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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd">
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<title>/Volumes/unix-files/u/ntl-new/ntl-9.9.0dev/doc/mat_RR.cpp.html</title>
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<font color="#0000ed"><i>/*</i></font><font color="#0000ed"><i>*************************************************************************\</i></font><br>
<br>
<font color="#0000ed"><i>MODULE: mat_RR</i></font><br>
<br>
<font color="#0000ed"><i>SUMMARY:</i></font><br>
<br>
<font color="#0000ed"><i>Defines the class mat_RR.</i></font><br>
<br>
<font color="#0000ed"><i>\*************************************************************************</i></font><font color="#0000ed"><i>*/</i></font><br>
<br>
<br>
<font color="#1773cc">#include </font><font color="#4a6f8b">&lt;NTL/matrix.h&gt;</font><br>
<font color="#1773cc">#include </font><font color="#4a6f8b">&lt;NTL/vec_vec_RR.h&gt;</font><br>
<br>
<font color="#008b00"><b>typedef</b></font>&nbsp;Mat&lt;RR&gt; mat_RR; <font color="#0000ed"><i>// backward compatibility</i></font><br>
<br>
<font color="#008b00"><b>void</b></font>&nbsp;add(mat_RR&amp; X, <font color="#008b00"><b>const</b></font>&nbsp;mat_RR&amp; A, <font color="#008b00"><b>const</b></font>&nbsp;mat_RR&amp; B); <br>
<font color="#0000ed"><i>// X = A + B</i></font><br>
<br>
<font color="#008b00"><b>void</b></font>&nbsp;sub(mat_RR&amp; X, <font color="#008b00"><b>const</b></font>&nbsp;mat_RR&amp; A, <font color="#008b00"><b>const</b></font>&nbsp;mat_RR&amp; B); <br>
<font color="#0000ed"><i>// X = A - B</i></font><br>
<br>
<font color="#008b00"><b>void</b></font>&nbsp;negate(mat_RR&amp; X, <font color="#008b00"><b>const</b></font>&nbsp;mat_RR&amp; A); <br>
<font color="#0000ed"><i>// X = - A</i></font><br>
<br>
<font color="#008b00"><b>void</b></font>&nbsp;mul(mat_RR&amp; X, <font color="#008b00"><b>const</b></font>&nbsp;mat_RR&amp; A, <font color="#008b00"><b>const</b></font>&nbsp;mat_RR&amp; B); <br>
<font color="#0000ed"><i>// X = A * B</i></font><br>
<br>
<font color="#008b00"><b>void</b></font>&nbsp;mul(vec_RR&amp; x, <font color="#008b00"><b>const</b></font>&nbsp;mat_RR&amp; A, <font color="#008b00"><b>const</b></font>&nbsp;vec_RR&amp; b); <br>
<font color="#0000ed"><i>// x = A * b</i></font><br>
<br>
<font color="#008b00"><b>void</b></font>&nbsp;mul(vec_RR&amp; x, <font color="#008b00"><b>const</b></font>&nbsp;vec_RR&amp; a, <font color="#008b00"><b>const</b></font>&nbsp;mat_RR&amp; B); <br>
<font color="#0000ed"><i>// x = a * B</i></font><br>
<br>
<font color="#008b00"><b>void</b></font>&nbsp;mul(mat_RR&amp; X, <font color="#008b00"><b>const</b></font>&nbsp;mat_RR&amp; A, <font color="#008b00"><b>const</b></font>&nbsp;RR&amp; b);<br>
<font color="#008b00"><b>void</b></font>&nbsp;mul(mat_RR&amp; X, <font color="#008b00"><b>const</b></font>&nbsp;mat_RR&amp; A, <font color="#008b00"><b>double</b></font>&nbsp;b);<br>
<font color="#0000ed"><i>// X = A * b</i></font><br>
<br>
<font color="#008b00"><b>void</b></font>&nbsp;mul(mat_RR&amp; X, <font color="#008b00"><b>const</b></font>&nbsp;RR&amp; a, <font color="#008b00"><b>const</b></font>&nbsp;mat_RR&amp; B);<br>
<font color="#008b00"><b>void</b></font>&nbsp;mul(mat_RR&amp; X, <font color="#008b00"><b>double</b></font>&nbsp;a, <font color="#008b00"><b>const</b></font>&nbsp;mat_RR&amp; B);<br>
<font color="#0000ed"><i>// X = a * B</i></font><br>
<br>
<br>
<font color="#008b00"><b>void</b></font>&nbsp;determinant(RR&amp; d, <font color="#008b00"><b>const</b></font>&nbsp;mat_RR&amp; A);<br>
RR determinant(<font color="#008b00"><b>const</b></font>&nbsp;mat_RR&amp; A);<br>
<font color="#0000ed"><i>// d = determinant(A)</i></font><br>
<br>
<br>
<font color="#008b00"><b>void</b></font>&nbsp;transpose(mat_RR&amp; X, <font color="#008b00"><b>const</b></font>&nbsp;mat_RR&amp; A);<br>
mat_RR transpose(<font color="#008b00"><b>const</b></font>&nbsp;mat_RR&amp; A);<br>
<font color="#0000ed"><i>// X = transpose of A</i></font><br>
<br>
<font color="#008b00"><b>void</b></font>&nbsp;solve(RR&amp; d, vec_RR&amp; X,<br>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; <font color="#008b00"><b>const</b></font>&nbsp;mat_RR&amp; A, <font color="#008b00"><b>const</b></font>&nbsp;vec_RR&amp; b);<br>
<font color="#0000ed"><i>// A is an n x n matrix, b is a length n vector.&nbsp;&nbsp;Computes d =</i></font><br>
<font color="#0000ed"><i>// determinant(A).&nbsp;&nbsp;If d != 0, solves x*A = b.</i></font><br>
<br>
<font color="#008b00"><b>void</b></font>&nbsp;inv(RR&amp; d, mat_RR&amp; X, <font color="#008b00"><b>const</b></font>&nbsp;mat_RR&amp; A);<br>
<font color="#0000ed"><i>// A is an n x n matrix.&nbsp;&nbsp;Computes d = determinant(A).&nbsp;&nbsp;If d != 0,</i></font><br>
<font color="#0000ed"><i>// computes X = A^{-1}.</i></font><br>
<br>
<font color="#008b00"><b>void</b></font>&nbsp;sqr(mat_RR&amp; X, <font color="#008b00"><b>const</b></font>&nbsp;mat_RR&amp; A);<br>
mat_RR sqr(<font color="#008b00"><b>const</b></font>&nbsp;mat_RR&amp; A);<br>
<font color="#0000ed"><i>// X = A*A</i></font><br>
<br>
<font color="#008b00"><b>void</b></font>&nbsp;inv(mat_RR&amp; X, <font color="#008b00"><b>const</b></font>&nbsp;mat_RR&amp; A);<br>
mat_RR inv(<font color="#008b00"><b>const</b></font>&nbsp;mat_RR&amp; A);<br>
<font color="#0000ed"><i>// X = A^{-1}; error is raised if A is&nbsp;&nbsp;singular</i></font><br>
<br>
<font color="#008b00"><b>void</b></font>&nbsp;power(mat_RR&amp; X, <font color="#008b00"><b>const</b></font>&nbsp;mat_RR&amp; A, <font color="#008b00"><b>const</b></font>&nbsp;ZZ&amp; e);<br>
mat_RR power(<font color="#008b00"><b>const</b></font>&nbsp;mat_RR&amp; A, <font color="#008b00"><b>const</b></font>&nbsp;ZZ&amp; e);<br>
<br>
<font color="#008b00"><b>void</b></font>&nbsp;power(mat_RR&amp; X, <font color="#008b00"><b>const</b></font>&nbsp;mat_RR&amp; A, <font color="#008b00"><b>long</b></font>&nbsp;e);<br>
mat_RR power(<font color="#008b00"><b>const</b></font>&nbsp;mat_RR&amp; A, <font color="#008b00"><b>long</b></font>&nbsp;e);<br>
<font color="#0000ed"><i>// X = A^e; e may be negative (in which case A must be nonsingular).</i></font><br>
<br>
<font color="#008b00"><b>void</b></font>&nbsp;ident(mat_RR&amp; X, <font color="#008b00"><b>long</b></font>&nbsp;n);<br>
mat_RR ident_mat_RR(<font color="#008b00"><b>long</b></font>&nbsp;n);<br>
<font color="#0000ed"><i>// X = n x n identity matrix</i></font><br>
<br>
<font color="#008b00"><b>long</b></font>&nbsp;IsIdent(<font color="#008b00"><b>const</b></font>&nbsp;mat_RR&amp; A, <font color="#008b00"><b>long</b></font>&nbsp;n);<br>
<font color="#0000ed"><i>// test if A is the n x n identity matrix</i></font><br>
<br>
<font color="#008b00"><b>void</b></font>&nbsp;diag(mat_RR&amp; X, <font color="#008b00"><b>long</b></font>&nbsp;n, <font color="#008b00"><b>const</b></font>&nbsp;RR&amp; d);<br>
mat_RR diag(<font color="#008b00"><b>long</b></font>&nbsp;n, <font color="#008b00"><b>const</b></font>&nbsp;RR&amp; d);<br>
<font color="#0000ed"><i>// X = n x n diagonal matrix with d on diagonal</i></font><br>
<br>
<font color="#008b00"><b>long</b></font>&nbsp;IsDiag(<font color="#008b00"><b>const</b></font>&nbsp;mat_RR&amp; A, <font color="#008b00"><b>long</b></font>&nbsp;n, <font color="#008b00"><b>const</b></font>&nbsp;RR&amp; d);<br>
<font color="#0000ed"><i>// test if X is an&nbsp;&nbsp;n x n diagonal matrix with d on diagonal</i></font><br>
<br>
<br>
<br>
<br>
<br>
<font color="#0000ed"><i>// miscellaneous:</i></font><br>
<br>
<font color="#008b00"><b>void</b></font>&nbsp;clear(mat_RR&amp; a);<br>
<font color="#0000ed"><i>// x = 0 (dimension unchanged)</i></font><br>
<br>
<font color="#008b00"><b>long</b></font>&nbsp;IsZero(<font color="#008b00"><b>const</b></font>&nbsp;mat_RR&amp; a);<br>
<font color="#0000ed"><i>// test if a is the zero matrix (any dimension)</i></font><br>
<br>
<br>
<font color="#0000ed"><i>// operator notation:</i></font><br>
<br>
mat_RR <font color="#b02f60"><b>operator</b></font>+(<font color="#008b00"><b>const</b></font>&nbsp;mat_RR&amp; a, <font color="#008b00"><b>const</b></font>&nbsp;mat_RR&amp; b);<br>
mat_RR <font color="#b02f60"><b>operator</b></font>-(<font color="#008b00"><b>const</b></font>&nbsp;mat_RR&amp; a, <font color="#008b00"><b>const</b></font>&nbsp;mat_RR&amp; b);<br>
mat_RR <font color="#b02f60"><b>operator</b></font>*(<font color="#008b00"><b>const</b></font>&nbsp;mat_RR&amp; a, <font color="#008b00"><b>const</b></font>&nbsp;mat_RR&amp; b);<br>
<br>
mat_RR <font color="#b02f60"><b>operator</b></font>-(<font color="#008b00"><b>const</b></font>&nbsp;mat_RR&amp; a);<br>
<br>
<br>
<font color="#0000ed"><i>// matrix/scalar multiplication:</i></font><br>
<br>
mat_RR <font color="#b02f60"><b>operator</b></font>*(<font color="#008b00"><b>const</b></font>&nbsp;mat_RR&amp; a, <font color="#008b00"><b>const</b></font>&nbsp;RR&amp; b);<br>
mat_RR <font color="#b02f60"><b>operator</b></font>*(<font color="#008b00"><b>const</b></font>&nbsp;mat_RR&amp; a, <font color="#008b00"><b>double</b></font>&nbsp;b);<br>
<br>
mat_RR <font color="#b02f60"><b>operator</b></font>*(<font color="#008b00"><b>const</b></font>&nbsp;RR&amp; a, <font color="#008b00"><b>const</b></font>&nbsp;mat_RR&amp; b);<br>
mat_RR <font color="#b02f60"><b>operator</b></font>*(<font color="#008b00"><b>double</b></font>&nbsp;a, <font color="#008b00"><b>const</b></font>&nbsp;mat_RR&amp; b);<br>
<br>
<br>
<font color="#0000ed"><i>// matrix/vector multiplication:</i></font><br>
<br>
vec_RR <font color="#b02f60"><b>operator</b></font>*(<font color="#008b00"><b>const</b></font>&nbsp;mat_RR&amp; a, <font color="#008b00"><b>const</b></font>&nbsp;vec_RR&amp; b);<br>
<br>
vec_RR <font color="#b02f60"><b>operator</b></font>*(<font color="#008b00"><b>const</b></font>&nbsp;vec_RR&amp; a, <font color="#008b00"><b>const</b></font>&nbsp;mat_RR&amp; b);<br>
<br>
<br>
<font color="#0000ed"><i>// assignment operator notation:</i></font><br>
<br>
mat_RR&amp; <font color="#b02f60"><b>operator</b></font>+=(mat_RR&amp; x, <font color="#008b00"><b>const</b></font>&nbsp;mat_RR&amp; a);<br>
mat_RR&amp; <font color="#b02f60"><b>operator</b></font>-=(mat_RR&amp; x, <font color="#008b00"><b>const</b></font>&nbsp;mat_RR&amp; a);<br>
mat_RR&amp; <font color="#b02f60"><b>operator</b></font>*=(mat_RR&amp; x, <font color="#008b00"><b>const</b></font>&nbsp;mat_RR&amp; a);<br>
<br>
mat_RR&amp; <font color="#b02f60"><b>operator</b></font>*=(mat_RR&amp; x, <font color="#008b00"><b>const</b></font>&nbsp;RR&amp; a);<br>
mat_RR&amp; <font color="#b02f60"><b>operator</b></font>*=(mat_RR&amp; x, <font color="#008b00"><b>double</b></font>&nbsp;a);<br>
<br>
vec_RR&amp; <font color="#b02f60"><b>operator</b></font>*=(vec_RR&amp; x, <font color="#008b00"><b>const</b></font>&nbsp;mat_RR&amp; a);<br>
<br>
<br>
<br>
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