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Prepare to build v55
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apete committed Sep 28, 2024
1 parent 1f0ccf7 commit c74f193
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2 changes: 2 additions & 0 deletions CHANGELOG.md
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Expand Up @@ -11,6 +11,8 @@ Added / Changed / Deprecated / Fixed / Removed / Security

> Corresponds to changes in the `develop` branch since the last release
## [55.0.0] – 2024-09-28

### Changed

#### org.ojalgo.function
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1,586 changes: 794 additions & 792 deletions jdeps.txt

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6 changes: 3 additions & 3 deletions pom.xml
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Expand Up @@ -2,7 +2,7 @@
<modelVersion>4.0.0</modelVersion>
<groupId>org.ojalgo</groupId>
<artifactId>ojalgo</artifactId>
<version>55.0.0-SNAPSHOT</version>
<version>55.0.0</version>
<name>ojAlgo</name>
<description>oj! Algorithms - ojAlgo - is Open Source Java code that has to do with mathematics, linear algebra and optimisation.</description>
<packaging>jar</packaging>
Expand Down Expand Up @@ -48,7 +48,7 @@
<properties>
<project.build.sourceEncoding>UTF-8</project.build.sourceEncoding>
<version.java>11</version.java>
<version.org.junit.jupiter>5.11.0</version.org.junit.jupiter>
<version.org.junit.jupiter>5.11.1</version.org.junit.jupiter>
<version.org.openjdk.jmh>1.37</version.org.openjdk.jmh>
</properties>
<dependencies>
Expand Down Expand Up @@ -163,7 +163,7 @@
<plugin>
<groupId>org.apache.maven.plugins</groupId>
<artifactId>maven-gpg-plugin</artifactId>
<version>3.2.6</version>
<version>3.2.7</version>
<executions>
<execution>
<id>sign-artifacts</id>
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9 changes: 6 additions & 3 deletions src/main/java/org/ojalgo/function/constant/BigMath.java
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Expand Up @@ -92,15 +92,18 @@ public static class Prefix {
/**
* https://oeis.org/A001113/constant
*/
public static final BigDecimal E = new BigDecimal("2.71828182845904523536028747135266249775724709369995957496696762772407663035354759457138217852516642742746");
public static final BigDecimal E = new BigDecimal(
"2.71828182845904523536028747135266249775724709369995957496696762772407663035354759457138217852516642742746");
/**
* https://oeis.org/A000796/constant
*/
public static final BigDecimal PI = new BigDecimal("3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798214");
public static final BigDecimal PI = new BigDecimal(
"3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798214");
/**
* https://oeis.org/A001622/constant
*/
public static final BigDecimal GOLDEN_RATIO = new BigDecimal("1.61803398874989484820458683436563811772030917980576286213544862270526046281890244970720720418939113748475");
public static final BigDecimal GOLDEN_RATIO = new BigDecimal(
"1.61803398874989484820458683436563811772030917980576286213544862270526046281890244970720720418939113748475");

public static final BigDecimal HALF_PI = HALF.multiply(PI);
public static final BigDecimal TWO_PI = TWO.multiply(PI);
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Expand Up @@ -37,7 +37,8 @@ public static ConstraintsMetaData newEntityMap(final int nbConstraints) {
}

public static ConstraintsMetaData newInstance(final int nbConstraints, final boolean inclDefs) {
EntryPair<ModelEntity<?>, ConstraintType>[] definitions = inclDefs ? (EntryPair<ModelEntity<?>, ConstraintType>[]) new EntryPair<?, ?>[nbConstraints] : null;
EntryPair<ModelEntity<?>, ConstraintType>[] definitions = inclDefs ? (EntryPair<ModelEntity<?>, ConstraintType>[]) new EntryPair<?, ?>[nbConstraints]
: null;
boolean[] negated = new boolean[nbConstraints];
return new ConstraintsMetaData(definitions, negated);
}
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Expand Up @@ -168,8 +168,6 @@ static Equation doGomoryMixedInteger(final Primitive1D body, final int index, fi

if (j < nbVariables) {



double aj = body.doubleValue(j);

if (!ACCURACY.isZero(aj)) {
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Expand Up @@ -475,11 +475,13 @@ public void testP20181204() {
public void testP20200821() {

MatrixR064.Factory matrixFactory = MatrixR064.FACTORY;
MatrixR064 cov = matrixFactory.copy(RawStore.wrap(new double[][] { { 0.19828575384387814, 0.19939590712485014, 0.04848819110209297, 0.001060547131952715 },
{ 0.19939590712485014, 0.17420946085220315, 0.05503998250848539, 0.09756310857237219 },
{ 0.04848819110209297, 0.05503998250848539, 0.03544331442632964, 0.08244505440089961 },
{ 0.001060547131952715, 0.09756310857237219, 0.08244505440089961, 0.18516185344938874 } }));
MatrixR064 ret = matrixFactory.copy(RawStore.wrap(new double[][] { { 0.16373354541629026 }, { 0.007304578002244022 }, { 0.05247478842401128 }, { 0.12286070470561875 } }));
MatrixR064 cov = matrixFactory
.copy(RawStore.wrap(new double[][] { { 0.19828575384387814, 0.19939590712485014, 0.04848819110209297, 0.001060547131952715 },
{ 0.19939590712485014, 0.17420946085220315, 0.05503998250848539, 0.09756310857237219 },
{ 0.04848819110209297, 0.05503998250848539, 0.03544331442632964, 0.08244505440089961 },
{ 0.001060547131952715, 0.09756310857237219, 0.08244505440089961, 0.18516185344938874 } }));
MatrixR064 ret = matrixFactory
.copy(RawStore.wrap(new double[][] { { 0.16373354541629026 }, { 0.007304578002244022 }, { 0.05247478842401128 }, { 0.12286070470561875 } }));

MarketEquilibrium marketEquilibrium = new MarketEquilibrium(cov);

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17 changes: 9 additions & 8 deletions src/test/java/org/ojalgo/matrix/P20030422Case.java
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Expand Up @@ -38,14 +38,15 @@ public class P20030422Case extends BasicMatrixTest {
private static final NumberContext DEFINITION = NumberContext.of(7, 6);

public static MatrixQ128 getProblematic() {
MatrixQ128 tmpMtrx = MatrixQ128.FACTORY.copy(RawStore.wrap(new double[][] { { 0.973950, 0.132128, -0.009493, 0.052934, -0.069248, 0.015658, -0.008564, 0.004549 },
{ -0.006969, -0.829742, -0.036236, 0.161777, -0.210089, 0.047385, -0.025882, 0.013746 },
{ 0.000143, 0.006440, -0.998445, -0.016720, 0.021093, -0.004711, 0.002560, -0.001359 },
{ -0.000036, -0.001408, 0.000752, -0.955688, -0.169493, 0.027513, -0.013046, 0.006811 },
{ 0.000020, 0.000783, -0.000406, 0.058420, -0.910235, -0.074152, 0.023345, -0.011574 },
{ -0.000003, -0.000101, 0.000052, -0.006126, 0.031007, -0.993209, -0.006144, 0.007871 },
{ 0.000000, 0.000009, -0.000004, 0.000458, -0.001702, 0.002139, -0.946651, 0.219946 },
{ 0.000000, 0.000002, -0.000001, 0.000085, -0.000388, -0.004230, -0.222064, 0.051624 } }));
MatrixQ128 tmpMtrx = MatrixQ128.FACTORY
.copy(RawStore.wrap(new double[][] { { 0.973950, 0.132128, -0.009493, 0.052934, -0.069248, 0.015658, -0.008564, 0.004549 },
{ -0.006969, -0.829742, -0.036236, 0.161777, -0.210089, 0.047385, -0.025882, 0.013746 },
{ 0.000143, 0.006440, -0.998445, -0.016720, 0.021093, -0.004711, 0.002560, -0.001359 },
{ -0.000036, -0.001408, 0.000752, -0.955688, -0.169493, 0.027513, -0.013046, 0.006811 },
{ 0.000020, 0.000783, -0.000406, 0.058420, -0.910235, -0.074152, 0.023345, -0.011574 },
{ -0.000003, -0.000101, 0.000052, -0.006126, 0.031007, -0.993209, -0.006144, 0.007871 },
{ 0.000000, 0.000009, -0.000004, 0.000458, -0.001702, 0.002139, -0.946651, 0.219946 },
{ 0.000000, 0.000002, -0.000001, 0.000085, -0.000388, -0.004230, -0.222064, 0.051624 } }));
return tmpMtrx.enforce(DEFINITION);
}

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32 changes: 16 additions & 16 deletions src/test/java/org/ojalgo/matrix/P20030512Case.java
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Expand Up @@ -40,22 +40,22 @@ public class P20030512Case extends BasicMatrixTest {
public static MatrixQ128 getProblematic() {

MatrixQ128 problematic = MatrixQ128.FACTORY.copy(RawStore.wrap(new double[][] {
{ -0.9739496281920735, 0.13212842225762753, -0.009493226825028579, 0.05293424713580207, -0.06924760059060892, 0.015657944731764042,
-0.008564346745847575, 0.004549185362729688 },
{ -0.006968800104298036, -0.8297418413337506, -0.0362355854907016, 0.16177736191417533, -0.2100891795366892, 0.047384677993178616,
-0.025882286895646086, 0.013745556592708215 },
{ 1.4340062938542994E-4, 0.006439566493351905, -0.9984450518018704, -0.01672049883731471, 0.021092888666976884, -0.004711245310661291,
0.0025599032294949626, -0.0013585613015492993 },
{ -3.622792387280378E-5, -0.0014079037419939427, 7.516302232185491E-4, -0.9556877762343504, -0.16949291959105728, 0.027512985877230767,
-0.013046496305597954, 0.006810504406440988 },
{ 2.0250340119662656E-5, 7.831989621712412E-4, -4.0564464234332884E-4, 0.058420413927192494, -0.9102354879995057, -0.07415158327826854,
0.02334549865104649, -0.011573691137110015 },
{ -2.6229700444995062E-6, -1.0131708540961972E-4, 5.206744734581627E-5, -0.0061256425235909915, 0.031006541861310723, -0.9932086467025747,
-0.006143996013045335, 0.007870602318658423 },
{ 2.229928791772293E-7, 8.605627003794518E-6, -4.397793602224121E-6, 4.5796561576393096E-4, -0.0017021220200960682, 0.002139079626942216,
-0.9466510330795804, 0.21994580987160817 },
{ 4.2787387020086915E-8, 1.6510244524754327E-6, -8.431008420700906E-7, 8.524039438893604E-5, -3.878467110438371E-4, -0.00423012863453722,
-0.22206406664227266, 0.05162429369962791 } }));
{ -0.9739496281920735, 0.13212842225762753, -0.009493226825028579, 0.05293424713580207, -0.06924760059060892, 0.015657944731764042,
-0.008564346745847575, 0.004549185362729688 },
{ -0.006968800104298036, -0.8297418413337506, -0.0362355854907016, 0.16177736191417533, -0.2100891795366892, 0.047384677993178616,
-0.025882286895646086, 0.013745556592708215 },
{ 1.4340062938542994E-4, 0.006439566493351905, -0.9984450518018704, -0.01672049883731471, 0.021092888666976884, -0.004711245310661291,
0.0025599032294949626, -0.0013585613015492993 },
{ -3.622792387280378E-5, -0.0014079037419939427, 7.516302232185491E-4, -0.9556877762343504, -0.16949291959105728, 0.027512985877230767,
-0.013046496305597954, 0.006810504406440988 },
{ 2.0250340119662656E-5, 7.831989621712412E-4, -4.0564464234332884E-4, 0.058420413927192494, -0.9102354879995057, -0.07415158327826854,
0.02334549865104649, -0.011573691137110015 },
{ -2.6229700444995062E-6, -1.0131708540961972E-4, 5.206744734581627E-5, -0.0061256425235909915, 0.031006541861310723, -0.9932086467025747,
-0.006143996013045335, 0.007870602318658423 },
{ 2.229928791772293E-7, 8.605627003794518E-6, -4.397793602224121E-6, 4.5796561576393096E-4, -0.0017021220200960682, 0.002139079626942216,
-0.9466510330795804, 0.21994580987160817 },
{ 4.2787387020086915E-8, 1.6510244524754327E-6, -8.431008420700906E-7, 8.524039438893604E-5, -3.878467110438371E-4, -0.00423012863453722,
-0.22206406664227266, 0.05162429369962791 } }));

return problematic.enforce(DEFINITION);
}
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3 changes: 2 additions & 1 deletion src/test/java/org/ojalgo/matrix/P20030528Case.java
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Expand Up @@ -42,7 +42,8 @@ public class P20030528Case extends BasicMatrixTest {
private static final NumberContext DEFINITION = NumberContext.of(7, 1);

public static MatrixR064 getProblematic() {
MatrixR064 tmpMtrx = MatrixR064.FACTORY.copy(RawStore.wrap(new double[][] { { 1, 0, 0, 0, 0, 0, 1 }, { 0, 1, 0, 0, 0, 1, 0 }, { 0, 0, 1, 0, 1, 0, 0 }, { 0, 0, 0, 1, 0, 0, 0 } }));
MatrixR064 tmpMtrx = MatrixR064.FACTORY
.copy(RawStore.wrap(new double[][] { { 1, 0, 0, 0, 0, 0, 1 }, { 0, 1, 0, 0, 0, 1, 0 }, { 0, 0, 1, 0, 1, 0, 0 }, { 0, 0, 0, 1, 0, 0, 0 } }));
return tmpMtrx.enforce(DEFINITION);
}

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2 changes: 1 addition & 1 deletion src/test/java/org/ojalgo/matrix/P20061119Case.java
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Expand Up @@ -55,7 +55,7 @@ public class P20061119Case extends BasicMatrixTest {
public static MatrixR064 getProblematic() {

MatrixR064 retVal = MatrixR064.FACTORY.copy(RawStore.wrap(new double[][] { { 9.28, 0.48, -2.72, 1.28, -8.32 }, { 4.48, 0.68, -6.52, 2.48, -1.12 },
{ -8.32, -0.12, 8.68, -2.32, 2.08 }, { 7.68, 0.88, -10.32, 3.68, -1.92 }, { -13.12, -1.92, 10.88, -5.12, 9.28 } }));
{ -8.32, -0.12, 8.68, -2.32, 2.08 }, { 7.68, 0.88, -10.32, 3.68, -1.92 }, { -13.12, -1.92, 10.88, -5.12, 9.28 } }));

return retVal.enforce(DEFINITION);
}
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6 changes: 4 additions & 2 deletions src/test/java/org/ojalgo/matrix/SimpleCholeskyCase.java
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Expand Up @@ -49,11 +49,13 @@ public static MatrixR064 getOriginal() {
}

private static MatrixR064 getFactorL() {
return MatrixR064.FACTORY.copy(RawStore.wrap(new double[][] { { 1.7321, 0.0, 0.0 }, { -0.5774, 1.6330, 0.0 }, { -0.5774, -0.8165, 1.4142 } })).enforce(DEFINITION);
return MatrixR064.FACTORY.copy(RawStore.wrap(new double[][] { { 1.7321, 0.0, 0.0 }, { -0.5774, 1.6330, 0.0 }, { -0.5774, -0.8165, 1.4142 } }))
.enforce(DEFINITION);
}

private static MatrixR064 getFactorR() {
return MatrixR064.FACTORY.copy(RawStore.wrap(new double[][] { { 1.7321, -0.5774, -0.5774 }, { 0.0, 1.6330, -0.8165 }, { 0.0, 0.0, 1.4142 } })).enforce(DEFINITION);
return MatrixR064.FACTORY.copy(RawStore.wrap(new double[][] { { 1.7321, -0.5774, -0.5774 }, { 0.0, 1.6330, -0.8165 }, { 0.0, 0.0, 1.4142 } }))
.enforce(DEFINITION);
}

@Override
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6 changes: 4 additions & 2 deletions src/test/java/org/ojalgo/matrix/SimpleLeastSquaresCase.java
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Expand Up @@ -38,7 +38,8 @@ public class SimpleLeastSquaresCase extends BasicMatrixTest {
private static final NumberContext DEFINITION = NumberContext.of(7, 4);

public static MatrixR064 getBody() {
MatrixR064 tmpMtrx = MatrixR064.FACTORY.copy(RawStore.wrap(new double[][] { { 1.0, 0.0, 0.0 }, { 0.0, 1.0, 0.0 }, { 0.0, 0.0, 1.0 }, { -1.0, 1.0, 0.0 }, { -1.0, 0.0, 1.0 }, { 0.0, -1.0, 1.0 } }));
MatrixR064 tmpMtrx = MatrixR064.FACTORY.copy(RawStore
.wrap(new double[][] { { 1.0, 0.0, 0.0 }, { 0.0, 1.0, 0.0 }, { 0.0, 0.0, 1.0 }, { -1.0, 1.0, 0.0 }, { -1.0, 0.0, 1.0 }, { 0.0, -1.0, 1.0 } }));
return tmpMtrx.enforce(DEFINITION);
}

Expand All @@ -53,7 +54,8 @@ public static MatrixR064 getSolution() {
}

private static MatrixR064 getFactorR() {
MatrixR064 tmpMtrx = MatrixR064.FACTORY.copy(RawStore.wrap(new double[][] { { -1.7321, 0.5774, 0.5774 }, { 0.0, -1.6330, 0.8165 }, { 0.0, 0.0, -1.4142 } }));
MatrixR064 tmpMtrx = MatrixR064.FACTORY
.copy(RawStore.wrap(new double[][] { { -1.7321, 0.5774, 0.5774 }, { 0.0, -1.6330, 0.8165 }, { 0.0, 0.0, -1.4142 } }));
return tmpMtrx.enforce(DEFINITION);
}

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2 changes: 1 addition & 1 deletion src/test/java/org/ojalgo/matrix/SimpleQRCase.java
Original file line number Diff line number Diff line change
Expand Up @@ -48,7 +48,7 @@ public static MatrixR064 getOriginal() {

private static MatrixR064 getFactorQ() {
MatrixR064 tmpMtrx = MatrixR064.FACTORY.copy(RawStore.wrap(new double[][] { { 1.0 / 3.0, 0.0 }, { 2.0 / 3.0, 1.0 / PrimitiveMath.SQRT.invoke(2.0) },
{ 2.0 / 3.0, -1.0 / PrimitiveMath.SQRT.invoke(2.0) } }));
{ 2.0 / 3.0, -1.0 / PrimitiveMath.SQRT.invoke(2.0) } }));
return tmpMtrx.enforce(DEFINITION);
}

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22 changes: 13 additions & 9 deletions src/test/java/org/ojalgo/matrix/decomposition/CaseTridiagonal.java
Original file line number Diff line number Diff line change
Expand Up @@ -56,7 +56,8 @@ public void minimiseAllBranchLimits() {
@Test
public void testFullertonExample1and2() {

final PhysicalStore<Double> tmpMtrxA = RawStore.wrap(new double[][] { { 4.0, 2.0, 2.0, 1.0 }, { 2.0, -3.0, 1.0, 1.0 }, { 2.0, 1.0, 3.0, 1.0 }, { 1.0, 1.0, 1.0, 2.0 } });
final PhysicalStore<Double> tmpMtrxA = RawStore
.wrap(new double[][] { { 4.0, 2.0, 2.0, 1.0 }, { 2.0, -3.0, 1.0, 1.0 }, { 2.0, 1.0, 3.0, 1.0 }, { 1.0, 1.0, 1.0, 2.0 } });
final PhysicalStore<Double> tmpMtrxD = RawStore
.wrap(new double[][] { { 4.0, -3.0, 0.0, 0.0 }, { -3.0, 2.0, 3.16227766, 0.0 }, { 0.0, 3.16227766, -1.4, -0.2 }, { 0.0, 0.0, -0.2, 1.4 } });

Expand All @@ -71,9 +72,10 @@ public void testFullertonExample1and2() {
public void testFullertonExercise3() {

final PhysicalStore<Double> tmpMtrxA = RawStore.wrap(new double[][] { { 5.0, 1.0, 2.0, 2.0, 4.0 }, { 1.0, 1.0, 2.0, 1.0, 0.0 },
{ 2.0, 2.0, 0.0, 2.0, 1.0 }, { 2.0, 1.0, 2.0, 1.0, 2.0 }, { 4.0, 0.0, 1.0, 2.0, 4.0 } });
final PhysicalStore<Double> tmpMtrxD = RawStore.wrap(new double[][] { { 5.0, -5.0, 0.0, 0.0, 0.0 }, { -5.0, 5.8, -0.8246211251, 0.0, 0.0 }, { 0.0, -0.8246211251, -0.8823529412, -1.577874704, 0.0 },
{ 0.0, 0.0, -1.577874704, 1.373213515, 1.279015421 }, { 0.0, 0.0, 0.0, 1.279015421, -0.2908605737 } });
{ 2.0, 2.0, 0.0, 2.0, 1.0 }, { 2.0, 1.0, 2.0, 1.0, 2.0 }, { 4.0, 0.0, 1.0, 2.0, 4.0 } });
final PhysicalStore<Double> tmpMtrxD = RawStore.wrap(
new double[][] { { 5.0, -5.0, 0.0, 0.0, 0.0 }, { -5.0, 5.8, -0.8246211251, 0.0, 0.0 }, { 0.0, -0.8246211251, -0.8823529412, -1.577874704, 0.0 },
{ 0.0, 0.0, -1.577874704, 1.373213515, 1.279015421 }, { 0.0, 0.0, 0.0, 1.279015421, -0.2908605737 } });

this.doTheTest(tmpMtrxA, tmpMtrxD);
}
Expand All @@ -87,10 +89,11 @@ public void testFullertonExercise3() {
public void testFullertonExercise4and5() {

final PhysicalStore<Double> tmpMtrxA = RawStore.wrap(new double[][] { { 4.0, 1.0, 2.0, -5.0, 1.0, 4.0 }, { 1.0, 2.0, 0.0, 4.0, 5.0, 3.0 },
{ 2.0, 0.0, 3.0, -1.0, 2.0, 1.0 }, { -5.0, 4.0, -1.0, 1.0, 5.0, 2.0 }, { 1.0, 5.0, 2.0, 5.0, -2.0, 4.0 }, { 4.0, 3.0, 1.0, 2.0, 4.0, 1.0 } });
final PhysicalStore<Double> tmpMtrxD = RawStore.wrap(new double[][] { { 4.0, -6.8556546, 0.0, 0.0, 0.0, 0.0 }, { -6.8556546, -0.1489361702, 2.924429193, 0.0, 0.0, 0.0 },
{ 0.0, 2.924429193, 1.268510593, 4.758239905, 0.0, 0.0 }, { 0.0, 0.0, 4.758239905, 2.664908905, -7.994421195, 0.0 },
{ 0.0, 0.0, 0.0, -7.994421195, 3.358186868, 1.759360415 }, { 0.0, 0.0, 0.0, 0.0, 1.759360415, -2.142670196 } });
{ 2.0, 0.0, 3.0, -1.0, 2.0, 1.0 }, { -5.0, 4.0, -1.0, 1.0, 5.0, 2.0 }, { 1.0, 5.0, 2.0, 5.0, -2.0, 4.0 }, { 4.0, 3.0, 1.0, 2.0, 4.0, 1.0 } });
final PhysicalStore<Double> tmpMtrxD = RawStore
.wrap(new double[][] { { 4.0, -6.8556546, 0.0, 0.0, 0.0, 0.0 }, { -6.8556546, -0.1489361702, 2.924429193, 0.0, 0.0, 0.0 },
{ 0.0, 2.924429193, 1.268510593, 4.758239905, 0.0, 0.0 }, { 0.0, 0.0, 4.758239905, 2.664908905, -7.994421195, 0.0 },
{ 0.0, 0.0, 0.0, -7.994421195, 3.358186868, 1.759360415 }, { 0.0, 0.0, 0.0, 0.0, 1.759360415, -2.142670196 } });

this.doTheTest(tmpMtrxA, tmpMtrxD);
}
Expand Down Expand Up @@ -147,7 +150,8 @@ public void testTypesWithRandom() {
@Test
public void testWikipediaExample() {

final PhysicalStore<Double> tmpMtrxA = RawStore.wrap(new double[][] { { 4.0, 1.0, -2.0, 2.0 }, { 1.0, 2.0, 0.0, 1.0 }, { -2.0, 0.0, 3.0, -2.0 }, { 2.0, 1.0, -2.0, -1.0 } });
final PhysicalStore<Double> tmpMtrxA = RawStore
.wrap(new double[][] { { 4.0, 1.0, -2.0, 2.0 }, { 1.0, 2.0, 0.0, 1.0 }, { -2.0, 0.0, 3.0, -2.0 }, { 2.0, 1.0, -2.0, -1.0 } });
final PhysicalStore<Double> tmpMtrxD = RawStore.wrap(new double[][] { { 4.0, -3.0, 0.0, 0.0 }, { -3.0, 10.0 / 3.0, -5.0 / 3.0, 0.0 },
{ 0.0, -5.0 / 3.0, -33.0 / 25.0, 68.0 / 75.0 }, { 0.0, 0.0, 68.0 / 75.0, 149.0 / 75.0 } });

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