Resolve #18: Levinson (chapter 5) implementation coverage testing

- removed prints from implementations and tests, added proper logging instead

.gitignore

@@ -3,8 +3,13 @@ __pycache__
 *.egg-info
 env
 .pyenv*
+.env*
 .coverage
 .vscode
 
 .ipynb_checkpoints
 
+dsp
+
+# images
+*.svg

pyssp/lattice.py

@@ -1,11 +1,14 @@
 """Implementation of algorithm from Chapter 6."""
 
+import logging
 from typing import NoReturn
 
 import numpy as np
 import scipy as sp
 from numpy.typing import ArrayLike
 
+logger = logging.getLogger(__name__)
+
 
 def fcov(x: ArrayLike, p: int) -> tuple[ArrayLike, ArrayLike]:
     """Figure 6.15, Page 310.
@@ -26,19 +29,18 @@ def fcov(x: ArrayLike, p: int) -> tuple[ArrayLike, ArrayLike]:
     err = np.empty((p, 1))
 
     for j in range(p):
-        print(j)
+        logger.info(j)
         N = N - 1
-        # print(f"{eplus=}, {eplus.shape=}")
-        # print(f"{eminus=}, {eminus.shape=}")
+        logger.info(f"{eplus=}, {eplus.shape=}")
+        logger.info(f"{eminus=}, {eminus.shape=}")
         gamma[j] = (np.transpose(-eminus) @ eplus) / (np.transpose(eminus) @ eminus)
         temp1 = eplus + gamma[j] * eminus
         temp2 = eminus + np.conjugate(gamma[j]) * eplus
         err[j] = np.transpose(temp1) @ temp1
         eplus = temp1[1:N]
         eminus = temp2[:N - 1]
-        print(gamma)
-        print(err)
-        print()
+        logger.info(gamma)
+        logger.info(err)
 
     return gamma, err
 
@@ -60,10 +62,10 @@ def burg(x: ArrayLike, p: int) -> tuple[ArrayLike, ArrayLike]:
     err = np.empty((p, 1))
 
     for j in range(p):
-        print(j)
+        logger.info(j)
         N = N - 1
-        # print(f"{eplus=}, {eplus.shape=}")
-        # print(f"{eminus=}, {eminus.shape=}")
+        logger.info(f"{eplus=}, {eplus.shape=}")
+        logger.info(f"{eminus=}, {eminus.shape=}")
         eplusmag = np.transpose(eplus) @ eplus
         eminusmag = np.transpose(eplus) @ eplus
         gamma[j] = (np.transpose(-2 * eminus) @ eplus) / (eplusmag + eminusmag)
@@ -72,7 +74,6 @@ def burg(x: ArrayLike, p: int) -> tuple[ArrayLike, ArrayLike]:
         err[j] = np.transpose(temp1) @ temp1 + np.transpose(temp2) @ temp2
         eplus = temp1[1:N]
         eminus = temp2[:N - 1]
-        print()
 
     return gamma, err
 
@@ -105,7 +106,6 @@ def mcov(x: ArrayLike, p: int) -> tuple[ArrayLike, ArrayLike]:
     b = b1 + b2
     a = sp.linalg.solve_toeplitz(Rx[:, 1], b)
     a = np.concatenate(([1], a))
-    # print(a.shape)
     err = np.dot(R[0], a) + np.dot(np.flip(R[p]), a)
 
     return a, err

pyssp/levinson.py

@@ -1,9 +1,13 @@
 """Chapter 5 algorithm implementations."""
 
+import logging
+from typing import NoReturn
 
 import numpy as np
 from numpy.typing import ArrayLike
 
+logger = logging.getLogger()
+
 
 def rtoa(r: ArrayLike) -> tuple[np.ndarray, float]:
     """Recursively map a set of autocorrelations to a set of model parameters.
@@ -22,8 +26,8 @@ def rtoa(r: ArrayLike) -> tuple[np.ndarray, float]:
         anT = np.conjugate(np.flipud(a))
         a = an + gamma * np.concatenate((np.zeros(1), anT.ravel())).reshape(-1, 1)
         epsilon = epsilon * (1 - np.abs(gamma)**2)
-        print(f"{gamma=},\n{a=},\n{epsilon=}\n")
-    return a, epsilon
+        logger.info(f"{gamma=},\n{a=},\n{epsilon=}\n")
+    return a.ravel(), epsilon.ravel()[0]
 
 
 def gtoa(gamma: ArrayLike) -> ArrayLike:
@@ -40,13 +44,13 @@ def gtoa(gamma: ArrayLike) -> ArrayLike:
     a = np.ones((1, 1))
     _g = np.array(gamma)
     p = len(_g)
-    for j in range(1, p):
+    for j in range(1, p + 1):
         a = np.concatenate((a, np.zeros((1, 1))))
         _a = a.copy()
         af = np.conjugate(np.flipud(_a))
-        a = a + _g[j] * af
+        a = a + _g[j - 1] * af
 
-    return a
+    return a.ravel()
 
 
 def atog(a: ArrayLike) -> ArrayLike:
@@ -70,23 +74,25 @@ def atog(a: ArrayLike) -> ArrayLike:
     gamma[p - 2] = _a[p - 2]
 
     for j in range(p - 2, 0, -1):
-        # print(f"{gamma=}, {_a=}")
+        # logger.info(f"{gamma=}, {_a=}")
         ai1 = _a[:j].copy()
         ai2 = _a[:j].copy()
         af = np.flipud(np.conjugate(ai1))
-        # print(f"{ai1=}, {ai2=}, {af=}")
+        # logger.info(f"{ai1=}, {ai2=}, {af=}")
         s1 = ai2 - gamma[j] * af
         s2 = 1 - np.abs(gamma[j])**2
         _a = np.divide(s1, s2)
-        # print(f"{s1=}, {s2=}, {_a=}")
+        # logger.info(f"{s1=}, {s2=}, {_a=}")
         gamma[j - 1] = _a[j - 1]
 
-    return gamma
+    return gamma.ravel()
 
 
 def gtor(gamma: ArrayLike, epsilon: None | float = None) -> ArrayLike:
     """Find the autocorrelation sequence from the reflection coefficients and the modeling error.
 
+    Also called the Inverse Levinson-Durbin Recursion.
+
     Page 241, Figure 5.9.
     """
     _g = np.array(gamma)
@@ -99,19 +105,18 @@ def gtor(gamma: ArrayLike, epsilon: None | float = None) -> ArrayLike:
         aa0 = np.concatenate((aa, np.zeros((1, 1)))).reshape(-1, 1)
         aaf = np.conjugate(np.flipud(aa1))
         aa = aa0 + _g[j] * aaf
-        print(aa)
+        logger.info(aa)
         rf = -np.fliplr(r) @ aa
-        print(rf)
-        print(rf.shape)
-        print(r)
-        print(r.shape)
-        print()
+        logger.info(rf)
+        logger.info(rf.shape)
+        logger.info(r)
+        logger.info(r.shape)
         r = np.concatenate((r[0], rf[0])).reshape(1, -1)
 
     if epsilon is not None:
         r = r * epsilon / np.prod(1 - np.abs(gamma)**2)
 
-    return r
+    return r.ravel()
 
 
 def ator(a: ArrayLike, b: float) -> ArrayLike:
@@ -147,27 +152,39 @@ def glev(r: ArrayLike, b: ArrayLike) -> ArrayLike:
     x = np.array([_b[0] / _r[0]]).reshape(-1, 1)
     epsilon = _r[0]
     for j in range(1, p):
-        print(j)
-        print(f"{_r=}, {_r.shape=}")
+        logger.info(j)
+        logger.info(f"{_r=}, {_r.shape=}")
         _r1 = np.transpose(np.array(_r[1:j + 1]))
-        print(f"{_r1=}, {_r1.shape=}")
-        print(f"{x=}, {x.shape=}")
-        print(f"{a=}, {a.shape=}")
+        logger.info(f"{_r1=}, {_r1.shape=}")
+        logger.info(f"{x=}, {x.shape=}")
+        logger.info(f"{a=}, {a.shape=}")
         g = _r1 @ np.flipud(a)
-        print(f"{g=}, {g.shape=}")
+        logger.info(f"{g=}, {g.shape=}")
         gamma = -g / epsilon
-        print(f"{gamma=}, {gamma.shape=}")
+        logger.info(f"{gamma=}, {gamma.shape=}")
         _a0 = np.concatenate([a, [[0]]])
         _af = np.conjugate(np.flipud(_a0))
-        print(f"{_a0=}, {_a0.shape=}")
-        print(f"{_af=}, {_af.shape=}")
+        logger.info(f"{_a0=}, {_a0.shape=}")
+        logger.info(f"{_af=}, {_af.shape=}")
         a = _a0 + gamma * _af
         epsilon = epsilon * (1 - np.abs(gamma)**2)
-        print(f"{epsilon=}")
+        logger.info(f"{epsilon=}")
         delta = _r1 @ np.flipud(x)
         q = (_b[j] - delta[0, 0]) / epsilon
         x = np.concatenate([x, [[0]]])
         x = x + q * np.conjugate(np.flipud(a))
-        print()
 
-    return x
+    return x.ravel()
+
+
+def shur_cohn_test() -> NoReturn:
+    """Check stability of any rational filter."""
+    raise NotImplementedError()
+
+
+def splitlev(r: ArrayLike, b: ArrayLike) -> ArrayLike:
+    """Implement the split levinson recursion.
+
+    Table 5.7, Page 274.
+    """
+    raise NotImplementedError()

pyssp/modeling.py

@@ -142,7 +142,7 @@ def covm(x: ArrayLike, p: int)-> tuple[ArrayLike, float]:
     X = convm(_x, p + 1)
     Xq = X[p - 1:N - 1, :p].copy()
     Xsol = np.linalg.lstsq(-Xq, X[p:N, 0], rcond=None)[0]
-    logger.warning(f"{Xsol=}")
+    logger.info(f"{Xsol=}")
     a = np.hstack(([1], Xsol))
     err = np.abs(X[p:N,0] @ X[p:N,] @ a)
     return a, err.ravel()[0]

pyssp/optimal.py

@@ -1,10 +1,13 @@
 """Optimal Filters, Chapter 7."""
 
+import logging
 from typing import NoReturn
 
 import numpy as np
 from numpy.typing import ArrayLike
 
+logger = logging.getLogger(__name__)
+
 
 def kalman(y: list[float], A: ArrayLike, C: ArrayLike, sigmaw: list[float],
            sigmav: list[float]) -> tuple[np.ndarray, ...]:
@@ -22,11 +25,11 @@ def kalman(y: list[float], A: ArrayLike, C: ArrayLike, sigmaw: list[float],
     Qw = np.diag(np.array(sigmaw, ndmin=1))
     Qv = np.diag(np.array(sigmav, ndmin=1))
     N = np.shape(_y)[1]
-    print(_y)
+    logger.info(_y)
 
     p = np.shape(_A)[0]
     q = np.shape(_C)[0]
-    print(f"{p}, {q}, {N=}")
+    logger.info(f"{p}, {q}, {N=}")
 
     # The a priori error covariance matrix
     P0 = np.zeros((N + 1, p, p))
@@ -66,12 +69,12 @@ def kalman(y: list[float], A: ArrayLike, C: ArrayLike, sigmaw: list[float],
     return P0, P1, K, xhat0, xhat1
 
 
-def wiener_denoise() -> None:
+def wiener_denoise() -> NoReturn:
     """Denoising based on IIR wiener filters."""
     raise NotImplementedError()
 
 
-def wiener_systemid() -> None:
+def wiener_systemid() -> NoReturn:
     """Systemid based on FIR wiener filters."""
     raise NotImplementedError()
 

tests/test_levinson.py

@@ -1,24 +1,93 @@
-""""""
+"""Test validation of levinson based recursion routines."""
 
+import logging
 
 import numpy as np
-from pyssp.levinson import glev, gtor
+from pyssp import levinson
+
+
+logger = logging.getLogger(__name__)
 
 
 def test_glev():
     '''Example 5.3.1, Page 266'''
     r = [4, 2, 1]
     b = [9, 6, 12]
 
-    res = glev(r, b)
-    print(res)
+    expected = [2, -1, 3]
+
+    sol = levinson.glev(r, b)
+    logger.info(sol)
+
+    assert np.allclose(sol, expected)
 
 
-def test_gtor():
+def test_gtor() -> None:
     '''Based on example 5.2.6'''
+    expected_rx = np.array([2, -1, -1/4, 1/8])
 
     gamma = [1/2, 1/2, 1/2]
     epsilon = 2 * (3 / 4)**3
-    res = gtor(gamma, epsilon)
-    true_results = np.array([2, -1, -1/4, 1/8])
-    print(res)
+    rx = levinson.gtor(gamma, epsilon)
+    assert np.allclose(rx, expected_rx)
+
+
+def test_atog() -> None:
+
+    a = [1, 0.5, -0.1, -0.5]
+    expected_g = np.array([0.5, 0.2, -0.5])
+
+    gamma = levinson.atog(a)
+    logger.info(gamma)
+    logger.info(expected_g)
+
+    assert np.allclose(gamma, expected_g)
+
+
+def test_rtog() -> None:
+    rx = [2, -1, -1/4, 1/8]
+    expected_g = np.array([0.5, 0.5, 0.5])
+
+    gamma = levinson.rtog(rx)
+    logger.info(gamma)
+    logger.info(expected_g)
+
+    assert np.allclose(gamma, expected_g)
+
+
+def test_ator() -> None:
+    a = [1, 1, 7/8, 1/2]
+    epsilon = 2 * (3 / 4)**3
+    b = epsilon**2
+    expected_rx = np.array([2, -1, -1/4, 1/8])
+
+    rx = levinson.ator(a, b = b)
+    logger.info(rx)
+    logger.info(expected_rx)
+
+    assert np.array_equal(rx, expected_rx)
+
+
+def test_gtoa() -> None:
+    gamma = [0.5, 0.2, -0.5]
+    expected_a = np.array([1, 0.5, -0.1, -0.5])
+
+    a = levinson.gtoa(gamma)
+    logger.info(a)
+    logger.info(expected_a)
+
+    assert np.allclose(a, expected_a)
+
+def test_rtoa() -> None:
+    rx = np.array([2, -1, -1/4, 1/8])
+    expected_a = [1, 1, 7/8, 1/2]
+    expected_eps = 2 * (3 / 4)**3
+
+    a, eps = levinson.rtoa(rx)
+
+    logger.info(f"{a=}")
+    logger.info(f"{expected_a=}")
+    logger.info(f"{eps=}")
+    logger.info(f"{expected_eps=}")
+
+    assert np.allclose(a, expected_a) and np.allclose(eps, expected_eps)