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author dwinter
date Tue, 04 Jan 2011 10:00:53 +0100
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15 <title>Math - The Commons Math User Guide - Complex Numbers</title>
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67 <h5>User Guide</h5>
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103 <strong>Complex Numbers</strong>
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149 <div class="section"><h2><a name="a7_Complex_Numbers"></a>7 Complex Numbers</h2>
150 <div class="section"><h3><a name="a7.1_Overview"></a>7.1 Overview</h3>
151 <p>
152 The complex packages provides a complex number type as well as complex
153 versions of common transcendental functions and complex number
154 formatting.
155 </p>
156 </div>
157 <div class="section"><h3><a name="a7.2_Complex_Numbers"></a>7.2 Complex Numbers</h3>
158 <p><a href="../apidocs/org/apache/commons/math/complex/Complex.html">
159 org.apache.commons.math.complex.Complex</a> provides a complex number
160 type that forms the basis for the complex functionality found in
161 commons-math.
162 </p>
163 <p>
164 Complex functions and arithmetic operations are implemented in
165 commons-math by applying standard computational formulas and
166 following the rules for <code>java.lang.Double</code> arithmetic in
167 handling infinite and <code>NaN</code> values. No attempt is made
168 to comply with ANSII/IEC C99x Annex G or any other standard for
169 Complex arithmetic. See the class and method javadocs for the
170 <a href="../apidocs/org/apache/commons/math/complex/Complex.html">
171 Complex</a> and
172 <a href="../apidocs/org/apache/commons/math/complex/ComplexUtils.html">
173 ComplexUtils</a> classes for details on computing formulas.
174 </p>
175 <p>
176 To create a complex number, simply call the constructor passing in two
177 floating-point arguments, the first being the real part of the
178 complex number and the second being the imaginary part:
179 <div class="source"><pre>Complex c = new Complex(1.0, 3.0); // 1 + 3i</pre>
180 </div>
181 </p>
182 <p>
183 Complex numbers may also be created from polar representations
184 using the <code>polar2Complex</code> method in
185 <code>ComplexUtils</code>.
186 </p>
187 <p>
188 The <code>Complex</code> class provides basic unary and binary
189 complex number operations. These operations provide the means to add,
190 subtract, multiply and divide complex numbers along with other
191 complex number functions similar to the real number functions found in
192 <code>java.math.BigDecimal</code>:
193 <div class="source"><pre>Complex lhs = new Complex(1.0, 3.0);
194 Complex rhs = new Complex(2.0, 5.0);
195
196 Complex answer = lhs.add(rhs); // add two complex numbers
197 answer = lhs.subtract(rhs); // subtract two complex numbers
198 answer = lhs.abs(); // absolute value
199 answer = lhs.conjugate(rhs); // complex conjugate</pre>
200 </div>
201 </p>
202 </div>
203 <div class="section"><h3><a name="a7.3_Complex_Transcendental_Functions"></a>7.3 Complex Transcendental Functions</h3>
204 <p><a href="../apidocs/org/apache/commons/math/complex/Complex.html">
205 org.apache.commons.math.complex.Complex</a> also provides
206 implementations of serveral transcendental functions involving complex
207 number arguments. Prior to version 1.2, these functions were provided
208 by <a href="../apidocs/org/apache/commons/math/complex/ComplexUtils.html">
209 org.apache.commons.math.complex.ComplexUtils</a> in a way similar to the real
210 number functions found in <code>java.lang.Math</code>, but this has been
211 deprecated. These operations provide the means to compute the log, sine,
212 tangent, and other complex values :
213 <div class="source"><pre>Complex first = new Complex(1.0, 3.0);
214 Complex second = new Complex(2.0, 5.0);
215
216 Complex answer = first.log(); // natural logarithm.
217 answer = first.cos(); // cosine
218 answer = first.pow(second); // first raised to the power of second</pre>
219 </div>
220 </p>
221 </div>
222 <div class="section"><h3><a name="a7.4_Complex_Formatting_and_Parsing"></a>7.4 Complex Formatting and Parsing</h3>
223 <p><code>Complex</code> instances can be converted to and from strings
224 using the<a href="../apidocs/org/apache/commons/math/complex/ComplexFormat.html">
225 org.apache.commons.math.complex.ComplexFormat</a> class.
226 <code>ComplexFormat</code> is a <code>java.text.Format</code>
227 extension and, as such, is used like other formatting objects (e.g.
228 <code>java.text.SimpleDateFormat</code>):
229 <div class="source"><pre>ComplexFormat format = new ComplexFormat(); // default format
230 Complex c = new Complex(1.1111, 2.2222);
231 String s = format.format(c); // s contains &quot;1.11 + 2.22i&quot;</pre>
232 </div>
233 </p>
234 <p>
235 To customize the formatting output, one or two
236 <code>java.text.NumberFormat</code> instances can be used to construct
237 a <code>ComplexFormat</code>. These number formats control the
238 formatting of the real and imaginary values of the complex number:
239 <div class="source"><pre>NumberFormat nf = NumberFormat.getInstance();
240 nf.setMinimumFractionDigits(3);
241 nf.setMaximumFractionDigits(3);
242
243 // create complex format with custom number format
244 // when one number format is used, both real and
245 // imaginary parts are formatted the same
246 ComplexFormat cf = new ComplexFormat(nf);
247 Complex c = new Complex(1.11, 2.2222);
248 String s = format.format(c); // s contains &quot;1.110 + 2.222i&quot;
249
250 NumberFormat nf2 = NumberFormat.getInstance();
251 nf.setMinimumFractionDigits(1);
252 nf.setMaximumFractionDigits(1);
253
254 // create complex format with custom number formats
255 cf = new ComplexFormat(nf, nf2);
256 s = format.format(c); // s contains &quot;1.110 + 2.2i&quot;</pre>
257 </div>
258 </p>
259 <p>
260 Another formatting customization provided by
261 <code>ComplexFormat</code> is the text used for the imaginary
262 designation. By default, the imaginary notation is &quot;i&quot; but, it can be
263 manipulated using the <code>setImaginaryCharacter</code> method.
264 </p>
265 <p>
266 Formatting inverse operation, parsing, can also be performed by
267 <code>ComplexFormat</code>. Parse a complex number from a string,
268 simply call the <code>parse</code> method:
269 <div class="source"><pre>ComplexFormat cf = new ComplexFormat();
270 Complex c = cf.parse(&quot;1.110 + 2.222i&quot;);</pre>
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