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0000000..aebf7d3 Binary files /dev/null and b/homeworks/reports/report_8.pdf differ diff --git a/homeworks/reports/report_8.tex b/homeworks/reports/report_8.tex new file mode 100644 index 0000000..f883d6d --- /dev/null +++ b/homeworks/reports/report_8.tex @@ -0,0 +1,56 @@ +\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} \ No newline at end of file diff --git a/main.cpp b/main.cpp index 58aa01d..cb302cc 100644 --- a/main.cpp +++ b/main.cpp @@ -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; } \ No newline at end of file