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+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import numpy as np\n",
+    "import msprime\n",
+    "import lshmm\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Input data\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# First, let's simulate some haplotypes to use as a reference panel.\n",
+    "seed = 1208\n",
+    "ts = msprime.sim_mutations(\n",
+    "    msprime.sim_ancestry(\n",
+    "        samples=10,\n",
+    "        ploidy=1,\n",
+    "        sequence_length=1e4,\n",
+    "        discrete_genome=True,\n",
+    "        recombination_rate=1e-4,\n",
+    "        random_seed=seed,\n",
+    "    ),\n",
+    "    rate=1e-4,\n",
+    "    random_seed=seed,\n",
+    ")\n",
+    "ts\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# A reference panel must be of size (number of sites, number of haplotypes).\n",
+    "ref_panel = ts.genotype_matrix()\n",
+    "\n",
+    "# A query must be of size (1, number of sites).\n",
+    "# It can contain MISSING values, but not NONCOPY values.\n",
+    "query = ref_panel[:, 0].reshape(1, ts.num_sites)\n",
+    "\n",
+    "# The number of distinct alleles per site is needed to get per-site mutation rates.\n",
+    "num_alleles = lshmm.core.get_num_alleles(ref_panel, query)\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Per-site recombination and mutation probabilities are needed\n",
+    "# to parametrise the LS HMM.\n",
+    "rho = np.zeros(ts.num_sites, dtype=np.float64) + 1e-4\n",
+    "rho[0] = 0\n",
+    "mu = np.zeros(ts.num_sites, dtype=np.float64) + 1e-4\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Viterbi algorithm"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Let's determine the best copying path and its log-likelihood using the Viterbi algorithm.\n",
+    "path, log_lik = lshmm.api.viterbi(\n",
+    "    ref_panel,\n",
+    "    query,\n",
+    "    num_alleles,\n",
+    "    prob_recombination=rho,\n",
+    "    prob_mutation=mu,\n",
+    "    scale_mutation_rate=True,\n",
+    ")\n",
+    "print(f\"Parents in the path: {len(np.unique(path))}\")\n",
+    "print(f\"Log-likelihood: {log_lik}\")\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# There is a function to evaluate the log-likelihood of a copying path.\n",
+    "# Let's check that we get the same log-likelihood of the same copying path \n",
+    "# under the same parameters using the function.\n",
+    "log_lik_2 = lshmm.api.path_loglik(\n",
+    "    ref_panel,\n",
+    "    query,\n",
+    "    num_alleles,\n",
+    "    path,\n",
+    "    prob_recombination=rho,\n",
+    "    prob_mutation=mu,\n",
+    "    scale_mutation_rate=True,\n",
+    ")\n",
+    "print(f\"Is the log-likelihood identical? {log_lik == log_lik_2}\")\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# We should get a different log-likelihood value if the parameters are not the same.\n",
+    "# Let's check the log-likelihood of the same copying path under different parameters.\n",
+    "log_lik_3 = lshmm.api.path_loglik(\n",
+    "    ref_panel,\n",
+    "    query,\n",
+    "    num_alleles,\n",
+    "    path,\n",
+    "    prob_recombination=rho,\n",
+    "    prob_mutation=mu + 1e-5,    # Increase\n",
+    "    scale_mutation_rate=True,\n",
+    ")\n",
+    "print(f\"Is the log-likelihood identical? {log_lik == log_lik_3}\")\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Forward-backward algorithm"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# To calculate the forward probability matrix of a query,\n",
+    "# let's use the forward algorithm.\n",
+    "np.set_printoptions(linewidth=100, precision=4)\n",
+    "fwd_mat, norm_factor, log_lik = lshmm.api.forwards(\n",
+    "    ref_panel,\n",
+    "    query,\n",
+    "    num_alleles=num_alleles,\n",
+    "    prob_recombination=rho,\n",
+    "    prob_mutation=mu,\n",
+    "    scale_mutation_rate=True,\n",
+    "    normalise=True,\n",
+    ")\n",
+    "fwd_mat\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Now, to calculate the backward probability matrix of the same query,\n",
+    "# let's use the backward algorithm.\n",
+    "np.set_printoptions(linewidth=100, precision=4)\n",
+    "bwd_mat = lshmm.api.backwards(\n",
+    "    ref_panel,\n",
+    "    query,\n",
+    "    num_alleles,\n",
+    "    normalisation_factor_from_forward=norm_factor,\n",
+    "    prob_recombination=rho,\n",
+    "    prob_mutation=mu,\n",
+    "    scale_mutation_rate=True,\n",
+    ")\n",
+    "bwd_mat\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Check the integrity of the matrices.\n",
+    "np.allclose(np.sum(fwd_mat * bwd_mat, axis=1), 1.0)\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.12.3"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}