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Merge branch 'main' of https://github.com/numericalalgorithmsgroup/NAGJavaExamples into development
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‎QCQP/Readme.md

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> ## Important Information
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> This repository can viewed as a regular github [repository](https://github.com/numericalalgorithmsgroup/NAGJavaExamples/tree/main/QCQP) or as a [webpage](https://numericalalgorithmsgroup.github.io/NAGJavaExamples/QCQP).
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> This file has a lot of Latex and GitHub currently cannot render it on Markdown files. You can read all the math clearly as a [webpage](https://numericalalgorithmsgroup.github.io/NAGJavaExamples/QCQP/) or access this as a regular github [repository](https://github.com/numericalalgorithmsgroup/NAGJavaExamples/tree/main/QCQP)
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>
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> The source of this example can be found [here](https://github.com/numericalalgorithmsgroup/NAGJavaExamples/blob/main/QCQP/portfolioOptimizationQCQP.java).
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>
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> See the top directory of this repository for instructions to set up the [NAG Library for Java](https://github.com/numericalalgorithmsgroup/NAGJavaExamples).
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# Quadratically constrained quadratic programming and its applications in portfolio optimization
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# Correct Rendering of this notebook
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This file has a lot of Latex and GitHub currently cannot render it on Markdown files. [Here](https://numericalalgorithmsgroup.github.io/NAGJavaExamples/QCQP/) you can read it clearly.
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The source of this example can be found [here](https://github.com/numericalalgorithmsgroup/NAGJavaExamples/blob/main/QCQP/portfolioOptimizationQCQP.java).
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# Introduction
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Quadratically constrained quadratic programming (QCQP) is a type of optimization problem in which both the objective function and the constraints involve quadratic functions. A general QCQP problem has the following form

‎README.md

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> ## Important Information
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> This repository is still under development.
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>
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> This repository can viewed as a regular github [repository](https://github.com/numericalalgorithmsgroup/NAGJavaExamples/) or as a [webpage](https://numericalalgorithmsgroup.github.io/NAGJavaExamples/).
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# Examples using the NAG Library for Java

‎nearest_correlation_matrices/Readme.md

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> ## Important Information
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> This repository can viewed as a regular github [repository](https://github.com/numericalalgorithmsgroup/NAGJavaExamples/tree/main/nearest_correlation_matrices) or as a [webpage](https://numericalalgorithmsgroup.github.io/NAGJavaExamples/nearest_correlation_matrices).
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> This file has a lot of Latex and GitHub currently cannot render it on Markdown files. You can read all the math clearly as a [webpage](https://numericalalgorithmsgroup.github.io/NAGJavaExamples/nearest_correlation_matrices) or access this as a regular github [repository](https://github.com/numericalalgorithmsgroup/NAGJavaExamples/tree/main/nearest_correlation_matrices).
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>
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> The source of this example can be found [here](https://github.com/numericalalgorithmsgroup/NAGJavaExamples/blob/main/nearest_correlation_matrices/NcmNag.java).
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>
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> See the top directory of this repository for instructions to set up the [NAG Library for Java](https://github.com/numericalalgorithmsgroup/NAGJavaExamples).
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# Nearest Correlation Matrices
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This notebook looks at computing *nearest correlation matrices* using the NAG Library for *Java*.
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The source of this example can be found [here](https://github.com/numericalalgorithmsgroup/NAGJavaExamples/blob/main/nearest_correlation_matrices/NcmNag.java).
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## Correlation Matrices
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* An $$n$$ by $$n$$ matrix is a correlation matrix if:

‎simple_examples/source/int64_unsupported/A00AAJE.java

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import com.nag.exceptions.NAGBadIntegerException;
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import com.nag.routines.A00.A00AA;
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import com.nag.routines.Routine;
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public class A00AAJE {
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public static void main (String[] args) throws NAGBadIntegerException {
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Routine.init();
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A00AA a00aa = new A00AA();
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System.out.println(" A00AAJ Example Program Results\n");
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a00aa.eval();
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}
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}

‎simple_examples/source/int64_unsupported/A00ADJE.java

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import com.nag.exceptions.NAGBadIntegerException;
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import com.nag.routines.A00.A00AD;
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import com.nag.routines.Routine;
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import java.util.Arrays;
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public class A00ADJE {
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/* Parameters */
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public static final int MSGLEN = 15;
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/** A00ADJ Example Program */
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public static void main (String[] args) throws NAGBadIntegerException {
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/* Local Scalars */
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int i;
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long mkmaj, mkmin;
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boolean licval;
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String fcomp = getBlankString(80), hdware = getBlankString(80),
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impl = getBlankString(80), opsys = getBlankString(80),
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pcode = getBlankString(80), prec = getBlankString(80),
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vend = getBlankString(80);
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/* Local Arrays */
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int[] itime = new int[7];
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String[] msg = new String[MSGLEN];
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// Instantiate arguments
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mkmaj = 0;
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mkmin = 0;
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licval = false;
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// Strings must be length expected by Fortran
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fcomp = getBlankString(80);
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hdware = getBlankString(80);
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impl = getBlankString(80);
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opsys = getBlankString(80);
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pcode = getBlankString(80);
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prec = getBlankString(80);
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vend = getBlankString(80);
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for (i = 0; i < MSGLEN; i++) msg[i] = getBlankString(102);
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Routine.init();
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System.out.println(" A00ADJ Example Program Results\n");
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A00AD a00ad = new A00AD();
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a00ad.eval(impl, prec, pcode, mkmaj, mkmin, hdware, opsys, fcomp, vend, licval);
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impl = a00ad.getIMPL();
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prec = a00ad.getPREC();
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pcode = a00ad.getPCODE();
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mkmaj = a00ad.getMKMAJ();
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mkmin = a00ad.getMKMIN();
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hdware = a00ad.getHDWARE();
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opsys = a00ad.getOPSYS();
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fcomp = a00ad.getFCOMP();
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vend = a00ad.getVEND();
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licval = a00ad.getLICVAL();
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/* Print implementation details */
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System.out.println("*** Start of NAG Library implementation details ***");
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System.out.println();
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System.out.println("Implementation title: " + impl.trim());
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System.out.println(" Precision: " + prec.trim());
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System.out.println(" Product code: " + pcode.trim());
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if (mkmin < 10) {
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System.out.printf(" Mark: %2d.%1d\n", mkmaj, mkmin);
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}
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else {
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System.out.printf(" Mark: %2d.%2d\n", mkmaj, mkmin);
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}
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if (vend.trim().equals("(self-contained)")) {
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System.out.println(" Vendor Library: None");
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}
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else {
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System.out.println(" Vendor Library: " + vend.trim());
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}
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System.out.println("Applicable to:");
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System.out.println(" hardware: " + hdware.trim());
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System.out.println(" operating system: " + opsys.trim());
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System.out.println(" Fortran compiler: " + fcomp.trim());
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System.out.println("and compatible systems.");
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if (!licval) {
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System.out.println(" Licence query: Unsuccessful");
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}
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else {
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System.out.println(" Licence query: Successful");
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}
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System.out.println();
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System.out.println("*** End of NAG Library implementation details ***");
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}
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/**
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* Returns a new String, filled with spaces to the specified length
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*
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* @param len the required length of the String
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* @returns a String of spaces of the specified length
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*/
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public static String getBlankString(int len) {
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if (len > 0) {
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char[] arr = new char[len];
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Arrays.fill(arr, ' ');
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return new String(arr);
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}
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return "";
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}
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}

‎simple_examples/source/int64_unsupported/C05AYJE.java

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import com.nag.exceptions.NAGBadIntegerException;
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import com.nag.routines.C05.C05AY;
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import com.nag.routines.Routine;
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public class C05AYJE {
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public static void main(String[] args) throws NAGBadIntegerException {
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C05AY c05ay = new C05AY();
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OBJFUN f = new OBJFUN();
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double a = 0.0, b = 1.0, eps = 1.0e-5, eta = 0.0, x = 0.0;
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long ifail = 0;
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long[] iuser = new long[1];
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double[] ruser = new double[1];
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System.out.println("C05AYJ Example Program Results");
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System.out.println();
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Routine.init();
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c05ay.eval(a, b, eps, eta, f, x, iuser, ruser, ifail);
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x = c05ay.getX();
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switch ((int)ifail) {
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case 0:
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System.out.printf("Zero at x = %12.5f\n", x);
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break;
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case 2: case 3:
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System.out.printf("Final point = %12.5f\n", x);
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break;
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default:
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System.out.println("Unexpected ifail = " + ifail);
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}
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}
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private static class OBJFUN extends C05AY.Abstract_C05AY_F {
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public double eval() {
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return Math.exp(-X) - X;
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}
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}
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}

‎simple_examples/source/int64_unsupported/C05AZJE.java

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import com.nag.exceptions.NAGBadIntegerException;
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import com.nag.routines.C05.C05AZ;
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import com.nag.routines.Routine;
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import java.util.logging.Level;
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import java.util.logging.Logger;
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public class C05AZJE {
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public static void main (String[] args)throws NAGBadIntegerException{
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double tolx = 0.00001, x = 0.0, y = 1.0, fx;
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long ir = 0, ind = 1, ifail = -1;
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double[] c = new double[17];
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boolean keepOn = true;
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Routine.init();
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C05AZ c05az = new C05AZ();
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fx = fun(x);
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int ite = 0;
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System.out.println(" C05AZJ Example Program Results\n");
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System.out.println(" Iterations\n");
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while (keepOn) {
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++ite;
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c05az.eval(x,y,fx,tolx,ir,c,ind,ifail);
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x = c05az.getX();
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y = c05az.getY();
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tolx = c05az.getTOLX();
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ir = c05az.getIR();
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ind = c05az.getIND();
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ifail = c05az.getIFAIL();
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if(ind == 0){
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keepOn = false;
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}
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else{
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fx = fun(x);
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System.out.printf(" X = %7.5f FX = %11.4E IND = %1d\n", x, fx, ind);
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}
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}
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switch ((int)ifail) {
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case 0:
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System.out.println("\n Solution\n");
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System.out.printf(" X = %8.5f Y = %8.5f\n",x,y);
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break;
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case 4:
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case 5:
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System.out.printf(" X = %8.5f Y = %8.5f\n",x,y);
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break;
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default:
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System.out.printf("Unexpected error ifail=%d\n",ifail);
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}
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}
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private static double fun(double x) {
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double res = (Math.expm1(-x) + 1) - x;
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return res;
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}
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}

‎simple_examples/source/int64_unsupported/C05MBJE.java

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import com.nag.exceptions.NAGBadIntegerException;
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import com.nag.routines.Routine;
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import com.nag.routines.C05.C05MB;
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import com.nag.routines.F06.DNRM2;
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import com.nag.routines.X02.X02AJ;
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/**
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* C05MBJ Example Program Text
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* @author joed
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* @since 27.0
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*/
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/* ** There have been at least 200*(n+1) calls to fcn.
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** Consider restarting the calculation from the point held in x.
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** ABNORMAL EXIT from NAG Library routine
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** NAG soft failure - control returned
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*/
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public class C05MBJE {
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private static final int n = 4;
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private static class FCN extends C05MB.Abstract_C05MB_FCN {
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public void eval() {
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FVEC[0] = Math.cos(X[2]) - X[0];
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FVEC[1] = Math.sqrt(1.0 - Math.pow(X[3],2)) - X[1];
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FVEC[2] = Math.sin(X[0]) - X[2];
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FVEC[3] = Math.pow(X[1], 2) - X[3];
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// Set iflag negative to terminate execution for any reason
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IFLAG = 0;
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return;
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}
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}
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/**
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* C05MBJ Example Main Program
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*/
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public static void main(String[] args) throws NAGBadIntegerException {
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C05MB c05mb = new C05MB();
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DNRM2 dnrm2 = new DNRM2();
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X02AJ x02aj = new X02AJ();
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FCN fcn = new FCN();
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long cpuser;
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double atol, cndtol, fnorm, machpr, rtol;
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long astart, ifail, m;
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int i;
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double[] fvec, x;
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double[] ruser = new double[1];
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long[] iuser = new long[1];
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System.out.println("C05MBJ Example Program Results\n");
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// Initialise NAG for Java
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Routine.init();
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// Get machine precision from X02AJ
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machpr = (new X02AJ()).eval();
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fvec = new double[n];
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x = new double[n];
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// The following starting values provide a rough solution
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x = new double[]{2.0, 0.5, 2.0, 0.5};
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m = 2;
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atol = Math.sqrt(machpr);
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rtol = Math.sqrt(machpr);
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cndtol = 0.0;
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astart = 0;
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cpuser = 0;
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ifail = -1;
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c05mb.eval(fcn, n, x, fvec, atol, rtol, m, cndtol, astart, iuser, ruser,
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cpuser, ifail);
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ifail = c05mb.getIFAIL();
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if (ifail==0 || ifail==8 || ifail==9) {
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if (ifail==0) {
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// The NAG name equivalent of dnrm2 is f06ej
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fnorm = dnrm2.eval(n, fvec, 1);
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System.out.println();
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System.out.printf("Final 2-norm of the residuals = %12.4e\n", fnorm);
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System.out.println();
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System.out.println("Final approximate solution");
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}
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else {
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System.out.println();
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System.out.println("Approximate solution");
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}
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System.out.println();
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for (i = 1; i <= n; i++) {
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System.out.printf("%12.4f", x[i-1]);
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}
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System.out.printf("\n");
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}
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}
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}

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