From 305e940411d98e32539b9a8e32ae92771f62b1fe Mon Sep 17 00:00:00 2001 From: BariscanTosyali Date: Mon, 16 Mar 2026 16:03:57 +0300 Subject: [PATCH] =?UTF-8?q?Markov=20Zincirleri=20g=C3=B6revleri=20ve=20g?= =?UTF-8?q?=C3=B6rselle=C5=9Ftirmesi=20tamamland=C4=B1?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- markov_chains.ipynb | 316 +++++++++++++++++++++++++++++++++++++++----- 1 file changed, 286 insertions(+), 30 deletions(-) diff --git a/markov_chains.ipynb b/markov_chains.ipynb index 9db9ef7..75c5a70 100644 --- a/markov_chains.ipynb +++ b/markov_chains.ipynb @@ -2,6 +2,7 @@ "cells": [ { "cell_type": "markdown", + "id": "0b2e679f", "metadata": {}, "source": [ "# Markov Zincirleri" @@ -9,8 +10,17 @@ }, { "cell_type": "code", - "execution_count": null, - "metadata": {}, + "execution_count": 1, + "id": "0a5ff2be", + "metadata": { + "execution": { + "iopub.execute_input": "2026-03-16T12:45:32.733435Z", + "iopub.status.busy": "2026-03-16T12:45:32.732893Z", + "iopub.status.idle": "2026-03-16T12:45:33.858828Z", + "shell.execute_reply": "2026-03-16T12:45:33.856618Z", + "shell.execute_reply.started": "2026-03-16T12:45:32.733399Z" + } + }, "outputs": [], "source": [ "import numpy as np\n", @@ -19,6 +29,7 @@ }, { "cell_type": "markdown", + "id": "11ceb7d1", "metadata": {}, "source": [ "💫 Hayal et ki senin ve kedinin bir süper gücü var: ışınlanma gücü 💫\n", @@ -54,6 +65,7 @@ }, { "cell_type": "markdown", + "id": "b27135b1", "metadata": {}, "source": [ "## 🐱 1) Kedinin hareketini modellemek" @@ -61,6 +73,7 @@ }, { "cell_type": "markdown", + "id": "78a22fcc", "metadata": {}, "source": [ "### 1.1) Draft" @@ -68,6 +81,7 @@ }, { "cell_type": "markdown", + "id": "f96629ab", "metadata": {}, "source": [ "✍️ Emily’nin hareketlerini görselleştirmek için bir kalem ve bir kâğıt al." @@ -75,6 +89,7 @@ }, { "cell_type": "markdown", + "id": "ddc7b7f4", "metadata": {}, "source": [ "
\n", @@ -87,6 +102,7 @@ }, { "cell_type": "markdown", + "id": "ed994922", "metadata": {}, "source": [ "### ✈️ 1.2) Transitions" @@ -94,6 +110,7 @@ }, { "cell_type": "markdown", + "id": "be4edcd1", "metadata": {}, "source": [ "[\"paris\", \"london\", \"berlin\"] şehirleri arasındaki hareketleri temsil eden[`transition_matrix`](https://en.wikipedia.org/wiki/Stochastic_matrix) yani geçiş matrisini senin için oluşturacağız.\n", @@ -115,6 +132,7 @@ { "cell_type": "code", "execution_count": null, + "id": "9d0ec85f", "metadata": {}, "outputs": [], "source": [ @@ -128,6 +146,7 @@ }, { "cell_type": "markdown", + "id": "b3507ccb", "metadata": {}, "source": [ "**`stochastic matrixes`** olarak da adlandırılan bu matrislerin dikkat çekici bir özelliği vardır:\n", @@ -136,6 +155,7 @@ }, { "cell_type": "markdown", + "id": "287f9394", "metadata": {}, "source": [ "👉 Emily’nin başlangıçta Paris’te olduğunu hayal edelim.\n", @@ -144,9 +164,35 @@ }, { "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], + "execution_count": 2, + "id": "21689fbd", + "metadata": { + "execution": { + "iopub.execute_input": "2026-03-16T12:46:17.594532Z", + "iopub.status.busy": "2026-03-16T12:46:17.592876Z", + "iopub.status.idle": "2026-03-16T12:46:17.606357Z", + "shell.execute_reply": "2026-03-16T12:46:17.604995Z", + "shell.execute_reply.started": "2026-03-16T12:46:17.594464Z" + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[1, 0, 0]])" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "shape: (1, 3)\n" + ] + } + ], "source": [ "initial_position = np.array([[1,0,0]])\n", "display(initial_position)\n", @@ -155,6 +201,7 @@ }, { "cell_type": "markdown", + "id": "92e3018d", "metadata": {}, "source": [ "❓ Emily’nin bir sonraki adımda paris/london/berlin’de olma olasılığı nedir?\n", @@ -164,8 +211,17 @@ }, { "cell_type": "code", - "execution_count": null, - "metadata": {}, + "execution_count": 3, + "id": "39070b2d", + "metadata": { + "execution": { + "iopub.execute_input": "2026-03-16T12:46:25.369873Z", + "iopub.status.busy": "2026-03-16T12:46:25.369442Z", + "iopub.status.idle": "2026-03-16T12:46:25.376770Z", + "shell.execute_reply": "2026-03-16T12:46:25.374962Z", + "shell.execute_reply.started": "2026-03-16T12:46:25.369843Z" + } + }, "outputs": [], "source": [ "proba_paris_to_paris = None # one-liner dot product\n", @@ -175,6 +231,7 @@ }, { "cell_type": "markdown", + "id": "646491a9", "metadata": {}, "source": [ "
\n", @@ -191,6 +248,7 @@ }, { "cell_type": "markdown", + "id": "856c1dc3", "metadata": {}, "source": [ "ℹ️ Şimdi, kedinin en son nerede görüldüğünü bilmiyorsun ama bir başlangıç tahminin var: Emily başlangıçta\n", @@ -203,19 +261,43 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 4, + "id": "640ecc2c", "metadata": { + "execution": { + "iopub.execute_input": "2026-03-16T12:47:31.472058Z", + "iopub.status.busy": "2026-03-16T12:47:31.471420Z", + "iopub.status.idle": "2026-03-16T12:47:31.483901Z", + "shell.execute_reply": "2026-03-16T12:47:31.481891Z", + "shell.execute_reply.started": "2026-03-16T12:47:31.472016Z" + }, "tags": [ "challengify" ] }, - "outputs": [], - "source": [ - "# SENİN KODUN BURAYA" + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Initial Position Array:\n", + " [[0.3 0.4 0.3]]\n", + "Shape: (1, 3)\n" + ] + } + ], + "source": [ + "# Başlangıç olasılıkları: Paris %30, Londra %40, Berlin %30\n", + "initial_position = np.array([[0.3, 0.4, 0.3]])\n", + "\n", + "# Kontrol için ekrana basalım\n", + "print(\"Initial Position Array:\\n\", initial_position)\n", + "print(\"Shape:\", initial_position.shape)" ] }, { "cell_type": "markdown", + "id": "425bb186", "metadata": {}, "source": [ "❓Kedinin 1. günde her şehirde olma olasılıklarını veren $ (1,3) $ boyutundaki `day_1` array’ini, şık bir matematiksel formülle hesapla ❓\n", @@ -232,19 +314,48 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 6, + "id": "82939f30", "metadata": { + "execution": { + "iopub.execute_input": "2026-03-16T12:48:55.260529Z", + "iopub.status.busy": "2026-03-16T12:48:55.259155Z", + "iopub.status.idle": "2026-03-16T12:48:55.269737Z", + "shell.execute_reply": "2026-03-16T12:48:55.267944Z", + "shell.execute_reply.started": "2026-03-16T12:48:55.260470Z" + }, "tags": [ "challengify" ] }, - "outputs": [], - "source": [ - "# SENİN KODUN BURAYA" + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "1. Gün Olasılık Dağılımı (Paris, Londra, Berlin):\n", + "[[0.285 0.3 0.415]]\n" + ] + } + ], + "source": [ + "# Önce Q matrisini tanımlayalım (Eğer yukarıdaki hücreyi çalıştırmadıysan diye)\n", + "Q = np.array([\n", + " [1/3, 1/3, 1/3],\n", + " [0.35, 0.35, 0.3],\n", + " [0.15, 0.2, 0.65]])\n", + "\n", + "# 1. Gün olasılıklarını matris çarpımı (dot product) ile hesapla\n", + "day_1 = initial_position.dot(Q)\n", + "\n", + "# Sonucu görüntüle\n", + "print(\"1. Gün Olasılık Dağılımı (Paris, Londra, Berlin):\")\n", + "print(day_1)" ] }, { "cell_type": "markdown", + "id": "f05e0e34", "metadata": {}, "source": [ "
\n", @@ -261,6 +372,7 @@ }, { "cell_type": "markdown", + "id": "55f35621", "metadata": {}, "source": [ "❓ Emily’nin 2. günde Paris’te olma olasılığı nedir? Peki ya Londra ve Berlin için olasılıklar nedir? ❓" @@ -268,19 +380,46 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 7, + "id": "776e1c18", "metadata": { + "execution": { + "iopub.execute_input": "2026-03-16T12:49:36.994905Z", + "iopub.status.busy": "2026-03-16T12:49:36.994521Z", + "iopub.status.idle": "2026-03-16T12:49:37.004288Z", + "shell.execute_reply": "2026-03-16T12:49:37.002910Z", + "shell.execute_reply.started": "2026-03-16T12:49:36.994880Z" + }, "tags": [ "challengify" ] }, - "outputs": [], - "source": [ - "# SENİN KODUN BURAYA" + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "2. Gün Olasılık Dağılımı:\n", + "Paris: 0.2622\n", + "Londra: 0.2830\n", + "Berlin: 0.4547\n" + ] + } + ], + "source": [ + "# 2. Gün olasılıklarını hesapla\n", + "day_2 = day_1.dot(Q)\n", + "\n", + "# Sonuçları yazdır\n", + "print(\"2. Gün Olasılık Dağılımı:\")\n", + "print(f\"Paris: {day_2[0][0]:.4f}\")\n", + "print(f\"Londra: {day_2[0][1]:.4f}\")\n", + "print(f\"Berlin: {day_2[0][2]:.4f}\")" ] }, { "cell_type": "markdown", + "id": "edac689c", "metadata": {}, "source": [ "### ⏳ 1.3) Kedi *n* gün sonra nerede olur? " @@ -288,6 +427,7 @@ }, { "cell_type": "markdown", + "id": "a0f9634f", "metadata": {}, "source": [ "❓ emily adında bir fonksiyon oluştur. Bu fonksiyon, Emily’nin n gün sonra Paris, Berlin ve Londra’da olma olasılıklarını hesaplamalı. ❓\n", @@ -298,16 +438,33 @@ }, { "cell_type": "code", - "execution_count": null, - "metadata": {}, + "execution_count": 8, + "id": "a2ca225c", + "metadata": { + "execution": { + "iopub.execute_input": "2026-03-16T12:50:39.995585Z", + "iopub.status.busy": "2026-03-16T12:50:39.994796Z", + "iopub.status.idle": "2026-03-16T12:50:40.004140Z", + "shell.execute_reply": "2026-03-16T12:50:40.002777Z", + "shell.execute_reply.started": "2026-03-16T12:50:39.995545Z" + } + }, "outputs": [], "source": [ "def emily(initial_position, transition_matrix, n_days):\n", - " pass # SENİN KODUN BURAYA" + " # Başlangıç pozisyonunu koruyalım\n", + " current_position = initial_position\n", + " \n", + " # n_days kadar gün boyunca matris çarpımı işlemini tekrarla\n", + " for i in range(n_days):\n", + " current_position = current_position.dot(transition_matrix)\n", + " \n", + " return current_position" ] }, { "cell_type": "markdown", + "id": "064cf9f1", "metadata": {}, "source": [ "❓ Peki, Emily 100 gün sonra nerede olacak? ❓" @@ -315,19 +472,41 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 9, + "id": "4127cad5", "metadata": { + "execution": { + "iopub.execute_input": "2026-03-16T12:50:49.935788Z", + "iopub.status.busy": "2026-03-16T12:50:49.935370Z", + "iopub.status.idle": "2026-03-16T12:50:49.945349Z", + "shell.execute_reply": "2026-03-16T12:50:49.943173Z", + "shell.execute_reply.started": "2026-03-16T12:50:49.935754Z" + }, "tags": [ "challengify" ] }, - "outputs": [], - "source": [ - "# SENİN KODUN BURAYA" + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "100 Gün Sonra Olasılık Dağılımı:\n", + "[[0.25093633 0.27465668 0.47440699]]\n" + ] + } + ], + "source": [ + "# Fonksiyonu 100 gün için çalıştıralım\n", + "day_100 = emily(initial_position, Q, 100)\n", + "\n", + "print(\"100 Gün Sonra Olasılık Dağılımı:\")\n", + "print(day_100)" ] }, { "cell_type": "markdown", + "id": "06b59a73", "metadata": {}, "source": [ "### 📈 1.4) Zaman İçinde Olasılıkların Görselleştirilmesi" @@ -335,6 +514,7 @@ }, { "cell_type": "markdown", + "id": "da7e60aa", "metadata": {}, "source": [ "❓ Zaman içinde her şehirde olma olasılıklarını gösteren bir grafik çiz\n", @@ -344,16 +524,78 @@ }, { "cell_type": "code", - "execution_count": null, - "metadata": {}, + "execution_count": 10, + "id": "bd9837a7", + "metadata": { + "execution": { + "iopub.execute_input": "2026-03-16T12:51:44.035757Z", + "iopub.status.busy": "2026-03-16T12:51:44.035322Z", + "iopub.status.idle": "2026-03-16T12:51:44.044026Z", + "shell.execute_reply": "2026-03-16T12:51:44.042639Z", + "shell.execute_reply.started": "2026-03-16T12:51:44.035724Z" + } + }, "outputs": [], "source": [ "def emily_over_time(initial_position, transition_matrix, n_days):\n", - " pass # SENİN KODUN BURAYA" + " # Olasılık geçmişini tutmak için bir liste oluştur (ilk durumu ekle)\n", + " history = [initial_position.flatten()]\n", + " current_position = initial_position\n", + " \n", + " for _ in range(n_days):\n", + " current_position = current_position.dot(transition_matrix)\n", + " history.append(current_position.flatten())\n", + " \n", + " return np.array(history)" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "80227165-a80a-453e-995d-22af0945fe01", + "metadata": { + "execution": { + "iopub.execute_input": "2026-03-16T12:52:10.379453Z", + "iopub.status.busy": "2026-03-16T12:52:10.378241Z", + "iopub.status.idle": "2026-03-16T12:52:10.631425Z", + "shell.execute_reply": "2026-03-16T12:52:10.630338Z", + "shell.execute_reply.started": "2026-03-16T12:52:10.379416Z" + } + }, + "outputs": [ + { + "data": { + "image/png": "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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Veriyi hazırla (20 gün için)\n", + "n_days = 20\n", + "history = emily_over_time(initial_position, Q, n_days)\n", + "\n", + "# Çizim yapalım\n", + "plt.figure(figsize=(10, 6))\n", + "plt.plot(history[:, 0], label='Paris', marker='o')\n", + "plt.plot(history[:, 1], label='London', marker='s')\n", + "plt.plot(history[:, 2], label='Berlin', marker='^')\n", + "\n", + "plt.title('Zaman İçinde Şehir Olasılıklarının Değişimi', fontsize=14)\n", + "plt.xlabel('Gün', fontsize=12)\n", + "plt.ylabel('Olasılık', fontsize=12)\n", + "plt.legend()\n", + "plt.grid(True, linestyle='--', alpha=0.7)\n", + "plt.show()" ] }, { "cell_type": "markdown", + "id": "b24a355a", "metadata": {}, "source": [ "## 🥡 2) Takeaways" @@ -361,6 +603,7 @@ }, { "cell_type": "markdown", + "id": "a98f6a9e", "metadata": {}, "source": [ "❤️ `Emily in Paris`,dizisinden sonra, uzun vadede muhtemelen `Emily in Berlin` göreceğiz!\n", @@ -375,6 +618,7 @@ }, { "cell_type": "markdown", + "id": "a6518cb9", "metadata": {}, "source": [ "🏁 Tebrikler!\n", @@ -390,9 +634,21 @@ ], "metadata": { "kernelspec": { - "display_name": "Python 3", + "display_name": "Python 3 (ipykernel)", "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": "3.12.9" } }, "nbformat": 4,