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<TITLE> 矩陣運算函數 </TITLE>
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<H1><FONT SIZE=6 COLOR=#0000FF>4.7 矩陣運算函數 </FONT><FONT FACE="新細明體"></FONT>
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先介紹幾個與矩陣轉角有關的函數：<FONT COLOR=#FF0000>rot90</FONT>,<FONT COLOR=#FF0000>
fliplr</FONT>, <FONT COLOR=#FF0000>flipud</FONT>，它們的用法及說明請參考以下的例子。
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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) % 將A矩陣逆時針轉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); % 將A矩陣從左向右翻</FONT>
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<FONT COLOR=#FF0000>>> C=flipud(A); % 將A矩陣從上向下翻</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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另外函數 <FONT COLOR=#FF0000>reshape</FONT> 則是用來調整矩陣改形，即是在矩陣的元素總數不變下，改變其列及行的大小。見以下范例。
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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); % 將A矩陣改成 4x2
的矩陣</FONT>
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<FONT COLOR=#FF0000>>> C=reshape(A,1,8); % 將A矩陣改成 8x1
的矩陣</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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我們如果要將矩陣內的特定元素讀取出來，或是將特定元素以其它值取代，以下的函數<FONT COLOR=#FF0000>diag</FONT>,
<FONT COLOR=#FF0000>triu</FONT>, <FONT COLOR=#FF0000>tril</FONT>
提供了這方面的功能。<FONT COLOR=#FF0000>diag</FONT>是只保留原矩陣的主對角線
(main diagonal) 的元素，其余的元素以零取代。<FONT COLOR=#FF0000>triu</FONT>,
<FONT COLOR=#FF0000>tril</FONT> 則是分別產生上三角形及下三角形矩陣，其余的元素也以零取代。以下的例子詳細的說明這三個函數的用法：
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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>
</FONT>
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