@@ -361,6 +361,69 @@

     "learner.plot()"

    ]

   },

+  {

+   "cell_type": "markdown",

+   "metadata": {},

+   "source": [

+    "# 1D learner with vector output: `f:ℝ → ℝ^N`"

+   ]

+  },

+  {

+   "cell_type": "markdown",

+   "metadata": {},

+   "source": [

+    "Some 1D functions return multiple numbers, such as the following function:"

+   ]

+  },

+  {

+   "cell_type": "code",

+   "execution_count": null,

+   "metadata": {},

+   "outputs": [],

+   "source": [

+    "random.seed(0)\n",

+    "offsets = [random.uniform(-0.8, 0.8) for _ in range(3)]\n",

+    "def f_levels(x, offsets=offsets):\n",

+    "    a = 0.01\n",

+    "    return np.array([offset + x + a**2 / (a**2 + (x - offset)**2)\n",

+    "                     for offset in offsets])"

+   ]

+  },

+  {

+   "cell_type": "markdown",

+   "metadata": {},

+   "source": [

+    "This is again a function with sharp peaks at different x-values and with different constant backgrounds. To learn this function we can use a `Learner1D` with the argument `vector_output=True`."

+   ]

+  },

+  {

+   "cell_type": "code",

+   "execution_count": null,

+   "metadata": {},

+   "outputs": [],

+   "source": [

+    "from adaptive.runner import SequentialExecutor\n",

+    "\n",

+    "learner = adaptive.Learner1D(f_levels, bounds=(-1, 1), vector_output=True)\n",

+    "runner = adaptive.Runner(learner, SequentialExecutor(), goal=lambda l: l.loss() < 0.05)"

+   ]

+  },

+  {

+   "cell_type": "markdown",

+   "metadata": {},

+   "source": [

+    "In the plot below we see that the function gets more densely sampled around the peaks, which is the behaviour we want."

+   ]

+  },

+  {

+   "cell_type": "code",

+   "execution_count": null,

+   "metadata": {},

+   "outputs": [],

+   "source": [

+    "adaptive.live_plot(runner)"

+   ]

+  },

   {

    "cell_type": "markdown",

    "metadata": {},