mirror of
https://github.com/MartinThoma/LaTeX-examples.git
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65 lines
2.6 KiB
TeX
65 lines
2.6 KiB
TeX
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\documentclass{article}
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\usepackage[pdftex,active,tightpage]{preview}
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\setlength\PreviewBorder{2mm}
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\usepackage[utf8]{inputenc} % this is needed for umlauts
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\usepackage[ngerman]{babel} % this is needed for umlauts
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\usepackage[T1]{fontenc} % this is needed for correct output of umlauts in pdf
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\usepackage{amssymb,amsmath,amsfonts} % nice math rendering
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\usepackage{braket} % needed for \Set
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\usepackage{algorithm,algpseudocode}
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\begin{document}
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\begin{preview}
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\begin{algorithm}[H]
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\begin{algorithmic}
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\Function{Gauss}{$A \in \mathbb{R}^{n \times {n+1}}$}
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\For{($i=1$; $\;i \leq n$; $\;i$++)}
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\State // Search for maximum in this column
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\State $maxEl = |A_{i,i}|$
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\State $maxRow = i$
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\For{($k=i+1$; $\;k \leq n$; $\;k$++)}
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\If{$|A_{k,i}| > maxEl$}
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\State $maxEl = A_{k,i}$
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\State $maxRow = k$
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\EndIf
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\EndFor
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\\
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\State // Swap maximum row with current row
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\For{($k=i$; $\;k \leq n$; $\;k$++)}
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\State $tmp = A_{maxRow,k}$
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\State $A_{maxRow,k} = A_{i,k}$
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\State $A_{i,k} = tmp$
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\EndFor
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\\
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\State // Make all rows below this one 0 in current column
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\For{($k=i+1$; $\;k \leq n$; $\;k$++)}
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\State $c = -\frac{A_{k,i}}{A_{i,i}}$
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\For{($j=i$; $\;j \leq n$; $\;j$++)}
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\If{$i == j$}
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\State $A_{k,j} = 0$
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\Else
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\State $A_{k,j} += c \cdot A_{i,j}$
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\EndIf
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\EndFor
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\EndFor
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\EndFor
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\\
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\State // Solve equation for an upper triangular matrix
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\State $x = \Set{0} \in \mathbb{R^n}$
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\For{($i=n$; $\;i \geq 1$; $\;i$-\--)}
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\State $x_i = \frac{A_{i,n+1}}{A_{i,i}}$
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\For{($k=i-1$; $\;k \geq 1$; $\;k$-\--)}
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\State $A_{k,n+1} -= A_{k,i} \cdot x_{i}$
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\EndFor
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\EndFor
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\\
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\State \Return $x$
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\EndFunction
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\end{algorithmic}
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\caption{Gaussian elimination}
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\label{alg:seq1}
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\end{algorithm}
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\end{preview}
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\end{document}
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