Continuous Wavelet Transforms, a Java Implementation

Mark H Bishop

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7 Mar 2015CPOL12 min read

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This article presents a Java example application that performs continuous wavelet transforms.

CwtSrc.zip
- CwtDemo
  - .classpath
  - .project
  - .settings
    - org.eclipse.jdt.core.prefs
  - bin
    - Colors.class
    - ComplexCalc.class
    - ComplexNumber.class
    - ConsoleTest.class
    - CWT$Wavelet.class
    - CWT.class
    - Examples.class
    - Fft.class
    - FileOps.class
    - Gamma.class
    - Hermite.class
    - ImagePanel.class
    - MainForm$1.class
    - MainForm$10.class
    - MainForm$11.class
    - MainForm$12.class
    - MainForm$13.class
    - MainForm$14.class
    - MainForm$15.class
    - MainForm$16.class
    - MainForm$17.class
    - MainForm$18.class
    - MainForm$19.class
    - MainForm$2.class
    - MainForm$20.class
    - MainForm$21.class
    - MainForm$22.class
    - MainForm$23.class
    - MainForm$24.class
    - MainForm$25.class
    - MainForm$26.class
    - MainForm$3.class
    - MainForm$4.class
    - MainForm$5.class
    - MainForm$6.class
    - MainForm$7.class
    - MainForm$8.class
    - MainForm$9.class
    - MainForm.class
    - MatrixOps.class
    - MraForm$1.class
    - MraForm$2.class
    - MraForm$3.class
    - MraForm$4.class
    - MraForm$5.class
    - MraForm$6.class
    - MraForm$7.class
    - MraForm$8.class
    - MraForm$Colors.class
    - MraForm.class
    - ParameterInputCwt$1.class
    - ParameterInputCwt$2.class
    - ParameterInputCwt$3.class
    - ParameterInputCwt$4.class
    - ParameterInputCwt.class
    - PlotFrame$1.class
    - PlotFrame$10.class
    - PlotFrame$11.class
    - PlotFrame$12.class
    - PlotFrame$13.class
    - PlotFrame$2.class
    - PlotFrame$3.class
    - PlotFrame$4.class
    - PlotFrame$5.class
    - PlotFrame$6.class
    - PlotFrame$7.class
    - PlotFrame$8.class
    - PlotFrame$9.class
    - PlotFrame.class
    - PlotVisiblePicker$1.class
    - PlotVisiblePicker$2.class
    - PlotVisiblePicker$3.class
    - PlotVisiblePicker.class
    - Scalogram$1.class
    - Scalogram$2.class
    - Scalogram$3.class
    - Scalogram$4.class
    - Scalogram$5.class
    - Scalogram$6.class
    - Scalogram.class
    - Signal$RangeOption$1.class
    - Signal$RangeOption$2.class
    - Signal$RangeOption.class
    - Signal.class
    - StringUtils.class
    - VariableProvider.class
    - XYForm$1.class
    - XYForm$2.class
    - XYForm$3.class
    - XYForm$4.class
    - XYForm$5.class
    - XYForm.class
  - GNU_v3.txt
  - jel-2.0.1
    - CODEGEN_HOW_TO
    - COPYING
    - docs
      - api
        
        allclasses-frame.html
        
        allclasses-noframe.html
        
        constant-values.html
        
        deprecated-list.html
        
        gnu
        
        jel
        
        ClassFile.html
        
        class-use
        
        ClassFile.html
        
        CompilationException.html
        
        CompiledExpression.html
        
        DVMap.html
        
        Evaluator.html
        
        ImageLoader.html
        
        Library.html
        
        LocalField.html
        
        LocalMethod.html
        
        OP.html
        
        OPbinary.html
        
        OPcall.html
        
        OPcondtnl.html
        
        OPload.html
        
        OPunary.html
        
        Parser.html
        
        TableKeeper.html
        
        TableWriter.html
        
        CompilationException.html
        
        CompiledExpression.html
        
        debug
        
        class-use
        
        Debug.html
        
        Debug.html
        
        package-frame.html
        
        package-summary.html
        
        package-tree.html
        
        package-use.html
        
        DVMap.html
        
        Evaluator.html
        
        ImageLoader.html
        
        Library.html
        
        LocalField.html
        
        LocalMethod.html
        
        OP.html
        
        OPbinary.html
        
        OPcall.html
        
        OPcondtnl.html
        
        OPload.html
        
        OPunary.html
        
        package-frame.html
        
        package-summary.html
        
        package-tree.html
        
        package-use.html
        
        Parser.html
        
        reflect
        
        Boolean.html
        
        Byte.html
        
        Character.html
        
        class-use
        
        Boolean.html
        
        Byte.html
        
        Character.html
        
        Double.html
        
        Float.html
        
        Integer.html
        
        Long.html
        
        Short.html
        
        String.html
        
        Double.html
        
        Float.html
        
        Integer.html
        
        Long.html
        
        package-frame.html
        
        package-summary.html
        
        package-tree.html
        
        package-use.html
        
        Short.html
        
        String.html
        
        TableKeeper.html
        
        TableWriter.html
        
        help-doc.html
        
        index.html
        
        index-all.html
        
        overview-frame.html
        
        overview-summary.html
        
        overview-tree.html
        
        package-list
        
        resources
        
        inherit.gif
        
        serialized-form.html
        
        stylesheet.css
      - back1.gif
      - EC.html
      - gnu-head-sm-transp.jpg
      - gnu-head-sm-transp.png
      - jel.css
      - license.txt
      - manual.html
    - Java Expressions Library.html
    - lib
      - jel.jar
      - jel_g.jar
    - README
    - RELNOTES
    - samples
      - calculator
        
        Calculator.class
        
        Calculator.java
        
        README
      - testbed
        
        Data.java
        
        DVResolverProvider.java
        
        GlobalContext.java
        
        YourTestBed.java
      - testsuite
        
        README
        
        tests.jar
    - source
      - build.xml
      - src
        
        docs
        
        CODEGEN_HOW_TO
        
        COPYING
        
        html
        
        back1.gif
        
        EC.html
        
        gnu-head-sm-transp.png
        
        index.html
        
        jel.css
        
        license.txt
        
        manual.html
        
        manual.xml
        
        README
        
        README.calculator
        
        README.testbed
        
        README.testsuite
        
        RELNOTES
        
        java
        
        Calculator.java
        
        Data.java
        
        DVResolverProvider.java
        
        GlobalContext.java
        
        gnu
        
        jel
        
        ClassFile.java
        
        CompilationException.java
        
        CompiledExpression.java
        
        debug
        
        Debug.java
        
        DVMap.java
        
        Evaluator.java
        
        ImageLoader.java
        
        IntegerStack.java
        
        JEL.properties
        
        Library.java
        
        LocalField.java
        
        LocalMethod.java
        
        OP.java
        
        OPbinary.java
        
        OPcall.java
        
        OPcondtnl.java
        
        OPload.java
        
        OPunary.java
        
        Parser.java
        
        reflect
        
        Boolean.java
        
        Byte.java
        
        Character.java
        
        Double.java
        
        Float.java
        
        Integer.java
        
        Long.java
        
        Short.java
        
        String.java
        
        TableKeeper.java
        
        TableWriter.java
        
        YourTestBed.java
        
        tests
        
        gnu
        
        jel
        
        ClassFileExprTest.java
        
        ClassFileTest.java
        
        IntegerStackTest.java
        
        IntegralDotOperatorTest.java
        
        IntegralDowncastingTest.java
        
        IntegralDynamicVariablesTest.java
        
        IntegralErrorTest.java
        
        IntegralExceptionsPassingTest.java
        
        IntegralPrimitiveOPsTest.java
        
        IntegralReferencesWideningTest.java
        
        IntegralStaticTest.java
        
        IntegralVarARRTest.java
        
        IntegralVirtualTest.java
        
        JELTestSuite.java
        
        LibraryDotOPTest.java
        
        LibraryTest.java
        
        ParserTest.java
        
        TestingUtils.java
        
        tests
        
        BooleanObject.java
        
        ByteObject.java
        
        CharacterObject.java
        
        DoubleObject.java
        
        FloatObject.java
        
        IntegerObject.java
        
        LongObject.java
        
        ShortObject.java
        
        StringObject.java
        
        VariableProvider.java
      - third-party
        
        junit.jar
  - Readme.txt
  - runnable
    - CwtRunnable.jar
    - TestSignal.csv
    - whiteNoise.csv
  - src
  - TestSignal.csv
  - whiteNoise.csv
CwtRunnable.zip
- CwtRunnable
  - CwtRunnable.jar
  - GNU_v3.txt
  - Readme.txt
  - TestSignal.csv
  - whiteNoise.csv

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gnu.jel</FONT>
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Class Evaluator</H2>
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java.lang.Object
  <IMG SRC="../../resources/inherit.gif" ALT="extended by "><B>gnu.jel.Evaluator</B>
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<DT><PRE>public class <B>Evaluator</B><DT>extends java.lang.Object</DL>
</PRE>

<P>
This is the main frontend to JEL.
 <P>It is intended for compilation of algebraic expressions involving 
 functions.
 <P> Syntax allows variables, which can be either a public fields of
 certain objects or functions with no arguments.  If a method like
 "<TT>double x() {}</TT>;" is defined in the dynamic library class
 (see <tt>gnu.jel.Library</tt> documentation on how to do this), an
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 and function <TT>Math.sin()</TT> ) each time it is evaluated.
 Static methods in namespace are assumed to be stateless (unless
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 <P>It is possible to have any type of intermediate object
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 values and parameters stay compatible. The compiler can
 do all the type conversions permissible in Java language and more 
 (e.g. between reflection wrappers <tt>java.lang.Integer</tt>,... and
 primitives). Widening type conversions (not leading to precision loss)
 are applied by JEL automatically, narrowing should be explicitly 
 requested.
 <P>There is variant of the "compile" function with three arguments,
 which allows to fix the type of the expression result. For example:
 <PRE>
 CompiledExpression expression=compile("2*6+6",lib,Double.TYPE); 
 </PRE> 
 will produce a compiled expression, whose return type is always
 <TT>double</TT>. For additional information on how to use this
 feature to eliminate object allocation overhead see
 <TT>gnu.jel.CompiledExpression</TT> documentation.
 
 <P> Care should be taken during the assembly of static and dynamic libraries
 to avoid conflicts and unexpected return types.

 <P>(c) 1998-2003, by Konstantin Metlov<BR>
 Prague, CZ
<P>

<P>
<DL>
<DT><B>See Also:</B><DD><A HREF="../../gnu/jel/CompiledExpression.html" title="class in gnu.jel"><CODE>CompiledExpression</CODE></A>, 
<A HREF="../../gnu/jel/Library.html" title="class in gnu.jel"><CODE>Library</CODE></A></DL>
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<CODE>protected static&nbsp;<A HREF="../../gnu/jel/ClassFile.html" title="class in gnu.jel">ClassFile</A></CODE></FONT></TD>
<TD><CODE><B><A HREF="../../gnu/jel/Evaluator.html#cf_orig">cf_orig</A></B></CODE>

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&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</TD>
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<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>protected static&nbsp;<A HREF="../../gnu/jel/LocalMethod.html" title="class in gnu.jel">LocalMethod</A>[]</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../gnu/jel/Evaluator.html#eval_methods">eval_methods</A></B></CODE>

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&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</TD>
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<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>protected static&nbsp;int</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../gnu/jel/Evaluator.html#retID_patchback">retID_patchback</A></B></CODE>

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&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</TD>
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<CODE>protected static&nbsp;int</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../gnu/jel/Evaluator.html#retIDC_patchback">retIDC_patchback</A></B></CODE>

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&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</TD>
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<TD><CODE><B><A HREF="../../gnu/jel/Evaluator.html#Evaluator()">Evaluator</A></B>()</CODE>

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<CODE>static&nbsp;<A HREF="../../gnu/jel/CompiledExpression.html" title="class in gnu.jel">CompiledExpression</A></CODE></FONT></TD>
<TD><CODE><B><A HREF="../../gnu/jel/Evaluator.html#compile(java.lang.String, gnu.jel.Library)">compile</A></B>(java.lang.String&nbsp;expression,
        <A HREF="../../gnu/jel/Library.html" title="class in gnu.jel">Library</A>&nbsp;lib)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Compiles expression, resolving the function names in the library.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>static&nbsp;<A HREF="../../gnu/jel/CompiledExpression.html" title="class in gnu.jel">CompiledExpression</A></CODE></FONT></TD>
<TD><CODE><B><A HREF="../../gnu/jel/Evaluator.html#compile(java.lang.String, gnu.jel.Library, java.lang.Class)">compile</A></B>(java.lang.String&nbsp;expression,
        <A HREF="../../gnu/jel/Library.html" title="class in gnu.jel">Library</A>&nbsp;lib,
        java.lang.Class&nbsp;resultType)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Compiles expression, resolving the function names in the library.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>static&nbsp;byte[]</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../gnu/jel/Evaluator.html#compileBits(java.lang.String, gnu.jel.Library)">compileBits</A></B>(java.lang.String&nbsp;expression,
            <A HREF="../../gnu/jel/Library.html" title="class in gnu.jel">Library</A>&nbsp;lib)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Compiles expression, resolving the function names in the library.</TD>
</TR>
<TR BGCOLOR="white" CLASS="TableRowColor">
<TD ALIGN="right" VALIGN="top" WIDTH="1%"><FONT SIZE="-1">
<CODE>static&nbsp;byte[]</CODE></FONT></TD>
<TD><CODE><B><A HREF="../../gnu/jel/Evaluator.html#compileBits(java.lang.String, gnu.jel.Library, java.lang.Class)">compileBits</A></B>(java.lang.String&nbsp;expression,
            <A HREF="../../gnu/jel/Library.html" title="class in gnu.jel">Library</A>&nbsp;lib,
            java.lang.Class&nbsp;resultType)</CODE>

<BR>
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Compiles expression, resolving the function names in the library.</TD>
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<TD><CODE>clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait</CODE></TD>
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<A NAME="cf_orig"><!-- --></A><H3>
cf_orig</H3>
<PRE>
protected static <A HREF="../../gnu/jel/ClassFile.html" title="class in gnu.jel">ClassFile</A> <B>cf_orig</B></PRE>
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<DL>
</DL>
</DL>
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<A NAME="retID_patchback"><!-- --></A><H3>
retID_patchback</H3>
<PRE>
protected static int <B>retID_patchback</B></PRE>
<DL>
<DL>
</DL>
</DL>
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<A NAME="retIDC_patchback"><!-- --></A><H3>
retIDC_patchback</H3>
<PRE>
protected static int <B>retIDC_patchback</B></PRE>
<DL>
<DL>
</DL>
</DL>
<HR>

<A NAME="eval_methods"><!-- --></A><H3>
eval_methods</H3>
<PRE>
protected static <A HREF="../../gnu/jel/LocalMethod.html" title="class in gnu.jel">LocalMethod</A>[] <B>eval_methods</B></PRE>
<DL>
<DL>
</DL>
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<A NAME="Evaluator()"><!-- --></A><H3>
Evaluator</H3>
<PRE>
public <B>Evaluator</B>()</PRE>
<DL>
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<A NAME="compile(java.lang.String, gnu.jel.Library, java.lang.Class)"><!-- --></A><H3>
compile</H3>
<PRE>
public static <A HREF="../../gnu/jel/CompiledExpression.html" title="class in gnu.jel">CompiledExpression</A> <B>compile</B>(java.lang.String&nbsp;expression,
                                         <A HREF="../../gnu/jel/Library.html" title="class in gnu.jel">Library</A>&nbsp;lib,
                                         java.lang.Class&nbsp;resultType)
                                  throws <A HREF="../../gnu/jel/CompilationException.html" title="class in gnu.jel">CompilationException</A></PRE>
<DL>
<DD>Compiles expression, resolving the function names in the library.
<P>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>expression</CODE> - is the expression to compile. i.e. "sin(666)" .<DD><CODE>lib</CODE> - Library of functions exported for use in expression.<DD><CODE>resultType</CODE> - identifies the type result should be converted to. Can
        be null, in this case the result type is not fixed.
<DT><B>Returns:</B><DD>Instance of the CompiledExpression subclass, implementing
   the specified expression evaluation.
<DT><B>Throws:</B>
<DD><CODE><A HREF="../../gnu/jel/CompilationException.html" title="class in gnu.jel">CompilationException</A></CODE> - if the expression is not
  syntactically or semantically correct.<DT><B>See Also:</B><DD><A HREF="../../gnu/jel/CompiledExpression.html" title="class in gnu.jel"><CODE>CompiledExpression</CODE></A></DL>
</DD>
</DL>
<HR>

<A NAME="compileBits(java.lang.String, gnu.jel.Library, java.lang.Class)"><!-- --></A><H3>
compileBits</H3>
<PRE>
public static byte[] <B>compileBits</B>(java.lang.String&nbsp;expression,
                                 <A HREF="../../gnu/jel/Library.html" title="class in gnu.jel">Library</A>&nbsp;lib,
                                 java.lang.Class&nbsp;resultType)
                          throws <A HREF="../../gnu/jel/CompilationException.html" title="class in gnu.jel">CompilationException</A></PRE>
<DL>
<DD>Compiles expression, resolving the function names in the library.
 <P>This variant of compile allows to store expressions in a 
 <TT>java.io.OutputStream</TT> using Java serialization mechanism.
<P>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>expression</CODE> - is the expression to compile. i.e. "sin(666)" .<DD><CODE>lib</CODE> - Library of functions exported for use in expression.<DD><CODE>resultType</CODE> - identifies the type result should be converted to. Can
        be null, in this case the result type is not fixed.
<DT><B>Returns:</B><DD>Byte array, representing the expression
 in a standard Java classfile format. It can be conveniently 
 loaded (with renaming, if necessary)
 into Java VM using <tt>gnu.jel.ImageLoader</tt>.
<DT><B>Throws:</B>
<DD><CODE><A HREF="../../gnu/jel/CompilationException.html" title="class in gnu.jel">CompilationException</A></CODE> - if the expression is not
  syntactically or semantically correct.<DT><B>See Also:</B><DD><A HREF="../../gnu/jel/CompiledExpression.html" title="class in gnu.jel"><CODE>CompiledExpression</CODE></A>, 
<A HREF="../../gnu/jel/ImageLoader.html" title="class in gnu.jel"><CODE>ImageLoader</CODE></A></DL>
</DD>
</DL>
<HR>

<A NAME="compile(java.lang.String, gnu.jel.Library)"><!-- --></A><H3>
compile</H3>
<PRE>
public static <A HREF="../../gnu/jel/CompiledExpression.html" title="class in gnu.jel">CompiledExpression</A> <B>compile</B>(java.lang.String&nbsp;expression,
                                         <A HREF="../../gnu/jel/Library.html" title="class in gnu.jel">Library</A>&nbsp;lib)
                                  throws <A HREF="../../gnu/jel/CompilationException.html" title="class in gnu.jel">CompilationException</A></PRE>
<DL>
<DD>Compiles expression, resolving the function names in the library.
<P>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>expression</CODE> - is the expression to compile. i.e. "sin(666)" .<DD><CODE>lib</CODE> - Library of functions exported for use in expression.
<DT><B>Returns:</B><DD>Instance of the CompiledExpression subclass, implementing
   the specified expression evaluation.
<DT><B>Throws:</B>
<DD><CODE><A HREF="../../gnu/jel/CompilationException.html" title="class in gnu.jel">CompilationException</A></CODE> - if the expression is not
  syntactically or semantically correct.<DT><B>See Also:</B><DD><A HREF="../../gnu/jel/CompiledExpression.html" title="class in gnu.jel"><CODE>CompiledExpression</CODE></A></DL>
</DD>
</DL>
<HR>

<A NAME="compileBits(java.lang.String, gnu.jel.Library)"><!-- --></A><H3>
compileBits</H3>
<PRE>
public static byte[] <B>compileBits</B>(java.lang.String&nbsp;expression,
                                 <A HREF="../../gnu/jel/Library.html" title="class in gnu.jel">Library</A>&nbsp;lib)
                          throws <A HREF="../../gnu/jel/CompilationException.html" title="class in gnu.jel">CompilationException</A></PRE>
<DL>
<DD>Compiles expression, resolving the function names in the library.
 <P>This variant of compile allows to store expressions in a 
 <TT>java.io.OutputStream</TT> using Java serialization mechanism.
<P>
<DD><DL>
<DT><B>Parameters:</B><DD><CODE>expression</CODE> - is the expression to compile. i.e. "sin(666)" .<DD><CODE>lib</CODE> - Library of functions exported for use in expression.
<DT><B>Returns:</B><DD>Byte array, representing the expression
 in a standard Java classfile format. It can be conveniently 
 loaded (with renaming, if necessary)
 into Java VM using <tt>gnu.jel.ImageLoader</tt>.
<DT><B>Throws:</B>
<DD><CODE><A HREF="../../gnu/jel/CompilationException.html" title="class in gnu.jel">CompilationException</A></CODE> - if the expression is not
  syntactically or semantically correct.<DT><B>See Also:</B><DD><A HREF="../../gnu/jel/CompiledExpression.html" title="class in gnu.jel"><CODE>CompiledExpression</CODE></A>, 
<A HREF="../../gnu/jel/ImageLoader.html" title="class in gnu.jel"><CODE>ImageLoader</CODE></A></DL>
</DD>
</DL>
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This article, along with any associated source code and files, is licensed under The Code Project Open License (CPOL)

Written By

Mark H Bishop

Founder PEI Watershed Alliance, Inc.

United States

I am an analytical chemist and an educator. I program primarily to perform matrix computations for regression analysis, process signals, acquire data from sensors, and to control devices.

I participate in many open source development communities and Linux user forums. I do contract work for an environmental analytical laboratory, where I am primarily focused on LIMS programming and network administration.

I am a member of several community-interest groups such as the Prince Edward Island Watershed Alliance, the Lot 11 and Area Watershed Management Group, and the Petersham Historic Commission.

Continuous Wavelet Transforms, a Java Implementation

License

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