public void estimate(final Access1D<?> x, final Access1D<?> y) {
final int tmpRowDim = (int) Math.min(x.count(), y.count());
final int tmpColDim = this.size();
final PhysicalStore<ComplexNumber> tmpBody =
ComplexDenseStore.FACTORY.makeZero(tmpRowDim, tmpColDim);
final PhysicalStore<ComplexNumber> tmpRHS = ComplexDenseStore.FACTORY.makeZero(tmpRowDim, 1);
for (int i = 0; i < tmpRowDim; i++) {
ComplexNumber tmpX = ComplexNumber.ONE;
final ComplexNumber tmpXfactor = ComplexNumber.valueOf((Number) x.get(i));
final ComplexNumber tmpY = ComplexNumber.valueOf((Number) y.get(i));
for (int j = 0; j < tmpColDim; j++) {
tmpBody.set(i, j, tmpX);
tmpX = tmpX.multiply(tmpXfactor);
}
tmpRHS.set(i, 0, tmpY);
}
final QR<ComplexNumber> tmpQR = QR.makeComplex();
tmpQR.decompose(tmpBody);
this.set(tmpQR.solve(tmpRHS));
}
@Override
protected Rotation<ComplexNumber>[] rotations(
final PhysicalStore<ComplexNumber> aStore,
final int aLowInd,
final int aHighInd,
final Rotation<ComplexNumber>[] retVal) {
final ComplexNumber a00 = aStore.get(aLowInd, aLowInd);
final ComplexNumber a01 = aStore.get(aLowInd, aHighInd);
final ComplexNumber a10 = aStore.get(aHighInd, aLowInd);
final ComplexNumber a11 = aStore.get(aHighInd, aHighInd);
final ComplexNumber x = a00.add(a11);
final ComplexNumber y = a10.subtract(a01);
ComplexNumber t; // tan, cot or something temporary
// Symmetrise - Givens
final ComplexNumber cg; // cos Givens
final ComplexNumber sg; // sin Givens
if (ComplexNumber.isSmall(PrimitiveMath.ONE, y)) {
cg = x.signum();
sg = ComplexNumber.ZERO;
} else if (ComplexNumber.isSmall(PrimitiveMath.ONE, x)) {
sg = y.signum();
cg = ComplexNumber.ZERO;
} else if (y.compareTo(x) == 1) {
t = x.divide(y); // cot
sg = y.signum().divide(ComplexFunction.SQRT1PX2.invoke(t));
cg = sg.multiply(t);
} else {
t = y.divide(x); // tan
cg = x.signum().divide(ComplexFunction.SQRT1PX2.invoke(t));
sg = cg.multiply(t);
}
final ComplexNumber b00 = cg.multiply(a00).add(sg.multiply(a10));
final ComplexNumber b11 = cg.multiply(a11).subtract(sg.multiply(a01));
final ComplexNumber b2 =
cg.multiply(a01.add(a10)).add(sg.multiply(a11.subtract(a00))); // b01 + b10
t = b11.subtract(b00).divide(b2);
t = t.signum().divide(ComplexFunction.SQRT1PX2.invoke(t).add(t.norm()));
// Annihilate - Jacobi
final ComplexNumber cj = ComplexFunction.SQRT1PX2.invoke(t).invert(); // Cos Jacobi
final ComplexNumber sj = cj.multiply(t); // Sin Jacobi
retVal[1] = new Rotation.Complex(aLowInd, aHighInd, cj, sj); // Jacobi
retVal[0] =
new Rotation.Complex(
aLowInd,
aHighInd,
cj.multiply(cg).add(sj.multiply(sg)),
cj.multiply(sg).subtract(sj.multiply(cg))); // Givens - Jacobi
return retVal;
}
@Override
protected Rotation<Double>[] rotations(
final PhysicalStore<Double> aStore,
final int aLowInd,
final int aHighInd,
final Rotation<Double>[] retVal) {
final double a00 = aStore.doubleValue(aLowInd, aLowInd);
final double a01 = aStore.doubleValue(aLowInd, aHighInd);
final double a10 = aStore.doubleValue(aHighInd, aLowInd);
final double a11 = aStore.doubleValue(aHighInd, aHighInd);
final double x = a00 + a11;
final double y = a10 - a01;
double t; // tan, cot or something temporary
// Symmetrise - Givens
final double cg; // cos Givens
final double sg; // sin Givens
if (TypeUtils.isZero(y)) {
cg = Math.signum(x);
sg = PrimitiveMath.ZERO;
} else if (TypeUtils.isZero(x)) {
sg = Math.signum(y);
cg = PrimitiveMath.ZERO;
} else if (Math.abs(y) > Math.abs(x)) {
t = x / y; // cot
sg = Math.signum(y) / PrimitiveFunction.SQRT1PX2.invoke(t);
cg = sg * t;
} else {
t = y / x; // tan
cg = Math.signum(x) / PrimitiveFunction.SQRT1PX2.invoke(t);
sg = cg * t;
}
final double b00 = (cg * a00) + (sg * a10);
final double b11 = (cg * a11) - (sg * a01);
final double b2 = (cg * (a01 + a10)) + (sg * (a11 - a00)); // b01 + b10
t = (b11 - b00) / b2;
t = Math.signum(t) / (PrimitiveFunction.SQRT1PX2.invoke(t) + Math.abs(t)); // tan Jacobi
// Annihilate - Jacobi
final double cj = PrimitiveMath.ONE / PrimitiveFunction.SQRT1PX2.invoke(t); // cos Jacobi
final double sj = cj * t; // sin Jacobi
retVal[1] = new Rotation.Primitive(aLowInd, aHighInd, cj, sj); // Jacobi
retVal[0] =
new Rotation.Primitive(
aLowInd,
aHighInd,
((cj * cg) + (sj * sg)),
((cj * sg) - (sj * cg))); // Givens - Jacobi
return retVal;
}
private QuadraticSolver buildIterationSolver(final boolean addSmallDiagonal) {
MatrixStore<Double> tmpQ = this.getQ();
final MatrixStore<Double> tmpC = this.getC();
if (addSmallDiagonal) {
final PhysicalStore<Double> tmpCopyQ = tmpQ.copy();
final double tmpLargest = tmpCopyQ.aggregateAll(Aggregator.LARGEST);
final double tmpRelativelySmall = MACHINE_DOUBLE_ERROR * tmpLargest;
final double tmpPracticalLimit = MACHINE_DOUBLE_ERROR + IS_ZERO;
final double tmpSmallToAdd = Math.max(tmpRelativelySmall, tmpPracticalLimit);
final UnaryFunction<Double> tmpFunc = ADD.second(tmpSmallToAdd);
tmpCopyQ.modifyDiagonal(0, 0, tmpFunc);
tmpQ = tmpCopyQ;
}
if (this.hasEqualityConstraints()) {
final MatrixStore<Double> tmpAE = this.getAE();
final MatrixStore<Double> tmpBE = this.getBE();
final int tmpZeroSize = tmpAE.getRowDim();
final MatrixStore<Double> tmpUpperLeftAE = tmpQ;
final MatrixStore<Double> tmpUpperRightAE = tmpAE.builder().transpose().build();
final MatrixStore<Double> tmpLowerLefAE = tmpAE;
final MatrixStore<Double> tmpLowerRightAE = ZeroStore.makePrimitive(tmpZeroSize, tmpZeroSize);
final MatrixStore<Double> tmpSubAE =
new AboveBelowStore<Double>(
new LeftRightStore<Double>(tmpUpperLeftAE, tmpUpperRightAE),
new LeftRightStore<Double>(tmpLowerLefAE, tmpLowerRightAE));
final MatrixStore<Double> tmpUpperBE = tmpC;
final MatrixStore<Double> tmpLowerBE = tmpBE;
final MatrixStore<Double> tmpSubBE = new AboveBelowStore<Double>(tmpUpperBE, tmpLowerBE);
return new Builder().equalities(tmpSubAE, tmpSubBE).build(options);
} else {
return new Builder().equalities(tmpQ, tmpC).build(options);
}
}
@SuppressWarnings("unchecked")
static void copy(
final ExpressionsBasedModel sourceModel, final QuadraticSolver.Builder destinationBuilder) {
final List<Variable> tmpFreeVariables = sourceModel.getFreeVariables();
final Set<Index> tmpFixedVariables = sourceModel.getFixedVariables();
final int tmpFreeVarDim = tmpFreeVariables.size();
final Array1D<Double> tmpCurrentSolution = Array1D.PRIMITIVE.makeZero(tmpFreeVarDim);
for (int i = 0; i < tmpFreeVariables.size(); i++) {
final BigDecimal tmpValue = tmpFreeVariables.get(i).getValue();
if (tmpValue != null) {
tmpCurrentSolution.set(i, tmpValue.doubleValue());
}
}
final Optimisation.Result tmpKickStarter =
new Optimisation.Result(Optimisation.State.UNEXPLORED, Double.NaN, tmpCurrentSolution);
// AE & BE
final List<Expression> tmpEqExpr = sourceModel.selectExpressionsLinearEquality();
final int tmpEqExprDim = tmpEqExpr.size();
if (tmpEqExprDim > 0) {
final PhysicalStore<Double> tmpAE = FACTORY.makeZero(tmpEqExprDim, tmpFreeVarDim);
final PhysicalStore<Double> tmpBE = FACTORY.makeZero(tmpEqExprDim, 1);
for (int i = 0; i < tmpEqExprDim; i++) {
final Expression tmpExpression = tmpEqExpr.get(i);
for (final Expression.Index tmpKey : tmpExpression.getLinearFactorKeys()) {
final int tmpIndex = sourceModel.indexOfFreeVariable(tmpKey.index);
if (tmpIndex >= 0) {
tmpAE.set(i, tmpIndex, tmpExpression.getAdjustedLinearFactor(tmpKey));
}
}
tmpBE.set(i, 0, tmpExpression.getCompensatedUpperLimit(tmpFixedVariables));
}
destinationBuilder.equalities(tmpAE, tmpBE);
}
// Q & C
final Expression tmpObjExpr = sourceModel.getObjectiveExpression();
PhysicalStore<Double> tmpQ = null;
if (tmpObjExpr.isAnyQuadraticFactorNonZero()) {
tmpQ = FACTORY.makeZero(tmpFreeVarDim, tmpFreeVarDim);
final BinaryFunction<Double> tmpBaseFunc = sourceModel.isMaximisation() ? SUBTRACT : ADD;
UnaryFunction<Double> tmpModifier;
for (final Expression.RowColumn tmpKey : tmpObjExpr.getQuadraticFactorKeys()) {
final int tmpRow = sourceModel.indexOfFreeVariable(tmpKey.row);
final int tmpColumn = sourceModel.indexOfFreeVariable(tmpKey.column);
if ((tmpRow >= 0) && (tmpColumn >= 0)) {
tmpModifier = tmpBaseFunc.second(tmpObjExpr.getAdjustedQuadraticFactor(tmpKey));
tmpQ.modifyOne(tmpRow, tmpColumn, tmpModifier);
tmpQ.modifyOne(tmpColumn, tmpRow, tmpModifier);
}
}
}
PhysicalStore<Double> tmpC = null;
if (tmpObjExpr.isAnyLinearFactorNonZero()) {
tmpC = FACTORY.makeZero(tmpFreeVarDim, 1);
if (sourceModel.isMinimisation()) {
for (final Expression.Index tmpKey : tmpObjExpr.getLinearFactorKeys()) {
final int tmpIndex = sourceModel.indexOfFreeVariable(tmpKey.index);
if (tmpIndex >= 0) {
tmpC.set(tmpIndex, 0, -tmpObjExpr.getAdjustedLinearFactor(tmpKey));
}
}
} else {
for (final Expression.Index tmpKey : tmpObjExpr.getLinearFactorKeys()) {
final int tmpIndex = sourceModel.indexOfFreeVariable(tmpKey.index);
if (tmpIndex >= 0) {
tmpC.set(tmpIndex, 0, tmpObjExpr.getAdjustedLinearFactor(tmpKey));
}
}
}
}
destinationBuilder.objective(tmpQ, tmpC);
// AI & BI
final List<Expression> tmpUpExpr = sourceModel.selectExpressionsLinearUpper();
final int tmpUpExprDim = tmpUpExpr.size();
final List<Variable> tmpUpVar = sourceModel.selectVariablesFreeUpper();
final int tmpUpVarDim = tmpUpVar.size();
final List<Expression> tmpLoExpr = sourceModel.selectExpressionsLinearLower();
final int tmpLoExprDim = tmpLoExpr.size();
final List<Variable> tmpLoVar = sourceModel.selectVariablesFreeLower();
final int tmpLoVarDim = tmpLoVar.size();
if ((tmpUpExprDim + tmpUpVarDim + tmpLoExprDim + tmpLoVarDim) > 0) {
final ModelEntity<?>[] tmpEntities =
new ModelEntity<?>[tmpUpExprDim + tmpUpVarDim + tmpLoExprDim + tmpLoVarDim];
final PhysicalStore<Double> tmpUAI =
FACTORY.makeZero(tmpUpExprDim + tmpUpVarDim, tmpFreeVarDim);
final PhysicalStore<Double> tmpUBI = FACTORY.makeZero(tmpUpExprDim + tmpUpVarDim, 1);
if (tmpUpExprDim > 0) {
for (int i = 0; i < tmpUpExprDim; i++) {
final Expression tmpExpression = tmpUpExpr.get(i);
for (final Expression.Index tmpKey : tmpExpression.getLinearFactorKeys()) {
final int tmpIndex = sourceModel.indexOfFreeVariable(tmpKey.index);
if (tmpIndex >= 0) {
tmpUAI.set(i, tmpIndex, tmpExpression.getAdjustedLinearFactor(tmpKey));
}
}
tmpUBI.set(i, 0, tmpExpression.getCompensatedUpperLimit(tmpFixedVariables));
tmpEntities[i] = tmpExpression;
}
}
if (tmpUpVarDim > 0) {
for (int i = 0; i < tmpUpVarDim; i++) {
final Variable tmpVariable = tmpUpVar.get(i);
tmpUAI.set(
tmpUpExprDim + i,
sourceModel.indexOfFreeVariable(tmpVariable),
tmpVariable.getAdjustmentFactor());
tmpUBI.set(tmpUpExprDim + i, 0, tmpVariable.getAdjustedUpperLimit());
tmpEntities[tmpUpExprDim + i] = tmpVariable;
}
}
final PhysicalStore<Double> tmpLAI =
FACTORY.makeZero(tmpLoExprDim + tmpLoVarDim, tmpFreeVarDim);
final PhysicalStore<Double> tmpLBI = FACTORY.makeZero(tmpLoExprDim + tmpLoVarDim, 1);
if (tmpLoExprDim > 0) {
for (int i = 0; i < tmpLoExprDim; i++) {
final Expression tmpExpression = tmpLoExpr.get(i);
for (final Expression.Index tmpKey : tmpExpression.getLinearFactorKeys()) {
final int tmpIndex = sourceModel.indexOfFreeVariable(tmpKey.index);
if (tmpIndex >= 0) {
tmpLAI.set(i, tmpIndex, -tmpExpression.getAdjustedLinearFactor(tmpKey));
}
}
tmpLBI.set(i, 0, -tmpExpression.getCompensatedLowerLimit(tmpFixedVariables));
tmpEntities[tmpUpExprDim + tmpUpVarDim + i] = tmpExpression;
}
}
if (tmpLoVarDim > 0) {
for (int i = 0; i < tmpLoVarDim; i++) {
final Variable tmpVariable = tmpLoVar.get(i);
tmpLAI.set(
tmpLoExprDim + i,
sourceModel.indexOfFreeVariable(tmpVariable),
-tmpVariable.getAdjustmentFactor());
tmpLBI.set(tmpLoExprDim + i, 0, -tmpVariable.getAdjustedLowerLimit());
tmpEntities[tmpUpExprDim + tmpUpVarDim + tmpLoExprDim + i] = tmpVariable;
}
}
final MatrixStore<Double> tmpAI = tmpLAI.builder().above(tmpUAI).build();
final MatrixStore<Double> tmpBI = tmpLBI.builder().above(tmpUBI).build();
destinationBuilder.inequalities(tmpAI, tmpBI, tmpEntities);
final IndexSelector tmpSelector = new IndexSelector(tmpEntities.length);
for (int i = 0; i < tmpEntities.length; i++) {
if (tmpEntities[i].isActiveInequalityConstraint()) {
tmpSelector.include(i);
}
}
tmpKickStarter.activeSet(tmpSelector.getIncluded());
}
destinationBuilder.setKickStarter(tmpKickStarter);
}
@Override
protected Rotation<BigDecimal>[] rotations(
final PhysicalStore<BigDecimal> aStore,
final int aLowInd,
final int aHighInd,
final Rotation<BigDecimal>[] retVal) {
final BigDecimal a00 = aStore.get(aLowInd, aLowInd);
final BigDecimal a01 = aStore.get(aLowInd, aHighInd);
final BigDecimal a10 = aStore.get(aHighInd, aLowInd);
final BigDecimal a11 = aStore.get(aHighInd, aHighInd);
final BigDecimal x = a00.add(a11);
final BigDecimal y = a10.subtract(a01);
BigDecimal t; // tan, cot or something temporary
// Symmetrise - Givens
final BigDecimal cg; // cos Givens
final BigDecimal sg; // sin Givens
if (y.signum() == 0) {
cg = BigFunction.SIGNUM.invoke(x);
sg = BigMath.ZERO;
} else if (x.signum() == 0) {
sg = BigFunction.SIGNUM.invoke(y);
cg = BigMath.ZERO;
} else if (y.abs().compareTo(x.abs()) == 1) {
t = BigFunction.DIVIDE.invoke(x, y); // cot
sg =
BigFunction.DIVIDE.invoke(BigFunction.SIGNUM.invoke(y), BigFunction.SQRT1PX2.invoke(t));
cg = sg.multiply(t);
} else {
t = BigFunction.DIVIDE.invoke(y, x); // tan
cg =
BigFunction.DIVIDE.invoke(BigFunction.SIGNUM.invoke(x), BigFunction.SQRT1PX2.invoke(t));
sg = cg.multiply(t);
}
final BigDecimal b00 = cg.multiply(a00).add(sg.multiply(a10));
final BigDecimal b11 = cg.multiply(a11).subtract(sg.multiply(a01));
final BigDecimal b2 =
cg.multiply(a01.add(a10)).add(sg.multiply(a11.subtract(a00))); // b01 + b10
t = BigFunction.DIVIDE.invoke(b11.subtract(b00), b2);
t =
BigFunction.DIVIDE.invoke(
BigFunction.SIGNUM.invoke(t), BigFunction.SQRT1PX2.invoke(t).add(t.abs()));
// Annihilate - Jacobi
final BigDecimal cj =
BigFunction.DIVIDE.invoke(BigMath.ONE, BigFunction.SQRT1PX2.invoke(t)); // Cos Jacobi
final BigDecimal sj = cj.multiply(t); // Sin Jacobi
retVal[1] = new Rotation.Big(aLowInd, aHighInd, cj, sj); // Jacobi
retVal[0] =
new Rotation.Big(
aLowInd,
aHighInd,
cj.multiply(cg).add(sj.multiply(sg)),
cj.multiply(sg).subtract(sj.multiply(cg))); // Givens - Jacobi
return retVal;
}
