0.34.1

docs and tests

Author: bartzbeielstein

notebooks/00_spotPython_tests.ipynb

@@ -14670,6 +14670,137 @@
     "S.surrogate.plot()"
    ]
   },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Cross-correlation matrix K(A, B):\n",
+      " [[0.99904559 0.99144306]\n",
+      " [0.99904559 0.99904559]]\n"
+     ]
+    }
+   ],
+   "source": [
+    "import numpy as np\n",
+    "from spotpython.surrogate.kriging import Kriging\n",
+    "X_train = np.array([[0.0, 0.0], [0.5, 0.5], [1.0, 1.0]])\n",
+    "y_train = np.array([0.1, 0.2, 0.3])\n",
+    "# Fit the Kriging model\n",
+    "model = Kriging().fit(X_train, y_train)\n",
+    "# Create two sets of points A and B\n",
+    "A = np.array([[0.0, 0.0], [1.0, 1.0]])\n",
+    "B = np.array([[0.5, 0.5], [1.5, 1.5]])\n",
+    "# Compute the cross-correlation matrix K(A, B)\n",
+    "K_AB = model._kernel_cross(A, B)\n",
+    "print(\"Cross-correlation matrix K(A, B):\\n\", K_AB)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Negative Log-Likelihood: -7.829213113186723\n",
+      "Correlation matrix Psi:\n",
+      " [[1.000001   0.60653066 0.13533528]\n",
+      " [0.60653066 1.000001   0.60653066]\n",
+      " [0.13533528 0.60653066 1.000001  ]]\n",
+      "Cholesky factor U (lower triangular):\n",
+      " [[1.0000005  0.         0.        ]\n",
+      " [0.60653036 0.79506096 0.        ]\n",
+      " [0.13533522 0.6596296  0.73930655]]\n"
+     ]
+    }
+   ],
+   "source": [
+    "import numpy as np\n",
+    "from spotpython.surrogate.kriging import Kriging\n",
+    "# Training data\n",
+    "X_train = np.array([[0.0, 0.0], [0.5, 0.5], [1.0, 1.0]])\n",
+    "y_train = np.array([0.1, 0.2, 0.3])\n",
+    "# Fit the Kriging model\n",
+    "model = Kriging().fit(X_train, y_train)\n",
+    "log_theta = np.array([0.0, 0.0, -6.0]) # nugget: -6 => 10**(-6) = 1e-6\n",
+    "negLnLike, Psi, U = model._likelihood_exact(log_theta)\n",
+    "print(\"Negative Log-Likelihood:\", negLnLike)\n",
+    "print(\"Correlation matrix Psi:\\n\", Psi)\n",
+    "print(\"Cholesky factor U (lower triangular):\\n\", U)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Landmark indices: [4 2 3]\n",
+      "Landmark points (X_m_):\n",
+      " [[0.75 0.75]\n",
+      " [1.   1.  ]\n",
+      " [0.25 0.25]]\n",
+      "Cholesky factor of W (W_chol_):\n",
+      " [[ 1.          0.          0.        ]\n",
+      " [ 0.97810062  0.20813259  0.        ]\n",
+      " [ 0.9152382  -0.36456734  0.17155086]]\n"
+     ]
+    }
+   ],
+   "source": [
+    "import numpy as np\n",
+    "from spotpython.surrogate.kriging import Kriging\n",
+    "# Training data\n",
+    "X_train = np.array([[0.0, 0.0], [0.5, 0.5], [1.0, 1.0], [0.25, 0.25], [0.75, 0.75]])\n",
+    "y_train = np.array([0.1, 0.2, 0.3, 0.15, 0.25])\n",
+    "# Fit the Kriging model with Nyström approximation\n",
+    "model = Kriging(use_nystrom=True, nystrom_m=3).fit(X_train, y_train)\n",
+    "model._nystrom_setup()\n",
+    "print(\"Landmark indices:\", model.landmark_idx_)\n",
+    "print(\"Landmark points (X_m_):\\n\", model.X_m_)\n",
+    "print(\"Cholesky factor of W (W_chol_):\\n\", model.W_chol_)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Result of R^{-1} v:\n",
+      " [-290115.82440447 -300201.80537958 -262514.38594912 -301405.32195489\n",
+      " -286648.86427461]\n"
+     ]
+    }
+   ],
+   "source": [
+    "import numpy as np\n",
+    "from spotpython.surrogate.kriging import Kriging\n",
+    "# Training data\n",
+    "X_train = np.array([[0.0, 0.0], [0.5, 0.5], [1.0, 1.0], [0.25, 0.25], [0.75, 0.75]])\n",
+    "y_train = np.array([0.1, 0.2, 0.3, 0.15, 0.25])\n",
+    "# Fit the Kriging model with Nyström approximation\n",
+    "model = Kriging(use_nystrom=True, nystrom_m=3).fit(X_train, y_train)\n",
+    "model._nystrom_setup()\n",
+    "v = np.array([1.0, 2.0, 3.0, 4.0, 5.0])\n",
+    "Rinv_v = model._woodbury_solve(v)\n",
+    "print(\"Result of R^{-1} v:\\n\", Rinv_v)\n",
+    "# Note: Ensure that model.M_chol_ is computed before calling this method."
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": null,