This class is subject to change. Programs using this class may require changes with a new version of VirtualLab.
This class is a matrix of complex values. If no imaginary part is needed (real valued fields) one can set a special flag that indicates a real valued field (ComplexField with imaginary part zero). This different internal representations are used to optimize the computer memory and computational time.
Operators ( \(a+b\), \(a-b\), \(a*b\) and \(a/b\)) can be used. Passing \(a\) or \(b\) as Complex or double is supported (Except of \(/\), only \(b\) may be a scalar). Operator \(a|b\) is used for calculation of inner product of two ComplexFields: \(a|b=\sum _{j=0}^{m}\sum _{i=0}^{n}a_{{i,j}}b_{{i,j}^{\star}}\) ( \(z^{\star}\) means conjugation of complex number.). IsComplex property is always taken from first operand. More...

Inheritance diagram for ComplexField:

Public Member Functions
void	AddConjugate ()
	Adds conjugated ComplexField to current one.

void	AddEqual (Complex c)
	Adds a Complex to current ComplexField. See important note on ComplexField.

void	AddEqual (ComplexField field)
	Adds a ComplexField to current one. Both field must have same number of sampling points. See important note on ComplexField.

void	ClipAmplitude (double clippingLevel)
	Sets all amplitude value greater than clippingLevel to clippingLevel.

	ComplexField ()
	Creates a ComplexField with 1x1 sampling points. The default precision is used and the internal data presentation is complex.

	ComplexField (ComplexField field)
	Copy constructor.

	ComplexField (Vector samplingPoints)
	Creates a ComplexField with given number of sampling points. The default precision is used and the internal data presentation is complex.

	ComplexField (Vector samplingPoints, bool createComplexField, Func< int, int, double > function, ParallelizationType parallelizationType=ParallelizationType.Always)
	Constructs a ComplexField object with given number of sampling points using a real-valued function which will be evaluated to fill in the complex amplitudes. The parameters x and y of the real function are measured in pixel coordinates whose origin is the upper left corner of the field.

	ComplexField (Vector samplingPoints, bool isComplex, PrecisionMode precision, Complex c)
	Creates a ComplexField with given number of sampling points using specified precision. The internal data representation can be complex or real. Field is filled with constant value. In case of a real valued complex field only the real part of constant value is stored.

	ComplexField (Vector samplingPoints, bool isComplex, PrecisionMode precision=PrecisionMode.Double, bool initializeValues=true)
	Creates a ComplexField with given number of sampling points using specified precision. The internal data representation can be complex or real.

	ComplexField (Vector samplingPoints, Complex c, bool isComplex=true)
	Creates a ComplexField with given number of sampling points using specified precision. The internal data representation can be complex or real. Field is filled with constant value. In case of a real valued complex field only the real part of constant value is stored.

	ComplexField (Vector samplingPoints, Func< int, int, Complex > function, ParallelizationType parallelizationType=ParallelizationType.Always)
	Constructs a ComplexField object with given number of sampling points using a complex-valued function which will be evaluated to fill in the complex amplitudes. The parameters x and y of the real function are measured in pixel coordinates whose origin is the upper left corner of the field.

void	Conjugate ()
	Conjugates current ComplexField.

void	ConvertTo2DDoubleArray (out double[,] doubleArrayReal, out double[,] doubleArrayImaginary)
	Public support method to convert the complex field into two double arrays. (real and imaginary part will be output separately) Remark: This function was implemented to realize compatibility to Python.

void	DivEqual (Complex c)
	Divides the present ComplexField by complex number. See important note on ComplexField.

void	DivEqual (ComplexField field)
	Divides the present ComplexField by passed one. Both field must have same number of sampling points. See important note on ComplexField.

void	EmbedCorner (Vector newSize)
	Embeds the current ComplexField into double side-length field of zero sampling points and places the original in bottom left corner of the new field. If the ComplexField is one-dimensional, only longer side of field is doubled.

virtual void	EmbedExtract ()
	Embeds the current ComplexField into double side-length field of zero sampling points and places the original in the middle of the new field. If the ComplexField is one-dimensional, only longer side of field is doubled.

virtual ComplexField	EmbedExtract (Rectangle rectangle)
	Extract a region of the current ComplexField including the bottom left corner but excluding the top right corner.

virtual void	EmbedExtract (Vector newSize)
	Embeds the current ComplexField into field of passed size of zero sampling points and places the original in the middle of the new field. By decreasing size, field can be extracted.

override bool	Equals (Object obj)
	Checks whether two complex fields represent the same values.

ComplexField	Extract (Vector size, VectorL position, bool elliptical=false)
	Extracts the given region at given position out of the current field. Points exceeding boundaries of current field will be ignored.

ComplexField	ExtractColumn (int colIndex)
	Extracts a column out of the current field. Points exceeding boundaries of current field will be set to zero.

ComplexField	ExtractRow (int rowIndex)
	Extracts a row out of the current field. Points exceeding boundaries of current field will be set to zero.

void	Fill (Complex c)
	Fills whole current ComplexField with the specified complex value.

void	Fill (Complex c, Rectangle marker, bool inside, bool elliptical=false)
	Fills whole ComplexField inside marker with the specified complex value. If inside is set to false, field outside marker will be filled.

void	GetAmplitude ()
	Returns ComplexField with zero phase and a magnitude equal to that of current ComplexField.

void	GetImaginaryPart ()
	Extracts the imaginary part of current ComplexField. The real part is set to zero.

void	GetIntensity ()
	Extracts the intensity of ComplexField and shifts to the real part of current ComplexField. The imaginary part is set to zero.

void	GetPhase ()
	Returns ComplexField with unit magnitude and a phase equal to that of current ComplexField.

void	GetRealPart ()
	Extracts the real part of current ComplexField. The imaginary part is set to zero.

void	HorizontalMirror ()
	Performs a horizontal mirroring of current ComplexField. [SamplingPoints.X - x - 1, y] = [x, y].

void	Insert (ComplexField field, VectorL position, bool elliptical=false)
	Inserts the given ComplexField into current field at given position. Points exceeding boundaries of current field will be ignored.

void	InsertColumn (int colIndex)
	Inserts or appends empty column.

void	InsertRow (int rowIndex)
	Inserts or appends empty row.

void	LiftPositive ()
	Lifts real part of current ComplexField to positive numbers. Function detects the minimum real number. If this number is smaller than zero it adds the absolute value of the minimum. If the minimum real number is larger than zero the present object is returned without changes.

double[]	LinearFit (VectorD samplDist)
	Linear regression on a real valued Complex Field (phase derivative of a CA in x resp. y) Excluded points are assumed to be marked by float.Epsilon.

void	ModifyComplexPart (ComplexPart complexPart, bool makeRealValuedIfSuitable=false, double thresholdForPhaseArtifacts=0, double amplitudeMaximum=0)
	Extract, shifts or swaps complex parts of the complex field.

void	ModifyPixels (Func< Complex, Complex > modificationMethod)
	Modifies all pixels in parallel. Can be used if the new pixel value depends only on the old pixel value (and maybe some fixed parameters).

void	ModifyPixels (Func< Complex, int, int, Complex > modificationMethod)
	Modifies all pixels in parallel. Can be used if the new pixel value depends on the old pixel value and the current position in pixel coordinates (and maybe some fixed parameters).

void	MultEqual (Complex c)
	Multiplies a Complex number to current ComplexField. See important note on ComplexField.

void	MultEqual (ComplexField field)
	Multiplies a ComplexField with current one. Both field must have same number of sampling points. See important note on ComplexField.

void	MultEqual (IRegion1D2D region, SamplingParameters samplingParameters)
	Multiplies a IRegion1D2D with this ComplexField.

void	Normalize (System.Drawing.Rectangle? rectangle=null)
	Normalizes ComplexField so that maximal amplitude inside rectangle is one.

void	PowerEqual (Complex c)
	Raises every element of current ComplexField to the power of passed complex number. See important note on ComplexField.

double	RadiusError (double constPart, double radius, double k, VectorD dist, bool computeInX)
	compute the fit measure of the spherical phase dependent on radius in partial phase derivative

void	Replicate (Vector newSize, VectorL shift)
	Replicates current ComplexField periodically. Needs new size.

void	Replicate_Periodic (Vector newSize)
	Replicates current ComplexField periodically, old field is at (0,0). Needs new size.

void	Rotate180 ()
	Rotates this ComplexField through 180° about the field center.

void	Shift (Vector shift, bool assumePeriodicField=false)
	Shifts current ComplexField by a specified distance. Size is not modified, so sampling points can get lost.

void	ShiftColumnFromOnePositionToAnother (int oldColIndex, int newColIndex)
	Shifts a single column from one pixel index to another.

void	ShiftRowFromOnePositionToAnother (int oldRowIndex, int newRowIndex)
	Shifts a single row from one pixel index to another.

void	SortColumns (int[] newColIndices)
	Method which brings all columns into a new, given order. Since this is not optimized, it shall not be used if a) the field is to be mirrored or b) only a single column is to be shifted.

void	SortRows (int[] newRowIndices)
	Method which brings all rows into a new, given order. Since this is not optimized, it shall not be used if a) the field is to be mirrored or b) only a single row is to be shifted.

void	SubEqual (Complex c)
	Subtracts a Complex from current ComplexField. See important note on ComplexField.

void	SubEqual (ComplexField field)
	Subtracts a ComplexField from current one. Both field must have same number of sampling points. See important note on ComplexField.

void	Transpose ()
	Transposes current ComplexField. This means [x, y] = [y, x].

void	VerticalMirror ()
	Performs a vertical mirroring of current ComplexField. [x, SamplingPoints.Y - y - 1] = [x, y].

Static Public Member Functions
static ComplexField	ConvertFrom2_1D_DoubleArrays (double[] doubleArray1, double[] doubleArray2)
	Converts two one-dimensional double arrays to a two dimensional complex field of dimensions 2 x doubleArray1.Length.

static ComplexField	ConvertFrom2D_DoubleArray (double[,] doubleArray)
	Converts a two dimensional double array to a two dimensional complex field.

static ComplexFieldDerivative1D	ConvertFrom_1D_ComplexArray (Complex[] complexArray)
	Converts one one-dimensional complex array to a one-dimensional complex field.

static CFieldDerivative1DReal	ConvertFrom_1D_DoubleArray (double[] doubleArray)
	Converts one one-dimensional double array to a one-dimensional complex field.

static double[]	ConvertTo1D_DoubleArray (ComplexField complexField, bool errorWhenComplex)
	Converts a one dimensional complex field to a one dimensional double array.

static double[,]	ConvertTo2D_DoubleArray (ComplexField complexField, bool errorWhenComplex)
	Converts a two dimensional complex field to a two dimensional double array.

static bool	operator!= (ComplexField field1, ComplexField field2)
	Compares two complex fields for equality.

static ComplexField	operator* (Complex c, ComplexField field)
	Multiplies a complex value to a complex field.

static ComplexField	operator* (ComplexField field, Complex c)
	Multiplies a complex value to a complex field.

static ComplexField	operator* (ComplexField field1, ComplexField field2)
	Multiplies two complex fields.

static ComplexField	operator+ (ComplexField field, Complex c)
	Adds a complex value to a complex field.

static ComplexField	operator+ (ComplexField field1, ComplexField field2)
	Adds two complex fields.

static ComplexField	operator- (Complex c, ComplexField field)
	Subtracts a complex number and a complex field.

static ComplexField	operator- (ComplexField field, Complex c)
	Subtracts a complex field and a complex number.

static ComplexField	operator- (ComplexField field1, ComplexField field2)
	Subtracts two complex fields.

static ComplexField	operator/ (ComplexField field, Complex c)
	Divides a complex field by a complex number.

static ComplexField	operator/ (ComplexField field1, ComplexField field2)
	Divide two complex fields.

static bool	operator== (ComplexField field1, ComplexField field2)
	Compares two complex fields for equality.

static Complex	operator\| (ComplexField field1, ComplexField field2)
	Computes the inner (or scalar) product of two complex fields as defined by (u\|v) := Integrate[u(x) * v^(x), {x, -Infinity, Infinity}].

Properties
virtual bool	IsComplex `[get, set]`
	Gets or sets the internal representation of the values of ComplexFieldGenerate Spheric. If IsComplex = true the real and imaginary part is stored. Is IsComplex = false only the real part is stored. It is assumed that the imagary part is zero. Setting the IsComplex property will convert the ComplexField from present representation to new one. Information can be lost during this conversion.

virtual bool	IsOneD `[get]`
	Indicates whether field is one-dimensional or not.

PrecisionMode	Precision `[get, set]`
	Changes the precision of the internal number representation. It is possible to switch between double (64 bit), single (32 bit) and integer precision (16bit). The different precisions are realized by using 3 different arrays of numbers. Only the array that corresponds to the selected precision is used and contains the values of the ComplexField. All other arrays are empty. Setting a different precision than the present will start a conversion of the ComplexField data to the new precision format. Information can be lost in case of a conversions to a lower accuracy.

virtual Vector	SamplingPoints `[get, set]`
	Gets or sets number of sampling points of ComplexField. Setting a new number of sampling points will embed the sampling points in zero samples or extract the central sampling points. See also EmbedExtract.

int	SamplingPointsOneD `[get]`
	Number of sampling points of one-dimensional field. An exception will be thrown, if field is two-dimensional.

virtual Complex	this[int x, int y] `[get, set]`
	Indexer to access complex values of complex field. Property performs a range checking before every access. If you try to read a complex value and index is out of range Complex(0) is returned. If you try to set a complex value and index is out of range nothing will happen. Indexer returns always a complex number in double precision independent on the internal complex number representation. During the setting of a complex value the indexer converts the complex number from double precision to the internal data representation. If internal precision is less accurate double precision information will be lost. Conversion to the less accurate precision is done by truncating the numbers after the last digit of the new precision. If IsComplex = false only the real part is stored.

Complex	this[long x, long y] `[get, set]`
	Indexer to access complex values of complex field. Property performs a range checking before every access. If you try to read a complex value and index is out of range Complex(0) is returned. If you try to set a complex value and index is out of range nothing will happen. Indexer returns always a complex number in double precision independent on the internal complex number representation. During the setting of a complex value the indexer converts the complex number from double precision to the internal data representation. If internal precision is less accurate double precision information will be lost. Conversion to the less accurate precision is done by truncating the numbers after the last digit of the new precision. If IsComplex = false only the real part is stored.

Detailed Description

This class is subject to change. Programs using this class may require changes with a new version of VirtualLab.
This class is a matrix of complex values. If no imaginary part is needed (real valued fields) one can set a special flag that indicates a real valued field (ComplexField with imaginary part zero). This different internal representations are used to optimize the computer memory and computational time.
Operators ( \(a+b\), \(a-b\), \(a*b\) and \(a/b\)) can be used. Passing \(a\) or \(b\) as Complex or double is supported (Except of \(/\), only \(b\) may be a scalar). Operator \(a|b\) is used for calculation of inner product of two ComplexFields: \(a|b=\sum _{j=0}^{m}\sum _{i=0}^{n}a_{{i,j}}b_{{i,j}^{\star}}\) ( \(z^{\star}\) means conjugation of complex number.). IsComplex property is always taken from first operand.

Constructor & Destructor Documentation

◆ ComplexField() [1/7]

ComplexField ( Vector samplingPoints )

Creates a ComplexField with given number of sampling points. The default precision is used and the internal data presentation is complex.

Parameters

samplingPoints Number of points in x and y direction.

◆ ComplexField() [2/7]

ComplexField ( ComplexField field )

Copy constructor.

Parameters

field Field to copy.

◆ ComplexField() [3/7]

ComplexField	(	Vector	samplingPoints,
		bool	isComplex,
		PrecisionMode	precision = `PrecisionMode::Double`,
		bool	initializeValues = `true`
	)

Creates a ComplexField with given number of sampling points using specified precision. The internal data representation can be complex or real.

Parameters

samplingPoints	Number of values in x and y direction.
isComplex	Indicates if new ComplexField should internally store real + imaginary part (complex = true) or the real part only (complex = false) (imaginary part is zero).
precision	Optional and obsolete PrecisionMode. Should not be used.
initializeValues	If this optional parameter is set to `false`, the field values are not initialized. Should be used only if the values are initialized immediately afterwards, but then performance is better.

◆ ComplexField() [4/7]

ComplexField	(	Vector	samplingPoints,
		bool	isComplex,
		PrecisionMode	precision,
		Complex	c
	)

Creates a ComplexField with given number of sampling points using specified precision. The internal data representation can be complex or real. Field is filled with constant value. In case of a real valued complex field only the real part of constant value is stored.

Parameters

samplingPoints	Number of values in x and y direction.
precision	Desired PrecisionMode.
isComplex	Indicates if the new ComplexField should internally store real + imaginary part (complex = true) or the real part only (complex = false) (imaginary part is zero).
c	Complex number with which the field is to be initialized.

◆ ComplexField() [5/7]

ComplexField	(	Vector	samplingPoints,
		Complex	c,
		bool	isComplex = `true`
	)

Creates a ComplexField with given number of sampling points using specified precision. The internal data representation can be complex or real. Field is filled with constant value. In case of a real valued complex field only the real part of constant value is stored.

Parameters

samplingPoints	Number of values in x and y direction.
isComplex	This optional parameter indicates if the new ComplexField should internally store real + imaginary part (`true`, which is the default) or the real part only (`false`) (imaginary part is zero).
c	Complex number with which the field is to be initialized.

◆ ComplexField() [6/7]

ComplexField	(	Vector	samplingPoints,
		bool	createComplexField,
		Func< int, int, double >	function,
		ParallelizationType	parallelizationType = `ParallelizationType::Always`
	)

Constructs a ComplexField object with given number of sampling points using a real-valued function which will be evaluated to fill in the complex amplitudes. The parameters x and y of the real function are measured in pixel coordinates whose origin is the upper left corner of the field.

Parameters

samplingPoints	Number of pixels in x-and y-direction.
createComplexField	Indicates if new ComplexField should internally store real + imaginary part (`createComplexField = true`) or the real part only (`createComplexField = false`).
function	Function to be evaluated.
parallelizationType	Optional type of the parallelization (ParallelizationType.AutomaticMeasure by default). Set it to ParallelizationType.NoParallelization if the method passed by the function is not thread-safe.

◆ ComplexField() [7/7]

ComplexField	(	Vector	samplingPoints,
		Func< int, int, Complex >	function,
		ParallelizationType	parallelizationType = `ParallelizationType::Always`
	)

Constructs a ComplexField object with given number of sampling points using a complex-valued function which will be evaluated to fill in the complex amplitudes. The parameters x and y of the real function are measured in pixel coordinates whose origin is the upper left corner of the field.

Parameters

samplingPoints	Number of pixels in x-and y-direction.
function	Function to be evaluated.
parallelizationType	Optional type of the parallelization (ParallelizationType.AutomaticMeasure by default). Set it to ParallelizationType.NoParallelization if the method passed by the function is not thread-safe.

Member Function Documentation

◆ AddEqual() [1/2]

void AddEqual ( Complex c )

Adds a Complex to current ComplexField. See important note on ComplexField.

Parameters

c	Complex number to add to current field.

◆ AddEqual() [2/2]

void AddEqual ( ComplexField field )

Adds a ComplexField to current one. Both field must have same number of sampling points. See important note on ComplexField.

Parameters

field Complex field to add to current field.

◆ ClipAmplitude()

void ClipAmplitude ( double clippingLevel )

Sets all amplitude value greater than clippingLevel to clippingLevel.

Parameters

clippingLevel Maximal value of amplitude.

◆ ConvertFrom2_1D_DoubleArrays()

static ComplexField ConvertFrom2_1D_DoubleArrays	(	double[]	doubleArray1,
		double[]	doubleArray2
	)

static

Converts two one-dimensional double arrays to a two dimensional complex field of dimensions 2 x doubleArray1.Length.

Parameters

doubleArray1	The first double array to convert
doubleArray2	The second double array to convert

Returns: Complex field, created from the double arrays

◆ ConvertFrom2D_DoubleArray()

static ComplexField ConvertFrom2D_DoubleArray ( double doubleArray[,] )

static

Converts a two dimensional double array to a two dimensional complex field.

Parameters

doubleArray The double array to convert

Returns: Complex field, created from the double array

◆ ConvertFrom_1D_ComplexArray()

static ComplexFieldDerivative1D ConvertFrom_1D_ComplexArray ( Complex[] complexArray )

static

Converts one one-dimensional complex array to a one-dimensional complex field.

Parameters

complexArray The complex array to convert

Returns: Complex field, created from the complex array

◆ ConvertFrom_1D_DoubleArray()

static CFieldDerivative1DReal ConvertFrom_1D_DoubleArray ( double[] doubleArray )

static

Converts one one-dimensional double array to a one-dimensional complex field.

Parameters

doubleArray The double array to convert

Returns: Complex field, created from the double array

◆ ConvertTo1D_DoubleArray()

static double[] ConvertTo1D_DoubleArray	(	ComplexField	complexField,
		bool	errorWhenComplex
	)

static

Converts a one dimensional complex field to a one dimensional double array.

Parameters

complexField	Complex field to convert
errorWhenComplex	Shall an exception be thrown if the complex field is not real valued? Please note: The Imaginary part will be ignored in every case!

Returns: Double array, created from the complex field

◆ ConvertTo2D_DoubleArray()

static double[,] ConvertTo2D_DoubleArray	(	ComplexField	complexField,
		bool	errorWhenComplex
	)

static

Converts a two dimensional complex field to a two dimensional double array.

Parameters

complexField	Complex field to convert
errorWhenComplex	Shall an exception be thrown if the complex field is not real valued? Please note: The Imaginary part will be ignored in every case!

Returns: Double array, created from the complex field

◆ ConvertTo2DDoubleArray()

void ConvertTo2DDoubleArray	(	out double	doubleArrayReal[,],
		out double	doubleArrayImaginary[,]
	)

Public support method to convert the complex field into two double arrays. (real and imaginary part will be output separately) Remark: This function was implemented to realize compatibility to Python.

Parameters

doubleArrayReal	The double array storing real part
doubleArrayImaginary	The double array storing imaginary part (remark: if the underlying complex field is real values, this data array will only contain zeroths

◆ DivEqual() [1/2]

void DivEqual ( Complex c )

Divides the present ComplexField by complex number. See important note on ComplexField.

Parameters

c	Complex number to divide.

◆ DivEqual() [2/2]

void DivEqual ( ComplexField field )

Divides the present ComplexField by passed one. Both field must have same number of sampling points. See important note on ComplexField.

Parameters

field Complex field used as divisor.

◆ EmbedCorner()

void EmbedCorner ( Vector newSize )

Embeds the current ComplexField into double side-length field of zero sampling points and places the original in bottom left corner of the new field. If the ComplexField is one-dimensional, only longer side of field is doubled.

Parameters

newSize New Size in pixel.

◆ EmbedExtract() [1/2]

virtual ComplexField EmbedExtract ( Rectangle rectangle )

virtual

Extract a region of the current ComplexField including the bottom left corner but excluding the top right corner.

Parameters

rectangle Region to extract.

Returns: Result of Operation.

Reimplemented in ComplexFieldDerivative1D.

◆ EmbedExtract() [2/2]

virtual void EmbedExtract ( Vector newSize )

virtual

Embeds the current ComplexField into field of passed size of zero sampling points and places the original in the middle of the new field. By decreasing size, field can be extracted.

Parameters

newSize New size in pixel.

Reimplemented in ComplexFieldDerivative1D.

◆ Equals()

override bool Equals ( Object obj )

Checks whether two complex fields represent the same values.

Parameters

obj	Complex field to be compared

Returns: True if both fields have the same size and the same values.

◆ Extract()

ComplexField Extract	(	Vector	size,
		VectorL	position,
		bool	elliptical = `false`
	)

Extracts the given region at given position out of the current field. Points exceeding boundaries of current field will be ignored.

Parameters

size	size of the region to extract.
position	Position at which field is to be extracted.
elliptical	Elliptical extraction?

Returns: The extracted field

◆ ExtractColumn()

ComplexField ExtractColumn ( int colIndex )

Extracts a column out of the current field. Points exceeding boundaries of current field will be set to zero.

Parameters

colIndex Index of the column to extract.

Returns: A ComplexField with only the extracted column.

◆ ExtractRow()

ComplexField ExtractRow ( int rowIndex )

Extracts a row out of the current field. Points exceeding boundaries of current field will be set to zero.

Parameters

rowIndex index of the row to extract.

Returns: A ComplexField with only the extracted row.

◆ Fill() [1/2]

void Fill ( Complex c )

Fills whole current ComplexField with the specified complex value.

Parameters

c	Complex value to fill the field with.

◆ Fill() [2/2]

void Fill	(	Complex	c,
		Rectangle	marker,
		bool	inside,
		bool	elliptical = `false`
	)

Fills whole ComplexField inside marker with the specified complex value. If inside is set to false, field outside marker will be filled.

Parameters

marker	Region that decides where to fill.
c	Complex value to fill the field with.
inside	Fill inside or outside of the marker.
elliptical	Fill elliptical instead of rectangular region?

◆ Insert()

void Insert	(	ComplexField	field,
		VectorL	position,
		bool	elliptical = `false`
	)

Inserts the given ComplexField into current field at given position. Points exceeding boundaries of current field will be ignored.

Parameters

field	Complex field to insert.
position	Position at which field is to be inserted (offset of 'field' to 'this').
elliptical	Elliptical insertion?

◆ InsertColumn()

void InsertColumn ( int colIndex )

Inserts or appends empty column.

Parameters

colIndex Index of column left of inserted column or -1 to append column.

◆ InsertRow()

void InsertRow ( int rowIndex )

Inserts or appends empty row.

Parameters

rowIndex Index of row below inserted row or -1 to append row.

◆ LinearFit()

double[] LinearFit ( VectorD samplDist )

Linear regression on a real valued Complex Field (phase derivative of a CA in x resp. y) Excluded points are assumed to be marked by float.Epsilon.

Parameters

samplDist dimensions of independent parameters (x,y)

Returns: model coefficients for linear fit dPhi = p0 + p1*x + p2*y

◆ ModifyComplexPart()

void ModifyComplexPart	(	ComplexPart	complexPart,
		bool	makeRealValuedIfSuitable = `false`,
		double	thresholdForPhaseArtifacts = `0`,
		double	amplitudeMaximum = `0`
	)

Extract, shifts or swaps complex parts of the complex field.

Parameters

complexPart	Enumerator element for desired action on ComplexField.
makeRealValuedIfSuitable	If this optional parameter is set to `true` the field is made real-valued if the imaginary part is zeroized. This is e.g. the case for extract amplitude and shift phase to real.
thresholdForPhaseArtifacts	Threshold for suppressing phase artifacts.
amplitudeMaximum	Amplitude maximum, needed for calculating an absolute artifacts threshold from the relative one.

◆ ModifyPixels() [1/2]

void ModifyPixels ( Func< Complex, Complex > modificationMethod )

Modifies all pixels in parallel. Can be used if the new pixel value depends only on the old pixel value (and maybe some fixed parameters).

Parameters

modificationMethod The modification method for each pixel.

◆ ModifyPixels() [2/2]

void ModifyPixels ( Func< Complex, int, int, Complex > modificationMethod )

Modifies all pixels in parallel. Can be used if the new pixel value depends on the old pixel value and the current position in pixel coordinates (and maybe some fixed parameters).

Parameters

modificationMethod The modification method for each pixel.

◆ MultEqual() [1/3]

void MultEqual ( Complex c )

Multiplies a Complex number to current ComplexField. See important note on ComplexField.

Parameters

c	Complex number used as factor.

◆ MultEqual() [2/3]

void MultEqual ( ComplexField field )

Multiplies a ComplexField with current one. Both field must have same number of sampling points. See important note on ComplexField.

Parameters

field Complex field used as factor.

◆ MultEqual() [3/3]

void MultEqual	(	IRegion1D2D	region,
		SamplingParameters	samplingParameters
	)

Multiplies a IRegion1D2D with this ComplexField.

Parameters

region	Region used as factor.
samplingParameters	The sampling parameters which apply to this complex field.

◆ Normalize()

void Normalize ( System::Drawing::Rectangle? rectangle = null )

Normalizes ComplexField so that maximal amplitude inside rectangle is one.

Parameters

rectangle If this optional parameter is set only the region within the specified rectangle is taken into account for the calculation of the maximum being the normalization reference.

◆ operator!=()

static bool operator!=	(	ComplexField	field1,
		ComplexField	field2
	)

static

Compares two complex fields for equality.

Parameters

field1	first field
field2	second field

Returns: True if both fields do not represent the same data.

◆ operator*() [1/3]

static ComplexField operator*	(	Complex	c,
		ComplexField	field
	)

static

Multiplies a complex value to a complex field.

Parameters

c	the complex value
field	the field

Returns: The result of the operator.

◆ operator*() [2/3]

static ComplexField operator*	(	ComplexField	field,
		Complex	c
	)

static

Multiplies a complex value to a complex field.

Parameters

field	the field
c	the complex value

Returns: The result of the operator.

◆ operator*() [3/3]

static ComplexField operator*	(	ComplexField	field1,
		ComplexField	field2
	)

static

Multiplies two complex fields.

Parameters

field1	the first field
field2	the second field

Returns: The result of the operator.

Exceptions

FieldSizesDontMatch

◆ operator+() [1/2]

static ComplexField operator+	(	ComplexField	field,
		Complex	c
	)

static

Adds a complex value to a complex field.

Parameters

field	the field
c	the complex value

Returns: The result of the operator.

◆ operator+() [2/2]

static ComplexField operator+	(	ComplexField	field1,
		ComplexField	field2
	)

static

Adds two complex fields.

Parameters

field1	the first field to be added
field2	the second field to be added

Returns: The result of the operator.

Exceptions

FieldSizesDontMatch

◆ operator-() [1/3]

static ComplexField operator-	(	Complex	c,
		ComplexField	field
	)

static

Subtracts a complex number and a complex field.

Parameters

c	Complex number.
field	Complex Field to subtract.

Returns: Difference of the complex field and the complex number.

◆ operator-() [2/3]

static ComplexField operator-	(	ComplexField	field,
		Complex	c
	)

static

Subtracts a complex field and a complex number.

Parameters

field	Complex Field.
c	Complex number to subtract.

Returns: Difference of the complex field and the complex number.

◆ operator-() [3/3]

static ComplexField operator-	(	ComplexField	field1,
		ComplexField	field2
	)

static

Subtracts two complex fields.

Parameters

field1	the first field
field2	the second field

Returns: The result of the operator.

Exceptions

FieldSizesDontMatch

◆ operator/() [1/2]

static ComplexField operator/	(	ComplexField	field,
		Complex	c
	)

static

Divides a complex field by a complex number.

Parameters

field	complex field
c	complex number

Returns: The result of the operation

◆ operator/() [2/2]

static ComplexField operator/	(	ComplexField	field1,
		ComplexField	field2
	)

static

Divide two complex fields.

Parameters

field1	the first field
field2	the second field

Returns: The result of the operation

◆ operator==()

static bool operator==	(	ComplexField	field1,
		ComplexField	field2
	)

static

Compares two complex fields for equality.

Parameters

field1	first field
field2	second field

Returns: True if both fields represent the same data.

◆ operator|()

static Complex operator\|	(	ComplexField	field1,
		ComplexField	field2
	)

static

Computes the inner (or scalar) product of two complex fields as defined by (u|v) := Integrate[u(x) * v^(x), {x, -Infinity, Infinity}].

Parameters

field1	the first field
field2	the second field

Returns: The inner product.

◆ PowerEqual()

void PowerEqual ( Complex c )

Raises every element of current ComplexField to the power of passed complex number. See important note on ComplexField.

Parameters

c	Complex exponent.

◆ RadiusError()

double RadiusError	(	double	constPart,
		double	radius,
		double	k,
		VectorD	dist,
		bool	computeInX
	)

compute the fit measure of the spherical phase dependent on radius in partial phase derivative

Parameters

constPart	value of phase derivative at x = y = 0
radius	radius of spherical phase
k	proportionality factor of spherical phase function
dist	sampling distance in original ComplexAmplitude
computeInX	is the ComplexField d_phi/dx or d_phi/dy

Returns: computed test value

◆ Replicate()

void Replicate	(	Vector	newSize,
		VectorL	shift
	)

Replicates current ComplexField periodically. Needs new size.

Parameters

newSize	New Size in pixel.
shift	Introduces a shift in pixels. If the shift is zero then the left bottom corner of the field to replicate is in the left bottom corner of the replicated field. Else the replication starts with the sampling point of the field to replicate at the position shift on the left bottom corner of the replicated field.

◆ Replicate_Periodic()

void Replicate_Periodic ( Vector newSize )

Replicates current ComplexField periodically, old field is at (0,0). Needs new size.

Parameters

newSize New Size in pixel.

◆ Shift()

void Shift	(	Vector	shift,
		bool	assumePeriodicField = `false`
	)

Shifts current ComplexField by a specified distance. Size is not modified, so sampling points can get lost.

Parameters

shift	Shift in pixel.
assumePeriodicField	If this optional parameter is set to `true` a periodic field is assumed. Else zeros occur outside of the shifted original field.

◆ ShiftColumnFromOnePositionToAnother()

void ShiftColumnFromOnePositionToAnother	(	int	oldColIndex,
		int	newColIndex
	)

Shifts a single column from one pixel index to another.

Parameters

oldColIndex	Old pixel index of column.
newColIndex	New pixel index of column.

◆ ShiftRowFromOnePositionToAnother()

void ShiftRowFromOnePositionToAnother	(	int	oldRowIndex,
		int	newRowIndex
	)

Shifts a single row from one pixel index to another.

Parameters

oldRowIndex	Old pixel index of row.
newRowIndex	New pixel index of row.

◆ SortColumns()

void SortColumns ( int[] newColIndices )

Method which brings all columns into a new, given order. Since this is not optimized, it shall not be used if a) the field is to be mirrored or b) only a single column is to be shifted.

Parameters

newColIndices Array with the new indices for all columns: the array index is the new index, the array item is the old index.

◆ SortRows()

void SortRows ( int[] newRowIndices )

Method which brings all rows into a new, given order. Since this is not optimized, it shall not be used if a) the field is to be mirrored or b) only a single row is to be shifted.

Parameters

newRowIndices Array with the new indices for all rows: the array index is the new index, the array item is the old index.

◆ SubEqual() [1/2]

void SubEqual ( Complex c )

Subtracts a Complex from current ComplexField. See important note on ComplexField.

Parameters

c	Complex number to subtract form current field.

◆ SubEqual() [2/2]

void SubEqual ( ComplexField field )

Subtracts a ComplexField from current one. Both field must have same number of sampling points. See important note on ComplexField.

Parameters

field Complex field to subtract form current field.

Property Documentation

◆ this[int x, int y]

virtual Complex this[int x, int y]

getset

Indexer to access complex values of complex field. Property performs a range checking before every access. If you try to read a complex value and index is out of range Complex(0) is returned. If you try to set a complex value and index is out of range nothing will happen. Indexer returns always a complex number in double precision independent on the internal complex number representation. During the setting of a complex value the indexer converts the complex number from double precision to the internal data representation. If internal precision is less accurate double precision information will be lost. Conversion to the less accurate precision is done by truncating the numbers after the last digit of the new precision. If IsComplex = false only the real part is stored.

Parameters

x	Index for x-coordinate
y	Index for y-coordinate

◆ this[long x, long y]

Complex this[long x, long y]

getset

Indexer to access complex values of complex field. Property performs a range checking before every access. If you try to read a complex value and index is out of range Complex(0) is returned. If you try to set a complex value and index is out of range nothing will happen. Indexer returns always a complex number in double precision independent on the internal complex number representation. During the setting of a complex value the indexer converts the complex number from double precision to the internal data representation. If internal precision is less accurate double precision information will be lost. Conversion to the less accurate precision is done by truncating the numbers after the last digit of the new precision. If IsComplex = false only the real part is stored.

Parameters

x	Index for x-coordinate
y	Index for y-coordinate

Public Member Functions

Static Public Member Functions

Properties

Detailed Description

Constructor & Destructor Documentation

◆ ComplexField() [1/7]

◆ ComplexField() [2/7]

◆ ComplexField() [3/7]

◆ ComplexField() [4/7]

◆ ComplexField() [5/7]

◆ ComplexField() [6/7]

◆ ComplexField() [7/7]

Member Function Documentation

◆ AddEqual() [1/2]

◆ AddEqual() [2/2]

◆ ClipAmplitude()

◆ ConvertFrom2_1D_DoubleArrays()

◆ ConvertFrom2D_DoubleArray()

◆ ConvertFrom_1D_ComplexArray()

◆ ConvertFrom_1D_DoubleArray()

◆ ConvertTo1D_DoubleArray()

◆ ConvertTo2D_DoubleArray()

◆ ConvertTo2DDoubleArray()

◆ DivEqual() [1/2]

◆ DivEqual() [2/2]

◆ EmbedCorner()

◆ EmbedExtract() [1/2]

◆ EmbedExtract() [2/2]

◆ Equals()

◆ Extract()

◆ ExtractColumn()

◆ ExtractRow()

◆ Fill() [1/2]

◆ Fill() [2/2]

◆ Insert()

◆ InsertColumn()

◆ InsertRow()

◆ LinearFit()

◆ ModifyComplexPart()

◆ ModifyPixels() [1/2]

◆ ModifyPixels() [2/2]

◆ MultEqual() [1/3]

◆ MultEqual() [2/3]

◆ MultEqual() [3/3]

◆ Normalize()

◆ operator!=()

◆ operator*() [1/3]

◆ operator*() [2/3]

◆ operator*() [3/3]

◆ operator+() [1/2]

◆ operator+() [2/2]

◆ operator-() [1/3]

◆ operator-() [2/3]

◆ operator-() [3/3]

◆ operator/() [1/2]

◆ operator/() [2/2]

◆ operator==()

◆ operator|()

◆ PowerEqual()

◆ RadiusError()

◆ Replicate()

◆ Replicate_Periodic()

◆ Shift()

◆ ShiftColumnFromOnePositionToAnother()

◆ ShiftRowFromOnePositionToAnother()

◆ SortColumns()

◆ SortRows()

◆ SubEqual() [1/2]

◆ SubEqual() [2/2]

Property Documentation

◆ this[int x, int y]

◆ this[long x, long y]