{"id":203133,"date":"2024-03-06T11:13:35","date_gmt":"2024-03-06T16:13:35","guid":{"rendered":"https:\/\/ibkrcampus.com\/?p=203133"},"modified":"2025-02-12T10:25:54","modified_gmt":"2025-02-12T15:25:54","slug":"r-symbolic-matrix-multiplications","status":"publish","type":"post","link":"https:\/\/www.interactivebrokers.com\/campus\/ibkr-quant-news\/r-symbolic-matrix-multiplications\/","title":{"rendered":"R: Symbolic Matrix Multiplications"},"content":{"rendered":"\n<p>This post shows how to perform symbolic matrix multiplications using two R libraries.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-symbolic-matrix-multiplications-in-r\">Symbolic Matrix Multiplications in R<\/h2>\n\n\n\n<p>Symbolic matrix multiplication is useful when trying to identify patterns in their products. To multiply two matrices with string elements (symbolic matrix), we can use the&nbsp;<strong>mx()<\/strong>&nbsp;function in the&nbsp;<strong>calculus<\/strong>&nbsp;R library, as follows.<\/p>\n\n\n\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"r\" data-enlighter-theme=\"\" data-enlighter-highlight=\"\" data-enlighter-linenumbers=\"\" data-enlighter-lineoffset=\"\" data-enlighter-title=\"\" data-enlighter-group=\"\">library(calculus) # mx\n \n# sample matrix with string elements\nm &lt;- matrix(\n    c(\"1\", \"0\", \"0\",\n      \"0\", \"a\", \"0\",\n      \"0\",\"-a\", \"a\"),\n    3,3, byrow = TRUE)\n \n# symblic matrix multiplication\nm2&lt;-mx(m, m); m2\nm3&lt;-mx(m, m2); m3<\/pre>\n\n\n\n<p>The output is satisfactory, but its length is excessive. A more concise representation would enhance its utility.<\/p>\n\n\n\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"r\" data-enlighter-theme=\"\" data-enlighter-highlight=\"\" data-enlighter-linenumbers=\"\" data-enlighter-lineoffset=\"\" data-enlighter-title=\"\" data-enlighter-group=\"\">> # symblic matrix multiplication\n> m2&lt;-mx(m, m); m2\n     [,1]        [,2]                      [,3]       \n[1,] \"(1) * (1)\" \"0\"                       \"0\"        \n[2,] \"0\"         \"(a) * (a)\"               \"0\"        \n[3,] \"0\"         \"(-a) * (a) + (a) * (-a)\" \"(a) * (a)\"\n> m3&lt;-mx(m, m2); m3\n     [,1]                [,2]                                                   [,3]               \n[1,] \"(1) * ((1) * (1))\" \"0\"                                                    \"0\"                \n[2,] \"0\"                 \"(a) * ((a) * (a))\"                                    \"0\"                \n[3,] \"0\"                 \"(-a) * ((a) * (a)) + (a) * ((-a) * (a) + (a) * (-a))\" \"(a) * ((a) * (a))\"<\/pre>\n\n\n\n<p>To compress the results, I make a user-defined function by utilizing the&nbsp;<strong>yacas(Expand(&#8220;string&#8221;))<\/strong>&nbsp;function in the&nbsp;<strong>Ryacas0<\/strong>&nbsp;R library, as demonstrated below.<\/p>\n\n\n\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"generic\" data-enlighter-theme=\"\" data-enlighter-highlight=\"\" data-enlighter-linenumbers=\"\" data-enlighter-lineoffset=\"\" data-enlighter-title=\"\" data-enlighter-group=\"\">library(Ryacas0)  # yacas\n \n# Function to apply yacas expression to each element \n# and replace with as.character(xx)\napply_yacas_and_replace &lt;- function(mat) {\n    ret_mat &lt;- matrix(nrow = nrow(mat), ncol = ncol(mat))\n    \n    for (i in 1:nrow(mat)) {\n        for (j in 1:ncol(mat)) {\n            # Apply yacas expression to each element\n            expr &lt;- yacas(paste(\"Expand(\", mat[i, j], \")\", \n                                sep = \"\"))\n            ret_mat[i, j] &lt;- as.character(expr)\n        }\n    }\n \n    # delete spaces\n    ret_mat&lt;- apply(ret_mat, c(1, 2), \n                    function(x) gsub(\"\\\\s\", \"\", x))\n    \n    return(ret_mat)\n}\n \n# Apply yacas expression and replace in the matrix\nm2_2 &lt;- apply_yacas_and_replace(m2); m2_2\nm3_2 &lt;- apply_yacas_and_replace(m3); m3_2<\/pre>\n\n\n\n<p>The outcomes now appear visually appealing, facilitating a more straightforward identification of potential patterns.<\/p>\n\n\n\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"r\" data-enlighter-theme=\"\" data-enlighter-highlight=\"\" data-enlighter-linenumbers=\"\" data-enlighter-lineoffset=\"\" data-enlighter-title=\"\" data-enlighter-group=\"\">> # Apply yacas expression and replace in the matrix\n> m2_2 &lt;- apply_yacas_and_replace(m2); m2_2\n     [,1] [,2]     [,3] \n[1,] \"1\"  \"0\"      \"0\"  \n[2,] \"0\"  \"a^2\"    \"0\"  \n[3,] \"0\"  \"-2*a^2\" \"a^2\"\n> m3_2 &lt;- apply_yacas_and_replace(m3); m3_2\n     [,1] [,2]     [,3] \n[1,] \"1\"  \"0\"      \"0\"  \n[2,] \"0\"  \"a^3\"    \"0\"  \n[3,] \"0\"  \"-3*a^3\" \"a^3\"\n> \n<\/pre>\n\n\n\n<p>In summary, the collaboration between these two R libraries has yielded relatively satisfactory results for symbolic matrix multiplication.<\/p>\n\n\n\n<p><em>Originally posted on <a href=\"https:\/\/shleeai.blogspot.com\/2024\/01\/r-symbolic-matrix-multiplications.html\">SHLee AI Financial Model<\/a> blog.<\/em><\/p>\n","protected":false},"excerpt":{"rendered":"<p>This post shows how to perform symbolic matrix multiplications using two R libraries.<\/p>\n","protected":false},"author":662,"featured_media":186467,"comment_status":"open","ping_status":"closed","sticky":true,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[339,343,338,341,342],"tags":[16788,806,16787,487,16789],"contributors-categories":[13728],"class_list":{"0":"post-203133","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-data-science","8":"category-programing-languages","9":"category-ibkr-quant-news","10":"category-quant-development","11":"category-r-development","12":"tag-calculus-r-library","13":"tag-data-science","14":"tag-matrix-multiplications","15":"tag-r","16":"tag-ryacas0-r-library","17":"contributors-categories-sh-fintech-modeling"},"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 v27.7) - 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