Math

Overview

Math utility functions.

Function List

qlCholeskyDecomposition ()
qlCovarianceDecomposition ()
qlCovarianceDecompositionCorrelationMatrix ()
qlCovarianceDecompositionStandardDeviations ()
qlCovarianceDecompositionVariances ()
qlGetCovariance ()
qlNormDist ()
qlNormInv ()
qlNormSDist ()
qlNormSInv ()
qlPrimeNumber ()
qlPseudoSqrt ()
qlRankReducedSqrt ()
qlSymmetricSchurDecomposition ()
qlSymmetricSchurDecompositionEigenvalues ()
qlSymmetricSchurDecompositionEigenvectors ()

Function Documentation

qlCholeskyDecomposition

vector<vector<double> > returnValue
 
qlCholeskyDecomposition(
        vector<vector<double> > Matrix
        bool Flexible
        any Trigger)

Description:

Returns the Cholesky decomposition of a real symmetric matrix.

Supported Platforms:

Excel

Parameters

Matrix	symmetric matrix (hopefully positive semi-definite at least).
Flexible	If TRUE it returns a result also for positive semi-definite matrix. Default value = false.
Trigger	dependency tracking trigger

qlCovarianceDecomposition

string returnValue
 
qlCovarianceDecomposition(
        string ObjectId
        vector<vector<double> > SymmetricMatrix
        double Tolerance
        bool Permanent
        any Trigger
        bool Overwrite)

Description:

Construct an object of class CovarianceDecomposition and return its id

Supported Platforms:

Excel

Parameters

ObjectId	id of object to be created
SymmetricMatrix	Symmetrix covariance matrix to be decomposed.
Tolerance	numerical tolerance for non symmetric matrix. Default value = 1.0e12.
Permanent	object permanent/nonpermanent
Trigger	dependency tracking trigger
Overwrite	overwrite flag

qlCovarianceDecompositionCorrelationMatrix

vector<vector<double> > returnValue
 
qlCovarianceDecompositionCorrelationMatrix(
        string ObjectId
        any Trigger)

Description:

Returns the correlation matrix for the given CovarianceDecomposition object.

Supported Platforms:

Excel

Parameters

ObjectId	id of existing QuantLib::CovarianceDecomposition object
Trigger	dependency tracking trigger

qlCovarianceDecompositionStandardDeviations

vector<double> returnValue
 
qlCovarianceDecompositionStandardDeviations(
        string ObjectId
        any Trigger)

Description:

Returns the standard deviation (i.e. volatility times square root of time) vector for the given CovarianceDecomposition object.

Supported Platforms:

Excel

Parameters

ObjectId	id of existing QuantLib::CovarianceDecomposition object
Trigger	dependency tracking trigger

qlCovarianceDecompositionVariances

vector<double> returnValue
 
qlCovarianceDecompositionVariances(
        string ObjectId
        any Trigger)

Description:

Returns the variance vector for the given CovarianceDecomposition object.

Supported Platforms:

Excel

Parameters

ObjectId	id of existing QuantLib::CovarianceDecomposition object
Trigger	dependency tracking trigger

qlGetCovariance

vector<vector<double> > returnValue
 
qlGetCovariance(
        vector<double> Vols
        vector<vector<double> > Matrix
        double Tolerance
        any Trigger)

Description:

Returns the covariance matrix generated using the correlation matrix and the standard deviation (i.e. volatility times square root of time) array.

Supported Platforms:

Excel

Parameters

Vols	volatility vector.
Matrix	symmetric matrix (hopefully positive semi-definite at least).
Tolerance	numerical tolerance for non symmetric matrix. Default value = 1.0e12.
Trigger	dependency tracking trigger

qlNormDist

double returnValue
 
qlNormDist(
        double X
        double Mean
        double Standard_dev
        bool Cumulative
        any Trigger)

Description:

Returns the normal cumulative distribution for the specified mean and standard deviation.

Supported Platforms:

Excel

Parameters

X	is the value for which you want the distribution.
Mean	is the arithmetic mean of the distribution. Default value = 0.0.
Standard_dev	is the standard deviation of the distribution, a positive number. Default value = 1.0.
Cumulative	is a logical value: for the cumulative distribution function, use TRUE; for the probability mass function, use FALSE. Default value = TRUE.
Trigger	dependency tracking trigger

qlNormInv

double returnValue
 
qlNormInv(
        double Probability
        double Mean
        double Standard_dev
        any Trigger)

Description:

Returns the inverse of the normal cumulative distribution for the specified mean and standard deviation.

Supported Platforms:

Excel

Parameters

Probability	is a probability corresponding to the normal distribution, a number between 0 and 1 inclusive.
Mean	is the arithmetic mean of the distribution. Default value = 0.0.
Standard_dev	is the standard deviation of the distribution, a positive number. Default value = 1.0.
Trigger	dependency tracking trigger

qlNormSDist

double returnValue
 
qlNormSDist(
        double Z
        any Trigger)

Description:

Returns the standard normal cumulative distribution (has a mean of zero and standard deviation of one).

Supported Platforms:

Excel

Parameters

Z	is the value for which you want the distribution.
Trigger	dependency tracking trigger

qlNormSInv

double returnValue
 
qlNormSInv(
        double Probability
        any Trigger)

Description:

Returns the inverse of the standard normal cumulative distribution (has a mean of zero and standard deviation of one).

Supported Platforms:

Excel

Parameters

Probability	is a probability corresponding to the normal distribution, a number between 0 and 1 inclusive.
Trigger	dependency tracking trigger

qlPrimeNumber

long returnValue
 
qlPrimeNumber(
        long N
        any Trigger)

Description:

returns the N-th prime number.

Supported Platforms:

Excel

Parameters

N	index of the prime number (e.g N=2 returns 3).
Trigger	dependency tracking trigger

qlPseudoSqrt

vector<vector<double> > returnValue
 
qlPseudoSqrt(
        vector<vector<double> > Matrix
        string SalvagingAlgorithm
        any Trigger)

Description:

Returns the pseudo square root of a real symmetric matrix.

Supported Platforms:

Excel

Parameters

Matrix	symmetric matrix (hopefully positive semi-definite at least).
SalvagingAlgorithm	Salvaging algorithm for symmetric matrix not positive semi-definite (None, Spectral).
Trigger	dependency tracking trigger

qlRankReducedSqrt

vector<vector<double> > returnValue
 
qlRankReducedSqrt(
        vector<vector<double> > Matrix
        long MaxRank
        double ComponentPercentage
        string SalvagingAlgorithm
        any Trigger)

Description:

Returns the rank reduced pseudo square root of a real symmetric matrix.

Supported Platforms:

Excel

Parameters

Matrix	symmetric matrix (hopefully positive semi-definite at least).
MaxRank	number of principal components retained, i.e. max rank for the result matrix.
ComponentPercentage	principal components retained as percentage of eigenvalues' sum.
SalvagingAlgorithm	Salvaging algorithm for symmetric matrix not positive semi-definite (None, Spectral).
Trigger	dependency tracking trigger

qlSymmetricSchurDecomposition

string returnValue
 
qlSymmetricSchurDecomposition(
        string ObjectId
        vector<vector<double> > SymmetricMatrix
        bool Permanent
        any Trigger
        bool Overwrite)

Description:

Construct an object of class SymmetricSchurDecomposition and return its id

Supported Platforms:

Excel

Parameters

ObjectId	id of object to be created
SymmetricMatrix	Symmetrix matrix to be decomposed.
Permanent	object permanent/nonpermanent
Trigger	dependency tracking trigger
Overwrite	overwrite flag

qlSymmetricSchurDecompositionEigenvalues

vector<double> returnValue
 
qlSymmetricSchurDecompositionEigenvalues(
        string ObjectId
        any Trigger)

Description:

Returns the eigenvalues for the given SymmetricSchurDecomposition object.

Supported Platforms:

Excel

Parameters

ObjectId	id of existing QuantLib::SymmetricSchurDecomposition object
Trigger	dependency tracking trigger

qlSymmetricSchurDecompositionEigenvectors

vector<vector<double> > returnValue
 
qlSymmetricSchurDecompositionEigenvectors(
        string ObjectId
        any Trigger)

Description:

Returns the eigenvectors for the given SymmetricSchurDecomposition object. Eigenvectors are returned columnwise.

Supported Platforms:

Excel

Parameters

ObjectId	id of existing QuantLib::SymmetricSchurDecomposition object
Trigger	dependency tracking trigger