func Brent(fn Diffable, x_lo, x_hi, epsAbs, epsRel float64) (float64, error) {
cfn := unsafe.Pointer(&fn)
result := C.double(0.0)
err := C.brentSolve(cfn, C.double(x_lo), C.double(x_hi), C.double(epsAbs), C.double(epsRel), &result)
if err != C.GSL_SUCCESS {
err_str := C.GoString(C.gsl_strerror(err))
return 0.0, fmt.Errorf("error in solve.Brent: %v\n", err_str)
}
return float64(result), nil
}
// Perform a fit for p = len(`start`) parameters on `n` functions `F` (with
// derivatives `Df`). F(x, i) and Df(x, i) must be defined for 0 <= i < n. If
// x (a vector of dimension p) is outside the domain of F or Df, they should
// return an error.
func MultiDim(F FitErrF, Df FitErrDf, n int, start vec.Vector, epsAbs, epsRel float64) (vec.Vector, error) {
fns := FitData{F, Df, n}
cfns := unsafe.Pointer(&fns)
p := C.size_t(len(start))
csolution, cstart := C.gsl_vector_alloc(p), C.gsl_vector_alloc(p)
vecToGSL(start, cstart)
err := C.multiFit(cfns, cstart, C.double(epsAbs), C.double(epsRel), C.size_t(n), csolution)
if err != C.GSL_SUCCESS {
err_str := C.GoString(C.gsl_strerror(err))
return nil, fmt.Errorf("error in fit.MultiDim: %v\n", err_str)
}
solution := vecFromGSL(csolution)
C.gsl_vector_free(csolution)
C.gsl_vector_free(cstart)
return solution, nil
}
// Numerical central derivative of fn(v) with respect to v_i within tolerance
// epsabs. h is the initial step size.
func Derivative(fn vec.FnDim0, v vec.Vector, i int, h, epsabs float64) (float64, error) {
v_i_initial := v[i]
iters, maxIters := 0, 100
// results are bad for h too small or too large; we iterate in both directions
hMin := h / 1e6
hMax := h * 1e6
hRising := true
hInitial := h
hOk := func(h float64) bool {
if !hRising && h > hMin {
return true
} else if hRising && h < hMax {
return true
}
return false
}
hAdvance := func(h float64) float64 {
if hRising {
if h*2.0 > hMax {
hRising = false
return hInitial / 2.0
}
return h * 2.0
}
return h / 2.0
}
fwi := unsafe.Pointer(&fnWithIndex{fn, v, i})
x := C.double(v[i])
result, abserr := C.double(0.0), C.double(math.MaxFloat64)
for iters < maxIters && hOk(h) {
err := C.centralDeriv(fwi, x, C.double(h), &result, &abserr)
if err != C.GSL_SUCCESS {
err_str := C.GoString(C.gsl_strerror(err))
v[i] = v_i_initial
return float64(result), fmt.Errorf("error in Derivative (GSL): %v\n", err_str)
}
if float64(abserr) < epsabs {
v[i] = v_i_initial
return float64(result), nil
}
iters++
h = hAdvance(h)
}
// if we get here, !hOk(h) || iters == maxIters
v[i] = v_i_initial
return float64(result), fmt.Errorf("Derivative exceeded maximum iterations\n")
}
// Multidimensional root-finder. Implemented by providing an interface to GSL
// implementation of Powell's Hybrid method (gsl_multiroot_fdfsolver_hybridsj).
// Callback passing through cgo follows the model at:
// http://stackoverflow.com/questions/6125683/call-go-functions-from-c/6147097#6147097
func MultiDim(fn DiffSystem, start vec.Vector, epsAbs, epsRel float64) (vec.Vector, error) {
cfn := unsafe.Pointer(&fn)
dim := C.size_t(fn.Dimension)
csolution, cstart := C.gsl_vector_alloc(dim), C.gsl_vector_alloc(dim)
VecToGSL(start, cstart)
err := C.powellSolve(cfn, cstart, C.double(epsAbs), C.double(epsRel), csolution)
if err != C.GSL_SUCCESS {
err_str := C.GoString(C.gsl_strerror(err))
return nil, fmt.Errorf("error in solve.MultiDim: %v\n", err_str)
}
solution := VecFromGSL(csolution)
val, solveErr := fn.F(solution)
if solveErr != nil || val.AbsMax() > epsAbs {
return nil, fmt.Errorf("solution is inaccurate; absolute error = %v", val)
}
C.gsl_vector_free(csolution)
C.gsl_vector_free(cstart)
return solution, nil
}
// Interface to gsl_integration_qags: "adaptive integration with [integrable]
// singularities". Integrate f from a to b and return the value of the
// integral and the absolute error.
func Qags(fn func(float64) float64, a, b, epsabs, epsrel float64) (result, absErr float64, err error) {
cfn := unsafe.Pointer(&fn)
C_result, C_absErr := C.double(0.0), C.double(0.0)
// guard against panics during integration
defer func() {
if x := recover(); x != nil {
result = 0.0
absErr = 0.0
err = x.(error)
}
}()
// perform integration
C_err := C.gslQags(cfn, C.double(a), C.double(b), C.double(epsabs), C.double(epsrel), &C_result, &C_absErr)
if C_err != C.GSL_SUCCESS {
err_str := C.GoString(C.gsl_strerror(C_err))
return 0.0, 0.0, fmt.Errorf("error in Qags (GSL): %v\n", err_str)
}
result = float64(C_result)
absErr = float64(C_absErr)
return
}
func (e *GSLError) Error() (what string) {
str := C.gsl_strerror(e.code)
what = C.GoString(str)
return
}
// const char * gsl_strerror (const GslError gsl_errno)
func (ge GslError) String() string {
return C.GoString(C.gsl_strerror(C.int(ge)))
}
func (e Error) Error() string {
return C.GoString(C.gsl_strerror(C.int(e)))
}
