Vector Record — MtxVec

type Vector = record;

Vector class for operator overloading (Delphi 2006 and later).

Declare Vector instead of TVec to take advantage of operator overloading in D2006 and later. Be carefull to declare Vector only for local variables with short lifetime. Call the Create method for Vector, if the variable is a global variable or a variable with a longer life. It also makes sense to continue to use TVec for global vars. If the Create method (constuctor) is not called, the Vector record obtains TVec object from object cache (fastest create). If the Create mehod is called, the TVec object is created in the usual way (slower). Object cache has limited size.

Examples

delphi

var b, c: Vector;
    bv: TVec;
begin
    b := Vector(TDoubleArray.Create(1,1,1,1));
    b := [1,1,1,1]; //or like this
    bv := b;  // b and bv point to same data object

    bv.Scale(2);
    TVec(b).Scale(2);  //an alternative way to scale
    c := b*2 + Cplx(2,3); c := b*2 + 2 + 3i

    c := b*bv; // mix Vector and TVec per element multiply

    bv.Add(c); //pass Vector type and implicitely convert to TVec
end;

Constructors

Name	Description
Create (4)	Uses TVec object as internal storage.

Properties

Name	Type	Description
Alfa	TCplx	Additional parameter for certain Lapack methods.
Beta	TCplx	Additional parameter for certain Lapack methods.
BlockEnd	Boolean	Returns true, if the currrent subrange of the vector was also the last subrange in the vector.
Capacity	Int64	Sizing the object will not allocate less than Capacity samples.
CapacityStep	Double	Specifies increment step for the Capacity property.
Caption	string	Vector Caption.
Complex	Boolean	Defines if object values are complex.
ConditionCheck	Boolean	Enables/disable inline condition checking.
FFTOddLength	Boolean	Defines if FFT transform length is odd.
FFTScrambled	Boolean	Leave FFT scrambeled.
FFTStorageFormat	TFFTStorageFormat	FFT storage format.
First	Double	First element in object Values array.
Firstc	TCplx	First element in object CValues array.
FloatPrecision	TMtxFloatPrecision	Defines the precision (single, float) and type (real, complex) of the floating point operations.
IsSubRange	Boolean	Set to true after the SetSubIndex or SetSubRange call.
Last	Double	Last element in object Values array.
Lastc	TCplx	Last complex element in object CValues array.
Length	Integer	Defines the length in number of samples.
Precision	TPrecision	Defines the precision used by streaming routines.
Rounding	TRounding	Defines the rounding used by streaming routines.
SubRangeLevel	Integer	Returns the current depth of SubRange stack.
Tag	Integer	Stores an integer value as a part of the object.
ZeroTolerance	Double	The tolerance used by Vector.IsEqual.

Methods

Name	Description
Abs (4)	Absolute values.
Add (18)	Adds complex Value to all calling object complex elements.
AddAndMul (50)	Compute (X + yScalar)*zScalar
AddProduct (2)	Add a product of two vectors.
AddScaled (25)	Add each of Vec elements to corresponding elements in the calling object.
AddScaledC (8)	Compute XxScale + YyScale + zScalar
AddScaledSqr (8)	Compute sqr(XxScale + YyScale)
Adopt	Adopts TVec object.
ArcCos (4)	The inverse cosine.
ArcCosh (4)	Inverse hyperbolic cosine.
ArcCot (4)	Inverse cotangens.
ArcCoth (4)	Inverse hyperbolic cotangens.
ArcCsc (4)	Inverse cosecant.
ArcCsch (4)	Inverse hyperbolic cosecant.
ArcSec (4)	Inverse secant.
ArcSech (4)	Inverse hyperbolic secant.
ArcSin (4)	The inverse sine.
ArcSinh (4)	Inverse hyperbolic sine.
ArcTan (4)	Inverse tangens.
ArcTan2 (2)	Inverse tangens of Y/X.
ArcTanh (4)	Inverse hyperbolic tangens.
AutoCorrBiased	Biased auto-correlation.
AutoCorrNormal	Normal auto-corellation.
AutoCorrUnBiased	Unbiased auto-correlation.
BinarySearch (2)	Finds a match for X in sorted object values using binary search.
BlockFinish	Deinitializes block processing before the final block is processed.
BlockInit (4)	Initializes block processing.
BlockNext	Obtains the next subrange of the data.
CartToPolar (2)	Converts elements from cartesian to polar coordinate form.
Cbrt (4)	The cube root.
Ceil (4)	Rounds towards positive infinity.
Clear	Sets vector size to zero.
Concat (2)	Concatenates an array of TVec objects.
CondDisable	Saves the current value of ConditionCheck property and sets it to false.
CondEnable	Sets the ConditionCheck property to whatever it was before the CondDisable was used.
Conj (4)	Conjugate.
ConjMul (4)	Conjugate and multiply.
Convolve	Single-rate finite, linear convolution of two sequences.
Copy (7)	Copy object values.
CopyFromArray (12)	Copies values from an array.
CopyTo (5)	Copy and if needed convert values to Dst.
CopyToArray (12)	Copy values to an array.
Cos (4)	Cosine.
Cosh (4)	Hyperbolic cosine.
Cot (4)	Cotangens.
Coth (4)	Hyperbolic cotangens.
CplxToReal (2)	Split complex calling object in real and imaginary part.
CrossCorr	The cross-correlation of two vectors.
Csc (4)	Cosecant.
Csch (4)	Hyperbolic cosecant.
CumProduct (4)	Calculate the cumulative product for all Vec elements.
CumSum (4)	Cumulative sum.
DCT (3)	The forward discrete cosine transform (DCT).
DegToRad (4)	Convert degrees to radians (in-place).
Diag	Copies the k-th diagonal from the TMtx object.
Difference (3)	Calculate the difference for all Vec elements and store the results in the calling vector.
DisableSelect	Prevents calls to MtxExpr.Select.
DisableSubrange	Prevents calls to Vector.SetSubRange.
Disown (2)	Disowns a calling vector values pointer by setting Values, CValues to nil and TMtxVecBase.Length to 0.
DivAndAdd (22)	Compute X/Y + zScalar
DivAndSub (22)	Compute X/Y - zScalar
Divide (14)	Compute xScalar / (Y*Z)
DivideBy (8)	Divide complex Value with elements of the calling object and store the result in the calling object.
DivideC (4)	Compute X / (Y*zScale)
DotProd (2)	Scalar product of two real arrays.
DotProdc (4)	Scalar product of two complex arrays.
DownSample (2)	Downsamples vector values.
EnableSelect	Enables calls to MtxExpr.Select.
EnableSubrange	Enables calls to Vector.SetSubRange.
Equal (2)	Compares vector elements and returns true if vectors are equal.
Erf (4)	Error function of self (in-place).
Erfc (4)	Complementary error function of self (in-place).
ErfInv (4)	Inverse error function of self (in-place).
Exp (4)	Exponent (e^).
Exp10 (4)	Exponent base 10 (10^).
Exp2 (4)	Exponent base 2 (2^).
Expj (3)	A complex exponential e^(j*W).
ExtendToComplex (3)	Extend Vec object to complex calling object.
FFT (3)	Calculate the FFT from all Vec elements.
FFTFromReal (3)	The forward Fast Fourier Transformation (FFT) from real to complex.
Find (2)	Compare complex value X with all calling object elements.
FindAndGather (3)	Finds and gathers vector elements.
FixAngle (4)	Sets angle in [-2Pi,2Pi].
Flip (4)	Flips the real and imaginary part of complex numbers.
FlipConj (4)	Flips the real and imaginary part of complex numbers and conjugates the complex numbers.
Floor (4)	Rounds towards negative infinity.
Frac (4)	Fractional part of values.
Gather	Gather vector elements.
GatherByIncr	Gather vector elements.
GatherByIndex	Gather vector elements.
GatherByMask	Gather vector elements.
GatherSplit	Gather a vector, split to two vectors.
GetCol (3)	Copies a column from matrix.
GetRow (3)	Copies a row from matrix.
GroupSum	Sums items from Src with matching corresponding indexes from Bins and places result in self.
GroupSumIteration	Sums items from Src with matching corresponding indexes from Bins and places result in self.
Hilbert	The fast hilbert transform (FFT based).
IDCT (3)	Calculate the inverse DCT in-pllace.
IFFT (3)	Calculate the inverse FFT from all Vec elements and store the results in the calling vector.
IFFTToReal (3)	Calculate the inverse FFT from all Vec elements.
ImagPart (2)	Gets the imaginary part of a complex object.
Integrate (2)	Integrate calling vector values.
IntPower (2)	Calculate the power Base^(Exponent) for all Base object elements using the integer Exponent value.
Inv (8)	Invert elements.
InvCbrt (4)	The inverse of cube root 1/(v)^1/3.
InvSqrt (4)	The inverse of square root 1/(v)^1/2.
IsEqual (8)	Compares complex Value with all calling object elements.
Kron	The Kronecker product between two vectors.
Kurtosis (2)	The Kurtosis (fourth central momentum).
Ln (4)	Natural logarithm.
LoadFromFile	Reads the header information and the values array content from the file.
LoadFromStream	Reads the header information and the values array content from a stream.
Log10 (4)	Log base 10.
Log2 (4)	Log base 2.
LogN (4)	Log base N.
Mag (4)	Magnitude.
Mask (3)	Assigns Value at indexes of the calling object, at which aMask is different from 0.
MaskNot (3)	Assigns Value at indexes of the calling object, at which aMask is equal to 0.
Max (5)	Maximum value.
Maxc (3)	Maximum value.
MaxEvery (4)	Vectorised maximum.
MaxMin (4)	Maximum and minimum value in a single pass.
Mean (3)	Mean value.
MeanAndStdDev (2)	Returns the standard deviation of all calling object elements.
Meanc (4)	Mean value.
Median (2)	Median.
Min (5)	Minimum value.
Minc (3)	Minimum value.
MinEvery (4)	Vectorised minimum.
Mul (18)	Multiply all calling object elements with complex Value in-place.
MulAndAdd (26)	Compute (X*yScalar) + zScalar
MulAndDiv (10)	Compute X * Y / zScalar
MulAndSub (26)	Compute XyScalar - ZzScale
MulI (4)	Multiply elements by imaginary unit I.
Norm	The norm of a vector.
Normalize (12)	Normalize by subtracting a complex constant SubOffset from Vec elements and dividing the result by complex constant DivFactor.
NormC (4)	Calculate the C-norm of calling vector.
NormL1 (4)	Calculate the L1-norm of the calling vector.
NormL2 (4)	Calculate the L2-norm of the calling vector.
Offset (4)	Add/Subtract a complex value.
Parse	Parses string content as vector.
PCValues1D	Obtains a pointer to the complex value of the vector at Index.
PhaseSpectrum (2)	The phase angles (spectrum) of object elements.
PixelDownSample (2)	Downsample the vectors Y and (optionaly) X starting at position Index and for Len samples.
PolarToCart (2)	Converts the polar magnitude/phase pairs to cartesian pairs.
Power (7)	Raises all calling vector elements to complex power Exponent in-place.
PowerSpectrum (2)	The power spectrum from object complex values.
PowerVec	Raises Base object elements to Exponent object elements power.
PrimeNumbers	Fills vector with prime numbers, starting from 2 up to the value of n.
Product (6)	Elements product.
Productc (2)	Elements product.
PValues1D	Obtains a pointer to the real value of the vector at Index.
RadToDeg (4)	Convert radians to degrees (in-place).
Ramp (7)	Fills the calling vector with a series following linear rule.
RandGauss (3)	The pseudo random sample generator with Gaussian distribution.
RandomShuffle	Randomly shuffles the content of the vector.
RandUniform (3)	The pseudo random sample generator with continuous uniform distribution.
Range (3)	Calculate the range from all calling object elements.
ReadHeader	Reads the header information from a stream to object.
ReadValues	Read values content from stream to object.
RealPart (2)	Gets real part of complex object values.
RealToCplx (2)	Constructs a complex object from two real objects.
Rem (4)	The Reminder after division X/Y.
Replace (4)	Search and replace a complex value.
ReplaceNAN (2)	Replaces all NAN values with Value.
Reset	Resets object properties to default values.
Resize (2)	Resizes vector size while preserving values.
Reverse (4)	Reverse vector elements.
RMS (2)	Root mean square (RMS).
Rotate (4)	Applies cyclic shift on Src vector elements and stores the result in Self.
Round (5)	Elements rounded to the nearest whole number.
SaveToFile	Write object header and values to a file.
SaveToStream	Writes the header information and the Values content to a stream.
Scale (4)	Multiply all calling object elements with a complex Value in-place.
Scatter	Scatter object elements.
ScatterByIncr	Scatter object elements.
ScatterByIndexes	Scatter object elements.
ScatterByMask	Scatter object elements.
Sec (4)	Secant.
Sech (4)	Hyperbolic secant.
SelectAll	Resets any defined selection.
SetCplx	Sets vector values (complex).
SetDouble (2)	Sets vector values (double).
SetFullRange	Resets any defined subrange.
SetInteger (2)	Sets vector values (integer).
SetIt (4)	Sets vector values.
SetSingle (2)	Sets vector values (single).
SetSubIndex (2)	Defines a subarray.
SetSubRange (4)	Sets the subarray size to full size.
SetSubRangeLevel (2)	Define a subvector of the Src vector starting at Index and ending at Index+Len-1.
SetVal (4)	Set all calling object complex elements to complex Value.
SetZero (2)	Initializes object elements to zero.
Sgn (4)	Computes signum function of calling object elements.
SgnMul	Signum.
Shift (4)	Shift vector elements left or right in the array.
Sign (4)	Changes elements sign.
Sin (4)	Sine.
SinCos (2)	Sine and cosine.
Sinh (4)	Hyperbolic sine.
SinhCosh (2)	Hyperbolic sine and cosine.
Size (4)	Size the object.
SizeFromArray (6)	Sets the size of the vector to match an array.
SizeToArray (6)	Sizes the array.
Skewness (2)	Skewness (third central momentum).
SortAscend (4)	Sorts vector elements in ascending order.
SortDescend (4)	Sorts vector elements in descending order.
Split (3)	Copy the contents of the calling TVec object to Vec1 and Vec2 objects.
Sqr (4)	Square.
SqrAddScaled (8)	Compute sqr(X)xScale + sqr(Y)yScale
Sqrt (4)	Square root.
StdDev (6)	Standard deviation.
StringsToValues (2)	Convert strings in aList to double or TCplx.
StripNanAndInf (3)	Copy Src into self, dropping every NAN/INF element and compacting the result.
Sub (18)	Subtracts complex Value from all calling object complex elements.
SubAndMul (50)	Compute (X - yScalar)*zScalar
SubFrom (8)	Subtract each of calling object elements from complex Value.
SubScaled (12)	Compute XxScale - YyScale - Z*zScale
SubScaledC (8)	Compute XxScale - YyScale - zScalar
Sum (5)	Sums vector values.
Sumc (2)	Sum (complex value).
SumOfSquares (2)	Calculate the Sum of squares of the calling vector.
Tan (4)	Tangens.
Tanh (4)	Hyperbolic tangens.
TensorProd (2)	Tensor product between vector and matrix.
ThreshAbsGT (4)	Perform threshold operation on all Src object values.
ThreshAbsLT (4)	Perform threshold operation on all Src object values.
ThreshBottom (4)	Perform threshold operation on all Src object values and store the results in calling object.
ThresholdGT (8)	Perform "greater than" threshold operation for complex numbers on all Vec object values and store the results in calling object.
ThresholdGT_LT (4)	Perform "greater than and less than" threshold operation on all Vec object values and store the results in calling object.
ThresholdLT (8)	Perform "less than" threshold operation for complex numbers on all Vec object values and store the results in calling object.
ThreshTop (4)	Perform threshold operation on all Src object values and store the results in calling object.
ToString	Returns content as a string.
Trunc (5)	Rounds a real number towards zero.
TruncAndFrac (2)	Rounds a real number towards zero and returns the fractional part.
UpSample (2)	Inserts zeroes between consecutive vector values.
ValuesToStrings (3)	Converts the content of the Values array of the calling vector to a list of strings.
WriteHeader	Writes the header information for the calling vector to a stream.
WriteValues	Writes object Values content to a stream.
ZScore (2)	Transforms vector into vector of standardized data in-place.

Operators

Name	Description
Add (7)	Add left to all elements in Right and return result.
Divide (7)	Divide Left with all elements Right.
Equal (7)	Returns true, if all elements of Right are equal to Left.
Explicit (7)	Explicitely convert TVec to Vector.
GreaterThan (5)	Returns true, if ALeft is greater from all elements in ARight.
GreaterThanOrEqual (5)	Returns true, if ALeft is greater or equal from all elements in ARight.
Implicit (12)	Implicit type conversion from an array of TCplx to Vector.
LessThan (5)	Returns true, if ALeft is smaller from all elements in ARight.
LessThanOrEqual (5)	Returns true, if ALeft is smaller or equal from all elements in ARight.
Multiply (7)	Multiply all elements in Right with Left.
Negative	Negates all values inside AValue.
NotEqual (7)	Returns true, if any elements of Right are not equal to Left.
Subtract (7)	Subtract all elements in Right from Left.