{"id":184976,"date":"2023-02-15T10:25:00","date_gmt":"2023-02-15T15:25:00","guid":{"rendered":"https:\/\/ibkrcampus.com\/?p=184976"},"modified":"2023-02-15T10:26:04","modified_gmt":"2023-02-15T15:26:04","slug":"can-chatgpt-self-improve-self-written-python-code-for-cholesky-decomposition","status":"publish","type":"post","link":"https:\/\/www.interactivebrokers.com\/campus\/ibkr-quant-news\/can-chatgpt-self-improve-self-written-python-code-for-cholesky-decomposition\/","title":{"rendered":"Can ChatGPT Self-Improve Self-Written Python Code for Cholesky Decomposition?"},"content":{"rendered":"\n<p>It is needless to say about next big thing in the field of artificial intelligence (AI) known as&nbsp;<a href=\"https:\/\/openai.com\/blog\/chatgpt\/\" rel=\"noreferrer noopener\" target=\"_blank\">ChatGPT<\/a>. ChatGPT is a large language model developed by OpenAI. It is based on the GPT (Generative Pre-training Transformer) architecture and is trained on a massive dataset of text data. This allows it to generate human-like text and perform a wide range of natural language processing tasks, such as language translation, text summarization, and question answering.<\/p>\n\n\n\n<p>One of the main advantages of ChatGPT is its ability to generate human-like text, which makes it useful for tasks such as writing essays, articles, and even code. It can be fine-tuned on specific tasks and domains, such as financial domain, allowing it to generate financial reports, financial predictions, code snippets and more.<\/p>\n\n\n\n<p>The model is trained on a large dataset of text, which allows it to understand and generate text in a variety of styles and formats. It can also generate text based on a given prompt, making it useful for tasks such as text completion, text generation, and text summarization.<\/p>\n\n\n\n<p><strong>1. ChatGPT for Quantitative Finance?<\/strong><\/p>\n\n\n\n<p>There is a lot of hype around the use of ChatGPT because it is a powerful and versatile language model that can perform a wide range of natural language processing tasks. ChatGPT can be useful in quantitative finance for several reasons:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Time-saving: it can generate code snippets quickly, allowing financial engineers and quantitative analysts to focus on more complex and high-level tasks.<\/li>\n\n\n\n<li>Consistency and accuracy: it can generate code that is consistent and accurate, reducing the risk of errors in financial computations.<\/li>\n\n\n\n<li>Flexibility: it can be used to generate code for a wide range of financial computations, from simple calculations to complex financial modeling.<\/li>\n\n\n\n<li>Scalability: it can be used to generate code for large-scale financial computations, such as portfolio optimization or risk management.<\/li>\n\n\n\n<li>Multi-language support: it can generate code in multiple programming languages, which allows for efficient and memory-friendly solutions for big computations.<\/li>\n\n\n\n<li>Efficient use of historical data: it can help generate code that makes the most of historical data, which is crucial in quantitative finance, where past performance is used to predict future outcomes.<\/li>\n\n\n\n<li>Repetitive task automation: it can help automate repetitive tasks, allowing financial engineers and quantitative analysts to focus on higher-level tasks and improve productivity.<\/li>\n\n\n\n<li>Cost-effective: it can help reduce costs by automating repetitive tasks, reducing human error and increasing productivity.<\/li>\n<\/ul>\n\n\n\n<p>Overall, ChatGPT can help financial engineers and quantitative analysts to work more efficiently, accurately and effectively, which can lead to better decision making and improved performance in financial markets.<\/p>\n\n\n\n<p><strong>2. So, Is It Reasonable to Use ChatGPT for Writing Python Code for Financial Applications?<\/strong><\/p>\n\n\n\n<p>ChatGPT can be used to write Python code for financial applications by providing concise, accurate and efficient code snippets for various financial computations. Some examples of financial computations that can be done using ChatGPT include:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Calculation of portfolio profit and loss<\/li>\n\n\n\n<li>Calculation of VaR (Value at Risk) and Liquidity VaR<\/li>\n\n\n\n<li>Calculation of expected shortfall for a portfolio<\/li>\n\n\n\n<li>Arbitrage on two FX currency pairs<\/li>\n\n\n\n<li>Cholesky decomposition for a given matrix<\/li>\n\n\n\n<li>Calculation of portfolio value given different trading strategies<\/li>\n\n\n\n<li>Filtering of noisy correlations in a correlation matrix<\/li>\n\n\n\n<li>Calculation of average loss for a cryptocurrency based on past performance<\/li>\n<\/ul>\n\n\n\n<p>ChatGPT can also be used to generate code in other languages like Rust, providing solutions that are efficient and memory-friendly. Rust, right after Solidity, is the language of choice for all recently-born blockchain developers, allowing Decentralised Finance (DeFi) application to blossom.<\/p>\n\n\n\n<p>It is important to note that the ChatGPT model is only able to provide the code based on the knowledge it has been trained on, and the performance of the generated code depends on the quality of the input data and the specific use case. It is always recommended to test and verify the generated code before using it in production environments.<\/p>\n\n\n\n<p><strong>3. Speaking of, Cholesky Decomposition. What code it can generate?<\/strong><\/p>\n\n\n\n<p>Cholesky decomposition is a method for decomposing a Hermitian, positive-definite matrix into the product of a lower triangular matrix and its conjugate transpose, which is useful for efficient numerical solutions, such as Monte Carlo simulations.<\/p>\n\n\n\n<p>Here is an example delivered by the model of a Python script that performs Cholesky decomposition on a matrix:<\/p>\n\n\n\n<pre class=\"wp-block-syntaxhighlighter-code\">import numpy as np\n \ndef cholesky(matrix):\n    \"\"\"\n    Perform Cholesky decomposition on a matrix\n    :param matrix: Square matrix to decompose\n    :return: Lower triangular matrix L\n    \"\"\"\n    n = matrix.shape[0]\n    L = np.zeros((n, n))\n    for i in range(n):\n        for j in range(i+1):\n            temp = sum(L[i][k] * L[j][k] for k in range(j))\n            if i == j:\n                L[i][j] = np.sqrt(matrix[i][i] - temp)\n            else:\n                L[i][j] = (1.0 \/ L[j][j] * (matrix[i][j] - temp))\n    return L\n \n# Example usage\nmatrix = np.array([[4, 12, -16], [12, 37, -43], [-16, -43, 98]])\nL = cholesky(matrix)\nprint(L)<\/pre>\n\n\n\n<p>In the above script the matrix is passed as an argument to the function&nbsp;<em>cholesky()<\/em>&nbsp;which decomposes the matrix and returns the lower triangular matrix.<br>Please note that the matrix passed to the function should be Hermitian, Positive-definite.<\/p>\n\n\n\n<p><strong>4. Code Self-Improved, Optimised for Speed? No Problem at All!<\/strong><\/p>\n\n\n\n<p>It looks like it can be done, too! No problem. In this can all we need is to ask politely ChatGPT \u201cCan you rewrite the following function optimised for speed, please?\u201d pasting the above script. Its response is quite optimistic, saying \u201cThere are multiple ways to optimize the function for speed, here is one possible way:\u201d<\/p>\n\n\n\n<pre class=\"wp-block-syntaxhighlighter-code\">import numpy as np\n \ndef cholesky(matrix):\n    \"\"\"\n    Perform Cholesky decomposition on a matrix\n    :param matrix: Square matrix to decompose\n    :return: Lower triangular matrix L\n    \"\"\"\n    n = matrix.shape[0]\n    L = np.zeros((n, n))\n    for i in range(n):\n        L[i][i] = np.sqrt(matrix[i][i] - np.dot(L[i, :i], L[i, :i]))\n        for j in range(i+1, n):\n            L[j][i] = (matrix[j][i] - np.dot(L[i, :i], L[j, :i])) \/ L[i][i]\n    return L<\/pre>\n\n\n\n<p>This implementation uses numpy\u2019s dot product function which is implemented in C and is therefore faster than using a Python for loop. This way it reduces the time complexity of the function and makes it faster.<\/p>\n\n\n\n<p>Additionally, the function uses only one for loop to calculate both the upper and lower triangular matrix. It also calculates the diagonal element of the matrix at the same time, which reduces the number of operations and improves performance.<\/p>\n\n\n\n<p><strong>5. Second Derivative, i.e. How to Self-Self-Improve Itself?<\/strong><\/p>\n\n\n\n<p>I have never thought I would be writing an article on such a bizarre topic. Never, ever, in my life. Until today! I asked again \u201cCan you rewrite the above function in order to make it run faster, please?\u201d And guess what? That soulless soul told me \u201cHere is one possible way to optimize the function for speed:\u201d<\/p>\n\n\n\n<pre class=\"wp-block-syntaxhighlighter-code\">import numpy as np\n \ndef cholesky(matrix):\n    \"\"\"\n    Perform Cholesky decomposition on a matrix\n    :param matrix: Square matrix to decompose\n    :return: Lower triangular matrix L\n    \"\"\"\n    n = matrix.shape[0]\n    L = np.zeros((n, n))\n    for i in range(n):\n        L[i, i:] = matrix[i, i:] - np.dot(L[:i, i:], L[:i, i:].T)\n        L[i, i:] \/= L[i, i]\n    return L<\/pre>\n\n\n\n<p>This implementation uses array slicing to access specific parts of the matrix and perform operations on them, which reduces the number of operations and improves performance.<\/p>\n\n\n\n<p><strong>6. Back to the Class-room?<\/strong><\/p>\n\n\n\n<p>My desire for asking and learning more continues with my next question \u201cCan you rewrite that function in Python as a class and add&nbsp;<em>n<\/em>&nbsp;as an input parameter provider by the user?\u201d Again, two seconds of \u201cthinking\u201d and this guy start printing:<\/p>\n\n\n\n<pre class=\"wp-block-syntaxhighlighter-code\">import numpy as np\n \nclass CholeskyDecomposition:\n    def __init__(self, n):\n        self.n = n\n    def decompose(self, matrix):\n        \"\"\"\n        Perform Cholesky decomposition on a matrix\n        :param matrix: Square matrix to decompose\n        :return: Lower triangular matrix L\n        \"\"\"\n        L = np.zeros((self.n, self.n))\n        for i in range(self.n):\n            L[i, i:] = matrix[i, i:] - np.dot(L[:i, i:], L[:i, i:].T)\n            L[i, i:] \/= L[i, i]\n        return L\n         \n# Example usage:\nn = 3\nmatrix = np.array([[4, 12, -16], [12, 37, -43], [-16, -43, 98]])\ncholesky_decomposition = CholeskyDecomposition(n)\nL = cholesky_decomposition.decompose(matrix)\nprint(L)<\/pre>\n\n\n\n<p>In this example, the user provides the value of&nbsp;<em>n<\/em>&nbsp;to the class constructor and the class uses it to define the shape of the matrix. This way the user can control the size of the matrix, and the class will be able to operate with any square matrix.<\/p>\n\n\n\n<p><strong>7. Parlez Vous Fran\u00e7ais?<\/strong><\/p>\n\n\n\n<p>Now an icing on the cake. It is 2023 and programming in Python became boring and too popular. If you want to feel the thrill and some adrenaline, go to France, try communication with other people using different language! What I\u2019m trying to say here is that taking Python code and translating it into, for example&nbsp;<a href=\"https:\/\/www.rust-lang.org\/\" rel=\"noreferrer noopener\" target=\"_blank\">Rust language<\/a>, now, is no longer an issue. Have a look. Just ask again \u201cRewrite the following Python function in Rust language, please.\u201d I do like to add \u201c, please\u201d at the end to get that personal touch to human-model conversation. I hope you know what I mean\u2026<\/p>\n\n\n\n<p>Here is an example of the Cholesky decomposition function implemented in Rust \u2013 the response appears without hesitation, followed by the code:<\/p>\n\n\n\n<pre class=\"wp-block-syntaxhighlighter-code\">use ndarray::{Array, Array2};\nuse ndarray_linalg::cholesky::cholesky_unpack;\n \nfn cholesky(matrix: Array2&lt;f64>) -> Array2&lt;f64> {\n    let (l, _) = cholesky_unpack(matrix);\n    l\n}\n \n\/\/ Example usage:\nlet matrix = array![[4.0, 12.0, -16.0], [12.0, 37.0, -43.0], [-16.0, -43.0, 98.0]];\nlet L = cholesky(matrix);\nprintln!(\"{}\", L);<\/pre>\n\n\n\n<p>Note that this example uses the ndarray and&nbsp;<em>ndarray_linalg<\/em>&nbsp;crates, which provide functionality for working with arrays and performing linear algebra operations. In this example, the input matrix is passed to the cholesky_unpack function from ndarray_linalg crate, which returns a tuple of lower triangular matrix and its transpose. The lower triangular matrix is then returned. This implementation is more concise and efficient than the previous one because it uses the optimized linear algebra libraries and doesn\u2019t require to iterate and perform the calculations manually.<\/p>\n\n\n\n<p>They say, in Rust you cannot do quantitative matrix operations! Not true! I ask ChatGPT for the last time \u201cWrite code in Rust performing Cholesky decomposiiton for matrix of size 500 by 500\u201d followed by repeated but reordered feedback \u201cHere is an example of how to perform Cholesky decomposition on a matrix of size 500\u00d7500 in Rust:\u201d<\/p>\n\n\n\n<pre class=\"wp-block-syntaxhighlighter-code\">use ndarray::{Array, Array2};\nuse ndarray_linalg::cholesky::cholesky_unpack;\n \nfn cholesky(matrix: Array2&lt;f64>) -> Array2&lt;f64> {\n    let (l, _) = cholesky_unpack(matrix);\n    l\n}\n \nfn main() {\n    let mut matrix = Array::zeros((500, 500));\n    \/\/ Fill the matrix with some values\n    \/\/ ...\n    let L = cholesky(matrix);\n    println!(\"{}\", L);\n}<\/pre>\n\n\n\n<p><\/p>\n\n\n\n<p>In this example, we first create a 2D array of size 500\u00d7500 using the&nbsp;<em>Array::zeros<\/em>&nbsp;function from the ndarray crate. Then we fill the matrix with some values, it could be from reading from a file or from some other calculation. Then we pass the matrix to the&nbsp;<em>cholesky_unpack<\/em>&nbsp;function from&nbsp;<em>ndarray_linalg<\/em>&nbsp;crate, which returns a tuple of lower triangular matrix and its transpose. The lower triangular matrix is then returned and printed. As we are working with a big matrix, it is recommended to use this implementation as it uses the optimized linear algebra libraries and doesn\u2019t require to iterate and perform the calculations manually.<\/p>\n\n\n\n<p><strong>Amazing!<\/strong><\/p>\n\n\n\n<p>Now I\u2019ll go and check if all these code lines actually work?!<\/p>\n\n\n\n<p><em>Originally posted on <a href=\"https:\/\/quantatrisk.com\/2023\/01\/13\/can-chatgpt-self-improve-self-written-python-code-for-cholesky-decomposition\/\">Quant at Risk<\/a> Blog.<\/em><\/p>\n","protected":false},"excerpt":{"rendered":"<p>ChatGPT is a large language model developed by OpenAI. It is based on the GPT (Generative Pre-training Transformer) architecture and is trained on a massive dataset of text data. <\/p>\n","protected":false},"author":710,"featured_media":185009,"comment_status":"closed","ping_status":"open","sticky":true,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[339,349,338,350,341,351,352,344,2197],"tags":[14403,14718,14717,12705,1225,14715,595,4921,14716,7946],"contributors-categories":[13732],"class_list":{"0":"post-184976","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-data-science","8":"category-python-development","9":"category-ibkr-quant-news","10":"category-quant-asia-pacific","11":"category-quant-development","12":"category-quant-europe","13":"category-quant-north-america","14":"category-quant-regions","15":"category-quant-south-america","16":"tag-chatgpt","17":"tag-cholesky-decomposition","18":"tag-decentralised-finance-defi","19":"tag-natural-language-processing-nlp","20":"tag-numpy","21":"tag-openai","22":"tag-python","23":"tag-quantitative-finance","24":"tag-rust","25":"tag-var","26":"contributors-categories-quant-at-risk"},"pp_statuses_selecting_workflow":false,"pp_workflow_action":"current","pp_status_selection":"publish","acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v26.9 (Yoast SEO v27.3) - https:\/\/yoast.com\/product\/yoast-seo-premium-wordpress\/ -->\n<title>Can ChatGPT Self-Improve Self-Written Python Code for Cholesky Decomposition?<\/title>\n<meta name=\"description\" content=\"ChatGPT is a large language model developed by OpenAI. It is based on the GPT (Generative Pre-training Transformer) architecture and is trained on a...\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.interactivebrokers.com\/campus\/wp-json\/wp\/v2\/posts\/184976\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Can ChatGPT Self-Improve Self-Written Python Code for Cholesky Decomposition? | IBKR Quant Blog\" \/>\n<meta property=\"og:description\" content=\"ChatGPT is a large language model developed by OpenAI. It is based on the GPT (Generative Pre-training Transformer) architecture and is trained on a massive dataset of text data.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/www.interactivebrokers.com\/campus\/ibkr-quant-news\/can-chatgpt-self-improve-self-written-python-code-for-cholesky-decomposition\/\" \/>\n<meta property=\"og:site_name\" content=\"IBKR Campus US\" \/>\n<meta property=\"article:published_time\" content=\"2023-02-15T15:25:00+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2023-02-15T15:26:04+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/www.interactivebrokers.com\/campus\/wp-content\/uploads\/sites\/2\/2023\/02\/quant-robot-ai.jpg\" \/>\n\t<meta property=\"og:image:width\" content=\"1000\" \/>\n\t<meta property=\"og:image:height\" content=\"563\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/jpeg\" \/>\n<meta name=\"author\" content=\"Dr. Pawel Lachowicz\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"Dr. Pawel Lachowicz\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"8 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\n\t    \"@context\": \"https:\\\/\\\/schema.org\",\n\t    \"@graph\": [\n\t        {\n\t            \"@type\": \"NewsArticle\",\n\t            \"@id\": \"https:\\\/\\\/www.interactivebrokers.com\\\/campus\\\/ibkr-quant-news\\\/can-chatgpt-self-improve-self-written-python-code-for-cholesky-decomposition\\\/#article\",\n\t            \"isPartOf\": {\n\t                \"@id\": \"https:\\\/\\\/www.interactivebrokers.com\\\/campus\\\/ibkr-quant-news\\\/can-chatgpt-self-improve-self-written-python-code-for-cholesky-decomposition\\\/\"\n\t            },\n\t            \"author\": {\n\t                \"name\": \"Dr. Pawel Lachowicz\",\n\t                \"@id\": \"https:\\\/\\\/ibkrcampus.com\\\/campus\\\/#\\\/schema\\\/person\\\/5097d856a095fc59920af69437fb1797\"\n\t            },\n\t            \"headline\": \"Can ChatGPT Self-Improve Self-Written Python Code for Cholesky Decomposition?\",\n\t            \"datePublished\": \"2023-02-15T15:25:00+00:00\",\n\t            \"dateModified\": \"2023-02-15T15:26:04+00:00\",\n\t            \"mainEntityOfPage\": {\n\t                \"@id\": \"https:\\\/\\\/www.interactivebrokers.com\\\/campus\\\/ibkr-quant-news\\\/can-chatgpt-self-improve-self-written-python-code-for-cholesky-decomposition\\\/\"\n\t            },\n\t            \"wordCount\": 1491,\n\t            \"publisher\": {\n\t                \"@id\": \"https:\\\/\\\/ibkrcampus.com\\\/campus\\\/#organization\"\n\t            },\n\t            \"image\": {\n\t                \"@id\": \"https:\\\/\\\/www.interactivebrokers.com\\\/campus\\\/ibkr-quant-news\\\/can-chatgpt-self-improve-self-written-python-code-for-cholesky-decomposition\\\/#primaryimage\"\n\t            },\n\t            \"thumbnailUrl\": \"https:\\\/\\\/www.interactivebrokers.com\\\/campus\\\/wp-content\\\/uploads\\\/sites\\\/2\\\/2023\\\/02\\\/quant-robot-ai.jpg\",\n\t            \"keywords\": [\n\t                \"ChatGPT\",\n\t                \"Cholesky Decomposition\",\n\t                \"Decentralised Finance (DeFi)\",\n\t                \"Natural Language Processing (NLP)\",\n\t                \"NumPy\",\n\t                \"OpenAI\",\n\t                \"Python\",\n\t                \"Quantitative Finance\",\n\t                \"Rust\",\n\t                \"VAR\"\n\t            ],\n\t            \"articleSection\": [\n\t                \"Data Science\",\n\t                \"Python Development\",\n\t                \"Quant\",\n\t                \"Quant Asia Pacific\",\n\t                \"Quant Development\",\n\t                \"Quant Europe\",\n\t                \"Quant North America\",\n\t                \"Quant Regions\",\n\t                \"Quant South America\"\n\t            ],\n\t            \"inLanguage\": \"en-US\"\n\t        },\n\t        {\n\t            \"@type\": \"WebPage\",\n\t            \"@id\": \"https:\\\/\\\/www.interactivebrokers.com\\\/campus\\\/ibkr-quant-news\\\/can-chatgpt-self-improve-self-written-python-code-for-cholesky-decomposition\\\/\",\n\t            \"url\": \"https:\\\/\\\/www.interactivebrokers.com\\\/campus\\\/ibkr-quant-news\\\/can-chatgpt-self-improve-self-written-python-code-for-cholesky-decomposition\\\/\",\n\t            \"name\": \"Can ChatGPT Self-Improve Self-Written Python Code for Cholesky Decomposition? | IBKR Quant Blog\",\n\t            \"isPartOf\": {\n\t                \"@id\": \"https:\\\/\\\/ibkrcampus.com\\\/campus\\\/#website\"\n\t            },\n\t            \"primaryImageOfPage\": {\n\t                \"@id\": \"https:\\\/\\\/www.interactivebrokers.com\\\/campus\\\/ibkr-quant-news\\\/can-chatgpt-self-improve-self-written-python-code-for-cholesky-decomposition\\\/#primaryimage\"\n\t            },\n\t            \"image\": {\n\t                \"@id\": \"https:\\\/\\\/www.interactivebrokers.com\\\/campus\\\/ibkr-quant-news\\\/can-chatgpt-self-improve-self-written-python-code-for-cholesky-decomposition\\\/#primaryimage\"\n\t            },\n\t            \"thumbnailUrl\": \"https:\\\/\\\/www.interactivebrokers.com\\\/campus\\\/wp-content\\\/uploads\\\/sites\\\/2\\\/2023\\\/02\\\/quant-robot-ai.jpg\",\n\t            \"datePublished\": \"2023-02-15T15:25:00+00:00\",\n\t            \"dateModified\": \"2023-02-15T15:26:04+00:00\",\n\t            \"description\": \"ChatGPT is a large language model developed by OpenAI. It is based on the GPT (Generative Pre-training Transformer) architecture and is trained on a massive dataset of text data.\",\n\t            \"inLanguage\": \"en-US\",\n\t            \"potentialAction\": [\n\t                {\n\t                    \"@type\": \"ReadAction\",\n\t                    \"target\": [\n\t                        \"https:\\\/\\\/www.interactivebrokers.com\\\/campus\\\/ibkr-quant-news\\\/can-chatgpt-self-improve-self-written-python-code-for-cholesky-decomposition\\\/\"\n\t                    ]\n\t                }\n\t            ]\n\t        },\n\t        {\n\t            \"@type\": \"ImageObject\",\n\t            \"inLanguage\": \"en-US\",\n\t            \"@id\": \"https:\\\/\\\/www.interactivebrokers.com\\\/campus\\\/ibkr-quant-news\\\/can-chatgpt-self-improve-self-written-python-code-for-cholesky-decomposition\\\/#primaryimage\",\n\t            \"url\": \"https:\\\/\\\/www.interactivebrokers.com\\\/campus\\\/wp-content\\\/uploads\\\/sites\\\/2\\\/2023\\\/02\\\/quant-robot-ai.jpg\",\n\t            \"contentUrl\": \"https:\\\/\\\/www.interactivebrokers.com\\\/campus\\\/wp-content\\\/uploads\\\/sites\\\/2\\\/2023\\\/02\\\/quant-robot-ai.jpg\",\n\t            \"width\": 1000,\n\t            \"height\": 563,\n\t            \"caption\": \"Quant\"\n\t        },\n\t        {\n\t            \"@type\": \"WebSite\",\n\t            \"@id\": \"https:\\\/\\\/ibkrcampus.com\\\/campus\\\/#website\",\n\t            \"url\": \"https:\\\/\\\/ibkrcampus.com\\\/campus\\\/\",\n\t            \"name\": \"IBKR Campus US\",\n\t            \"description\": \"Financial Education from Interactive Brokers\",\n\t            \"publisher\": {\n\t                \"@id\": \"https:\\\/\\\/ibkrcampus.com\\\/campus\\\/#organization\"\n\t            },\n\t            \"potentialAction\": [\n\t                {\n\t                    \"@type\": \"SearchAction\",\n\t                    \"target\": {\n\t                        \"@type\": \"EntryPoint\",\n\t                        \"urlTemplate\": \"https:\\\/\\\/ibkrcampus.com\\\/campus\\\/?s={search_term_string}\"\n\t                    },\n\t                    \"query-input\": {\n\t                        \"@type\": \"PropertyValueSpecification\",\n\t                        \"valueRequired\": true,\n\t                        \"valueName\": \"search_term_string\"\n\t                    }\n\t                }\n\t            ],\n\t            \"inLanguage\": \"en-US\"\n\t        },\n\t        {\n\t            \"@type\": \"Organization\",\n\t            \"@id\": \"https:\\\/\\\/ibkrcampus.com\\\/campus\\\/#organization\",\n\t            \"name\": \"Interactive Brokers\",\n\t            \"alternateName\": \"IBKR\",\n\t            \"url\": \"https:\\\/\\\/ibkrcampus.com\\\/campus\\\/\",\n\t            \"logo\": {\n\t                \"@type\": \"ImageObject\",\n\t                \"inLanguage\": \"en-US\",\n\t                \"@id\": \"https:\\\/\\\/ibkrcampus.com\\\/campus\\\/#\\\/schema\\\/logo\\\/image\\\/\",\n\t                \"url\": \"https:\\\/\\\/www.interactivebrokers.com\\\/campus\\\/wp-content\\\/uploads\\\/sites\\\/2\\\/2024\\\/05\\\/ibkr-campus-logo.jpg\",\n\t                \"contentUrl\": \"https:\\\/\\\/www.interactivebrokers.com\\\/campus\\\/wp-content\\\/uploads\\\/sites\\\/2\\\/2024\\\/05\\\/ibkr-campus-logo.jpg\",\n\t                \"width\": 669,\n\t                \"height\": 669,\n\t                \"caption\": \"Interactive Brokers\"\n\t            },\n\t            \"image\": {\n\t                \"@id\": \"https:\\\/\\\/ibkrcampus.com\\\/campus\\\/#\\\/schema\\\/logo\\\/image\\\/\"\n\t            },\n\t            \"publishingPrinciples\": \"https:\\\/\\\/www.interactivebrokers.com\\\/campus\\\/about-ibkr-campus\\\/\",\n\t            \"ethicsPolicy\": \"https:\\\/\\\/www.interactivebrokers.com\\\/campus\\\/cyber-security-notice\\\/\"\n\t        },\n\t        {\n\t            \"@type\": \"Person\",\n\t            \"@id\": \"https:\\\/\\\/ibkrcampus.com\\\/campus\\\/#\\\/schema\\\/person\\\/5097d856a095fc59920af69437fb1797\",\n\t            \"name\": \"Dr. Pawel Lachowicz\",\n\t            \"sameAs\": [\n\t                \"https:\\\/\\\/quantatrisk.com\\\/\"\n\t            ],\n\t            \"url\": \"https:\\\/\\\/www.interactivebrokers.com\\\/campus\\\/author\\\/pawellachowicz\\\/\"\n\t        }\n\t    ]\n\t}<\/script>\n<!-- \/ Yoast SEO Premium plugin. -->","yoast_head_json":{"title":"Can ChatGPT Self-Improve Self-Written Python Code for Cholesky Decomposition?","description":"ChatGPT is a large language model developed by OpenAI. It is based on the GPT (Generative Pre-training Transformer) architecture and is trained on a...","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/www.interactivebrokers.com\/campus\/wp-json\/wp\/v2\/posts\/184976\/","og_locale":"en_US","og_type":"article","og_title":"Can ChatGPT Self-Improve Self-Written Python Code for Cholesky Decomposition? | IBKR Quant Blog","og_description":"ChatGPT is a large language model developed by OpenAI. It is based on the GPT (Generative Pre-training Transformer) architecture and is trained on a massive dataset of text data.","og_url":"https:\/\/www.interactivebrokers.com\/campus\/ibkr-quant-news\/can-chatgpt-self-improve-self-written-python-code-for-cholesky-decomposition\/","og_site_name":"IBKR Campus US","article_published_time":"2023-02-15T15:25:00+00:00","article_modified_time":"2023-02-15T15:26:04+00:00","og_image":[{"width":1000,"height":563,"url":"https:\/\/www.interactivebrokers.com\/campus\/wp-content\/uploads\/sites\/2\/2023\/02\/quant-robot-ai.jpg","type":"image\/jpeg"}],"author":"Dr. Pawel Lachowicz","twitter_card":"summary_large_image","twitter_misc":{"Written by":"Dr. Pawel Lachowicz","Est. reading time":"8 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"NewsArticle","@id":"https:\/\/www.interactivebrokers.com\/campus\/ibkr-quant-news\/can-chatgpt-self-improve-self-written-python-code-for-cholesky-decomposition\/#article","isPartOf":{"@id":"https:\/\/www.interactivebrokers.com\/campus\/ibkr-quant-news\/can-chatgpt-self-improve-self-written-python-code-for-cholesky-decomposition\/"},"author":{"name":"Dr. Pawel Lachowicz","@id":"https:\/\/ibkrcampus.com\/campus\/#\/schema\/person\/5097d856a095fc59920af69437fb1797"},"headline":"Can ChatGPT Self-Improve Self-Written Python Code for Cholesky Decomposition?","datePublished":"2023-02-15T15:25:00+00:00","dateModified":"2023-02-15T15:26:04+00:00","mainEntityOfPage":{"@id":"https:\/\/www.interactivebrokers.com\/campus\/ibkr-quant-news\/can-chatgpt-self-improve-self-written-python-code-for-cholesky-decomposition\/"},"wordCount":1491,"publisher":{"@id":"https:\/\/ibkrcampus.com\/campus\/#organization"},"image":{"@id":"https:\/\/www.interactivebrokers.com\/campus\/ibkr-quant-news\/can-chatgpt-self-improve-self-written-python-code-for-cholesky-decomposition\/#primaryimage"},"thumbnailUrl":"https:\/\/www.interactivebrokers.com\/campus\/wp-content\/uploads\/sites\/2\/2023\/02\/quant-robot-ai.jpg","keywords":["ChatGPT","Cholesky Decomposition","Decentralised Finance (DeFi)","Natural Language Processing (NLP)","NumPy","OpenAI","Python","Quantitative Finance","Rust","VAR"],"articleSection":["Data Science","Python Development","Quant","Quant Asia Pacific","Quant Development","Quant Europe","Quant North America","Quant Regions","Quant South America"],"inLanguage":"en-US"},{"@type":"WebPage","@id":"https:\/\/www.interactivebrokers.com\/campus\/ibkr-quant-news\/can-chatgpt-self-improve-self-written-python-code-for-cholesky-decomposition\/","url":"https:\/\/www.interactivebrokers.com\/campus\/ibkr-quant-news\/can-chatgpt-self-improve-self-written-python-code-for-cholesky-decomposition\/","name":"Can ChatGPT Self-Improve Self-Written Python Code for Cholesky Decomposition? | IBKR Quant Blog","isPartOf":{"@id":"https:\/\/ibkrcampus.com\/campus\/#website"},"primaryImageOfPage":{"@id":"https:\/\/www.interactivebrokers.com\/campus\/ibkr-quant-news\/can-chatgpt-self-improve-self-written-python-code-for-cholesky-decomposition\/#primaryimage"},"image":{"@id":"https:\/\/www.interactivebrokers.com\/campus\/ibkr-quant-news\/can-chatgpt-self-improve-self-written-python-code-for-cholesky-decomposition\/#primaryimage"},"thumbnailUrl":"https:\/\/www.interactivebrokers.com\/campus\/wp-content\/uploads\/sites\/2\/2023\/02\/quant-robot-ai.jpg","datePublished":"2023-02-15T15:25:00+00:00","dateModified":"2023-02-15T15:26:04+00:00","description":"ChatGPT is a large language model developed by OpenAI. It is based on the GPT (Generative Pre-training Transformer) architecture and is trained on a massive dataset of text data.","inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/www.interactivebrokers.com\/campus\/ibkr-quant-news\/can-chatgpt-self-improve-self-written-python-code-for-cholesky-decomposition\/"]}]},{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/www.interactivebrokers.com\/campus\/ibkr-quant-news\/can-chatgpt-self-improve-self-written-python-code-for-cholesky-decomposition\/#primaryimage","url":"https:\/\/www.interactivebrokers.com\/campus\/wp-content\/uploads\/sites\/2\/2023\/02\/quant-robot-ai.jpg","contentUrl":"https:\/\/www.interactivebrokers.com\/campus\/wp-content\/uploads\/sites\/2\/2023\/02\/quant-robot-ai.jpg","width":1000,"height":563,"caption":"Quant"},{"@type":"WebSite","@id":"https:\/\/ibkrcampus.com\/campus\/#website","url":"https:\/\/ibkrcampus.com\/campus\/","name":"IBKR Campus US","description":"Financial Education from Interactive Brokers","publisher":{"@id":"https:\/\/ibkrcampus.com\/campus\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/ibkrcampus.com\/campus\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"en-US"},{"@type":"Organization","@id":"https:\/\/ibkrcampus.com\/campus\/#organization","name":"Interactive Brokers","alternateName":"IBKR","url":"https:\/\/ibkrcampus.com\/campus\/","logo":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/ibkrcampus.com\/campus\/#\/schema\/logo\/image\/","url":"https:\/\/www.interactivebrokers.com\/campus\/wp-content\/uploads\/sites\/2\/2024\/05\/ibkr-campus-logo.jpg","contentUrl":"https:\/\/www.interactivebrokers.com\/campus\/wp-content\/uploads\/sites\/2\/2024\/05\/ibkr-campus-logo.jpg","width":669,"height":669,"caption":"Interactive Brokers"},"image":{"@id":"https:\/\/ibkrcampus.com\/campus\/#\/schema\/logo\/image\/"},"publishingPrinciples":"https:\/\/www.interactivebrokers.com\/campus\/about-ibkr-campus\/","ethicsPolicy":"https:\/\/www.interactivebrokers.com\/campus\/cyber-security-notice\/"},{"@type":"Person","@id":"https:\/\/ibkrcampus.com\/campus\/#\/schema\/person\/5097d856a095fc59920af69437fb1797","name":"Dr. Pawel Lachowicz","sameAs":["https:\/\/quantatrisk.com\/"],"url":"https:\/\/www.interactivebrokers.com\/campus\/author\/pawellachowicz\/"}]}},"jetpack_featured_media_url":"https:\/\/www.interactivebrokers.com\/campus\/wp-content\/uploads\/sites\/2\/2023\/02\/quant-robot-ai.jpg","_links":{"self":[{"href":"https:\/\/ibkrcampus.com\/campus\/wp-json\/wp\/v2\/posts\/184976","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ibkrcampus.com\/campus\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/ibkrcampus.com\/campus\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/ibkrcampus.com\/campus\/wp-json\/wp\/v2\/users\/710"}],"replies":[{"embeddable":true,"href":"https:\/\/ibkrcampus.com\/campus\/wp-json\/wp\/v2\/comments?post=184976"}],"version-history":[{"count":0,"href":"https:\/\/ibkrcampus.com\/campus\/wp-json\/wp\/v2\/posts\/184976\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/ibkrcampus.com\/campus\/wp-json\/wp\/v2\/media\/185009"}],"wp:attachment":[{"href":"https:\/\/ibkrcampus.com\/campus\/wp-json\/wp\/v2\/media?parent=184976"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ibkrcampus.com\/campus\/wp-json\/wp\/v2\/categories?post=184976"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ibkrcampus.com\/campus\/wp-json\/wp\/v2\/tags?post=184976"},{"taxonomy":"contributors-categories","embeddable":true,"href":"https:\/\/ibkrcampus.com\/campus\/wp-json\/wp\/v2\/contributors-categories?post=184976"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}