Estimates the derivative of a data set by means of a naive implementation of a finite difference scheme based upon central differences.
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| real(kind=real64), | intent(in) | :: | dt |
The time step between data points. |
||
| real(kind=real64), | intent(in), | dimension(:) | :: | x |
An N-element array containing the data whose derivative is to be estimated. |
An N-element array containing the derivative estimate.
Computes an estimate to the derivative of an evenly-sampled data set using total variation regularization.
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| real(kind=real64), | intent(in), | dimension(:) | :: | t |
An N-element array containing the time points at which x was sampled. |
|
| real(kind=real64), | intent(in), | dimension(:) | :: | x |
An N-element array containing the data whose derivative is to be estimated. |
An N-element array containing the derivative estimate.
Estimates the derivative of a signal by utilization of a second-order system as a filter.
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| real(kind=real64), | intent(in) | :: | dt |
The time step between data points. |
||
| real(kind=real64), | intent(in), | dimension(:) | :: | x |
An N-element array containing the data whose derivative is to be estimated. |
|
| real(kind=real64), | intent(in) | :: | fc |
The filter cutoff frequency, in Hz. |
An N-element array containing the filtered signal in the first column and the derivative estimate in the second.
Utilizes a 5-point stencil to estimate the derivative of a data set.
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| real(kind=real64), | intent(in) | :: | dt |
The time step between data points. |
||
| real(kind=real64), | intent(in), | dimension(:) | :: | x |
An N-element array containing the data whose derivative is to be estimated. |
An N-element array containing the derivative estimate.
Utilizes a 5-point stencil to estimate the second derivative of a data set.
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| real(kind=real64), | intent(in) | :: | dt |
The time step between data points. |
||
| real(kind=real64), | intent(in), | dimension(:) | :: | x |
An N-element array containing the data whose derivative is to be estimated. |
An N-element array containing the derivative estimate.
Computes an estimate to the derivative of an evenly-sampled data set using total variation regularization.
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| real(kind=real64), | intent(in) | :: | dt |
The time step between data points. |
||
| real(kind=real64), | intent(in), | dimension(:) | :: | x |
An N-element array containing the data whose derivative is to be estimated. |
|
| real(kind=real64), | intent(in) | :: | alpha |
The regularization parameter. |
||
| integer(kind=int32), | intent(in), | optional | :: | maxiter |
The maximum number of iterations to allow. The default is 20 iterations. |
|
| real(kind=real64), | intent(in), | optional | :: | tol |
The convergence tolerance to use. The tolerance is applied to the difference in Euclidean norms of the derivative update vector. Once the norm of the update vector is changing less than this tolerance, the iteration process will terminate. The default is 1e-3. |
|
| integer(kind=int32), | intent(out), | optional | :: | niter |
The number of iterations actually performed. |
An N-element array containing the estimate of the derivative.