The Chicken sundials library provides bindings to the solvers from
the SUNDIALS library (http://computation.llnl.gov/casc/sundials/)
. SUNDIALS (SUite of Nonlinear and DIfferential/ALgebraic equation
Solvers) is a collection of solvers for systems of ordinary
differential equations and differential-algebraic equations.
The Chicken sundials library provides interfaces to the CVODE and
IDA solvers and has been tested with SUNDIALS versions 2.4.0 and 2.5.0.
(ida-create-solver TSTART TSTOP VARIABLES DERIVATIVES RESIDUAL-MAIN [RESIDUAL-INIT] [RESIDUAL-EVENT] [EVENTS] [ALG-OR-DIFF] [SUPPRESS] [IC] [USER-DATA] [RELTOL] [ABSTOL]) => IDA-SOLVER
Creates and initializes an object representing a problem to be solved with the IDA solver.
Arguments TSTART and TSTOP must be real numbers that represent
the beginning and end of the independent variable range.
Arguments VARIABLES and DERIVATIVES must be SRFI-4
f64vector objects that hold respectively the initial values and
derivatives of the system variables.
Argument RESIDUAL-MAIN is used to compute the residual function
F and must be a procedure of the following form:
(LAMBDA T YY YP DATA)
or
(LAMBDA T YY YP)
depending on whether the USER-DATA optional argument is set, where
; T : real-valued independent variable
; YY : SRFI-4 f64vector with current variable values
; YP : SRFI-4 f64vector with current variable derivatives
; DATA : is a user data object (if set)
This procedure must return a SRFI-4 f64vector containing the
residual vector.
Optional keyword argument RESIDUAL-EVENT must be a procedure of
the same form as RESIDUAL-MAIN, which computes a rootfinding
problem to be solved during the integration of the system. It is set
only if argument EVENTS is given.
Optional keyword argument EVENTS is an SRFI-4 s32vector that
is used for storage of root finding solutions. It must be given if
RESIDUAL-EVENT is given.
Optional keyword argument ALG-OR-DIFF must be an SRFI-4
s32vector which indicates the algebraic and differential variables
in the system. A value of 1 indiciates differential variable, and a
value of 0 indicates an algebraic one. This is required if the
SUPPRESS argument is given and true.
Optional keyword argument SUPPRESS is a boolean flag that
indicates whether algebraic variables must be suppressed in the local
error test. If it is true (suppress), then the argument
ALG-OR-DIFF must be given.
Optional keyword argument IC is a boolean flag that indicates
whether the solver must calculate consistent initial conditions, or
whether it must use the initial conditions given by VARIABLES.
Optional keyword argument USER-DATA is an object that will be
passed as an additional argument to the residual functions.
Optional keyword arguments RELTOL and ABSTOL specify relative
and absolute error tolerance, respectively. These both default to
1e-4.
(ida-reinit-solver IDA-SOLVER T0 Y0 YP0)
Re-initializes IDA for the solution of a problem.
(ida-destroy-solver IDA-SOLVER)
Deallocates the memory associated with the given solver.
(ida-solve IDA-SOLVER T)
Integrates the system over an interval in the independent
variable. This procedure returns either when the given T is
reached, or when a root is found.
(ida-yy IDA-SOLVER)
Returns the vector of current state values of the system.
(ida-yp IDA-SOLVER)
Returns the vector of current state derivative values of the system.
(ida-get-last-order IDA-SOLVER)
Returns the order used during the last solver step.
(ida-get-last-step IDA-SOLVER)
Returns the steps size used during the last solver step.
(ida-get-num-steps IDA-SOLVER)
Returns the cumulative number of steps taken by the solver.
(cvode-create-solver TSTART TSTOP VARIABLES RHS-FN [LMM] [ITER] [EWT-FN] [EVENT-FN] [EVENTS] [USER-DATA] [RELTOL] [ABSTOL]) => CVODE-SOLVER
Creates and initializes an object representing a problem to be solved with the CVODE solver.
Arguments TSTART and TSTOP must be real numbers that represent
the beginning and end of the independent variable range.
Arguments VARIABLES must be a SRFI-4 f64vector object that
holds the initial values of the system variables.
Argument RHS-FN is used to compute the right-hand side of the
equations, and must be a procedure of the following form:
(LAMBDA T YY DATA)
or
(LAMBDA T YY)
depending on whether the USER-DATA optional argument is set, where
; T : real-valued independent variable
; YY : SRFI-4 f64vector with current variable values
; DATA : is a user data object (if set)
This procedure must return a SRFI-4 f64vector containing the
residual vector.
Optional keyword argument EWT-FN must be a procedure of the same
form as (LAMBDA YY), which computes error weights for the system
variables, and which can be used in place of relative and absolute
error tolerance.
Optional keyword argument EVENT-FN must be a procedure of
the same form as RHS-FN, which computes a rootfinding
problem to be solved during the integration of the system. It is set
only if argument EVENTS is given.
Optional keyword argument EVENTS is an SRFI-4 s32vector that
is used for storage of root finding solutions. It must be given if
EVENT-FN is given.
Optional keyword argument LMM specifies the linear multistep
method to be used and can be one of cvode-lmm/adams (default) or
cvode-lmm/bdf. cvode-lmm/bdf is recommended for stiff
problems.
Optional keyword argument ITER specifies the iteration type to be
used and can be one of cvode-iter/functional (default) or
cvode-iter/newton. cvode-iter/newton is recommended for stiff
problems.
Optional keyword argument USER-DATA is an object that will be
passed as an additional argument to the residual functions.
Optional keyword arguments RELTOL and ABSTOL specify relative
and absolute error tolerance, respectively. These both default to
1e-4. They are only set of EWT-FN is not specified.
(cvode-reinit-solver CVODE-SOLVER T0 Y0 YP0)
Re-initializes CVODE for the solution of a problem.
(cvode-destroy-solver CVODE-SOLVER)
Deallocates the memory associated with the given solver.
(cvode-solve CVODE-SOLVER T)
Integrates the system over an interval in the independent
variable. This procedure returns either when the given T is
reached, or when a root is found.
(cvode-yy CVODE-SOLVER)
Returns the vector of current state values of the system.
;;
;; Hodgkin-Huxley model
;;
(use mathh sundials srfi-4)
(define neg -)
(define pow expt)
(define TEND 500.0)
;; Model parameters
(define (I_stim t) 10)
(define C_m 1)
(define E_Na 50)
(define E_K -77)
(define E_L -54.4)
(define gbar_Na 120)
(define gbar_K 36)
(define g_L 0.3)
;; Rate functions
(define (amf v) (* 0.1 (/ (+ v 40) (- 1.0 (exp (/ (neg (+ v 40)) 10))))))
(define (bmf v) (* 4.0 (exp (/ (neg (+ v 65)) 18))))
(define (ahf v) (* 0.07 (exp (/ (neg (+ v 65)) 20))))
(define (bhf v) (/ 1.0 (+ 1.0 (exp (/ (neg (+ v 35)) 10)))))
(define (anf v) (* 0.01 (/ (+ v 55) (- 1 (exp (/ (neg (+ v 55)) 10))))))
(define (bnf v) (* 0.125 (exp (/ (neg (+ v 65)) 80))))
;; State functions
(define (minf v) (* 0.5 (+ 1 (tanh (/ (- v v1) v2)))))
(define (winf v) (* 0.5 (+ 1 (tanh (/ (- v v3) v4)))))
(define (lamw v) (* phi (cosh (/ (- v v3) (* 2 v4)))))
;; Model equations
(define (rhs t yy)
(let ((v (f64vector-ref yy 0))
(m (f64vector-ref yy 1))
(h (f64vector-ref yy 2))
(n (f64vector-ref yy 3)))
;; transition rates at current step
(let ((am (amf v))
(an (anf v))
(ah (ahf v))
(bm (bmf v))
(bn (bnf v))
(bh (bhf v))
(g_Na (* gbar_Na (* h (pow m 3))))
(g_K (* gbar_K (pow n 4))))
(let (
;; currents
(I_Na (* (- v E_Na) g_Na))
(I_K (* (- v E_K) g_K))
(I_L (* g_L (- v E_L))))
(let (
;; state equations
(dm (- (* am (- 1 m)) (* bm m)))
(dh (- (* ah (- 1 h)) (* bh h)))
(dn (- (* an (- 1 n)) (* bn n)))
(dv (/ (- (I_stim t) I_L I_Na I_K) C_m))
)
(f64vector dv dm dh dn)
)))
))
(let ((yy (f64vector -65 0.052 0.596 0.317)) ;; v m h n
;; Integration limits
(t0 0.0)
(tf TEND)
(dt 1e-2))
;; CVODE initialization
(let ((solver (cvode-create-solver
t0 yy rhs
tstop: tf
abstol: 1e-4
reltol: 1e-4)))
;; In loop, call CVodeSolve, print results, and test for error.
(let recur ((tnext (+ t0 dt)) (iout 1))
(let ((flag (cvode-solve solver tnext)))
(if (negative? flag) (error 'main "CVODE solver error" flag))
(print-results solver tnext)
(if (< tnext tf)
(recur (+ tnext dt) (+ 1 iout)))
))
(cvode-destroy-solver solver)
(define (print-results solver t)
(let ((yy (cvode-yy solver)))
(printf "~A ~A ~A ~A ~A ~A ~A ~A~%"
t
(f64vector-ref yy 0)
(f64vector-ref yy 1)
(f64vector-ref yy 2)
(f64vector-ref yy 3)
(cvode-get-last-order solver)
(cvode-get-num-steps solver)
(cvode-get-last-step solver)
)))Copyright 2011-2016 Ivan Raikov. All rights reserved.
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