1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
|
<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII">
<title>posvx</title>
<link rel="stylesheet" href="../../../../boostbook.css" type="text/css">
<meta name="generator" content="DocBook XSL Stylesheets V1.75.2">
<link rel="home" href="../../../../index.html" title="Chapter 1. Boost.Numeric_Bindings">
<link rel="up" href="../driver_routines.html" title="Driver Routines">
<link rel="prev" href="posv.html" title="posv">
<link rel="next" href="ppsv.html" title="ppsv">
</head>
<body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF">
<table cellpadding="2" width="100%"><tr><td valign="top"></td></tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="posv.html"><img src="../../../../images/prev.png" alt="Prev"></a><a accesskey="u" href="../driver_routines.html"><img src="../../../../images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../images/home.png" alt="Home"></a><a accesskey="n" href="ppsv.html"><img src="../../../../images/next.png" alt="Next"></a>
</div>
<div class="section">
<div class="titlepage"><div><div><h5 class="title">
<a name="boost_numeric_bindings.reference.lapack.driver_routines.posvx"></a><a class="link" href="posvx.html" title="posvx">posvx</a>
</h5></div></div></div>
<a name="boost_numeric_bindings.reference.lapack.driver_routines.posvx.prototype"></a><h6>
<a name="id856713"></a>
<a class="link" href="posvx.html#boost_numeric_bindings.reference.lapack.driver_routines.posvx.prototype">Prototype</a>
</h6>
<p>
There is one prototype of <code class="computeroutput"><span class="identifier">posvx</span></code>
available, please see below.
</p>
<pre class="programlisting"><span class="identifier">posvx</span><span class="special">(</span> <span class="keyword">const</span> <span class="keyword">char</span> <span class="identifier">fact</span><span class="special">,</span> <span class="identifier">MatrixA</span><span class="special">&</span> <span class="identifier">a</span><span class="special">,</span> <span class="identifier">MatrixAF</span><span class="special">&</span> <span class="identifier">af</span><span class="special">,</span> <span class="keyword">char</span><span class="special">&</span> <span class="identifier">equed</span><span class="special">,</span>
<span class="identifier">VectorS</span><span class="special">&</span> <span class="identifier">s</span><span class="special">,</span> <span class="identifier">MatrixB</span><span class="special">&</span> <span class="identifier">b</span><span class="special">,</span> <span class="identifier">MatrixX</span><span class="special">&</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">Scalar</span> <span class="special">>,</span> <span class="identifier">VectorFERR</span><span class="special">&</span> <span class="identifier">ferr</span><span class="special">,</span>
<span class="identifier">VectorBERR</span><span class="special">&</span> <span class="identifier">berr</span> <span class="special">);</span>
</pre>
<p>
</p>
<a name="boost_numeric_bindings.reference.lapack.driver_routines.posvx.description"></a><h6>
<a name="id856991"></a>
<a class="link" href="posvx.html#boost_numeric_bindings.reference.lapack.driver_routines.posvx.description">Description</a>
</h6>
<p>
<code class="computeroutput"><span class="identifier">posvx</span></code> (short for $FRIENDLY_NAME)
provides a C++ interface to LAPACK routines SPOSVX, DPOSVX, CPOSVX, and
ZPOSVX. <code class="computeroutput"><span class="identifier">posvx</span></code> uses the
Cholesky factorization A = U**H*U or A = L<span class="bold"><strong>L</strong></span>*H
to compute the solution to a complex system of linear equations A * X
= B, where A is an N-by-N Hermitian positive definite matrix and X and
B are N-by-NRHS matrices.
</p>
<p>
Error bounds on the solution and a condition estimate are also provided.
</p>
<p>
Description <code class="literal">=</code><code class="literal">=</code><code class="literal">=</code>==
</p>
<p>
The following steps are performed:
</p>
<p>
1. If FACT = 'E', real scaling factors are computed to equilibrate the
system: diag(S) * A * diag(S) * inv(diag(S)) * X = diag(S) * B Whether
or not the system will be equilibrated depends on the scaling of the
matrix A, but if equilibration is used, A is overwritten by diag(S)*A*diag(S)
and B by diag(S)*B.
</p>
<p>
2. If FACT = 'N' or 'E', the Cholesky decomposition is used to factor
the matrix A (after equilibration if FACT = 'E') as A = U<span class="bold"><strong>*H</strong></span>
U, if UPLO = 'U', or A = L * L**H, if UPLO = 'L', where U is an upper
triangular matrix and L is a lower triangular matrix.
</p>
<p>
3. If the leading i-by-i principal minor is not positive definite, then
the routine returns with INFO = i. Otherwise, the factored form of A
is used to estimate the condition number of the matrix A. If the reciprocal
of the condition number is less than machine precision, INFO = N+1 is
returned as a warning, but the routine still goes on to solve for X and
compute error bounds as described below.
</p>
<p>
4. The system of equations is solved for X using the factored form of
A.
</p>
<p>
5. Iterative refinement is applied to improve the computed solution matrix
and calculate error bounds and backward error estimates for it.
</p>
<p>
6. If equilibration was used, the matrix X is premultiplied by diag(S)
so that it solves the original system before equilibration.
</p>
<p>
The selection of the LAPACK routine is done during compile-time, and
is determined by the type of values contained in type <code class="computeroutput"><span class="identifier">MatrixA</span></code>.
The type of values is obtained through the <code class="computeroutput"><span class="identifier">value_type</span></code>
meta-function <code class="computeroutput"><span class="keyword">typename</span> <span class="identifier">value_type</span><span class="special"><</span><span class="identifier">MatrixA</span><span class="special">>::</span><span class="identifier">type</span></code>. The dispatching table below illustrates
to which specific routine the code path will be generated.
</p>
<div class="table">
<a name="boost_numeric_bindings.reference.lapack.driver_routines.posvx.dispatching_of_posvx"></a><p class="title"><b>Table 1.142. Dispatching of posvx</b></p>
<div class="table-contents"><table class="table" summary="Dispatching of posvx">
<colgroup>
<col>
<col>
</colgroup>
<thead><tr>
<th>
<p>
Value type of MatrixA
</p>
</th>
<th>
<p>
LAPACK routine
</p>
</th>
</tr></thead>
<tbody>
<tr>
<td>
<p>
<code class="computeroutput"><span class="keyword">float</span></code>
</p>
</td>
<td>
<p>
SPOSVX
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="keyword">double</span></code>
</p>
</td>
<td>
<p>
DPOSVX
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">complex</span><span class="special"><</span><span class="keyword">float</span><span class="special">></span></code>
</p>
</td>
<td>
<p>
CPOSVX
</p>
</td>
</tr>
<tr>
<td>
<p>
<code class="computeroutput"><span class="identifier">complex</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span></code>
</p>
</td>
<td>
<p>
ZPOSVX
</p>
</td>
</tr>
</tbody>
</table></div>
</div>
<br class="table-break"><a name="boost_numeric_bindings.reference.lapack.driver_routines.posvx.definition"></a><h6>
<a name="id857416"></a>
<a class="link" href="posvx.html#boost_numeric_bindings.reference.lapack.driver_routines.posvx.definition">Definition</a>
</h6>
<p>
Defined in header <code class="computeroutput">boost/numeric/bindings/lapack/driver/posvx.hpp</code>.
</p>
<a name="boost_numeric_bindings.reference.lapack.driver_routines.posvx.parameters_or_requirements_on_types"></a><h6>
<a name="id857458"></a>
<a class="link" href="posvx.html#boost_numeric_bindings.reference.lapack.driver_routines.posvx.parameters_or_requirements_on_types">Parameters
or Requirements on Types</a>
</h6>
<div class="variablelist">
<p class="title"><b>Parameters</b></p>
<dl>
<dt><span class="term">MatrixA</span></dt>
<dd><p>
The definition of term 1
</p></dd>
<dt><span class="term">MatrixB</span></dt>
<dd><p>
The definition of term 2
</p></dd>
<dt><span class="term">MatrixC</span></dt>
<dd>
<p>
The definition of term 3.
</p>
<p>
Definitions may contain paragraphs.
</p>
</dd>
</dl>
</div>
<a name="boost_numeric_bindings.reference.lapack.driver_routines.posvx.complexity"></a><h6>
<a name="id857545"></a>
<a class="link" href="posvx.html#boost_numeric_bindings.reference.lapack.driver_routines.posvx.complexity">Complexity</a>
</h6>
<a name="boost_numeric_bindings.reference.lapack.driver_routines.posvx.example"></a><h6>
<a name="id857573"></a>
<a class="link" href="posvx.html#boost_numeric_bindings.reference.lapack.driver_routines.posvx.example">Example</a>
</h6>
<p>
</p>
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">numeric</span><span class="special">/</span><span class="identifier">bindings</span><span class="special">/</span><span class="identifier">lapack</span><span class="special">/</span><span class="identifier">driver</span><span class="special">/</span><span class="identifier">posvx</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span>
<span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">numeric</span><span class="special">::</span><span class="identifier">bindings</span><span class="special">;</span>
<span class="identifier">lapack</span><span class="special">::</span><span class="identifier">posvx</span><span class="special">(</span> <span class="identifier">x</span><span class="special">,</span> <span class="identifier">y</span><span class="special">,</span> <span class="identifier">z</span> <span class="special">);</span>
</pre>
<p>
</p>
<p>
this will output
</p>
<p>
</p>
<pre class="programlisting"><span class="special">[</span><span class="number">5</span><span class="special">]</span> <span class="number">0</span> <span class="number">1</span> <span class="number">2</span> <span class="number">3</span> <span class="number">4</span> <span class="number">5</span>
</pre>
<p>
</p>
<a name="boost_numeric_bindings.reference.lapack.driver_routines.posvx.notes"></a><h6>
<a name="id857857"></a>
<a class="link" href="posvx.html#boost_numeric_bindings.reference.lapack.driver_routines.posvx.notes">Notes</a>
</h6>
<a name="boost_numeric_bindings.reference.lapack.driver_routines.posvx.see_also"></a><h6>
<a name="id857883"></a>
<a class="link" href="posvx.html#boost_numeric_bindings.reference.lapack.driver_routines.posvx.see_also">See
Also</a>
</h6>
<div class="itemizedlist"><ul class="itemizedlist" type="disc"><li class="listitem">
Originating Fortran source files <a href="http://www.netlib.org/lapack/single/sposvx.f" target="_top">sposvx.f</a>,
<a href="http://www.netlib.org/lapack/double/dposvx.f" target="_top">dposvx.f</a>,
<a href="http://www.netlib.org/lapack/complex/cposvx.f" target="_top">cposvx.f</a>,
and <a href="http://www.netlib.org/lapack/complex16/zposvx.f" target="_top">zposvx.f</a>
at Netlib.
</li></ul></div>
</div>
<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr>
<td align="left"></td>
<td align="right"><div class="copyright-footer">Copyright © 2002 -2009 Rutger ter Borg, Krešimir Fresl, Thomas Klimpel,
Toon Knapen, Karl Meerbergen<p>
Distributed under the Boost Software License, Version 1.0. (See accompanying
file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
</p>
</div></td>
</tr></table>
<hr>
<div class="spirit-nav">
<a accesskey="p" href="posv.html"><img src="../../../../images/prev.png" alt="Prev"></a><a accesskey="u" href="../driver_routines.html"><img src="../../../../images/up.png" alt="Up"></a><a accesskey="h" href="../../../../index.html"><img src="../../../../images/home.png" alt="Home"></a><a accesskey="n" href="ppsv.html"><img src="../../../../images/next.png" alt="Next"></a>
</div>
</body>
</html>
|
