Lcurve.m - Revision history

Kuprov: sync with Spinach main f053e432: argument constraints, lam_opt output, corner-criterion notes; canonical section layout

2026-08-30T06:03:55Z

sync with Spinach main f053e432: argument constraints, lam_opt output, corner-criterion notes; canonical section layout

2026-06-06T18:38:34Z

Update function See also links and function index membership

2026-06-05T17:50:12Z

Rename Arguments section heading to Parameters

2026-06-05T16:41:12Z

Normalise preformatted blank lines in function documentation blocks

2026-06-05T16:26:39Z

Add missing Version/authors metadata and remove raw author emails

2026-04-25T11:26:54Z

Normalise sequential blank lines

2026-04-25T11:15:58Z

Add See also section to function-description page

2026-04-05T14:49:16Z

Restore pre-bulk-edit wiki content

2026-04-05T14:13:36Z

Normalise remaining wiki page to current Spinach source header

2026-04-05T14:12:07Z

Sync syntax/arguments/outputs with current Spinach source

@@ Line 1: / Line 1: @@
 {{DISPLAYTITLE:lcurve.m}} __NOTOC__
-L-curve analysis function. Syntax:
+==Syntax==
       lam_opt=lcurve(lam,err,reg,mode)
-Parameters:
+==Parameters==
-         lam - row vector of regularisation parameters
+         lam - row vector of regularisation parameters, must
-         err - row vector of least squares errors
+         err - row vector of least squares errors, must be
-         reg - row vector of regularisation functional values
+         reg - row vector of regularisation functional values,
         mode - 'log' for logarithmic coordinates and 'linear'
                for linear ones; 'log' is recommended
-The function returns the regularisation parameter at the point of the maximum curvature of the L-curve.
+==Outputs==
-==Parameters==
+==Notes==
+The corner is the point of the greatest curvature, which for a smooth asymmetric bend is not the intersection of the asymptotes; the criterion locates the regularisation parameter to within a factor of a few and is not convergent in the zero noise limit (Vogel, SIAM J. Numer. Anal. 34, 1996). Treat the answer as an order of magnitude estimate and inspect the plotted curve.
-       err - row vector of least squares errors
+The curvature maximum must fall inside the sampled interval; if it falls on either end, the corner is outside the range and this function refuses to return the endpoint as an answer.
 ==See also==

@@ Line 35: / Line 35: @@
 ==See also==
-[[tikhonov.m]], [[tikhoind.m]], [[ipcs.m]], [[Pseudocontact_shift_analysis|Pseudocontact shift analysis]]
+[[tikhonov.m]], [[tikhoind.m]], [[ipcs.m]], [[autoexec.m]], [[bos_product_table.m]], [[fft_freq_axis.m]], [[fwhm2rlx.m]], [[icm2hz.m]], [[ifft_time_axis.m]], [[intrep.m]], [[istraceless.m]], [[kq2lin.m]], [[kronm.m]], [[lin2kq.m]], [[min_int_type.m]], [[prune_subgraphs.m]], [[redfield_integral_async.m]], [[redfield_integral_serial.m]], [[repcols.m]], [[reprows.m]], [[serpentine.m]], [[st_product_table.m]], [[tikhol1n.m]], [[unihash.m]], [[which_subst.m]], [[xyz2hfc.m]], [[Kernel_utilities]], [[Pseudocontact_shift_analysis]]
 ''Version 1.9, authors: [[Ilya Kuprov]]''

← Older revision		Revision as of 17:50, 5 June 2026
Line 19:		Line 19:


−	==~~Arguments~~==	+	==Parameters==

	lam - row vector of regularisation parameters		lam - row vector of regularisation parameters

@@ Line 24: / Line 24: @@
         err - row vector of least squares errors
-−
         reg - row vector of regularisation functional values
-−
        mode - 'log' for logarithmic coordinates and 'linear'
               for linear ones; 'log' is recommended
-−
   The function returns the regularisation parameter at the point
   of the maximum curvature of the L-curve.

@@ Line 18: / Line 18: @@
 The function returns the regularisation parameter at the point of the maximum curvature of the L-curve.
 ==Arguments==
@@ Line 34: / Line 33: @@
   of the maximum curvature of the L-curve.
 ==See also==
 [[tikhonov.m]], [[tikhoind.m]], [[ipcs.m]], [[Pseudocontact_shift_analysis|Pseudocontact shift analysis]]

← Older revision		Revision as of 11:15, 25 April 2026
Line 37:		Line 37:

	ilya.kuprov@weizmann.ac.il		ilya.kuprov@weizmann.ac.il
		+
		+	==See also==
		+	[[tikhonov.m]], [[tikhoind.m]], [[ipcs.m]], [[Pseudocontact_shift_analysis\|Pseudocontact shift analysis]]

← Older revision		Revision as of 14:12, 5 April 2026
Line 1:		Line 1:
		+	{{DISPLAYTITLE:lcurve.m}} __NOTOC__
		+
	L-curve analysis function. Syntax:		L-curve analysis function. Syntax:

Line 19:		Line 21:

	''Version 1.9, authors: [[Ilya Kuprov]]''		''Version 1.9, authors: [[Ilya Kuprov]]''
		+
		+	==Arguments==
		+
		+	lam - row vector of regularisation parameters
		+
		+	err - row vector of least squares errors
		+
		+	reg - row vector of regularisation functional values
		+
		+	mode - 'log' for logarithmic coordinates and 'linear'
		+	for linear ones; 'log' is recommended
		+
		+	The function returns the regularisation parameter at the point
		+	of the maximum curvature of the L-curve.
		+
		+	ilya.kuprov@weizmann.ac.il