Refactor MB06 (#51)

* refactor to avoid loops

* apply Diego's suggestions

* remove useless return after error

pydomcfg/utils.py

@@ -2,7 +2,6 @@
 Utilities
 """
 
-# from itertools import product
 from typing import Hashable, Iterable, Iterator, Optional
 
 import numpy as np
@@ -80,10 +79,15 @@ def _calc_rmax(depth: DataArray) -> DataArray:
     return rmax.fillna(0)
 
 
-def _smooth_MB06(depth: DataArray, rmax: float) -> DataArray:
+def _smooth_MB06(
+    depth: DataArray,
+    rmax: float,
+    tol: float = 1.0e-8,
+    max_iter: int = 10_000,
+) -> DataArray:
     """
-    This is NEMO implementation of the direct iterative method
-    of Martinho and Batteen (2006).
+    Direct iterative method of Martinho and Batteen (2006) consistent
+    with NEMO implementation.
 
     The algorithm ensures that
 
@@ -100,87 +104,62 @@ def _smooth_MB06(depth: DataArray, rmax: float) -> DataArray:
     Parameters
     ----------
     depth: DataArray
-        Bottom depth (units: m).
+        Bottom depth.
     rmax: float
         Maximum slope parameter allowed
+    tol: float, default = 1.0e-8
+        Tolerance for the iterative method
+    max_iter: int, default = 10000
+        Maximum number of iterations
 
     Returns
     -------
     DataArray
         Smooth version of the bottom topography with
-        a maximum slope parameter < rmax (units: m).
-
+        a maximum slope parameter < rmax.
     """
 
-    # set scaling factor used for smoothing
+    # Set scaling factor used for smoothing
     zrfact = (1.0 - rmax) / (1.0 + rmax)
 
-    # getting the actual numpy array
-    # TO BE OPTIMISED
-    da_zenv = depth.copy()
-    zenv = da_zenv.data
-    nj = zenv.shape[0]
-    ni = zenv.shape[1]
-
-    # initialise temporary evelope depth arrays
-    ztmpi1 = zenv.copy()
-    ztmpi2 = zenv.copy()
-    ztmpj1 = zenv.copy()
-    ztmpj2 = zenv.copy()
-
-    # Computing the initial maximum slope parameter
-    zrmax = 1.0  # np.nanmax(_calc_rmax(depth))
-    zri = np.ones(zenv.shape)  # * zrmax
-    zrj = np.ones(zenv.shape)  # * zrmax
-
-    tol = 1.0e-8
-    itr = 0
-    max_itr = 10000
-
-    while itr <= max_itr and (zrmax - rmax) > tol:
-
-        itr += 1
-        zrmax = 0.0
-        # we set zrmax from previous r-values (zri and zrj) first
-        # if set after current r-value calculation (as previously)
-        # we could exit DO WHILE prematurely before checking r-value
-        # of current zenv
-        max_zri = np.nanmax(np.absolute(zri))
-        max_zrj = np.nanmax(np.absolute(zrj))
-        zrmax = np.nanmax([zrmax, max_zrj, max_zri])
-
-        print("Iter:", itr, "rmax: ", zrmax)
-
-        zri *= 0.0
-        zrj *= 0.0
-
-        for j in range(nj - 1):
-            for i in range(ni - 1):
-                ip1 = np.minimum(i + 1, ni)
-                jp1 = np.minimum(j + 1, nj)
-                if zenv[j, i] > 0.0 and zenv[j, ip1] > 0.0:
-                    zri[j, i] = (zenv[j, ip1] - zenv[j, i]) / (
-                        zenv[j, ip1] + zenv[j, i]
-                    )
-                if zenv[j, i] > 0.0 and zenv[jp1, i] > 0.0:
-                    zrj[j, i] = (zenv[jp1, i] - zenv[j, i]) / (
-                        zenv[jp1, i] + zenv[j, i]
-                    )
-                if zri[j, i] > rmax:
-                    ztmpi1[j, i] = zenv[j, ip1] * zrfact
-                if zri[j, i] < -rmax:
-                    ztmpi2[j, ip1] = zenv[j, i] * zrfact
-                if zrj[j, i] > rmax:
-                    ztmpj1[j, i] = zenv[jp1, i] * zrfact
-                if zrj[j, i] < -rmax:
-                    ztmpj2[jp1, i] = zenv[j, i] * zrfact
-
-        ztmpi = np.maximum(ztmpi1, ztmpi2)
-        ztmpj = np.maximum(ztmpj1, ztmpj2)
-        zenv = np.maximum(zenv, np.maximum(ztmpi, ztmpj))
-
-    da_zenv.data = zenv
-    return da_zenv
+    # Initialize envelope bathymetry
+    zenv = depth
+
+    for _ in range(max_iter):
+
+        # Initialize lists of DataArrays to concatenate
+        all_ztmp = []
+        all_zr = []
+        for dim in zenv.dims:
+
+            # Shifted arrays
+            zenv_m1 = zenv.shift({dim: -1})
+            zenv_p1 = zenv.shift({dim: +1})
+
+            # Compute zr
+            zr = (zenv_m1 - zenv) / (zenv_m1 + zenv)
+            zr = zr.where((zenv > 0) & (zenv_m1 > 0), 0)
+            for dim_name in zenv.dims:
+                zr[{dim_name: -1}] = 0
+            all_zr += [zr]
+
+            # Compute ztmp
+            zr_p1 = zr.shift({dim: +1})
+            all_ztmp += [zenv.where(zr <= rmax, zenv_m1 * zrfact)]
+            all_ztmp += [zenv.where(zr_p1 >= -rmax, zenv_p1 * zrfact)]
+
+        # Update envelope bathymetry
+        zenv = xr.concat([zenv] + all_ztmp, "dummy_dim").max("dummy_dim")
+
+        # Check target rmax
+        zr = xr.concat(all_zr, "dummy_dim")
+        if ((np.abs(zr) - rmax) <= tol).all():
+            return zenv
+
+    raise ValueError(
+        "Iterative method did NOT converge."
+        " You might want to increase the number of iterations and/or the tolerance."
+    )
 
 
 def generate_cartesian_grid(