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;ELC
;;; Compiled
;;; in Emacs version 26.1
;;; with all optimizations.

;;; This file uses dynamic docstrings, first added in Emacs 19.29.

;;; This file does not contain utf-8 non-ASCII characters,
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(byte-code "\300\301!\210\300\302!\207" [require calc-arith calcalg3] 2)
#@70 Return the parameters A and B for the best least squares fit y=a+bx.
(defalias 'math-nlfit-least-squares #[(xdata ydata &optional sdata sigmas) "G\n\203\306\307\n\"\202\310	\311\"\n\203\312\202	\312\211\312\211\313\203\274@@@\314
\203L\315\"\202N\"\314\203a\315\"\202c\"\314\203z\315\316\211\"\"\202\316\211\"\"\314\203\227\315\316\"\"\202\235\316\"\"\n\203\255\314\f\315\311\"\"+AAA\202+\317\316\f\"\316
\211\"\"\315\317\316\"\316
\"\"\"\315\317\316\f\"\316
\"\"\"\203.\315\"\320\315
\"!\315\f\" !\321\322!!E\321\322!E\323\211! E\323 EEE+\2023D.\n\207" [xdata n sdata s2data S Sx mapcar calcFunc-sqr make-list 1 0 nil math-add math-div math-mul math-sub math-neg sdev calcFunc-sqrt vec Sy Sxx Sxy D ydata s y x B A sigmas C22 C12 C11] 8 (#$ . 481)])
(defalias 'math-nlfit-get-rates-from-cumul #[(tdata qdata) "\303\304A@@\"\304	A@	@\"\"CG\305V\203J\306\307\310\303\304\3058A@\"\304\305	8	A@\"\"\303\304A@@\"\304	A@	@\"\"\"\"\nBA\211\202\303\304A@@\"\304	A@	@\"\"\nB\311\n!)\207" [qdata tdata pdata math-div math-sub 2 math-mul (float 5 -1) math-add reverse] 10])
(defalias 'math-nlfit-get-cumul-from-rates #[(tdata pdata q0) "C\nA\203+\304	@\305\211\306\304\nA@\n@\"\"\307A@@\"\"\"	B\nAA\202\310	!)\207" [q0 qdata pdata tdata math-add math-mul (float 5 -1) math-sub reverse] 8])
(defalias 'math-nlfit-find-qmax #[(qdata pdata tdata) "\306\307	#\310\n\"\311	@	A\"\312\307\fA@\f@\"!\313
\"\203,\314\315
\"\202.,\207" [pdata qdata ratios tdata lsdata qmax math-map-binop math-div math-nlfit-least-squares math-max-list math-neg math-lessp math-add (float 5 -1) a] 4])
(defalias 'math-nlfit-find-logistic-parameters #[(qdata pdata tdata) "\306	\n#\307\310\"\311\n\f\"\312
@!
A@E+\207" [qdata pdata tdata a newqdata bandc math-nlfit-find-qmax mapcar #[(q) "\302\303\304	\"\305\"!\207" [a q calcFunc-ln math-sub math-div 1] 5] math-nlfit-least-squares calcFunc-exp] 4])
(defalias 'math-nlfit-find-qmaxhalf #[(pdata tdata) "\304@A\"\305\306@\n\"\2031\307	\310\211\311\307A@@\"\"\312A@@\"\"\"AA\202		*\207" [pdata qmh pmax tdata math-max-list 0 math-lessp math-add math-mul (float 5 -1) math-sub] 8])
(defalias 'math-nlfit-find-q0 #[(pdata tdata) "\306	\"\307\310\n\"\311	#\312\313\314\315\f\"	#\307\316\317\n\"\"\"\203,\317\n\"\202\320\n\"\313\314\321\f\"	#\322\211\323W\203u\307\324\317
\"\"\312\313\314\325\f\"	#\307\326\317\n\"\"\"\203i\202lT\211\202B\307\327\317
\"\".\207" [pdata tdata qhalf q0 qdata qmin math-nlfit-find-qmaxhalf math-mul 2 math-nlfit-get-cumul-from-rates math-lessp math-nlfit-find-qmax mapcar #[(q) "\302	\"\207" [q0 q math-add] 3] (float 5 -1) math-add math-sub #[(q) "\302	\"\207" [q0 q math-add] 3] 0 10 (float 5 -1) #[(q) "\302	\"\207" [q0 q math-add] 3] (float 5 -1) (float 5 -1) qmax qt i] 8])
(defvar math-nlfit-delta '(float 1 -8))
(defvar math-nlfit-epsilon '(float 1 -5))
(defvar math-nlfit-max-its 100)
(defalias 'math-nlfit-set-elt #[(vec i x) "S	\233\n\240\207" [i vec x] 2])
(defalias 'math-nlfit-get-elt #[(vec i) "S	8\207" [i vec] 2])
(defalias 'math-nlfit-make-matrix #[(i j) "\305\306\"\307\306	\fW\203\310!\nB	T\211\202\n\n+\207" [j k mat row i make-list 0 nil copy-sequence] 4])
(defalias 'math-nlfit-set-matx-elt #[(mat i j x) "S	S\n8\233\240\207" [j i mat x] 3])
(defalias 'math-nlfit-get-matx-elt #[(mat i j) "S	S\n88\207" [j i mat] 3])
(defalias 'math-nlfit-givens #[(C d) "\306!\306	!@GG\307\310\311\"\310\311\"\312\211\312\211\f\nX\203\fT\211X\203w\313\f#\313\f\211# \314\311 \"\204m\315\316!\317!\316 !\"\"\203r\320 !\311\307\211\202\266\317\321!\322\323\317\211\"\317 \211\"\"!\"\324\"\320\324 \"!\315\316!\"\203\254\202\266\324\321!\" \325\f\211$\210\325\f$\210\fT\"\"\nX\203+\313\f\"##\313\"#$\326\317#\"\317$\"\"%\323\317#\"\317$\"\"$%#\325\"$$\210\325\f\"#$\210\"T\"+\202\323)\327	\"&\327	\f\"'\326\317'\"\317&\"\"%\323\317'\"\317&\"\"&%'\330	&#\210\330	\f'#\210+*T\211\2023)\fT\211\202)\n\312(\211\307Y\203\337\330
\311#\210\327	\"(T\211\"\nX\203\302\323(\317\313\"#\327\"\"\"\"(\"T\211\"\202\237)\330\320\324(\313\211#\"!#\210S\211\202\206*\nT\211X\203\376\330
\327	\"#\210T\211\202\345)\n\211\307Y\203\267\211\fTY\203\257\313\f#\314\307\"\203*\311\307\202b\315\316!\307\"\203G\322\326\307\317\211\"\"!\202b\324\307\316!\"\317\321!\322\326\307\317\211\"\"!\"\327
\"\327
\f\"\312%)*\323\317)\"\317*\"\"%\326\317*\"\317)\"\"*%)\330
*#\210\330
\f)#\210+S\211\202)\fS\211\202).\207" [C d n N j r copy-tree 1 make-list 0 nil math-nlfit-get-matx-elt math-equal math-lessp calcFunc-abs math-mul math-neg calcFunc-sign calcFunc-sqrt math-add math-div math-nlfit-set-matx-elt math-sub math-nlfit-get-elt math-nlfit-set-elt x w gamma sigma rho i cjj cij math-nlfit-delta k cjk cik h di dj s rj ri] 11])
(defalias 'math-nlfit-jacobian #[(grad xlist parms &optional slist) "\306	\203'\307\n	@#
\203\310\311\f\"\202\fB)
A	A\211\204\312!)\207" [j xlist grad parms row slist nil apply mapcar #[(x) "\302	@\"\207" [x slist math-div] 3] reverse] 5])
(defalias 'math-nlfit-make-ident #[(l n) "\304\211\"\305	X\203\306\n	\211$\210	T\211\202\n*\207" [n i m l math-nlfit-make-matrix 1 math-nlfit-set-matx-elt] 6])
(defalias 'math-nlfit-chi-sq #[(xlist ylist parms fn &optional slist) "\306	\2034\307\310\n	@#\f@\"\f\203\311
\f@\"\312\313
\211\"\")	A\fA\fA\f\202)\207" [cs xlist fn parms ylist c 0 math-sub apply math-div math-add math-mul slist] 5])
(defalias 'math-nlfit-init-lambda #[(C) "\305@GG\203-@\211\203%\306\307\f@\f@\"\"\fA\211\204)A\211\204
\310\311\307\n	\"\"!+\207" [C N n l row 0 math-add math-mul calcFunc-sqrt math-div] 7])
(defalias 'math-nlfit-make-Ctilda #[(C l) "@G\304\n	\"\305\"*\207" [C n l bot math-nlfit-make-ident append] 3])
(defalias 'math-nlfit-make-d #[(fn xdata ydata parms &optional sdata) "\306	\2032\307\310\n	@#\f@\"\203\311
@\"\202 
)B	A\fAA\202\312!)\207" [d xdata fn parms ydata dd nil math-sub apply math-div reverse sdata] 5])
(defalias 'math-nlfit-make-dtilda #[(d n) "\302\303	\304\"\"\207" [d n append make-list 0] 5])
(defalias 'math-nlfit-fit #[(xlist ylist parms fn grad &optional slist) "\306	\n$\307
	\n%\310	\n
%\311\f!\312\313\204\276W\203\276T\312\204\251\314\f\" \315\f@G\"!\316 !\"\"\317\320\321\n!\"##\310	#
%$\322$\"\203\236\322\323\324$\"$\"%\"\203\212\325\323\326\"$#\325\202\245\327\326\"-\202;\306	\n$\307
	\n%)\202&\n.D\207" [grad xlist parms slist C fn math-nlfit-jacobian math-nlfit-make-d math-nlfit-chi-sq math-nlfit-init-lambda nil 0 math-nlfit-make-Ctilda math-nlfit-make-dtilda math-nlfit-givens math-map-binop math-add copy-tree math-lessp math-div math-sub t 10 math-mul ylist d chisq lambda really-done iters math-nlfit-max-its done Ctilda dtilda zeta newparms newchisq math-nlfit-epsilon] 6])
(defalias 'math-nlfit-s-logistic-fn #[(x a b c) "\304\305\306\307	\310\307\n\"!\"\"\"\207" [a b c x math-div math-add 1 math-mul calcFunc-exp] 10])
(defalias 'math-nlfit-s-logistic-grad #[(x a b c) "\306\307	\"!\310\311\307\n\"\"\307\f\211\"\312\311\f\"\313\312\307\f\n\"
\"!\313\312\307\f\307\307	\n\"\"\"
\"!E+\207" [c x ep b d d2 calcFunc-exp math-mul math-add 1 math-div math-neg a] 11])
(defalias 'math-nlfit-b-logistic-fn #[(x a c d) "\305\306\307	\n\"\"!\310\306\f\"\311\312\"\306\f\211\")\")\207" [c x d ex a calcFunc-exp math-mul math-sub math-div math-add 1] 6])
(defalias 'math-nlfit-b-logistic-grad #[(x a c d) "\306\307\310	\n\"\"!\311\312\"\310	\n\"\313\f\307\211\")\"\310\313\307\307
\"\"\f\307\211\")\"\313\307\314\307\307
\307\211\")\"\"\"\315\f\316\"\"\"\310\313\307\314\307\307\307\211\")\"\"\"\315\f\316\"\"\313\307\307\"\"\f\307\211\")\"\"E+\207" [c x d ex ex1 xd calcFunc-exp math-mul math-sub math-add 1 math-div 2 math-pow 3 a] 13])
(defalias 'math-nlfit-find-covar #[(grad xlist pparms) "\304	\203\305\306\n	@#BB	A\211\204\305\307!B\310\311!\"\312!)\207" [j xlist grad pparms nil vec apply reverse math-mul calcFunc-trn calcFunc-inv] 6])
(defalias 'math-nlfit-get-sigmas #[(grad xlist pparms chisq) "\306\307	\n#\211GS\nG\310\f
V\2039\f
X\2035\311\f\211\f88!B\fT\211\f\202\312!\f-D\207" [sgs grad xlist pparms covar n nil math-nlfit-find-covar 1 calcFunc-sqrt reverse N i] 5])
(defalias 'math-nlfit-s-logistic-params #[(xdata ydata) "\303	\"\304	\n#)\207" [xdata ydata pdata math-nlfit-get-rates-from-cumul math-nlfit-find-logistic-parameters] 4])
(defalias 'math-nlfit-b-logistic-params #[(xdata ydata) "\306	\"\307	\n#\310	#\211A@\311\f8\312\313\f@\313
\"\"!\312\314\315
!\"!\314
\"\211E.\207" [ydata xdata q0 qdata abc B math-nlfit-find-q0 math-nlfit-get-cumul-from-rates math-nlfit-find-logistic-parameters 2 math-neg math-mul math-div calcFunc-ln C A D] 7])
(defalias 'math-nlfit-s-logistic-solnexpr #[(pms var) "@A@\3058\306\307\310\311\n\312\311	\fE!EEE+\207" [pms c b a var 2 / + 1 * calcFunc-exp] 10])
(defalias 'math-nlfit-b-logistic-solnexpr #[(pms var) "@A@\3058\306\307\310\307\n\311\f	EE!E\312\313\314\310\307\n\311\f	EE!E\305EE+\207" [pms d c a var 2 / * calcFunc-exp - ^ + 1] 11])
(defalias 'math-nlfit-enter-result #[(n prefix vals) "\304\n#\210\305 \207" [prefix calc-aborted-prefix n vals calc-pop-push-record-list calc-handle-whys] 4])
(defalias 'math-nlfit-fit-curve #[(fn grad solnexpr initparms &optional sdv) "\300\301`\"\207" [calc-do #[nil "\306=\206	\307=\310\311\312!\211A@AAA@A\313
!\205%\314\315
\"#\314\316
\"\310\211$%\312&\317\312\320\"'$A@(%A)*\f
\"+\321\f
+,-#&\211.A@/	\205o\322-\f/.@$0	\205x0@\2111\203\210\323\324/1#\202\212//2/(\"3\325\31045)\203\273\326)@/@E4B4/A/)A\211)\204\240\327\3304\237B!4\331\267\202\332\312\3333#\210\202\3106\330340A@\334.@\fG/G78#\20387V\203\335.@87Z\"\202\336*\2576\332\312\3376#\210)\202\332\312\3403#\210\3414\342\".\207" [sdv sdevv calc-display-working-message data xdata ydata calcFunc-efit calcFunc-xfit nil calc-top 1 math-contains-sdev-p mapcar #[(x) "\301\302\"\207" [x math-get-sdev t] 3] #[(x) "\301!\207" [x math-get-value] 2] calc-get-fit-variables 3 math-nlfit-fit math-nlfit-get-sigmas math-map-binop #[(x y) "\302	E\207" [x y sdev] 3] t calcFunc-eq calc-normalize vec #s(hash-table size 2 test eq rehash-size 1.5 rehash-threshold 0.8125 purecopy t data (calcFunc-efit 202 calcFunc-xfit 212)) math-nlfit-enter-result "efit" (vec) calcFunc-utpc (var nan var-nan) "xfit" "fit" calc-record "parm" sdata calc-curve-varnames calc-curve-coefnames calc-curve-nvars fitvars var parms initparms parmguess fn grad fit finalparms sigmacovar sigmas solnexpr soln traillist calc-fit-to-trail sln m n] 11]] 3])
(defalias 'calc-fit-s-shaped-logistic-curve #[(arg) "\301\302\303\304\305%\207" [arg math-nlfit-fit-curve math-nlfit-s-logistic-fn math-nlfit-s-logistic-grad math-nlfit-s-logistic-solnexpr math-nlfit-s-logistic-params] 6 nil "P"])
(defalias 'calc-fit-bell-shaped-logistic-curve #[(arg) "\301\302\303\304\305%\207" [arg math-nlfit-fit-curve math-nlfit-b-logistic-fn math-nlfit-b-logistic-grad math-nlfit-b-logistic-solnexpr math-nlfit-b-logistic-params] 6 nil "P"])
(defalias 'calc-fit-hubbert-linear-curve #[(&optional sdv) "\300\301`\"\207" [calc-do #[nil "\306=\206	\307=\310\311\312!\211A@AAA@A\313
!\205%\314\315
\"*\314\316
\"\317\320
\f#+\321\f+*	$\211,@\322\320,@,A@\"!D-\310\211./\3120\323\312\324\"1.A@2/A3\325-@\326\312\3272-A@EEE4\330\31056\331\3323@-@E\3323A@-A@EE5\333\267\202\376\334\312\3354#\210\202\310\336\f+-@A@-A@A@D\337*%78\33145\324,8\331\340\341\327\342\343EDE7\fG9*\203\3559\324V\203\355\34479\324Z\"\202\356\345)\2578\334\312\3468#\210*\202\334\312\3474#\210\3505\351\".\207" [sdv sdevv calc-display-working-message data qdata pdata calcFunc-efit calcFunc-xfit nil calc-top 1 math-contains-sdev-p mapcar #[(x) "\301\302\"\207" [x math-get-sdev t] 3] #[(x) "\301!\207" [x math-get-value] 2] math-map-binop math-div math-nlfit-least-squares math-neg calc-get-fit-variables 2 * - / t vec calcFunc-eq #s(hash-table size 2 test eq rehash-size 1.5 rehash-threshold 0.8125 purecopy t data (calcFunc-efit 155 calcFunc-xfit 165)) math-nlfit-enter-result "efit" math-nlfit-chi-sq #[(x a b) "\303\304\305\306	\n\"\"\"\207" [a x b math-mul math-sub 1 math-div] 7] (calcFunc-fitdummy 1) calcFunc-neg (calcFunc-fitdummy 1) (calcFunc-fitdummy 2) calcFunc-utpc (var nan var-nan) "xfit" "fit" calc-record "parm" sdata poverqdata parmvals finalparms calc-curve-varnames calc-curve-coefnames calc-curve-nvars fitvars var parms soln traillist calc-fit-to-trail chisq sln n] 11]] 3])
(provide 'calc-nlfit)