Uses of Class
org.episteme.core.mathematics.numbers.complex.Complex

Packages that use Complex

Package	Description
org.episteme.benchmarks.audit.mathematics.linearalgebra
org.episteme.benchmarks.benchmark.benchmarks
org.episteme.core.mathematics.algebra.groups
org.episteme.core.mathematics.algebra.intervals
org.episteme.core.mathematics.analysis.chaos
org.episteme.core.mathematics.analysis.fft
org.episteme.core.mathematics.analysis.fft.providers
org.episteme.core.mathematics.analysis.transform
org.episteme.core.mathematics.linearalgebra.vectors
org.episteme.core.mathematics.loaders.mathml	Provides the invalid reference org.episteme.core.ml.mathml module.
org.episteme.core.mathematics.numbers.complex
org.episteme.core.mathematics.sets
org.episteme.nativ.mathematics.analysis.fft.backends
org.episteme.nativ.mathematics.linearalgebra.backends
org.episteme.natural.physics.classical.waves
org.episteme.natural.physics.quantum
org.episteme.natural.physics.quantum.backends
org.episteme.natural.technical.backend.quantum

Uses of Complex in org.episteme.benchmarks.audit.mathematics.linearalgebra

Method parameters in org.episteme.benchmarks.audit.mathematics.linearalgebra with type arguments of type Complex

Modifier and Type	Method	Description
static void	HighPrecisionAuditOperations.runComplexAudit(LinearAlgebraProvider<Complex> p, int n, HighPrecisionAuditOperations.AuditAction<Complex> action)
static void	HighPrecisionAuditOperations.runComplexAudit(LinearAlgebraProvider<Complex> p, int n, HighPrecisionAuditOperations.AuditAction<Complex> action)
static void	HighPrecisionAuditOperations.testComplexAcos(LinearAlgebraProvider<Complex> prov, LinearAlgebraProvider<Complex> groundTruth)
static void	HighPrecisionAuditOperations.testComplexAdd(LinearAlgebraProvider<Complex> prov, LinearAlgebraProvider<Complex> groundTruth)
static void	HighPrecisionAuditOperations.testComplexAsin(LinearAlgebraProvider<Complex> prov, LinearAlgebraProvider<Complex> groundTruth)
static void	HighPrecisionAuditOperations.testComplexAtan(LinearAlgebraProvider<Complex> prov, LinearAlgebraProvider<Complex> groundTruth)
static void	HighPrecisionAuditOperations.testComplexBiCGSTAB(LinearAlgebraProvider<Complex> prov, LinearAlgebraProvider<Complex> groundTruth)
static void	HighPrecisionAuditOperations.testComplexCbrt(LinearAlgebraProvider<Complex> prov, LinearAlgebraProvider<Complex> groundTruth)
static void	HighPrecisionAuditOperations.testComplexCholesky(LinearAlgebraProvider<Complex> prov, LinearAlgebraProvider<Complex> groundTruth)
static void	HighPrecisionAuditOperations.testComplexConjugateGradient(LinearAlgebraProvider<Complex> prov, LinearAlgebraProvider<Complex> groundTruth)
static void	HighPrecisionAuditOperations.testComplexCos(LinearAlgebraProvider<Complex> prov, LinearAlgebraProvider<Complex> groundTruth)
static void	HighPrecisionAuditOperations.testComplexCosh(LinearAlgebraProvider<Complex> prov, LinearAlgebraProvider<Complex> groundTruth)
static void	HighPrecisionAuditOperations.testComplexDeterminant(LinearAlgebraProvider<Complex> prov, LinearAlgebraProvider<Complex> groundTruth)
static void	HighPrecisionAuditOperations.testComplexDot(LinearAlgebraProvider<Complex> prov, LinearAlgebraProvider<Complex> groundTruth)
static void	HighPrecisionAuditOperations.testComplexEigen(LinearAlgebraProvider<Complex> prov, LinearAlgebraProvider<Complex> groundTruth)
static void	HighPrecisionAuditOperations.testComplexExp(LinearAlgebraProvider<Complex> prov, LinearAlgebraProvider<Complex> groundTruth)
static void	HighPrecisionAuditOperations.testComplexGMRES(LinearAlgebraProvider<Complex> prov, LinearAlgebraProvider<Complex> groundTruth)
static void	HighPrecisionAuditOperations.testComplexInverse(LinearAlgebraProvider<Complex> prov, LinearAlgebraProvider<Complex> groundTruth)
static void	HighPrecisionAuditOperations.testComplexLog(LinearAlgebraProvider<Complex> prov, LinearAlgebraProvider<Complex> groundTruth)
static void	HighPrecisionAuditOperations.testComplexLog10(LinearAlgebraProvider<Complex> prov, LinearAlgebraProvider<Complex> groundTruth)
static void	HighPrecisionAuditOperations.testComplexLU(LinearAlgebraProvider<Complex> prov, LinearAlgebraProvider<Complex> groundTruth)
static void	HighPrecisionAuditOperations.testComplexMatVec(LinearAlgebraProvider<Complex> prov, LinearAlgebraProvider<Complex> groundTruth)
static void	HighPrecisionAuditOperations.testComplexMultiply(LinearAlgebraProvider<Complex> prov, LinearAlgebraProvider<Complex> groundTruth)
static void	HighPrecisionAuditOperations.testComplexNorm(LinearAlgebraProvider<Complex> prov, LinearAlgebraProvider<Complex> groundTruth)
static void	HighPrecisionAuditOperations.testComplexPow(LinearAlgebraProvider<Complex> prov, LinearAlgebraProvider<Complex> groundTruth)
static void	HighPrecisionAuditOperations.testComplexQR(LinearAlgebraProvider<Complex> prov, LinearAlgebraProvider<Complex> groundTruth)
static void	HighPrecisionAuditOperations.testComplexScale(LinearAlgebraProvider<Complex> prov, LinearAlgebraProvider<Complex> groundTruth)
static void	HighPrecisionAuditOperations.testComplexSin(LinearAlgebraProvider<Complex> prov, LinearAlgebraProvider<Complex> groundTruth)
static void	HighPrecisionAuditOperations.testComplexSinh(LinearAlgebraProvider<Complex> prov, LinearAlgebraProvider<Complex> groundTruth)
static void	HighPrecisionAuditOperations.testComplexSolve(LinearAlgebraProvider<Complex> prov, LinearAlgebraProvider<Complex> groundTruth)
static void	HighPrecisionAuditOperations.testComplexSqrt(LinearAlgebraProvider<Complex> prov, LinearAlgebraProvider<Complex> groundTruth)
static void	HighPrecisionAuditOperations.testComplexSubtract(LinearAlgebraProvider<Complex> prov, LinearAlgebraProvider<Complex> groundTruth)
static void	HighPrecisionAuditOperations.testComplexSVD(LinearAlgebraProvider<Complex> prov, LinearAlgebraProvider<Complex> groundTruth)
static void	HighPrecisionAuditOperations.testComplexTan(LinearAlgebraProvider<Complex> prov, LinearAlgebraProvider<Complex> groundTruth)
static void	HighPrecisionAuditOperations.testComplexTanh(LinearAlgebraProvider<Complex> prov, LinearAlgebraProvider<Complex> groundTruth)
static void	HighPrecisionAuditOperations.testComplexTranspose(LinearAlgebraProvider<Complex> prov, LinearAlgebraProvider<Complex> groundTruth)

Uses of Complex in org.episteme.benchmarks.benchmark.benchmarks

Classes in org.episteme.benchmarks.benchmark.benchmarks that implement interfaces with type arguments of type Complex

Modifier and Type	Class	Description
class	ComplexLinearAlgebraBenchmark	Systematic benchmark for High-Precision Complex Linear Algebra.
class	ComplexMatrixInversionBenchmark	Systematic benchmark for High-Precision Complex Matrix Inversion.
class	ComplexSolveBenchmark	Systematic benchmark for High-Precision Complex Matrix Solve.

Methods in org.episteme.benchmarks.benchmark.benchmarks that return types with arguments of type Complex

Modifier and Type	Method	Description
Class<LinearAlgebraProvider<Complex>>	ComplexLinearAlgebraBenchmark.getProviderClass()
Class<LinearAlgebraProvider<Complex>>	ComplexMatrixInversionBenchmark.getProviderClass()
Class<LinearAlgebraProvider<Complex>>	ComplexSolveBenchmark.getProviderClass()

Method parameters in org.episteme.benchmarks.benchmark.benchmarks with type arguments of type Complex

Modifier and Type	Method	Description
void	ComplexLinearAlgebraBenchmark.setProvider(LinearAlgebraProvider<Complex> provider)
void	ComplexMatrixInversionBenchmark.setProvider(LinearAlgebraProvider<Complex> provider)
void	ComplexSolveBenchmark.setProvider(LinearAlgebraProvider<Complex> provider)

Uses of Complex in org.episteme.core.mathematics.algebra.groups

Classes in org.episteme.core.mathematics.algebra.groups that implement interfaces with type arguments of type Complex

Modifier and Type	Class	Description
class	LieGroup	A Lie group is a group that is also a differentiable manifold.
class	SU2Group	The group of 2x2 unitary matrices with determinant 1.
class	SU3Group	The group of 3x3 unitary matrices with determinant 1.
class	U1Group	Represents the Unitary Group U(1).

Methods in org.episteme.core.mathematics.algebra.groups that return Complex

Modifier and Type	Method	Description
Complex	U1Group.fromPhase(double theta)	Creates a U(1) element from an angle (phase).
Complex	U1Group.identity()
Complex	U1Group.inverse(Complex element)
Complex	U1Group.operate(Complex left, Complex right)

Methods in org.episteme.core.mathematics.algebra.groups that return types with arguments of type Complex

Modifier and Type	Method	Description
Matrix<Complex>	LieGroup.getElement(Vector<Real> v)	Generates a group element near the identity using the exponential map approximation.
Matrix<Complex>	LieGroup.identity()
Matrix<Complex>	SU2Group.identity()
Matrix<Complex>	SU3Group.identity()
Matrix<Complex>	LieGroup.inverse(Matrix<Complex> element)
Matrix<Complex>	SU2Group.inverse(Matrix<Complex> element)
Matrix<Complex>	SU3Group.inverse(Matrix<Complex> element)
Matrix<Complex>	LieGroup.operate(Matrix<Complex> a, Matrix<Complex> b)
Matrix<Complex>	SU2Group.operate(Matrix<Complex> left, Matrix<Complex> right)
Matrix<Complex>	SU3Group.operate(Matrix<Complex> left, Matrix<Complex> right)

Methods in org.episteme.core.mathematics.algebra.groups with parameters of type Complex

Modifier and Type	Method	Description
boolean	U1Group.contains(Complex element)
Complex	U1Group.inverse(Complex element)
Complex	U1Group.operate(Complex left, Complex right)

Method parameters in org.episteme.core.mathematics.algebra.groups with type arguments of type Complex

Modifier and Type	Method	Description
boolean	LieGroup.contains(Matrix<Complex> element)
boolean	SU2Group.contains(Matrix<Complex> element)
boolean	SU3Group.contains(Matrix<Complex> element)
Matrix<Complex>	LieGroup.inverse(Matrix<Complex> element)
Matrix<Complex>	SU2Group.inverse(Matrix<Complex> element)
Matrix<Complex>	SU3Group.inverse(Matrix<Complex> element)
Matrix<Complex>	LieGroup.operate(Matrix<Complex> a, Matrix<Complex> b)
Matrix<Complex>	SU2Group.operate(Matrix<Complex> left, Matrix<Complex> right)
Matrix<Complex>	SU3Group.operate(Matrix<Complex> left, Matrix<Complex> right)

Uses of Complex in org.episteme.core.mathematics.algebra.intervals

Methods in org.episteme.core.mathematics.algebra.intervals that return Complex

Modifier and Type	Method	Description
static Complex	ComplexInterval.center(Interval<Real> region)	Returns the center of the complex region.

Methods in org.episteme.core.mathematics.algebra.intervals with parameters of type Complex

Modifier and Type	Method	Description
static boolean	ComplexInterval.contains(Interval<Real> region, Complex z)	Checks if a complex number is inside the region.
static FieldIntervalND<Real>	ComplexInterval.square(Complex center, Real halfWidth)	Creates a square region centered at a complex number.
static FieldIntervalND<Real>	ComplexInterval.translate(Interval<Real> region, Complex delta)	Creates a translated region.

Uses of Complex in org.episteme.core.mathematics.analysis.chaos

Classes in org.episteme.core.mathematics.analysis.chaos that implement interfaces with type arguments of type Complex

Modifier and Type	Class	Description
class	JuliaSet	Julia Set as a proper mathematical set.
class	MandelbrotSet	The Mandelbrot Set as a proper mathematical set.

Methods in org.episteme.core.mathematics.analysis.chaos that return Complex

Modifier and Type	Method	Description
Complex	JuliaSet.getParameter()

Methods in org.episteme.core.mathematics.analysis.chaos with parameters of type Complex

Modifier and Type	Method	Description
boolean	JuliaSet.contains(Complex z)
boolean	MandelbrotSet.contains(Complex c)
int	JuliaSet.escapeTime(Complex z)
int	MandelbrotSet.escapeTime(Complex c)

Constructors in org.episteme.core.mathematics.analysis.chaos with parameters of type Complex

Modifier	Constructor	Description
	JuliaSet(Complex c)
	JuliaSet(Complex c, int maxIterations)

Uses of Complex in org.episteme.core.mathematics.analysis.fft

Methods in org.episteme.core.mathematics.analysis.fft that return Complex

Modifier and Type	Method	Description
Complex[]	FFTProvider.inverseTransformComplex(Complex[] data)
Complex[][]	FFTProvider.inverseTransformComplex2D(Complex[][] data)
Complex[][][]	FFTProvider.inverseTransformComplex3D(Complex[][][] data)
Complex[]	FFTProvider.transformComplex(Complex[] data)
Complex[][]	FFTProvider.transformComplex2D(Complex[][] data)
Complex[][][]	FFTProvider.transformComplex3D(Complex[][][] data)

Methods in org.episteme.core.mathematics.analysis.fft with parameters of type Complex

Modifier and Type	Method	Description
Complex[]	FFTProvider.inverseTransformComplex(Complex[] data)
Complex[][]	FFTProvider.inverseTransformComplex2D(Complex[][] data)
Complex[][][]	FFTProvider.inverseTransformComplex3D(Complex[][][] data)
Complex[]	FFTProvider.transformComplex(Complex[] data)
Complex[][]	FFTProvider.transformComplex2D(Complex[][] data)
Complex[][][]	FFTProvider.transformComplex3D(Complex[][][] data)

Uses of Complex in org.episteme.core.mathematics.analysis.fft.providers

Methods in org.episteme.core.mathematics.analysis.fft.providers that return Complex

Modifier and Type	Method	Description
Complex[]	MulticoreFFTProvider.inverseTransformComplex(Complex[] data)
Complex[]	StandardFFTProvider.inverseTransformComplex(Complex[] data)
Complex[][]	MulticoreFFTProvider.inverseTransformComplex2D(Complex[][] data)
Complex[][]	StandardFFTProvider.inverseTransformComplex2D(Complex[][] data)
Complex[][][]	MulticoreFFTProvider.inverseTransformComplex3D(Complex[][][] data)
Complex[][][]	StandardFFTProvider.inverseTransformComplex3D(Complex[][][] data)
Complex[]	MulticoreFFTProvider.transformComplex(Complex[] data)
Complex[]	StandardFFTProvider.transformComplex(Complex[] data)
Complex[][]	MulticoreFFTProvider.transformComplex2D(Complex[][] data)
Complex[][]	StandardFFTProvider.transformComplex2D(Complex[][] data)
Complex[][][]	MulticoreFFTProvider.transformComplex3D(Complex[][][] data)
Complex[][][]	StandardFFTProvider.transformComplex3D(Complex[][][] data)

Methods in org.episteme.core.mathematics.analysis.fft.providers with parameters of type Complex

Modifier and Type	Method	Description
Complex[]	MulticoreFFTProvider.inverseTransformComplex(Complex[] data)
Complex[]	StandardFFTProvider.inverseTransformComplex(Complex[] data)
Complex[][]	MulticoreFFTProvider.inverseTransformComplex2D(Complex[][] data)
Complex[][]	StandardFFTProvider.inverseTransformComplex2D(Complex[][] data)
Complex[][][]	MulticoreFFTProvider.inverseTransformComplex3D(Complex[][][] data)
Complex[][][]	StandardFFTProvider.inverseTransformComplex3D(Complex[][][] data)
Complex[]	MulticoreFFTProvider.transformComplex(Complex[] data)
Complex[]	StandardFFTProvider.transformComplex(Complex[] data)
Complex[][]	MulticoreFFTProvider.transformComplex2D(Complex[][] data)
Complex[][]	StandardFFTProvider.transformComplex2D(Complex[][] data)
Complex[][][]	MulticoreFFTProvider.transformComplex3D(Complex[][][] data)
Complex[][][]	StandardFFTProvider.transformComplex3D(Complex[][][] data)

Uses of Complex in org.episteme.core.mathematics.analysis.transform

Classes in org.episteme.core.mathematics.analysis.transform that implement interfaces with type arguments of type Complex

Modifier and Type	Class	Description
class	DiscreteFourierTransform	Discrete Fourier Transform (DFT) using Fast Fourier Transform (FFT) algorithm.
class	DiscreteFourierTransform	Discrete Fourier Transform (DFT) using Fast Fourier Transform (FFT) algorithm.
class	DiscreteFourierTransform	Discrete Fourier Transform (DFT) using Fast Fourier Transform (FFT) algorithm.

Methods in org.episteme.core.mathematics.analysis.transform that return Complex

Modifier and Type	Method	Description
static Complex[]	DiscreteFourierTransform.transform(Complex[] data)	Static convenience method for FFT.

Methods in org.episteme.core.mathematics.analysis.transform that return types with arguments of type Complex

Modifier and Type	Method	Description
Vector<Complex>	DiscreteFourierTransform.evaluate(Vector<Complex> input)
Transform<Vector<Complex>, Vector<Complex>>	DiscreteFourierTransform.inverse()
Transform<Vector<Complex>, Vector<Complex>>	DiscreteFourierTransform.inverse()
static Vector<Complex>	AlgebraicFFT.inverseTransform(Vector<Complex> input)	Computes the Inverse FFT of a complex vector.
Matrix<Complex>	DiscreteFourierTransform.jacobian(Vector<Complex> point)
static Vector<Complex>	AlgebraicFFT.transform(Vector<Complex> input)	Computes the Forward FFT of a complex vector.

Methods in org.episteme.core.mathematics.analysis.transform with parameters of type Complex

Modifier and Type	Method	Description
static Complex[]	DiscreteFourierTransform.transform(Complex[] data)	Static convenience method for FFT.

Method parameters in org.episteme.core.mathematics.analysis.transform with type arguments of type Complex

Modifier and Type	Method	Description
Vector<Complex>	DiscreteFourierTransform.evaluate(Vector<Complex> input)
static Vector<Complex>	AlgebraicFFT.inverseTransform(Vector<Complex> input)	Computes the Inverse FFT of a complex vector.
Matrix<Complex>	DiscreteFourierTransform.jacobian(Vector<Complex> point)
static Vector<Complex>	AlgebraicFFT.transform(Vector<Complex> input)	Computes the Forward FFT of a complex vector.

Uses of Complex in org.episteme.core.mathematics.linearalgebra.vectors

Methods in org.episteme.core.mathematics.linearalgebra.vectors that return types with arguments of type Complex

Modifier and Type	Method	Description
static DenseVector<Complex>	DenseVector.valueOf(List<Complex> elements)
static SparseVector<Complex>	SparseVector.valueOf(List<Complex> elements)

Method parameters in org.episteme.core.mathematics.linearalgebra.vectors with type arguments of type Complex

Modifier and Type	Method	Description
static DenseVector<Complex>	DenseVector.valueOf(List<Complex> elements)
static SparseVector<Complex>	SparseVector.valueOf(List<Complex> elements)

Uses of Complex in org.episteme.core.mathematics.loaders.mathml

Methods in org.episteme.core.mathematics.loaders.mathml with parameters of type Complex

Modifier and Type	Method	Description
Element	MathMLDocumentEpistemeImpl.createNumber(Complex z)

Method parameters in org.episteme.core.mathematics.loaders.mathml with type arguments of type Complex

Modifier and Type	Method	Description
Element	MathMLDocumentEpistemeImpl.createComplexMatrix(DenseMatrix<Complex> m)
Element	MathMLDocumentEpistemeImpl.createComplexVector(DenseVector<Complex> v)

Uses of Complex in org.episteme.core.mathematics.numbers.complex

Classes in org.episteme.core.mathematics.numbers.complex that implement interfaces with type arguments of type Complex

Modifier and Type	Class	Description
final class	Complex	Represents a complex number (â„‚), defined as a + bi where a, b are Real numbers.
final class	Complex	Represents a complex number (â„‚), defined as a + bi where a, b are Real numbers.

Fields in org.episteme.core.mathematics.numbers.complex declared as Complex

Modifier and Type	Field	Description
static final Complex	Complex.I
static final Complex	Complex.ONE
static final Complex	Complex.ZERO

Methods in org.episteme.core.mathematics.numbers.complex that return Complex

Modifier and Type	Method	Description
Complex	Complex.acos()	Returns the arccosine of this complex number. acos(z) = -i * log(z + i*sqrt(1 - z^2))
Complex	Complex.acosh()	Returns the inverse hyperbolic cosine of this complex number. acosh(z) = log(z + sqrt(z^2 - 1))
Complex	Complex.add(Complex other)
Complex	Complex.add(Complex a, Complex b)
Complex	Complex.asin()	Returns the arcsine of this complex number. asin(z) = -i * log(iz + sqrt(1 - z^2))
Complex	Complex.asinh()	Returns the inverse hyperbolic sine of this complex number. asinh(z) = log(z + sqrt(z^2 + 1))
Complex	Complex.atan()	Returns the arctangent of this complex number. atan(z) = (i/2) * log((1-iz)/(1+iz))
Complex	Complex.atanh()	Returns the inverse hyperbolic tangent of this complex number. atanh(z) = 0.5 * log((1 + z) / (1 - z))
Complex	Complex.cbrt()	Returns the cube root of this complex number. cbrt(z) = z^(1/3)
Complex	Complex.conjugate()
Complex	Complex.cos()	Returns the cosine of this complex number. cos(a + bi) = cos(a)cosh(b) - i*sin(a)sinh(b)
Complex	Complex.cosh()	Returns the hyperbolic cosine of this complex number. cosh(z) = (exp(z) + exp(-z)) / 2
Complex	Complex.divide(Complex other)
Complex	Complex.divide(Complex a, Complex b)
Complex	Complex.exp()	Returns e raised to this complex number. exp(a + bi) = e^a * (cos(b) + i*sin(b))
Complex	Complex.inverse()
Complex	Complex.inverse(Complex a)
Complex	Complex.log()	Returns the natural logarithm of this complex number. log(z) = ln(|z|) + i*arg(z)
Complex	Complex.log10()	Returns the base-10 logarithm of this complex number. log10(z) = log(z) / log(10)
Complex	Complex.multiply(Complex other)
Complex	Complex.multiply(Complex a, Complex b)
Complex	Complex.negate()
Complex	Complex.negate(Complex a)
static Complex	Complex.of(double real)
static Complex	Complex.of(double real, double imaginary)
static Complex	Complex.of(float real)
static Complex	Complex.of(float real, float imaginary)
static Complex	Complex.of(Real real)
static Complex	Complex.of(Real real, Real imaginary)
static Complex	Complex.ofPolar(double magnitude, double phase)
Complex	Complex.one()
Complex	Complex.operate(Complex a, Complex b)
Complex	Complex.pow(double exponent)	Returns this complex number raised to a double power.
Complex	Complex.pow(Complex exponent)	Returns this complex number raised to a complex power. z^w = exp(w * log(z))
Complex	Complex.reciprocal()	Alias for inverse() to satisfy certain matrix operation requirements.
Complex	Complex.sin()	Returns the sine of this complex number. sin(a + bi) = sin(a)cosh(b) + i*cos(a)sinh(b)
Complex	Complex.sinh()	Returns the hyperbolic sine of this complex number. sinh(z) = (exp(z) - exp(-z)) / 2
Complex	Complex.sqrt()
Complex	Complex.subtract(Complex other)
Complex	Complex.subtract(Complex a, Complex b)
Complex	Complex.tan()	Returns the tangent of this complex number. tan(z) = sin(z) / cos(z)
Complex	Complex.tanh()	Returns the hyperbolic tangent of this complex number. tanh(z) = sinh(z) / cosh(z)
static Complex	Complex.valueOf(String s)
static Complex	Complex.valueOf(String realStr, String imagStr)
Complex	Complex.zero()

Methods in org.episteme.core.mathematics.numbers.complex that return types with arguments of type Complex

Modifier and Type	Method	Description
Ring<Complex>	Complex.getScalarRing()
static Ring<Complex>	Complex.ring()	Returns the ring structure for complex numbers.

Methods in org.episteme.core.mathematics.numbers.complex with parameters of type Complex

Modifier and Type	Method	Description
Complex	Complex.add(Complex other)
Complex	Complex.add(Complex a, Complex b)
boolean	Complex.contains(Complex element)
Complex	Complex.divide(Complex other)
Complex	Complex.divide(Complex a, Complex b)
static Octonion	Octonion.fromComplex(Complex c)	Creates an octonion from a complex number (last 6 components = 0).
Complex	Complex.inverse(Complex a)
Complex	Complex.multiply(Complex other)
Complex	Complex.multiply(Complex a, Complex b)
Complex	Complex.negate(Complex a)
Complex	Complex.operate(Complex a, Complex b)
Complex	Complex.pow(Complex exponent)	Returns this complex number raised to a complex power. z^w = exp(w * log(z))
Complex	Complex.subtract(Complex other)
Complex	Complex.subtract(Complex a, Complex b)

Uses of Complex in org.episteme.core.mathematics.sets

Classes in org.episteme.core.mathematics.sets that implement interfaces with type arguments of type Complex

Modifier and Type	Class	Description
final class	Complexes	The structure of complex numbers (â„‚).
final class	Complexes	The structure of complex numbers (â„‚).

Methods in org.episteme.core.mathematics.sets that return Complex

Modifier and Type	Method	Description
Complex	Complexes.add(Complex a, Complex b)
Complex	Complexes.divide(Complex a, Complex b)
Complex	Complexes.inverse(Complex element)
Complex	Complexes.multiply(Complex a, Complex b)
Complex	Complexes.negate(Complex element)
Complex	Complexes.one()
Complex	Complexes.operate(Complex a, Complex b)
Complex	Complexes.zero()

Methods in org.episteme.core.mathematics.sets with parameters of type Complex

Modifier and Type	Method	Description
Complex	Complexes.add(Complex a, Complex b)
boolean	Complexes.contains(Complex element)
Complex	Complexes.divide(Complex a, Complex b)
Complex	Complexes.inverse(Complex element)
Complex	Complexes.multiply(Complex a, Complex b)
Complex	Complexes.negate(Complex element)
Complex	Complexes.operate(Complex a, Complex b)

Uses of Complex in org.episteme.nativ.mathematics.analysis.fft.backends

Methods in org.episteme.nativ.mathematics.analysis.fft.backends that return Complex

Modifier and Type	Method	Description
Complex[]	NativeFFTBackend.inverseTransformComplex(Complex[] data)
Complex[]	NativeOpenCLFFTBackend.inverseTransformComplex(Complex[] data)
Complex[][]	NativeFFTBackend.inverseTransformComplex2D(Complex[][] data)
Complex[][]	NativeOpenCLFFTBackend.inverseTransformComplex2D(Complex[][] data)
Complex[][][]	NativeFFTBackend.inverseTransformComplex3D(Complex[][][] data)
Complex[][][]	NativeOpenCLFFTBackend.inverseTransformComplex3D(Complex[][][] data)
Complex[]	NativeFFTBackend.transformComplex(Complex[] data)
Complex[]	NativeOpenCLFFTBackend.transformComplex(Complex[] data)
Complex[][]	NativeFFTBackend.transformComplex2D(Complex[][] data)
Complex[][]	NativeOpenCLFFTBackend.transformComplex2D(Complex[][] data)
Complex[][][]	NativeFFTBackend.transformComplex3D(Complex[][][] data)
Complex[][][]	NativeOpenCLFFTBackend.transformComplex3D(Complex[][][] data)

Methods in org.episteme.nativ.mathematics.analysis.fft.backends with parameters of type Complex

Modifier and Type	Method	Description
Complex[]	NativeFFTBackend.inverseTransformComplex(Complex[] data)
Complex[]	NativeOpenCLFFTBackend.inverseTransformComplex(Complex[] data)
Complex[][]	NativeFFTBackend.inverseTransformComplex2D(Complex[][] data)
Complex[][]	NativeOpenCLFFTBackend.inverseTransformComplex2D(Complex[][] data)
Complex[][][]	NativeFFTBackend.inverseTransformComplex3D(Complex[][][] data)
Complex[][][]	NativeOpenCLFFTBackend.inverseTransformComplex3D(Complex[][][] data)
Complex[]	NativeFFTBackend.transformComplex(Complex[] data)
Complex[]	NativeOpenCLFFTBackend.transformComplex(Complex[] data)
Complex[][]	NativeFFTBackend.transformComplex2D(Complex[][] data)
Complex[][]	NativeOpenCLFFTBackend.transformComplex2D(Complex[][] data)
Complex[][][]	NativeFFTBackend.transformComplex3D(Complex[][][] data)
Complex[][][]	NativeOpenCLFFTBackend.transformComplex3D(Complex[][][] data)

Uses of Complex in org.episteme.nativ.mathematics.linearalgebra.backends

Subclasses with type arguments of type Complex in org.episteme.nativ.mathematics.linearalgebra.backends

Modifier and Type	Class	Description
class	NativeCPULinearAlgebraComplexBackend	Concrete Native CPU-BLAS provider for Complex numbers.
class	NativeFFMBLASComplexBackend	Native FFM BLAS/LAPACK provider specialized for Complex numbers.
class	NativeSIMDComplexBackend	Concrete Native SIMD provider for Complex numbers.

Uses of Complex in org.episteme.natural.physics.classical.waves

Methods in org.episteme.natural.physics.classical.waves that return Complex

Modifier and Type	Method	Description
Complex	Wave.phasor(Real x, Real t)	Complex phasor representation: $A e^{i(kx - \omega t + \phi)}$

Uses of Complex in org.episteme.natural.physics.quantum

Methods in org.episteme.natural.physics.quantum that return Complex

Modifier and Type	Method	Description
Complex	BraKet.dot(BraKet other)
static Complex[]	BlochSphere.fromBlochAngles(Real theta, Real phi)	Converts Bloch sphere coordinates back to qubit state.

Methods in org.episteme.natural.physics.quantum that return types with arguments of type Complex

Modifier and Type	Method	Description
DenseMatrix<Complex>	DensityMatrix.getMatrix()
DenseMatrix<Complex>	QuantumGate.getMatrix()
static DenseMatrix<Complex>	QuantumTensorProduct.kronecker(DenseMatrix<Complex> A, DenseMatrix<Complex> B)	Computes the tensor (Kronecker) product of two matrices.
Vector<Complex>	BraKet.vector()

Methods in org.episteme.natural.physics.quantum with parameters of type Complex

Modifier and Type	Method	Description
static Real[]	BlochSphere.toBlochCoordinates(Complex alpha, Complex beta)	Converts qubit amplitudes to Bloch sphere coordinates.

Method parameters in org.episteme.natural.physics.quantum with type arguments of type Complex

Modifier and Type	Method	Description
static DenseMatrix<Complex>	QuantumTensorProduct.kronecker(DenseMatrix<Complex> A, DenseMatrix<Complex> B)	Computes the tensor (Kronecker) product of two matrices.

Constructors in org.episteme.natural.physics.quantum with parameters of type Complex

Modifier	Constructor	Description
	BraKet(Complex... amplitudes)

Constructor parameters in org.episteme.natural.physics.quantum with type arguments of type Complex

Modifier	Constructor	Description
	BraKet(Vector<Complex> vector)
	DensityMatrix(DenseMatrix<Complex> matrix)
	QuantumGate(DenseMatrix<Complex> matrix)

Uses of Complex in org.episteme.natural.physics.quantum.backends

Methods in org.episteme.natural.physics.quantum.backends that return types with arguments of type Complex

Modifier and Type	Method	Description
Matrix<Complex>	AmazonBraketBackend.stateTomography(QuantumBackend.QuantumCircuit c, int s)
Matrix<Complex>	PythonQuantumBackend.stateTomography(QuantumBackend.QuantumCircuit c, int s)
Matrix<Complex>	QiskitBackend.stateTomography(QuantumBackend.QuantumCircuit c, int s)
Matrix<Complex>	Quantum4JBackend.stateTomography(QuantumBackend.QuantumCircuit c, int s)
Matrix<Complex>	StrangeBackend.stateTomography(QuantumBackend.QuantumCircuit c, int s)

Method parameters in org.episteme.natural.physics.quantum.backends with type arguments of type Complex

Modifier and Type	Method	Description
QuantumBackend.QuantumCircuit	AmazonBraketBackend.matrixToUnitary(Matrix<Complex> m)
QuantumBackend.QuantumCircuit	PythonQuantumBackend.matrixToUnitary(Matrix<Complex> m)
QuantumBackend.QuantumCircuit	QiskitBackend.matrixToUnitary(Matrix<Complex> m)
QuantumBackend.QuantumCircuit	Quantum4JBackend.matrixToUnitary(Matrix<Complex> m)
QuantumBackend.QuantumCircuit	StrangeBackend.matrixToUnitary(Matrix<Complex> m)
QuantumBackend.QuantumResult	AmazonBraketBackend.qaoa(Matrix<Complex> h, int l)
QuantumBackend.QuantumResult	PythonQuantumBackend.qaoa(Matrix<Complex> h, int l)
QuantumBackend.QuantumResult	QiskitBackend.qaoa(Matrix<Complex> h, int l)
QuantumBackend.QuantumResult	Quantum4JBackend.qaoa(Matrix<Complex> h, int l)
QuantumBackend.QuantumResult	StrangeBackend.qaoa(Matrix<Complex> h, int l)
double	AmazonBraketBackend.quantumPhaseEstimation(Matrix<Complex> u, Vector<Complex> e, int p)
double	AmazonBraketBackend.quantumPhaseEstimation(Matrix<Complex> u, Vector<Complex> e, int p)
double	PythonQuantumBackend.quantumPhaseEstimation(Matrix<Complex> u, Vector<Complex> e, int p)
double	PythonQuantumBackend.quantumPhaseEstimation(Matrix<Complex> u, Vector<Complex> e, int p)
double	QiskitBackend.quantumPhaseEstimation(Matrix<Complex> u, Vector<Complex> e, int p)
double	QiskitBackend.quantumPhaseEstimation(Matrix<Complex> u, Vector<Complex> e, int p)
double	Quantum4JBackend.quantumPhaseEstimation(Matrix<Complex> u, Vector<Complex> e, int p)
double	Quantum4JBackend.quantumPhaseEstimation(Matrix<Complex> u, Vector<Complex> e, int p)
double	StrangeBackend.quantumPhaseEstimation(Matrix<Complex> u, Vector<Complex> e, int p)
double	StrangeBackend.quantumPhaseEstimation(Matrix<Complex> u, Vector<Complex> e, int p)
double	AmazonBraketBackend.vqe(Matrix<Complex> h, QuantumBackend.QuantumCircuit a, String o)
double	PythonQuantumBackend.vqe(Matrix<Complex> hamiltonian, QuantumBackend.QuantumCircuit ansatz, String optimizer)
double	QiskitBackend.vqe(Matrix<Complex> h, QuantumBackend.QuantumCircuit a, String o)
double	Quantum4JBackend.vqe(Matrix<Complex> h, QuantumBackend.QuantumCircuit a, String o)
double	StrangeBackend.vqe(Matrix<Complex> h, QuantumBackend.QuantumCircuit a, String o)

Uses of Complex in org.episteme.natural.technical.backend.quantum

Methods in org.episteme.natural.technical.backend.quantum that return types with arguments of type Complex

Modifier and Type	Method	Description
Vector<Complex>	QuantumBackend.QuantumResult.getStatevector()
Matrix<Complex>	QuantumAlgorithmProvider.stateTomography(QuantumBackend.QuantumCircuit circuit, int shots)	Performs quantum state tomography to reconstruct a density matrix.

Method parameters in org.episteme.natural.technical.backend.quantum with type arguments of type Complex

Modifier and Type	Method	Description
QuantumBackend.QuantumCircuit	QuantumAlgorithmProvider.matrixToUnitary(Matrix<Complex> matrix)	Converts a classical matrix to a quantum unitary operator.
QuantumBackend.QuantumResult	QuantumAlgorithmProvider.qaoa(Matrix<Complex> costHamiltonian, int layers)	Performs Quantum Approximate Optimization Algorithm (QAOA).
double	QuantumAlgorithmProvider.quantumPhaseEstimation(Matrix<Complex> unitary, Vector<Complex> eigenstate, int precision)	Performs Quantum Phase Estimation (QPE).
double	QuantumAlgorithmProvider.quantumPhaseEstimation(Matrix<Complex> unitary, Vector<Complex> eigenstate, int precision)	Performs Quantum Phase Estimation (QPE).
double	QuantumAlgorithmProvider.vqe(Matrix<Complex> hamiltonian, QuantumBackend.QuantumCircuit ansatz, String optimizer)	Performs Variational Quantum Eigensolver (VQE) to find ground state energy.