Print, don't plot, the covar

nansencenter · Sep 20, 2023 · d7a1cdb · d7a1cdb
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diff --git a/notebooks/T8 - Monte-Carlo & ensembles.ipynb b/notebooks/T8 - Monte-Carlo & ensembles.ipynb
@@ -123,7 +123,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "311ffb67",
+   "id": "84bec352",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -136,22 +136,13 @@
     "# Using a loop (\"slow\")\n",
     "E = np.zeros((xDim, N))\n",
     "for n in range(N):\n",
-    "    E[:, n] = mu + L@Z[:, n]\n",
-    "\n",
-    "# Comparison to true values\n",
-    "fig, (ax1, ax2) = plt.subplots(ncols=2)\n",
-    "kws = dict(vmin=C.min(), vmax=C.max(), cmap=\"Blues\")\n",
-    "cc = ax1.matshow(C, **kws)\n",
-    "cc = ax2.matshow(np.cov(E), **kws)\n",
-    "fig.colorbar(cc, ax=(ax1, ax2), orientation='horizontal')\n",
-    "with np.printoptions(precision=1):\n",
-    "    print(\"Estimated mean =\", np.mean(E, axis=1))"
+    "    E[:, n] = mu + L@Z[:, n]"
    ]
   },
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "fae3cf5b",
+   "id": "4d254ff9",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -160,11 +151,24 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f6c91f60",
+   "id": "3f46e7f6",
    "metadata": {},
    "source": [
-    "Note that the estimates are not exact. \n",
-    "They contain some amount of random error, a.k.a. ***sampling error***."
+    "The following prints some numbers that can be used to ascertain if you got it right.\n",
+    "Note that the estimates will never be exact:\n",
+    "they contain some amount of random error, a.k.a. ***sampling error***."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "311ffb67",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "with np.printoptions(precision=1):\n",
+    "    print(\"Estimated mean =\", np.mean(E, axis=1))\n",
+    "    print(\"Estimated cov =\", np.cov(E), sep=\"\\n\")"
    ]
   },
   {
@@ -233,7 +237,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b541c271",
+   "id": "471bc6ef",
    "metadata": {},
    "source": [
     "It can be shown that the above estimators are ***consistent and unbiased***.\n",
@@ -303,7 +307,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e5cc312d",
+   "id": "67b387e8",
    "metadata": {},
    "source": [
     "**Exc (optional) -- Error notions:**\n",
@@ -317,7 +321,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "4417a07b",
+   "id": "a38ee124",
    "metadata": {},
    "outputs": [],
    "source": [

diff --git a/notebooks/scripts/T8 - Monte-Carlo & ensembles.py b/notebooks/scripts/T8 - Monte-Carlo & ensembles.py
@@ -99,22 +99,18 @@ def pdf_reconstructions(seed=5,       nbins=10,      bw=.3):
 for n in range(N):
     E[:, n] = mu + L@Z[:, n]
 
-# Comparison to true values
-fig, (ax1, ax2) = plt.subplots(ncols=2)
-kws = dict(vmin=C.min(), vmax=C.max(), cmap="Blues")
-cc = ax1.matshow(C, **kws)
-cc = ax2.matshow(np.cov(E), **kws)
-fig.colorbar(cc, ax=(ax1, ax2), orientation='horizontal')
-with np.printoptions(precision=1):
-    print("Estimated mean =", np.mean(E, axis=1))
-
-
 # +
 # show_answer('Gaussian sampling', 'b')
 # -
 
-# Note that the estimates are not exact. 
-# They contain some amount of random error, a.k.a. ***sampling error***.
+# The following prints some numbers that can be used to ascertain if you got it right.
+# Note that the estimates will never be exact:
+# they contain some amount of random error, a.k.a. ***sampling error***.
+
+with np.printoptions(precision=1):
+    print("Estimated mean =", np.mean(E, axis=1))
+    print("Estimated cov =", np.cov(E), sep="\n")
+
 
 # **Exc -- Moment estimation code:** Above, we used numpy's (`np`) functions to compute the sample-estimated mean and covariance matrix,
 # $\bx$ and $\barC$,