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ISpacedInterval Interface

[Missing <summary> documentation for "T:Altaxo.Calc.LinearAlgebra.ISpacedInterval"]


Namespace: Altaxo.Calc.LinearAlgebra
Assembly: AltaxoCore (in AltaxoCore.dll) Version: 4.8.3179.0 (4.8.3179.0)
Syntax
C#
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public interface ISpacedInterval : IReadOnlyList<double>, 
	IReadOnlyCollection<double>, IEnumerable<double>, IEnumerable, 
	IImmutable

The ISpacedInterval type exposes the following members.

Properties
 NameDescription
Public propertyCountGets the number of elements in the collection.
(Inherited from IReadOnlyCollectionDouble)
Public propertyEnd Start of the interval (inclusive if step can divide the interval by an integer number).
Public propertyIsCountEditable 
Public propertyIsEndEditable 
Public propertyIsStartEditable 
Public propertyIsStepEditable 
Public propertyItemGets the element at the specified index in the read-only list.
(Inherited from IReadOnlyListDouble)
Public propertyStart Start of the interval (inclusive).
Public propertyStep Gets the step size.
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Methods
 NameDescription
Public methodGetEnumeratorReturns an enumerator that iterates through the collection.
(Inherited from IEnumerableDouble)
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Extension Methods
 NameDescription
Public Extension MethodAny Determines whether the given vector contains any elements.
(Defined by VectorMath)
Public Extension MethodAny Determines whether any element of the vector satisfies a condition.
(Defined by VectorMath)
Public Extension MethodAny Determines whether any element of the vector satisfies a condition.
(Defined by VectorMath)
Public Extension MethodAverage Returns the average (=sum/N) of the elements in vector.
(Defined by VectorMath)
Public Extension MethodCompoundReturn Compound Monthly Return or Geometric Return or Annualized Return
(Defined by AbsoluteReturnMeasures)
Public Extension MethodCovariance 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)
Public Extension MethodDownsideDeviation 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)
Public Extension MethodElementsAtDouble
(Defined by VectorMath)
Public Extension MethodElementsWhereDouble
(Defined by VectorMath)
Public Extension MethodElementsWhereDouble
(Defined by VectorMath)
Public Extension MethodEmpiricalCDF Estimates the empirical cumulative distribution function (CDF) at x from the provided samples.
(Defined by Statistics)
Public Extension MethodEmpiricalCDFFunc Estimates the empirical cumulative distribution function (CDF) at x from the provided samples.
(Defined by Statistics)
Public Extension MethodEmpiricalInvCDF Estimates the empirical inverse CDF at tau from the provided samples.
(Defined by Statistics)
Public Extension MethodEmpiricalInvCDFFunc Estimates the empirical inverse CDF at tau from the provided samples.
(Defined by Statistics)
Public Extension MethodEuclideanNormGiven an n-vector x, this function calculates the euclidean norm of x.
(Defined by VectorMath)
Public Extension MethodExcessKurtosisOfNormalized 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)
Public Extension MethodFirstOrDouble Returns the first value of the enumeration, or, if the enumeration is empty, the other value provided in the arguments.
(Defined by EnumerableExtensions)
Public Extension MethodFiveNumberSummary Estimates {min, lower-quantile, median, upper-quantile, max} from the provided samples. Approximately median-unbiased regardless of the sample distribution (R8).
(Defined by Statistics)
Public Extension MethodFlattenFromRootToLeavesDouble Converts a recursive data structure into a flat list. The root element is enumerated before its corresponding child element(s).
(Defined by EnumerableExtensions)
Public Extension MethodForEachDoDouble Executes an action for each element of the sequence.
(Defined by EnumerableExtensions)
Public Extension MethodGainLossRatio 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)
Public Extension MethodGainMean 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)
Public Extension MethodGainStandardDeviation 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)
Public Extension MethodGeometricMean Evaluates the geometric mean. Returns NaN if data is empty or if any entry is NaN.
(Defined by Statistics)
Public Extension MethodGetDifferences Gets the differences x[i+1] - x[i], for i = 0 .. x.Count-2.
(Defined by EnumerableExtensions)
Public Extension MethodGetPossibleStepsToMoveTowardsHigherIndicesDouble 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)
Public Extension MethodGetPossibleStepsToMoveTowardsLowerIndicesDouble 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)
Public Extension MethodGetUsedLength 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)
Public Extension MethodGetUsedLength 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)
Public Extension MethodHarmonicMean Evaluates the harmonic mean. Returns NaN if data is empty or if any entry is NaN.
(Defined by Statistics)
Public Extension MethodHasSingleElementDouble Determines whether the specified enumeration has exactly one element.
(Defined by EnumerableExtensions)
Public Extension MethodIndexOfDouble Gets the index of an item in a enumeration or list.
(Defined by ListExtensions)
Public Extension MethodIndexOfFirstDouble Gets the index the of first item in list that fulfills the predicate predicate
(Defined by ListExtensions)
Public Extension MethodIndexOfFirstDouble Gets the index the of first item in list that fulfills the predicate predicate
(Defined by ListExtensions)
Public Extension MethodIndexOfMaxDoubleReturn 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)
Public Extension MethodIndexOfMaxAbsoluteValueReturn the index of the first element with the maximum absolute value in a vector
(Defined by VectorMath)
Public Extension MethodIndexOfMaxValueReturn the index of the first element with the maximum value in a vector
(Defined by VectorMath)
Public Extension MethodIndexOfMinDoubleReturn 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)
Public Extension MethodIndexOfMinAbsoluteValueReturn the index of the first element with the minimum absolute value in a vector
(Defined by VectorMath)
Public Extension MethodIndexOfMinValueReturn the index of the first element with the minimum value in a vector
(Defined by VectorMath)
Public Extension MethodIndicesInt32AndValuesWhereDouble 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)
Public Extension MethodIndicesInt32AndValuesWhereDouble 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)
Public Extension MethodIndicesInt32WhereDouble Returns the indices of the elements which fullfill a given condition, given by the element's value.
(Defined by EnumerableExtensions)
Public Extension MethodIndicesInt32WhereDouble Returns the indices of the elements which fullfill a given condition, given by the element's value and its index.
(Defined by EnumerableExtensions)
Public Extension MethodIndicesOfMinMaxDoubleReturn 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)
Public Extension MethodInterquartileRange Estimates the inter-quartile range from the provided samples. Approximately median-unbiased regardless of the sample distribution (R8).
(Defined by Statistics)
Public Extension MethodInterQuartileRange
(Defined by Statistics)
Public Extension MethodIsEmptyDouble Determines whether the specified enumeration is empty.
(Defined by EnumerableExtensions)
Public Extension MethodIsStrictlyDecreasing Returns true if the sequence given by the vector argument is strictly decreasing.
(Defined by VectorMath)
Public Extension MethodIsStrictlyIncreasing Returns true if the sequence given by the vector argument is strictly increasing.
(Defined by VectorMath)
Public Extension MethodIsStrictlyIncreasingOrDecreasing Returns true if the sequence given by the vector argument is strictly increasing or decreasing.
(Defined by VectorMath)
Public Extension MethodIsStrictlyIncreasingOrDecreasing Returns true if the sequence given by the vector argument is strictly increasing or decreasing.
(Defined by VectorMath)
Public Extension MethodJoinConditionalDouble, T2 Takes a join of two sequences, but only takes into account those pair, which fulfill a given condition.
(Defined by EnumerableExtensions)
Public Extension MethodJoinConditionalDouble, T2, TResult Takes a join of two sequences, but only takes into account those pair, which fulfill a given condition.
(Defined by EnumerableExtensions)
Public Extension MethodKurtosis 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)
Public Extension MethodKurtosis 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)
Public Extension MethodL1Norm Calculates the L1 norm of the vector (as the sum of the absolute values of the elements).
(Defined by VectorMath)
Public Extension MethodL2NormGiven an n-vector x, this function calculates the euclidean norm of x.
(Defined by VectorMath)
Public Extension MethodL2NormGiven an n-vector x, this function calculates the euclidean norm of x.
(Defined by VectorMath)
Public Extension MethodLastOrDouble Returns the last value of the enumeration, or, if the enumeration is empty, the other value provided in the arguments.
(Defined by EnumerableExtensions)
Public Extension MethodLInfinityNorm 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)
Public Extension MethodLossMean 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)
Public Extension MethodLossStandardDeviation 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)
Public Extension MethodLowerQuartile Estimates the first quartile value from the provided samples. Approximately median-unbiased regardless of the sample distribution (R8).
(Defined by Statistics)
Public Extension MethodLpNormCompute the p Norm of this vector.
(Defined by VectorMath)
Public Extension MethodMassDistribution
(Defined by Statistics)
Public Extension MethodMax Returns the maximum of the elements in vector.
(Defined by VectorMath)
Public Extension MethodMax Returns the maximum of the elements in vector.
(Defined by VectorMath)
Public Extension MethodMaxElementDouble, 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)
Public Extension MethodMaximum Returns the maximum value in the sample data. Returns NaN if data is empty or if any entry is NaN.
(Defined by Statistics)
Public Extension MethodMaximumAbsolute Returns the maximum absolute value in the sample data. Returns NaN if data is empty or if any entry is NaN.
(Defined by Statistics)
Public Extension MethodMaxOf Creates a new vector, whose elements are the maximum of the elements of a given input vector and a given number.
(Defined by VectorMath)
Public Extension MethodMaxOfValidElements Returns the maximum value of all the valid elements in x (nonvalid elements, i.e. NaN values are not considered).
(Defined by VectorMath)
Public Extension MethodMaxOrDefaultDouble, M Evaluates the maximum of a enumeration of elements, or returns a default value if the series is empty.
(Defined by EnumerableExtensions)
Public Extension MethodMean Returns the average (=sum/N) of the elements in vector.
(Defined by VectorMath)
Public Extension MethodMean
(Defined by Statistics)
Public Extension MethodMean 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)
Public Extension MethodMean
(Defined by Statistics)
Public Extension MethodMeanAndVariance 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)
Public Extension MethodMeanStandardDeviation 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)
Public Extension MethodMeanVariance 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)
Public Extension MethodMedian Estimates the sample median from the provided samples (R8).
(Defined by Statistics)
Public Extension MethodMin Returns the minimum of the elements in vector.
(Defined by VectorMath)
Public Extension MethodMin Returns the minimum of the elements in vector.
(Defined by VectorMath)
Public Extension MethodMinimum Returns the minimum value in the sample data. Returns NaN if data is empty or if any entry is NaN.
(Defined by Statistics)
Public Extension MethodMinimumAbsolute Returns the minimum absolute value in the sample data. Returns NaN if data is empty or if any entry is NaN.
(Defined by Statistics)
Public Extension MethodMinOfValidElements Returns the minimum value of all the valid elements in x (nonvalid elements, i.e. NaN values are not considered).
(Defined by VectorMath)
Public Extension MethodMovingAverage 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)
Public Extension MethodPercentile 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)
Public Extension MethodPercentileFunc 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)
Public Extension MethodPopulationCovariance 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)
Public Extension MethodPopulationKurtosis 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)
Public Extension MethodPopulationSkewness 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)
Public Extension MethodPopulationSkewnessKurtosis 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)
Public Extension MethodPopulationStandardDeviation 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)
Public Extension MethodPopulationVariance 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)
Public Extension MethodProbabilityDensity
(Defined by Statistics)
Public Extension MethodQuantile The quantile value of x.
(Defined by Statistics)
Public Extension MethodQuantile 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)
Public Extension MethodQuantile The quantile value of x.
(Defined by Statistics)
Public Extension MethodQuantileCustom 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)
Public Extension MethodQuantileCustomFunc 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)
Public Extension MethodQuantileFunc 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)
Public Extension MethodQuantileRank 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)
Public Extension MethodQuantileRankFunc 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)
Public Extension MethodRanks 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)
Public Extension MethodRootMeanSquare 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)
Public Extension MethodSelectCombinationDouble Select a random combination, without repetition, from a data sequence by selecting k elements in original order.
(Defined by Combinatorics)
Public Extension MethodSelectCombinationWithRepetitionDouble Select a random combination, with repetition, from a data sequence by selecting k elements in original order.
(Defined by Combinatorics)
Public Extension MethodSelectPermutationDouble Select a random permutation from a data sequence by returning the provided data in random order. Implemented using Fisher-Yates Shuffling.
(Defined by Combinatorics)
Public Extension MethodSelectVariationDouble 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)
Public Extension MethodSelectVariationWithRepetitionDouble Select a random variation, with repetition, from a data sequence by randomly selecting k elements in random order.
(Defined by Combinatorics)
Public Extension MethodSemiDeviation 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)
Public Extension MethodSkewness 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)
Public Extension MethodSkewnessKurtosis 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)
Public Extension MethodStandardDeviation
(Defined by Statistics)
Public Extension MethodStandardDeviation 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)
Public Extension MethodTakeAllButLastDouble Takes all elements of the enumeration except the last element.
(Defined by EnumerableExtensions)
Public Extension MethodThisOrEmptyDouble Returns either the provided enumeration, or if it is null, an empty enumeration.
(Defined by EnumerableExtensions)
Public Extension MethodToInverseROVector Wraps a double[] array to get an [!:IReadOnlyList<double>] with elements = 1 / elements of the original vector.
(Defined by VectorMath)
Public Extension MethodToInverseROVector Wraps a double[] array till a given length to get an [!:IReadOnlyList<double>] with elements = 1 / elements of the original vector.
(Defined by VectorMath)
Public Extension MethodToROVector Wraps a section of an original vector into a new vector.
(Defined by VectorMath)
Public Extension MethodTryGetFirstAndLastDouble Returns true and the first and last value of the enumeration, or, if the enumeration is empty, returns false.
(Defined by EnumerableExtensions)
Public Extension MethodTryGetSingleElementDouble Try to get the one and only element of the collection.
(Defined by EnumerableExtensions)
Public Extension MethodUpperQuartile Estimates the third quartile value from the provided samples. Approximately median-unbiased regardless of the sample distribution (R8).
(Defined by Statistics)
Public Extension MethodVariance 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)
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See Also