self, other)
 
-    def logical_xor(self, other: Union[Real, tensor]) -> tensor:
+    def logical_xor(self, other: Union[float, tensor]) -> tensor:
         """
         Logical xor for tensors
 
@@ -867,7 +866,7 @@ def reshape(self, shape: Tuple[int, ...]) -> tensor:
 
         return ttb.tensor.from_data(np.reshape(self.data, shape, order="F"), shape)
 
-    def squeeze(self) -> Union[tensor, np.ndarray, Real]:
+    def squeeze(self) -> Union[tensor, np.ndarray, float]:
         """
         Removes singleton dimensions from a tensor
 
@@ -1029,7 +1028,7 @@ def symmetrize(
     def ttm(
         self,
         matrix: Union[np.ndarray, List[np.ndarray]],
-        dims: Optional[Union[Real, np.ndarray]] = None,
+        dims: Optional[Union[float, np.ndarray]] = None,
         transpose: bool = False,
     ) -> tensor:
         """
@@ -1046,7 +1045,7 @@ def ttm(
             dims = np.arange(self.ndims)
         elif isinstance(dims, list):
             dims = np.array(dims)
-        elif isinstance(dims, Real):
+        elif isinstance(dims, (float, int, np.generic)):
             dims = np.array([dims])
 
         if isinstance(matrix, list):
@@ -1060,7 +1059,7 @@ def ttm(
             return Y
 
         if not isinstance(matrix, np.ndarray):
-            assert False, "matrix must be of type numpy.ndarray"
+            assert False, f"matrix must be of type numpy.ndarray but got:\n{matrix}"
 
         if not (dims.size == 1 and np.isin(dims, np.arange(self.ndims))):
             assert False, "dims must contain values in [0,self.dims)"

tests/test_hosvd.py

@@ -0,0 +1,67 @@
+import numpy as np
+import pytest
+
+import pyttb as ttb
+
+
+@pytest.fixture()
+def sample_tensor():
+    data = np.array([[29, 39.0], [63.0, 85.0]])
+    shape = (2, 2)
+    params = {"data": data, "shape": shape}
+    tensorInstance = ttb.tensor().from_data(data, shape)
+    return params, tensorInstance
+
+
+@pytest.mark.indevelopment
+def test_hosvd_simple_convergence(capsys, sample_tensor):
+    (data, T) = sample_tensor
+    tol = 1e-4
+    result = ttb.hosvd(T, tol)
+    assert (result.full() - T).norm() / T.norm() < tol, f"Failed to converge"
+
+    tol = 1e-4
+    result = ttb.hosvd(T, tol, sequential=False)
+    assert (
+        result.full() - T
+    ).norm() / T.norm() < tol, f"Failed to converge for non-sequential option"
+
+    impossible_tol = 1e-20
+    with pytest.warns(UserWarning):
+        result = ttb.hosvd(T, impossible_tol)
+    assert (
+        result.full() - T
+    ).norm() / T.norm() > impossible_tol, f"Converged beyond provided precision"
+
+
+@pytest.mark.indevelopment
+def test_hosvd_default_init(capsys, sample_tensor):
+    (data, T) = sample_tensor
+    _ = ttb.hosvd(T, 1)
+
+
+@pytest.mark.indevelopment
+def test_hosvd_smoke_test_verbosity(capsys, sample_tensor):
+    """For now just make sure verbosity calcs don't crash"""
+    (data, T) = sample_tensor
+    ttb.hosvd(T, 1, verbosity=10)
+
+
+@pytest.mark.indevelopment
+def test_hosvd_incorrect_ranks(capsys, sample_tensor):
+    (data, T) = sample_tensor
+    ranks = list(range(T.ndims - 1))
+    with pytest.raises(ValueError):
+        _ = ttb.hosvd(T, 1, ranks=ranks)
+
+
+@pytest.mark.indevelopment
+def test_hosvd_incorrect_dimorder(capsys, sample_tensor):
+    (data, T) = sample_tensor
+    dimorder = list(range(T.ndims - 1))
+    with pytest.raises(ValueError):
+        _ = ttb.hosvd(T, 1, dimorder=dimorder)
+
+    dimorder = 1
+    with pytest.raises(ValueError):
+        _ = ttb.hosvd(T, 1, dimorder=dimorder)