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% Document Info
\author{ThanhTrungK15}
\pdfinfo{
  /Title (convex-optimization.pdf)
  /Creator (Cheatography)
  /Author (ThanhTrungK15)
  /Subject (Convex Optimization Cheat Sheet)
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\noindent
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    {\parbox{\dimexpr\textwidth-2\fboxsep\relax}{\noindent
        \hspace*{-6pt}\includegraphics[width=5.8cm]{/web/www.cheatography.com/public/images/cheatography_logo.pdf}}
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    \vspace{-2pt}\large{\bf{\textcolor{DarkBackground}{\textrm{Convex Optimization Cheat Sheet}}}} \\
    \normalsize{by \textcolor{DarkBackground}{ThanhTrungK15} via \textcolor{DarkBackground}{\uline{cheatography.com/137592/cs/28908/}}}
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  \mymulticolumn{2}{p{5.377cm}}{\bf\textcolor{white}{Cheatographer}}  \\
  \vspace{-2pt}ThanhTrungK15 \\
  \uline{cheatography.com/thanhtrungk15} \\
  \end{tabulary}
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  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Cheat Sheet}}  \\
   \vspace{-2pt}Published 20th August, 2021.\\
   Updated 20th August, 2021.\\
   Page {\thepage} of \pageref{LastPage}.
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  Measure your website readability!\\
  www.readability-score.com
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\begin{tabularx}{8.4cm}{X}
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\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{CVXOPT}}  \tn
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\mymulticolumn{1}{x{8.4cm}}{The {\bf{CVXOPT}} is a free software package for convex optimization based on the Python programming language. Its main purpose is to make the development of software for convex optimization applications straightforward by building on Python's extensive standard library and on the strengths of Python as a high-level programming language. \newline % Row Count 7 (+ 7)
Use the following import convention: \newline % Row Count 8 (+ 1)
`\textgreater{}\textgreater{}\textgreater{} import cvxopt`% Row Count 9 (+ 1)
} \tn 
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\begin{tabularx}{8.4cm}{X}
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\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{Dense and Sparse Matrices}}  \tn
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\mymulticolumn{1}{x{8.4cm}}{{\bf{CVXOPT}} extends the built-in Python objects with two matrix objects: {\bf{{\emph{spmatrix}}}} for sparse matrix and {\bf{{\emph{matrix}}}} for dense matrix}  \tn 
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\begin{tabularx}{8.4cm}{X}
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\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{Dense Matrices}}  \tn
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\mymulticolumn{1}{x{8.4cm}}{-{}-{}- The function {\bf{{\emph{matrix}}}} -{}-{}- \newline \textgreater{}\textgreater{}\textgreater{} from cvxopt import matrix \newline \textgreater{}\textgreater{}\textgreater{} A = matrix(1, (1, 4)) \newline \textgreater{}\textgreater{}\textgreater{} print(A) \newline    {[} 1  1  1  1{]} \newline \textgreater{}\textgreater{}\textgreater{} A = matrix(1.0, (1, 4)) \newline \textgreater{}\textgreater{}\textgreater{} print(A) \newline    {[} 1.00e+00  1.00e+00  1.00e+00  1.00e+00{]} \newline \textgreater{}\textgreater{}\textgreater{} A = matrix(1 + 1j) \newline \textgreater{}\textgreater{}\textgreater{} print(A) \newline    {[} 1.00e+00+j1.00e+00{]} \newline  \newline -{}-{}- Several ways to define integer matrix -{}-{}- \newline \textgreater{}\textgreater{}\textgreater{} A = matrix({[}0, 1, 2, 3{]}, (2,2)) \newline \textgreater{}\textgreater{}\textgreater{} A = matrix((0, 1, 2, 3), (2,2)) \newline \textgreater{}\textgreater{}\textgreater{} A = matrix(range(4), (2,2)) \newline \textgreater{}\textgreater{}\textgreater{} from array import array \newline \textgreater{}\textgreater{}\textgreater{} A = matrix(array('i', {[}0,1,2,3{]}), (2,2)) \newline \textgreater{}\textgreater{}\textgreater{} print(A) \newline    {[} 0  2{]} \newline    {[} 1  3{]} \newline  \newline -{}-{}- {\bf{{\emph{NumPy}}}} arrays can be converted to matrices -{}-{}- \newline \textgreater{}\textgreater{}\textgreater{} from numpy import array \newline \textgreater{}\textgreater{}\textgreater{} x = array({[}{[}1., 2., 3.{]}, {[}4., 5., 6.{]}{]}) \newline \textgreater{}\textgreater{}\textgreater{} print(x) \newline    array({[}{[} 1.  2.  3.{]} \newline           {[} 4.  5.  6.{]}{]}) \newline \textgreater{}\textgreater{}\textgreater{} print(matrix(x)) \newline    {[} 1.00e+00  2.00e+00  3.00e+00{]} \newline    {[} 4.00e+00  5.00e+00  6.00e+00{]} \newline  \newline -{}-{}- Another ways to create dense matrix  -{}-{}- \newline \textgreater{}\textgreater{}\textgreater{} print(matrix({[}{[}1., 2.{]}, {[}3., 4.{]}, {[}5., 6.{]}{]})) \newline    {[} 1.00e+00  3.00e+00  5.00e+00{]} \newline    {[} 2.00e+00  4.00e+00  6.00e+00{]} \newline \textgreater{}\textgreater{}\textgreater{} B1 = matrix({[}6, 7, 8, 9, 10, 11{]}, (2,3)) \newline \textgreater{}\textgreater{}\textgreater{} B2 = matrix({[}12, 13, 14, 15, 16, 17{]}, (2,3)) \newline \textgreater{}\textgreater{}\textgreater{} B3 = matrix({[}18, 19, 20{]}, (1,3)) \newline \textgreater{}\textgreater{}\textgreater{} D = matrix({[}B1, B2, B3{]}) \newline \textgreater{}\textgreater{}\textgreater{} print(D) \newline    {[}  6   8  10{]} \newline    {[}  7   9  11{]} \newline    {[} 12  14  16{]} \newline    {[} 13  15  17{]} \newline    {[} 18  19  20{]}} \tn 
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\mymulticolumn{1}{x{8.4cm}}{\textgreater{}\textgreater{}\textgreater{} from cvxopt import matrix, spmatrix, sparse, spdiag \newline -{}-{}- The function {\bf{{\emph{spmatrix}}}}  -{}-{}- \newline \textgreater{}\textgreater{}\textgreater{} A = spmatrix(1.0, range(2), range(2)) \newline \textgreater{}\textgreater{}\textgreater{} print(A) \newline    {[} 1.00e+00     0    {]}                                                                                                    \newline    {[}    0      1.00e+00{]}  \newline \textgreater{}\textgreater{}\textgreater{} A = spmatrix({[}1, 2, 3, 4{]}, {[}0, 0, 1, 1{]}, {[}0, 1, 0, 1{]})                                                               \newline \textgreater{}\textgreater{}\textgreater{} print(A) \newline    {[} 1.00e+00  2.00e+00{]} \newline    {[} 3.00e+00  4.00e+00{]} \newline  \newline -{}-{}- The function {\bf{{\emph{sparse}}}} -{}-{}- \newline \textgreater{}\textgreater{}\textgreater{} A = matrix({[}{[}1, 2{]}, {[}5, 6{]}{]}) \newline \textgreater{}\textgreater{}\textgreater{} print(A) \newline    {[} 1  5{]} \newline    {[} 2  6{]} \newline \textgreater{}\textgreater{}\textgreater{} B = spmatrix({[}{]}, {[}{]}, {[}{]}, (2, 2)) \newline \textgreater{}\textgreater{}\textgreater{} print(B) \newline    {[}0 0{]} \newline    {[}0 0{]} \newline \textgreater{}\textgreater{}\textgreater{} C = spmatrix({[}4, 2, 1, 9{]}, {[}0, 0, 1, 1{]}, {[}0, 1, 1, 0{]}) \newline \textgreater{}\textgreater{}\textgreater{} print(C) \newline     {[} 4.00e+00  2.00e+00{]} \newline     {[} 9.00e+00  1.00e+00{]} \newline \textgreater{}\textgreater{}\textgreater{} D = sparse({[}{[}A, B{]}, {[}B, C{]}{]}) \newline \textgreater{}\textgreater{}\textgreater{} print(D) \newline    {[} 1.00e+00  5.00e+00     0         0    {]} \newline    {[} 2.00e+00  6.00e+00     0         0    {]} \newline    {[}    0         0      4.00e+00  2.00e+00{]} \newline    {[}    0         0      9.00e+00  1.00e+00{]} \newline \textgreater{}\textgreater{}\textgreater{} D = sparse({[}A, C{]}) \newline \textgreater{}\textgreater{}\textgreater{} print(D) \newline    {[} 1.00e+00  5.00e+00{]} \newline    {[} 2.00e+00  6.00e+00{]} \newline    {[} 4.00e+00  2.00e+00{]} \newline    {[} 9.00e+00  1.00e+00{]} \newline  \newline -{}-{}- The function {\bf{{\emph{spdiag}}}} -{}-{}- \newline \textgreater{}\textgreater{}\textgreater{} A = 3.0 \newline \textgreater{}\textgreater{}\textgreater{} print(A) \newline    3.0 \newline \textgreater{}\textgreater{}\textgreater{} B = matrix({[}{[}1, 2{]}, {[}4, 3{]}{]}) \newline \textgreater{}\textgreater{}\textgreater{} print(B) \newline    {[} 1  4{]} \newline    {[} 2  3{]} \newline \textgreater{}\textgreater{}\textgreater{} C = spmatrix({[}4, 5, 6, 7{]}, {[}0, 0, 1, 1{]}, {[}0, 1, 0, 1{]}) \newline \textgreater{}\textgreater{}\textgreater{} print(C) \newline    {[} 4.00e+00  5.00e+00{]} \newline    {[} 6.00e+00  7.00e+00{]} \newline \textgreater{}\textgreater{}\textgreater{} D = spdiag({[}A, B, C{]}) \newline \textgreater{}\textgreater{}\textgreater{} print(D) \newline    {[} 3.00e+00     0         0         0         0    {]} \newline    {[}    0      1.00e+00  4.00e+00     0         0    {]} \newline    {[}    0      2.00e+00  3.00e+00     0         0    {]} \newline    {[}    0         0         0      4.00e+00  5.00e+00{]} \newline    {[}    0         0         0      6.00e+00  7.00e+00{]}} \tn 
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\mymulticolumn{2}{x{8.4cm}}{`A` and `B` are dense or sparse matrices of compatible dimensions. \newline `c` is a scalar (a Python number or a dense 1 by 1 matrix) \newline `D` is a dense matrix. \newline `e` is a Python number}  \tn 
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% That's all folks
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