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Compute derivatives of HRF functions

Source: R/all_generic.R
deriv.Rd

Calculates the derivative of a Hemodynamic Response Function (HRF) at specified time points. This is useful for:

  • Understanding HRF dynamics and rate of change

  • Creating temporal derivative regressors for fMRI models

  • Analyzing HRF shape characteristics

  • Implementing advanced HRF basis sets

Usage

deriv(x, t, ...)

Arguments

x

An HRF object

t

Numeric vector of time points at which to evaluate the derivative

...

Additional arguments passed to specific methods

Value

Numeric vector or matrix of derivative values at the specified time points. For multi-basis HRFs, returns a matrix with one column per basis function.

Details

The derivative computation method depends on the HRF type:

  • Analytic derivatives are used when available (e.g., SPMG1, SPMG2, SPMG3)

  • Numeric finite-difference approximation is used as fallback

The default implementation uses numDeriv::grad for numerical differentiation when analytic derivatives are not available.

See also

[evaluate()], [HRF_objects], [numDeriv::grad()]

Other hrf: HRF_objects, penalty_matrix()

Examples

# Compute derivative of SPM canonical HRF
t <- seq(0, 20, by = 0.1)
hrf_deriv <- deriv(HRF_SPMG1, t)

# Plot HRF and its derivative
hrf_vals <- evaluate(HRF_SPMG1, t)
plot(t, hrf_vals, type = "l", col = "black",
     ylab = "Response", xlab = "Time (s)")
lines(t, hrf_deriv, col = "red", lty = 2)
legend("topright", c("HRF", "Derivative"),
       col = c("black", "red"), lty = c(1, 2))


# For multi-basis HRFs, returns matrix
deriv_matrix <- deriv(HRF_SPMG3, t)
# Returns derivatives for all 3 basis functions