patterncausality (version 0.1.3)

fillPCMatrix: Calculate and Record Causality Strengths

Description

Computes the causality strengths based on the comparison between predicted and real patterns and signatures in a system's dynamic model. It applies a normalization function to measure the intensity of causal influences and uses an error function for weighting if required.

Usage

fillPCMatrix(
  weighted,
  predictedPatternY,
  realPatternY,
  predictedSignatureY,
  realSignatureY,
  patternX,
  signatureX
)

Value

A dataframe with two columns: 'real' and 'predicted', representing the real and predicted causality strengths.

Arguments

weighted

Logical, if TRUE, the causality strength is calculated using the error function for normalization, otherwise a binary indication (1 for accurate prediction and 0 otherwise) is used.

predictedPatternY

Numeric vector, the predicted pattern of variable Y at a future time step.

realPatternY

Numeric vector, the actual observed pattern of variable Y at the same future time step.

predictedSignatureY

Numeric vector, the predicted signature vector derived from the system model for Y.

realSignatureY

Numeric vector, the actual observed signature vector for Y.

patternX

Numeric vector, the current observed pattern of variable X, used as the basis for prediction.

signatureX

Numeric vector, the current observed signature vector of variable X.

Details

Fill Pattern Causality Matrix with Causality Strengths

This function calculates and fills the causality strengths between predicted and real patterns and signatures for a complex system analysis. It evaluates the accuracy of predictions and computes the strength of causal relationships based on norm vectors and optionally weights these strengths using the error function (erf).

Examples

set.seed(123)
E <- 3
tau <- 1
Mx <- matrix(rnorm(200), nrow = 20)
My <- matrix(rnorm(200), nrow = 20)
Dx <- distanceMatrix(Mx, "minkowski")
Dy <- distanceMatrix(My, "minkowski")
SMx <- signatureSpace(Mx, E)
SMy <- signatureSpace(My, E)
PSMx <- patternSpace(SMx, E)
PSMy <- patternSpace(SMy, E)
CCSPAN <- (E - 1) * tau
NNSPAN <- E + 1
i <- 15
h <- 2
NNx <- pastNNsInfo(CCSPAN, NNSPAN, Mx, Dx, SMx, PSMx, i, h)
timesX <- NNx$times
projNNy <- projectedNNsInfo(My, Dy, SMy, PSMy, timesX, i, h)
pSY <- predictionY(E, projNNy, zeroTolerance = E - 1)$predictedSignatureY
pPY <- predictionY(E, projNNy, zeroTolerance = E - 1)$predictedPatternY[1]
rSY <- SMy[(i + h), ]
rPY <- PSMy[i + h]
signatureX <- SMx[i, ]
patternX <- PSMx[i, ]
weighted <- 0
pc <- fillPCMatrix(weighted, pPY, rPY, pSY, rSY, patternX, signatureX)