Linearly |
Defines a linearly spaced closed interval defined by start, end and step size.
Inheritance HierarchyNamespace: Altaxo.Calc.LinearAlgebra
Assembly: AltaxoCore (in AltaxoCore.dll) Version: 4.8.3179.0 (4.8.3179.0)
SyntaxC#
public class LinearlySpacedIntervalByStartEndStep : ISpacedInterval, IReadOnlyList<double>, IReadOnlyCollection<double>, IEnumerable<double>, IEnumerable, IImmutable, IEquatable<LinearlySpacedIntervalByStartEndStep>
The LinearlySpacedIntervalByStartEndStep type exposes the following members.
Constructors| Name | Description | |
|---|---|---|
 | LinearlySpacedIntervalByStartEndStep | Initializes a new default instance of the LinearlySpacedIntervalByStartEndStep class, with an interval [0,100], step size of 1 and count=101. |
| LinearlySpacedIntervalByStartEndStep(Double, Double, Double) | Initializes a new instance of the LinearlySpacedIntervalByStartEndStep class. |
Properties| Name | Description | |
|---|---|---|
 | Count | The number of elements. |
| End | Start of the interval (inclusive if step can divide the interval by an integer number). |
| IsCountEditable | |
| IsEndEditable | |
| IsStartEditable | |
| IsStepEditable | |
| Item | Gets the element at the specified index. |
| Start | Start of the interval (inclusive). |
| Step | Gets the step size. |
Methods| Name | Description | |
|---|---|---|
 | Finalize | Allows an object to try to free resources and perform other cleanup operations before it is reclaimed by garbage collection. (Inherited from Object) |
| GetEnumerator | Returns an enumerator that iterates through the collection. |
| GetType | Gets the Type of the current instance. (Inherited from Object) |
| MemberwiseClone | Creates a shallow copy of the current Object. (Inherited from Object) |
Extension Methods| Name | Description | |
|---|---|---|
 | Any |
Determines whether the given vector contains any elements.
(Defined by VectorMath) |
| Any |
Determines whether any element of the vector satisfies a condition.
(Defined by VectorMath) |
| Any |
Determines whether any element of the vector satisfies a condition.
(Defined by VectorMath) |
| Average |
Returns the average (=sum/N) of the elements in vector.
(Defined by VectorMath) |
| CompoundReturn |
Compound Monthly Return or Geometric Return or Annualized Return
(Defined by AbsoluteReturnMeasures) |
| Covariance |
Estimates the unbiased population covariance from the provided samples.
On a dataset of size N will use an N-1 normalizer (Bessel's correction).
Returns NaN if data has less than two entries or if any entry is NaN.
(Defined by Statistics) |
| DownsideDeviation |
This measure is similar to the loss standard deviation except the downside deviation
considers only returns that fall below a defined minimum acceptable return (MAR) rather than the arithmetic mean.
For example, if the MAR is 7%, the downside deviation would measure the variation of each period that falls below
7%. (The loss standard deviation, on the other hand, would take only losing periods, calculate an average return for
the losing periods, and then measure the variation between each losing return and the losing return average).
(Defined by AbsoluteRiskMeasures) |
| ElementsAtDouble | (Defined by VectorMath) |
| ElementsWhereDouble | (Defined by VectorMath) |
| ElementsWhereDouble | (Defined by VectorMath) |
| EmpiricalCDF |
Estimates the empirical cumulative distribution function (CDF) at x from the provided samples.
(Defined by Statistics) |
| EmpiricalCDFFunc |
Estimates the empirical cumulative distribution function (CDF) at x from the provided samples.
(Defined by Statistics) |
| EmpiricalInvCDF |
Estimates the empirical inverse CDF at tau from the provided samples.
(Defined by Statistics) |
| EmpiricalInvCDFFunc |
Estimates the empirical inverse CDF at tau from the provided samples.
(Defined by Statistics) |
| EuclideanNorm | Given an n-vector x, this function calculates the euclidean norm of x. (Defined by VectorMath) |
| ExcessKurtosisOfNormalized |
Returns the excess kurtosis of the elements in vector. The excess kurtosis is defined as
excesskurtosis(X) = E{X^4} - 3(E{X²})².
(Defined by VectorMath) |
| FirstOrDouble |
Returns the first value of the enumeration, or, if the enumeration is empty, the other value provided in the arguments.
(Defined by EnumerableExtensions) |
| FiveNumberSummary |
Estimates {min, lower-quantile, median, upper-quantile, max} from the provided samples.
Approximately median-unbiased regardless of the sample distribution (R8).
(Defined by Statistics) |
| FlattenFromRootToLeavesDouble |
Converts a recursive data structure into a flat list. The root element is enumerated before its corresponding child element(s).
(Defined by EnumerableExtensions) |
| ForEachDoDouble |
Executes an action for each element of the sequence.
(Defined by EnumerableExtensions) |
| GainLossRatio |
Measures a fund’s average gain in a gain period divided by the fund’s average loss in a losing
period. Periods can be monthly or quarterly depending on the data frequency.
(Defined by AbsoluteRiskMeasures) |
| GainMean |
Average Gain or Gain Mean
This is a simple average (arithmetic mean) of the periods with a gain. It is calculated by summing the returns for gain periods (return 0)
and then dividing the total by the number of gain periods.
(Defined by AbsoluteReturnMeasures) |
| GainStandardDeviation |
Calculation is similar to Standard Deviation , except it calculates an average (mean) return only for periods with a gain
and measures the variation of only the gain periods around the gain mean. Measures the volatility of upside performance.
© Copyright 1996, 1999 Gary L.Gastineau. First Edition. © 1992 Swiss Bank Corporation.
(Defined by AbsoluteRiskMeasures) |
| GeometricMean |
Evaluates the geometric mean.
Returns NaN if data is empty or if any entry is NaN.
(Defined by Statistics) |
| GetDifferences |
Gets the differences x[i+1] - x[i], for i = 0 .. x.Count-2.
(Defined by EnumerableExtensions) |
| GetPossibleStepsToMoveTowardsHigherIndicesDouble |
Return the number of steps that selected items can be moved towards higher indices. The selected item with the highest index determines that value.
(Defined by ListExtensions) |
| GetPossibleStepsToMoveTowardsLowerIndicesDouble |
Return the number of steps that selected items can be moved towards lower indices. The selected item with the lowest index determines that value.
(Defined by ListExtensions) |
| GetUsedLength |
Returns the used length of the vector. This is one more than the highest index of the element that is different from NaN.
(Defined by VectorMath) |
| GetUsedLength |
Returns the used length of the vector. This is one more than the highest index of the element that is different from Double.NaN.
(Defined by VectorMath) |
| HarmonicMean |
Evaluates the harmonic mean.
Returns NaN if data is empty or if any entry is NaN.
(Defined by Statistics) |
| HasSingleElementDouble |
Determines whether the specified enumeration has exactly one element.
(Defined by EnumerableExtensions) |
| IndexOfDouble |
Gets the index of an item in a enumeration or list.
(Defined by ListExtensions) |
| IndexOfFirstDouble |
Gets the index the of first item in list that fulfills the predicate predicate (Defined by ListExtensions) |
| IndexOfFirstDouble |
Gets the index the of first item in list that fulfills the predicate predicate (Defined by ListExtensions) |
| IndexOfMaxDouble | Return the index of the element with the maximum value in an enumerable.
If multiple elements with the same minimal value exist, the index of the first element in the sequence is returned. (Defined by EnumerableExtensions) |
| IndexOfMaxAbsoluteValue | Return the index of the first element with the maximum absolute value in a vector (Defined by VectorMath) |
| IndexOfMaxValue | Return the index of the first element with the maximum value in a vector (Defined by VectorMath) |
| IndexOfMinDouble | Return the index of the element with the minimum value in an enumerable.
If multiple elements with the same minimal value exist, the index of the first element in the sequence is returned. (Defined by EnumerableExtensions) |
| IndexOfMinAbsoluteValue | Return the index of the first element with the minimum absolute value in a vector (Defined by VectorMath) |
| IndexOfMinValue | Return the index of the first element with the minimum value in a vector (Defined by VectorMath) |
| IndicesInt32AndValuesWhereDouble |
Returns tuples of index and element of all elements in an enumeration which fullfill a given condition, given by the element's value.
(Defined by EnumerableExtensions) |
| IndicesInt32AndValuesWhereDouble |
Returns tuples of index and element of all elements in an enumeration which fullfill a given condition, given by the element's value and its index.
(Defined by EnumerableExtensions) |
| IndicesInt32WhereDouble |
Returns the indices of the elements which fullfill a given condition, given by the element's value.
(Defined by EnumerableExtensions) |
| IndicesInt32WhereDouble |
Returns the indices of the elements which fullfill a given condition, given by the element's value and its index.
(Defined by EnumerableExtensions) |
| IndicesOfMinMaxDouble | Return the index of the element with the minimum value in an enumerable.
If multiple elements with the same minimal value exist, the index of the first element in the sequence is returned. (Defined by EnumerableExtensions) |
| InterquartileRange |
Estimates the inter-quartile range from the provided samples.
Approximately median-unbiased regardless of the sample distribution (R8).
(Defined by Statistics) |
| InterQuartileRange | (Defined by Statistics) |
| IsEmptyDouble |
Determines whether the specified enumeration is empty.
(Defined by EnumerableExtensions) |
| IsStrictlyDecreasing |
Returns true if the sequence given by the vector argument is strictly decreasing.
(Defined by VectorMath) |
| IsStrictlyIncreasing |
Returns true if the sequence given by the vector argument is strictly increasing.
(Defined by VectorMath) |
| IsStrictlyIncreasingOrDecreasing |
Returns true if the sequence given by the vector argument is strictly increasing or decreasing.
(Defined by VectorMath) |
| IsStrictlyIncreasingOrDecreasing |
Returns true if the sequence given by the vector argument is strictly increasing or decreasing.
(Defined by VectorMath) |
| JoinConditionalDouble, T2 |
Takes a join of two sequences, but only takes into account those pair, which fulfill a given condition.
(Defined by EnumerableExtensions) |
| JoinConditionalDouble, T2, TResult |
Takes a join of two sequences, but only takes into account those pair, which fulfill a given condition.
(Defined by EnumerableExtensions) |
| Kurtosis |
Returns the kurtosis of the elements in vector. The kurtosis is defined as
kurtosis(X) = E{(X-µ)^4}/((E{(X-µ)²})².
(Defined by VectorMath) |
| Kurtosis |
Estimates the unbiased population kurtosis from the provided samples.
Uses a normalizer (Bessel's correction; type 2).
Returns NaN if data has less than four entries or if any entry is NaN.
(Defined by Statistics) |
| L1Norm |
Calculates the L1 norm of the vector (as the sum of the absolute values of the elements).
(Defined by VectorMath) |
| L2Norm | Given an n-vector x, this function calculates the euclidean norm of x. (Defined by VectorMath) |
| L2Norm | Given an n-vector x, this function calculates the euclidean norm of x. (Defined by VectorMath) |
| LastOrDouble |
Returns the last value of the enumeration, or, if the enumeration is empty, the other value provided in the arguments.
(Defined by EnumerableExtensions) |
| LInfinityNorm |
Returns the L-infinity norm of the provided vector (as is the maximum of the absolute value of the elements). If one
of the elements of the vector is invalid, the return value is also invalid (for the floating point types).
(Defined by VectorMath) |
| LossMean |
Average Loss or LossMean
This is a simple average (arithmetic mean) of the periods with a loss. It is calculated by summing the returns for loss periods (return < 0)
and then dividing the total by the number of loss periods.
(Defined by AbsoluteReturnMeasures) |
| LossStandardDeviation |
Similar to standard deviation, except this statistic calculates an average (mean) return for only the periods with a loss and then
measures the variation of only the losing periods around this loss mean. This statistic measures the volatility of downside performance.
(Defined by AbsoluteRiskMeasures) |
| LowerQuartile |
Estimates the first quartile value from the provided samples.
Approximately median-unbiased regardless of the sample distribution (R8).
(Defined by Statistics) |
| LpNorm | Compute the p Norm of this vector. (Defined by VectorMath) |
| MassDistribution | (Defined by Statistics) |
| Max |
Returns the maximum of the elements in vector.
(Defined by VectorMath) |
| Max |
Returns the maximum of the elements in vector.
(Defined by VectorMath) |
| MaxElementDouble, M |
Gets the element of a IEnumerabe that evaluates by means of a conversion function to the maximal value.
This is different from Select(x => conversion(x)).Max() insofar as it not returns the maximum value, but the original element x which converts to the maximum value.
(Defined by EnumerableExtensions) |
| Maximum |
Returns the maximum value in the sample data.
Returns NaN if data is empty or if any entry is NaN.
(Defined by Statistics) |
| MaximumAbsolute |
Returns the maximum absolute value in the sample data.
Returns NaN if data is empty or if any entry is NaN.
(Defined by Statistics) |
| MaxOf |
Creates a new vector, whose elements are the maximum of the elements of a given input vector and a given number.
(Defined by VectorMath) |
| MaxOfValidElements |
Returns the maximum value of all the valid elements in x (nonvalid elements, i.e. NaN values are not considered).
(Defined by VectorMath) |
| MaxOrDefaultDouble, M |
Evaluates the maximum of a enumeration of elements, or returns a default value if the series is empty.
(Defined by EnumerableExtensions) |
| Mean |
Returns the average (=sum/N) of the elements in vector.
(Defined by VectorMath) |
| Mean | (Defined by Statistics) |
| Mean |
Evaluates the sample mean, an estimate of the population mean.
Returns NaN if data is empty or if any entry is NaN.
(Defined by Statistics) |
| Mean | (Defined by Statistics) |
| MeanAndVariance |
Returns the average (=sum/N) of the elements in vector, as well as the variance (sum of squares of the mean centered values divided by length of the vector).
(Defined by VectorMath) |
| MeanStandardDeviation |
Estimates the sample mean and the unbiased population standard deviation from the provided samples.
On a dataset of size N will use an N-1 normalizer (Bessel's correction).
Returns NaN for mean if data is empty or if any entry is NaN and NaN for standard deviation if data has less than two entries or if any entry is NaN.
(Defined by Statistics) |
| MeanVariance |
Estimates the sample mean and the unbiased population variance from the provided samples.
On a dataset of size N will use an N-1 normalizer (Bessel's correction).
Returns NaN for mean if data is empty or if any entry is NaN and NaN for variance if data has less than two entries or if any entry is NaN.
(Defined by Statistics) |
| Median |
Estimates the sample median from the provided samples (R8).
(Defined by Statistics) |
| Min |
Returns the minimum of the elements in vector.
(Defined by VectorMath) |
| Min |
Returns the minimum of the elements in vector.
(Defined by VectorMath) |
| Minimum |
Returns the minimum value in the sample data.
Returns NaN if data is empty or if any entry is NaN.
(Defined by Statistics) |
| MinimumAbsolute |
Returns the minimum absolute value in the sample data.
Returns NaN if data is empty or if any entry is NaN.
(Defined by Statistics) |
| MinOfValidElements |
Returns the minimum value of all the valid elements in x (nonvalid elements, i.e. NaN values are not considered).
(Defined by VectorMath) |
| MovingAverage |
Evaluates the sample mean over a moving window, for each samples.
Returns NaN if no data is empty or if any entry is NaN.
(Defined by Statistics) |
| Percentile |
Estimates the p-Percentile value from the provided samples.
If a non-integer Percentile is needed, use Quantile instead.
Approximately median-unbiased regardless of the sample distribution (R8).
(Defined by Statistics) |
| PercentileFunc |
Estimates the p-Percentile value from the provided samples.
If a non-integer Percentile is needed, use Quantile instead.
Approximately median-unbiased regardless of the sample distribution (R8).
(Defined by Statistics) |
| PopulationCovariance |
Evaluates the population covariance from the provided full populations.
On a dataset of size N will use an N normalizer and would thus be biased if applied to a subset.
Returns NaN if data is empty or if any entry is NaN.
(Defined by Statistics) |
| PopulationKurtosis |
Evaluates the kurtosis from the full population.
Does not use a normalizer and would thus be biased if applied to a subset (type 1).
Returns NaN if data has less than three entries or if any entry is NaN.
(Defined by Statistics) |
| PopulationSkewness |
Evaluates the skewness from the full population.
Does not use a normalizer and would thus be biased if applied to a subset (type 1).
Returns NaN if data has less than two entries or if any entry is NaN.
(Defined by Statistics) |
| PopulationSkewnessKurtosis |
Evaluates the skewness and kurtosis from the full population.
Does not use a normalizer and would thus be biased if applied to a subset (type 1).
(Defined by Statistics) |
| PopulationStandardDeviation |
Evaluates the standard deviation from the provided full population.
On a dataset of size N will use an N normalizer and would thus be biased if applied to a subset.
Returns NaN if data is empty or if any entry is NaN.
(Defined by Statistics) |
| PopulationVariance |
Evaluates the variance from the provided full population.
On a dataset of size N will use an N normalizer and would thus be biased if applied to a subset.
Returns NaN if data is empty or if any entry is NaN.
(Defined by Statistics) |
| ProbabilityDensity | (Defined by Statistics) |
| Quantile |
The quantile value of x.
(Defined by Statistics) |
| Quantile |
Estimates the tau-th quantile from the provided samples.
The tau-th quantile is the data value where the cumulative distribution
function crosses tau.
Approximately median-unbiased regardless of the sample distribution (R8).
(Defined by Statistics) |
| Quantile |
The quantile value of x.
(Defined by Statistics) |
| QuantileCustom |
Estimates the tau-th quantile from the provided samples.
The tau-th quantile is the data value where the cumulative distribution
function crosses tau. The quantile definition can be specified to be compatible
with an existing system.
(Defined by Statistics) |
| QuantileCustomFunc |
Estimates the tau-th quantile from the provided samples.
The tau-th quantile is the data value where the cumulative distribution
function crosses tau. The quantile definition can be specified to be compatible
with an existing system.
(Defined by Statistics) |
| QuantileFunc |
Estimates the tau-th quantile from the provided samples.
The tau-th quantile is the data value where the cumulative distribution
function crosses tau.
Approximately median-unbiased regardless of the sample distribution (R8).
(Defined by Statistics) |
| QuantileRank |
Estimates the quantile tau from the provided samples.
The tau-th quantile is the data value where the cumulative distribution
function crosses tau. The quantile definition can be specified to be compatible
with an existing system.
(Defined by Statistics) |
| QuantileRankFunc |
Estimates the quantile tau from the provided samples.
The tau-th quantile is the data value where the cumulative distribution
function crosses tau. The quantile definition can be specified to be compatible
with an existing system.
(Defined by Statistics) |
| Ranks |
Evaluates the rank of each entry of the provided samples.
The rank definition can be specified to be compatible
with an existing system.
(Defined by Statistics) |
| RootMeanSquare |
Evaluates the root mean square (RMS) also known as quadratic mean.
Returns NaN if data is empty or if any entry is NaN.
(Defined by Statistics) |
| SelectCombinationDouble |
Select a random combination, without repetition, from a data sequence by selecting k elements in original order.
(Defined by Combinatorics) |
| SelectCombinationWithRepetitionDouble |
Select a random combination, with repetition, from a data sequence by selecting k elements in original order.
(Defined by Combinatorics) |
| SelectPermutationDouble |
Select a random permutation from a data sequence by returning the provided data in random order.
Implemented using Fisher-Yates Shuffling.
(Defined by Combinatorics) |
| SelectVariationDouble |
Select a random variation, without repetition, from a data sequence by randomly selecting k elements in random order.
Implemented using partial Fisher-Yates Shuffling.
(Defined by Combinatorics) |
| SelectVariationWithRepetitionDouble |
Select a random variation, with repetition, from a data sequence by randomly selecting k elements in random order.
(Defined by Combinatorics) |
| SemiDeviation |
A measure of volatility in returns below the mean. It's similar to standard deviation, but it only
looks at periods where the investment return was less than average return.
(Defined by AbsoluteRiskMeasures) |
| Skewness |
Estimates the unbiased population skewness from the provided samples.
Uses a normalizer (Bessel's correction; type 2).
Returns NaN if data has less than three entries or if any entry is NaN.
(Defined by Statistics) |
| SkewnessKurtosis |
Estimates the unbiased population skewness and kurtosis from the provided samples in a single pass.
Uses a normalizer (Bessel's correction; type 2).
(Defined by Statistics) |
| StandardDeviation | (Defined by Statistics) |
| StandardDeviation |
Estimates the unbiased population standard deviation from the provided samples.
On a dataset of size N will use an N-1 normalizer (Bessel's correction).
Returns NaN if data has less than two entries or if any entry is NaN.
(Defined by Statistics) |
| TakeAllButLastDouble |
Takes all elements of the enumeration except the last element.
(Defined by EnumerableExtensions) |
| ThisOrEmptyDouble |
Returns either the provided enumeration, or if it is null, an empty enumeration.
(Defined by EnumerableExtensions) |
| ToInverseROVector |
Wraps a double[] array to get an [!:IReadOnlyList<double>] with elements = 1 / elements of the original vector.
(Defined by VectorMath) |
| ToInverseROVector |
Wraps a double[] array till a given length to get an [!:IReadOnlyList<double>] with elements = 1 / elements of the original vector.
(Defined by VectorMath) |
| ToROVector |
Wraps a section of an original vector into a new vector.
(Defined by VectorMath) |
| TryGetFirstAndLastDouble |
Returns true and the first and last value of the enumeration, or, if the enumeration is empty, returns false.
(Defined by EnumerableExtensions) |
| TryGetSingleElementDouble |
Try to get the one and only element of the collection.
(Defined by EnumerableExtensions) |
| UpperQuartile |
Estimates the third quartile value from the provided samples.
Approximately median-unbiased regardless of the sample distribution (R8).
(Defined by Statistics) |
| Variance |
Estimates the unbiased population variance from the provided samples.
On a dataset of size N will use an N-1 normalizer (Bessel's correction).
Returns NaN if data has less than two entries or if any entry is NaN.
(Defined by Statistics) |
See Also