GNU Scientific Library Reference Manual - Third Edition (v1.12)by M. Galassi, J. Davies, J. Theiler, B. Gough, G. Jungman, P. Alken, M. Booth, F. Rossi Paperback (6"x9"), 592 pages, 60 figures ISBN 0954612078 RRP £24.95 ($39.95) |

## 27.1 Functions

__Function:__int**gsl_deriv_central***(const gsl_function **`f`, double`x`, double`h`, double *`result`, double *`abserr`)- This function computes the numerical derivative of the function
`f`at the point`x`using an adaptive central difference algorithm with a step-size of`h`. The derivative is returned in`result`and an estimate of its absolute error is returned in`abserr`.The initial value of

`h`is used to estimate an optimal step-size, based on the scaling of the truncation error and round-off error in the derivative calculation. The derivative is computed using a 5-point rule for equally spaced abscissae at x-h, x-h/2, x, x+h/2, x+h, with an error estimate taken from the difference between the 5-point rule and the corresponding 3-point rule x-h, x, x+h. Note that the value of the function at x does not contribute to the derivative calculation, so only 4-points are actually used.

__Function:__int**gsl_deriv_forward***(const gsl_function **`f`, double`x`, double`h`, double *`result`, double *`abserr`)- This function computes the numerical derivative of the function
`f`at the point`x`using an adaptive forward difference algorithm with a step-size of`h`. The function is evaluated only at points greater than`x`, and never at`x`itself. The derivative is returned in`result`and an estimate of its absolute error is returned in`abserr`. This function should be used if f(x) has a discontinuity at`x`, or is undefined for values less than`x`.The initial value of

`h`is used to estimate an optimal step-size, based on the scaling of the truncation error and round-off error in the derivative calculation. The derivative at x is computed using an “open” 4-point rule for equally spaced abscissae at x+h/4, x+h/2, x+3h/4, x+h, with an error estimate taken from the difference between the 4-point rule and the corresponding 2-point rule x+h/2, x+h.

__Function:__int**gsl_deriv_backward***(const gsl_function **`f`, double`x`, double`h`, double *`result`, double *`abserr`)- This function computes the numerical derivative of the function
`f`at the point`x`using an adaptive backward difference algorithm with a step-size of`h`. The function is evaluated only at points less than`x`, and never at`x`itself. The derivative is returned in`result`and an estimate of its absolute error is returned in`abserr`. This function should be used if f(x) has a discontinuity at`x`, or is undefined for values greater than`x`.This function is equivalent to calling

`gsl_deriv_forward`

with a negative step-size.

ISBN 0954612078 | GNU Scientific Library Reference Manual - Third Edition (v1.12) | See the print edition |