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feat: add homework_7 report
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tiankaima committed Jan 3, 2024
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77 changes: 77 additions & 0 deletions homeworks/reports/data/report_8_output.txt
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iterations: 61053
time spent: 2837150us
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Binary file added homeworks/reports/report_8.pdf
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56 changes: 56 additions & 0 deletions homeworks/reports/report_8.tex
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\documentclass{article}
\usepackage[UTF8]{ctex}
\usepackage{hyperref,float,indentfirst,verbatim,fancyhdr,graphicx,listings,longtable,amsmath, amsfonts,amssymb}
\newenvironment{metaverbatim}{\verbatim}{\endverbatim}

\textheight 23.5cm \textwidth 15.8cm
\topmargin -1.5cm \oddsidemargin 0.3cm \evensidemargin -0.3cm

\title{数值代数实验报告 8}
\author{马天开}

\begin{document}
\maketitle

\section{问题描述}

\subsection{SVD 迭代}

参考课本 7.6.2 节 (P234-240)SVD 迭代完成 SVD 算法 7.6.3, 并对附件 svddata.txt 中的矩阵作 SVD 分解 $A = P\Sigma Q$。并计算 $PP^T-I, QQ^T-I, P\Sigma Q-A$ 的绝对值最大的元素，依次用 ep, eq, et 表示。

\begin{metaverbatim}
输出格式为：
迭代次数：x
奇异值从小到大：
ep = xx
eq = xx
et = xx

A=PTQ
T= [矩阵]
P= [矩阵]
Q= [矩阵]
\end{metaverbatim}


\section{算法说明}

必须实现的算法有：

\begin{enumerate}
\item SVD 迭代 $\Rightarrow$ \verb|SVDMethod/SVDMethod|
\end{enumerate}

其中 SVD 分解中 2x2 的实现参考了：
\url{https://www.math.ucla.edu/~cffjiang/research/svd/svd.pdf}，
在此表示感谢。

\section{运行结果}

也可在 \verb|homeworks/reports/data/report_8_output.txt| 中查看。

\verbatiminput{data/report_8_output.txt}

\newpage

\end{document}
7 changes: 7 additions & 0 deletions main.cpp
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Expand Up @@ -59,5 +59,12 @@ int main() {
<< "eq = " << MatrixNorm_Infinity(r.V.transpose() * r.V - Matrix::identity(n)) << std::endl
<< "et = " << MatrixNorm_Infinity(r.U * A * r.V - r.B) << std::endl;

std::cout << "T=" << std::endl;
r.B.print();
std::cout << "P=" << std::endl;
r.U.print();
std::cout << "Q=" << std::endl;
r.V.print();

return 0;
}

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