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<TITLE> 矩阵运算函数 </TITLE>
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<H1><FONT SIZE=6 COLOR=#0000FF>4.7 矩阵运算函数 </FONT><FONT FACE="新细明体"></FONT>
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先介绍几个与矩阵转角有关的函数：<FONT COLOR=#FF0000>rot90</FONT>,<FONT COLOR=#FF0000>
fliplr</FONT>, <FONT COLOR=#FF0000>flipud</FONT>，它们的用法及说明请参考以下的例子。
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<FONT COLOR=#FF0000>>> A=[2 1 0; -2 5 -1; 3 4 6];</FONT>
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<FONT COLOR=#FF0000>>> B=rot90(A) % 将A矩阵逆时针转90度</FONT>
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<FONT COLOR=#FF0000>B =</FONT>
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<FONT COLOR=#FF0000>0 -1 6</FONT>
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<FONT COLOR=#FF0000>1 5 4</FONT>
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<FONT COLOR=#FF0000>2 -2 3<BR>
</FONT>
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<FONT COLOR=#FF0000>>> A=[1 2; 4 8; -2 0];</FONT>
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<FONT COLOR=#FF0000>>> B=fliplr(A); % 将A矩阵从左向右翻</FONT>
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<FONT COLOR=#FF0000>>> C=flipud(A); % 将A矩阵从上向下翻</FONT>
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<FONT COLOR=#FF0000>>> B, C<BR>
</FONT>
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<FONT COLOR=#FF0000>B =</FONT>
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<FONT COLOR=#FF0000>2 1</FONT>
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<FONT COLOR=#FF0000>8 4</FONT>
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<FONT COLOR=#FF0000>0 -2</FONT>
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<FONT COLOR=#FF0000>C =</FONT>
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<FONT COLOR=#FF0000>-2 0</FONT>
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<FONT COLOR=#FF0000>4 8</FONT>
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<FONT COLOR=#FF0000>1 2<BR>
</FONT>
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另外函数 <FONT COLOR=#FF0000>reshape</FONT> 则是用来调整矩阵改形，即是在矩阵的元素总数不变下，改变其列及行的大小。见以下范例。
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<FONT COLOR=#FF0000>>> A=[2 5 6 -1; 3 -2 10 0];</FONT>
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<FONT COLOR=#FF0000>>> B=reshape(A,4,2); % 将A矩阵改成 4x2
的矩阵</FONT>
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<FONT COLOR=#FF0000>>> C=reshape(A,1,8); % 将A矩阵改成 8x1
的矩阵</FONT>
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<FONT COLOR=#FF0000>>> B, C</FONT>
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<FONT COLOR=#FF0000>B =</FONT>
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<FONT COLOR=#FF0000>2 6</FONT>
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<FONT COLOR=#FF0000>3 10</FONT>
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<FONT COLOR=#FF0000>5 -1</FONT>
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<FONT COLOR=#FF0000>-2 0<BR>
C =</FONT>
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<FONT COLOR=#FF0000> 2 5</FONT>
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<FONT COLOR=#FF0000> 6 1</FONT>
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<FONT COLOR=#FF0000> 3 -2</FONT>
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<FONT COLOR=#FF0000>10 0</FONT>
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我们如果要将矩阵内的特定元素读取出来，或是将特定元素以其它值取代，以下的函数<FONT COLOR=#FF0000>diag</FONT>,
<FONT COLOR=#FF0000>triu</FONT>, <FONT COLOR=#FF0000>tril</FONT>
提供了这方面的功能。<FONT COLOR=#FF0000>diag</FONT>是只保留原矩阵的主对角线
(main diagonal) 的元素，其余的元素以零取代。<FONT COLOR=#FF0000>triu</FONT>,
<FONT COLOR=#FF0000>tril</FONT> 则是分别产生上三角形及下三角形矩阵，其余的元素也以零取代。以下的例子详细的说明这三个函数的用法：
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<FONT COLOR=#FF0000>>> V=[1 2 3];</FONT>
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<FONT COLOR=#FF0000>>> A=diag(V)</FONT>
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<FONT COLOR=#FF0000>A =</FONT>
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<FONT COLOR=#FF0000>1 0 0</FONT>
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<FONT COLOR=#FF0000>0 2 0</FONT>
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<FONT COLOR=#FF0000>0 0 3<BR>
</FONT>
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<FONT COLOR=#FF0000>>> A=[1:2:7; 3:3:12; 4:-1:1; 1:4]</FONT>
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<FONT COLOR=#FF0000>A =</FONT>
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<FONT COLOR=#FF0000>1 3 5 7</FONT>
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<FONT COLOR=#FF0000>3 6 9 12</FONT>
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<FONT COLOR=#FF0000>4 3 2 1</FONT>
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<FONT COLOR=#FF0000>1 2 3 4</FONT>
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<FONT COLOR=#FF0000>>> B=triu(A)</FONT>
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<FONT COLOR=#FF0000>B =</FONT>
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<FONT COLOR=#FF0000>1 3 5 7</FONT>
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<FONT COLOR=#FF0000>0 6 9 12</FONT>
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<FONT COLOR=#FF0000>0 0 2 1</FONT>
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<FONT COLOR=#FF0000>0 0 0 4</FONT>
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<FONT COLOR=#FF0000>>> C=triu(A,-1)</FONT>
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<FONT COLOR=#FF0000>C =</FONT>
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<FONT COLOR=#FF0000>1 3 5 7</FONT>
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<FONT COLOR=#FF0000>3 6 9 12</FONT>
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<FONT COLOR=#FF0000>0 3 2 1</FONT>
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<FONT COLOR=#FF0000>0 0 3 4</FONT>
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<FONT COLOR=#FF0000>>> D=triu(A,3)</FONT>
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<FONT COLOR=#FF0000>D =</FONT>
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<FONT COLOR=#FF0000>0 0 0 7</FONT>
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<FONT COLOR=#FF0000>0 0 0 0</FONT>
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<FONT COLOR=#FF0000>0 0 0 0</FONT>
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<FONT COLOR=#FF0000>0 0 0 0<BR>
</FONT>
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<FONT COLOR=#FF0000>>> B=tril(A)</FONT>
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<FONT COLOR=#FF0000>B =</FONT>
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<FONT COLOR=#FF0000>1 0 0 0</FONT>
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<FONT COLOR=#FF0000>3 6 0 0</FONT>
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<FONT COLOR=#FF0000>4 3 2 0</FONT>
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<FONT COLOR=#FF0000>1 2 3 4</FONT>
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<FONT COLOR=#FF0000>>> C=triu(A,-1)</FONT>
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<FONT COLOR=#FF0000>C =</FONT>
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<FONT COLOR=#FF0000>0 0 0 0</FONT>
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<FONT COLOR=#FF0000>3 0 0 0</FONT>
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<FONT COLOR=#FF0000>4 3 0 0</FONT>
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<FONT COLOR=#FF0000>1 2 3 0</FONT>
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<FONT COLOR=#FF0000>>> D=triu(A,3)</FONT>
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<FONT COLOR=#FF0000>D =</FONT>
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<FONT COLOR=#FF0000>1 3 5 7</FONT>
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<FONT COLOR=#FF0000>3 6 9 12</FONT>
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<FONT COLOR=#FF0000>4 3 2 1</FONT>
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<FONT COLOR=#FF0000>1 2 3 4<BR>
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