Commit 3da5fec4 by Francesco Montanari

### Check convergence for Simpson's rule (commented code)

```* cosmo.el (cosmo-trapzd, cosmo-qsimp): Adapt Simpson's rule to
automatically check convergence. At similar accuracy, the code is
about one order of magnitude slower than the previous
implementation. Try to improve efficiency by replacing loops with
more functional solutions. For the time being the newly added code
is commented out, the old implementation is used.```
parent a76d7c92
 ... ... @@ -70,8 +70,6 @@ ;; automatically (the user should only pass a max number of steps) ;; or an error should be shown if the result does not converge. ;; ;; - Consider using Calc as a library for quadrature, and maybe to plot. ;; ;; - Refactor tests, now the code is too cumbersome and repetitive. ;; ;; - Add all quantities from Hogg 1999. ... ... @@ -193,6 +191,61 @@ Example: (* 4 sum1) (* 2 sum2))))))) ;; (defun cosmo-trapzd (func lo hi sum niter) ;; "Extended trapezoidal rule to integrate FUNC from LO to HI. ;; Compute the refinement to an old SUM result, previous to the ;; current NITER stage of refinement. The function must be called ;; for NITER = 1, 2, 3, ... in order. Boundaries LO and HI are ;; always converted to floats." ;; (let ((lo (float lo)) ; Always assume float boundaries. ;; (hi (float hi))) ;; ;; NITER=1 corresponds simply to integrate(func(x), x, lo, hi) ;; (if (= niter 1) ;; (* 0.5 (- hi lo) (+ (funcall func lo) (funcall func hi))) ;; ;; Subsequent calls NITER = 2, 3, ... (in order) improve the ;; ;; accuracy by adding 2^(NITER-2) interior points. ;; (let* ((iter (expt 2 (- niter 2))) ;; (step (/ (- hi lo) iter)) ;; (xval (+ lo (* 0.5 step))) ;; (sumf 0.0) ;; (j 0)) ;; (while (< j iter) ;; (setq sumf (+ sumf (funcall func xval))) ;; (setq xval (+ xval step)) ;; (setq j (1+ j))) ;; (* 0.5 (+ sum (* (- hi lo) (/ sumf iter)))))))) ;; (defun cosmo-qsimp (func lo hi &optional eps jmax) ;; "Simpson's integration. ;; Argument FUNC integrand. ;; Argument LO lower bound. ;; Argument HI upper bound. ;; Optional argument EPS fractional accuracy. ;; Optional argument JMAX maximum number of steps. ;; " ;; (let ((eps (or eps 1e-6)) ; Set defaults. ;; (jmax (or jmax 20)) ;; (nsum 0.0) ; N-th iteration sum. ;; (nsumt 0.0) ;; (osum 0.0) ; Old sum. ;; (osumt 0.0) ;; (converged nil) ;; (j 1)) ;; (while (and (<= j jmax) (not converged)) ;; (setq nsumt (cosmo-trapzd func lo hi nsum j)) ;; (setq nsum (/ (- (* 4.0 nsumt) osumt) 3.0)) ;; (if (and (> j 5) ; Avoid spurious early convergence. ;; (or (< (abs (- nsum osum)) (* eps (abs osum))) ;; (and (= nsum 0.0) (= osum 0.0)))) ;; (setq converged t)) ;; (setq osum nsum) ;; (setq osumt nsumt) ;; (setq j (1+ j))) ;; (if converged ;; nsum ;; (error "Error: The integral did not converge. Try to ;; increase the number of steps")))) ;;; Compute cosmological functions. ... ... @@ -254,6 +307,7 @@ Example: "Line-of-sight comoving distance [Mpc] for Lambda-CDM at a given REDSHIFT." (let ((DH (cosmo-get-hubble-distance)) (int (cosmo-simps #'cosmo-inv-efunc 0.0 redshift 1000))) ;; (int (cosmo-qsimp #'cosmo-inv-efunc 0.0 redshift 1e-3 20))) (* DH int))) (defun cosmo-los-comoving-distance () ... ...
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