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;;; -*- Mode: lisp -*-
;;; Simple Maxima interface to minpack routines
(in-package #:maxima)
(defmvar $debug_minpack nil
"Set to true to enable debugging messages from minpack routines")
(defmfun $minpack_lsquares (fcns vars init-x
&key
(jacobian t)
(tolerance #.(sqrt double-float-epsilon)))
"Minimize the sum of the squares of m functions in n unknowns (n <= m)
VARS list of the variables
INIT-X initial guess
FCNS list of the m functions
Optional keyword args (key = val)
TOLERANCE tolerance in solution
JACOBIAN If true, maxima computes the Jacobian directly from FCNS.
If false, the Jacobian is internally computed using a
forward-difference approximation.
Otherwise, it is a function returning the Jacobian"
(unless (and (listp fcns) (eq (caar fcns) 'mlist))
(merror "~M: ~M is not a list of functions" %%pretty-fname fcns))
(unless (and (listp vars) (eq (caar vars) 'mlist))
(merror "~M: ~M is not a list of variables" %%pretty-fname vars))
(unless (and (listp init-x) (eq (caar init-x) 'mlist))
(merror "~M: ~M is not a list of initial values" %%pretty-fname init-x))
(setf tolerance ($float tolerance))
(unless (and (realp tolerance) (plusp tolerance))
(merror "~M: tolerance must be a non-negative real number, not: ~M"
%%pretty-fname tolerance))
(let* ((n (length (cdr vars)))
(m (length (cdr fcns)))
(x (make-array n :element-type 'double-float
:initial-contents (mapcar #'(lambda (z)
($float z))
(cdr init-x))))
(fvec (make-array m :element-type 'double-float))
(fjac (make-array (* m n) :element-type 'double-float))
(ldfjac m)
(info 0)
(ipvt (make-array n :element-type 'f2cl-lib:integer4))
(fv (coerce-float-fun fcns vars))
(fj (cond ((eq jacobian t)
;; T means compute it ourselves
(meval `(($jacobian) ,fcns ,vars)))
(jacobian
;; Use the specified Jacobian
)
(t
;; No jacobian at all
nil))))
;; Massage the Jacobian into a function
(when jacobian
(setf fj (coerce-float-fun fj vars)))
(cond
(jacobian
;; Jacobian given (or computed by maxima), so use lmder1
(let* ((lwa (+ m (* 5 n)))
(wa (make-array lwa :element-type 'double-float)))
(labels ((fcn-and-jacobian (m n x fvec fjac ldfjac iflag)
(declare (type f2cl-lib:integer4 m n ldfjac iflag)
(type (cl:array double-float (*)) x fvec fjac))
(ecase iflag
(1
;; Compute function at point x, placing result
;; in fvec (subseq needed because sometimes
;; we're called with vector that is longer than
;; we want. Perfectly valid Fortran, though.)
(let ((val (apply 'funcall fv (subseq (coerce x 'list) 0 n))))
(unless (consp val)
(merror "Unable to evaluate function at the point ~M"
(list* '(mlist) (subseq (coerce x 'list) 0 n))))
(when $debug_minpack
(format t "f(~{~A~^, ~}) =~%[~@<~{~A~^, ~:_~}~:>]~%"
(coerce x 'list)
(cdr val)))
(replace fvec (mapcar #'(lambda (z)
(cl:float z 1d0))
(cdr val)))))
(2
;; Compute Jacobian at point x, placing result in fjac
(let ((j (apply 'funcall fj (subseq (coerce x 'list) 0 n))))
(unless (consp j)
(merror "Unable to evaluate Jacobian at the point ~M"
(list* '(mlist) (subseq (coerce x 'list) 0 n))))
;; Extract out elements of Jacobian and place into
;; fjac, in column-major order.
(let ((row-index 0))
(dolist (row (cdr j))
(let ((col-index 0))
(dolist (col (cdr row))
(setf (aref fjac (+ row-index (* ldfjac col-index)))
(cl:float col 1d0))
(incf col-index)))
(incf row-index))))))
(values m n nil nil nil ldfjac iflag)))
(multiple-value-bind (var-0 var-1 var-2 var-3 var-4 var-5 ldfjac var-6 info)
(minpack:lmder1 #'fcn-and-jacobian
m
n
x
fvec
fjac
ldfjac
tolerance
info
ipvt
wa
lwa)
(declare (ignore ldfjac var-0 var-1 var-2 var-3 var-4 var-5 var-6))
;; Return a list of the solution and the info flag
(list '(mlist)
(list* '(mlist) (coerce x 'list))
(minpack:enorm m fvec)
info)))))
(t
;; No Jacobian given so we need to use differences to compute
;; a numerical Jacobian. Use lmdif1.
(let* ((lwa (+ m (* 5 n) (* m n)))
(wa (make-array lwa :element-type 'double-float)))
(labels ((fval (m n x fvec iflag)
(declare (type f2cl-lib:integer4 m n ldfjac iflag)
(type (cl:array double-float (*)) x fvec fjac))
;; Compute function at point x, placing result in fvec
(let ((val (apply 'funcall fv (subseq (coerce x 'list) 0 n))))
(unless (consp val)
(merror "Unable to evaluate function at the point ~M"
(list* '(mlist) (subseq (coerce x 'list) 0 n))))
(when $debug_minpack
(format t "f(~{~A~^, ~}) =~%[~@<~{~A~^, ~:_~}~:>]~%"
(coerce x 'list)
(cdr val)))
(replace fvec (mapcar #'(lambda (z)
(cl:float z 1d0))
(cdr val))))
(values m n nil nil iflag)))
(multiple-value-bind (var-0 var-1 var-2 var-3 var-4 var-5 info)
(minpack:lmdif1 #'fval
m
n
x
fvec
tolerance
info
ipvt
wa
lwa)
(declare (ignore var-0 var-1 var-2 var-3 var-4 var-5))
;; Return a list of the solution and the info flag
(list '(mlist)
(list* '(mlist) (coerce x 'list))
(minpack:enorm m fvec)
info))))))))
(defmfun $minpack_solve (fcns vars init-x
&key
(jacobian t)
(tolerance #.(sqrt double-float-epsilon)))
"Solve the system of n equations in n unknowns
VARS list of the n variables
INIT-X initial guess
FCNS list of the n functions
Optional keyword args (key = val)
TOLERANCE tolerance in solution
JACOBIAN If true, maxima computes the Jacobian directly from FCNS.
If false, the Jacobian is internally computed using a
forward-difference approximation.
Otherwise, it is a function returning the Jacobian"
(unless (and (listp fcns) (eq (caar fcns) 'mlist))
(merror "~M: ~M is not a list of functions"
%%pretty-fname fcns))
(unless (and (listp vars) (eq (caar vars) 'mlist))
(merror "~M: ~M is not a list of variables"
%%pretty-fname vars))
(unless (and (listp init-x) (eq (caar init-x) 'mlist))
(merror "~M: ~M is not a list of initial values"
%%pretty-fname init-x))
(unless (and (realp tolerance) (plusp tolerance))
(merror "~M: tolerance must be a non-negative real number, not: ~M"
%%pretty-fname tolerance))
(let* ((n (length (cdr vars)))
(x (make-array n :element-type 'double-float
:initial-contents (mapcar #'(lambda (z)
($float z))
(cdr init-x))))
(fvec (make-array n :element-type 'double-float))
(fjac (make-array (* n n) :element-type 'double-float))
(ldfjac n)
(info 0)
(fv (coerce-float-fun fcns vars))
(fj (cond ((eq jacobian t)
;; T means compute it ourselves
(mfuncall '$jacobian fcns vars))
(jacobian
;; Use the specified Jacobian
)
(t
;; No jacobian at all
nil))))
;; Massage the Jacobian into a function
(when jacobian
(setf fj (coerce-float-fun fj vars)))
(cond
(jacobian
;; Jacobian given (or computed by maxima), so use lmder1
(let* ((lwa (/ (* n (+ n 13)) 2))
(wa (make-array lwa :element-type 'double-float)))
(labels ((fcn-and-jacobian (n x fvec fjac ldfjac iflag)
(declare (type f2cl-lib:integer4 n ldfjac iflag)
(type (cl:array double-float (*)) x fvec fjac))
(ecase iflag
(1
;; Compute function at point x, placing result
;; in fvec (subseq needed because sometimes
;; we're called with vector that is longer than
;; we want. Perfectly valid Fortran, though.)
(let ((val (apply 'funcall fv (subseq (coerce x 'list) 0 n))))
(replace fvec (mapcar #'(lambda (z)
(cl:float z 1d0))
(cdr val)))))
(2
;; Compute Jacobian at point x, placing result in fjac
(let ((j (apply 'funcall fj (subseq (coerce x 'list) 0 n))))
;; Extract out elements of Jacobian and place into
;; fjac, in column-major order.
(let ((row-index 0))
(dolist (row (cdr j))
(let ((col-index 0))
(dolist (col (cdr row))
(setf (aref fjac (+ row-index (* ldfjac col-index)))
(cl:float col 1d0))
(incf col-index)))
(incf row-index))))))
(values n nil nil nil ldfjac iflag)))
(multiple-value-bind (var-0 var-1 var-2 var-3 var-4 ldfjac var-6 info)
(minpack:hybrj1 #'fcn-and-jacobian
n
x
fvec
fjac
ldfjac
tolerance
info
wa
lwa)
(declare (ignore ldfjac var-0 var-1 var-2 var-3 var-4 var-6))
;; Return a list of the solution and the info flag
(list '(mlist)
(list* '(mlist) (coerce x 'list))
(minpack:enorm n fvec)
info)))))
(t
;; No Jacobian given so we need to use differences to compute
;; a numerical Jacobian. Use lmdif1.
(let* ((lwa (/ (* n (+ (* 3 n) 13)) 2))
(wa (make-array lwa :element-type 'double-float)))
(labels ((fval (n x fvec iflag)
(declare (type f2cl-lib:integer4 n ldfjac iflag)
(type (cl:array double-float (*)) x fvec fjac))
;; Compute function at point x, placing result in fvec
(let ((val (apply 'funcall fv (subseq (coerce x 'list) 0 n))))
(replace fvec (mapcar #'(lambda (z)
(cl:float z 1d0))
(cdr val))))
(values n nil nil iflag)))
(multiple-value-bind (var-0 var-1 var-2 var-3 var-4 info)
(minpack:hybrd1 #'fval
n
x
fvec
tolerance
info
wa
lwa)
(declare (ignore var-0 var-1 var-2 var-3 var-4))
;; Return a list of the solution and the info flag
(list '(mlist)
(list* '(mlist) (coerce x 'list))
(minpack:enorm n fvec)
info))))))))
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