_odepackmodule.c

/* MULTIPACK module by Travis Oliphant

Copyright (c) 2002 Travis Oliphant all rights reserved
oliphant.travis@ieee.org
Permission to use, modify, and distribute this software is given under the
terms of the SciPy (BSD style) license.  See LICENSE.txt that came with
this distribution for specifics.

NO WARRANTY IS EXPRESSED OR IMPLIED.  USE AT YOUR OWN RISK.
*/


/* This extension module is a collection of wrapper functions around
common FORTRAN code in the package ODEPACK.

The wrappers are meant to be nearly direct translations between the
FORTRAN code and Python.  Some parameters like sizes do not need to be
passed since they are available from the objects.

It is anticipated that a pure Python module be written to call these lower
level routines and make a simpler user interface.  All of the routines define
default values for little-used parameters so that even the raw routines are
quite useful without a separate wrapper.

FORTRAN Outputs that are not either an error indicator or the sought-after
results are placed in a dictionary and returned as an optional member of
the result tuple when the full_output argument is non-zero.
*/

#include "Python.h"
#include "numpy/npy_3kcompat.h"

#include "numpy/arrayobject.h"

#define PYERR(errobj,message) {\
    PyErr_SetString(errobj,message); \
    goto fail; \
}
#define PYERR2(errobj,message) { \
    PyErr_Print(); \
    PyErr_SetString(errobj, message); \
    goto fail; \
}

typedef struct _odepack_globals {
    PyObject *python_function;
    PyObject *python_jacobian;
    PyObject *extra_arguments;  /* a tuple */
    int jac_transpose;
    int jac_type;
    int tfirst;
} odepack_params;

static odepack_params global_params = {NULL, NULL, NULL, 0, 0, 0};

static
PyObject *call_odeint_user_function(PyObject *func, npy_intp n, double *x,
                                    double t, int tfirst,
                                    PyObject *args, PyObject *error_obj)
{
    /*
    This function is the C wrapper of the user's Python functions that
    define the differential equations (and also the Jacobian function).
    The Fortran code calls ode_function() and ode_jacobian_function(),
    and those functions call this function to call the Python functions
    provided to odeint by the user.

    If an error occurs, NULL is returned.  Otherwise, a numpy array
    is returned.
    */

    PyArrayObject *sequence = NULL;
    PyObject *tfloat = NULL;
    PyObject *firstargs = NULL;
    PyObject *arglist = NULL;
    PyObject *result = NULL;
    PyArrayObject *result_array = NULL;

    /* Build sequence argument from inputs */
    sequence = (PyArrayObject *) PyArray_SimpleNewFromData(1, &n, NPY_DOUBLE,
                                                           (char *) x);
    if (sequence == NULL) {
        goto fail;
    }

    tfloat = PyFloat_FromDouble(t);
    if (tfloat == NULL) {
        goto fail;
    }

    /* firstargs is a tuple that will hold the first two arguments. */
    firstargs = PyTuple_New(2);
    if (firstargs == NULL) {
        goto fail;
    }

    if (tfirst == 0) {
        PyTuple_SET_ITEM(firstargs, 0, (PyObject *) sequence);
        PyTuple_SET_ITEM(firstargs, 1, tfloat);
    } else {
        PyTuple_SET_ITEM(firstargs, 0, tfloat);
        PyTuple_SET_ITEM(firstargs, 1, (PyObject *) sequence);
    }
    /* firstargs now owns the sequence and tfloat references. */
    sequence = NULL;
    tfloat = NULL;

    arglist = PySequence_Concat(firstargs, args);
    if (arglist == NULL) {
        goto fail;
    }

    /* Call the Python function. */
    result = PyEval_CallObject(func, arglist);
    if (result == NULL) {
        goto fail;
    }

    result_array = (PyArrayObject *)
                   PyArray_ContiguousFromObject(result, NPY_DOUBLE, 0, 0);

fail:
    Py_XDECREF(sequence);
    Py_XDECREF(tfloat);
    Py_XDECREF(firstargs);
    Py_XDECREF(arglist);
    Py_XDECREF(result);
    return (PyObject *) result_array;
}


static PyObject *odepack_error;

#if defined(UPPERCASE_FORTRAN)
    #if defined(NO_APPEND_FORTRAN)
        /* nothing to do here */
    #else
        #define LSODA  LSODA_
    #endif
#else
    #if defined(NO_APPEND_FORTRAN)
        #define LSODA  lsoda
    #else
        #define LSODA  lsoda_
    #endif
#endif

void LSODA();

/*
void ode_function(int *n, double *t, double *y, double *ydot)
{
  ydot[0] = -0.04*y[0] + 1e4*y[1]*y[2];
  ydot[2] = 3e7*y[1]*y[1];
  ydot[1] = -ydot[0] - ydot[2];
  return;
}
*/

void
ode_function(int *n, double *t, double *y, double *ydot)
{
    /*
    This is the function called from the Fortran code. It should
        -- use call_odeint_user_function to get a multiarrayobject result
        -- check for errors and set *n to -1 if any
        -- otherwise place result of calculation in ydot
    */

    PyArrayObject *result_array = NULL;

    result_array = (PyArrayObject *)
                   call_odeint_user_function(global_params.python_function,
                                             *n, y, *t, global_params.tfirst,
                                             global_params.extra_arguments,
                                             odepack_error);
    if (result_array == NULL) {
        *n = -1;
        return;
    }

    if (PyArray_NDIM(result_array) > 1) {
        *n = -1;
        PyErr_Format(PyExc_RuntimeError,
                "The array return by func must be one-dimensional, but got ndim=%d.",
                PyArray_NDIM(result_array));
        Py_DECREF(result_array);
        return;
    }

    if (PyArray_Size((PyObject *)result_array) != *n) {
        PyErr_Format(PyExc_RuntimeError,
            "The size of the array returned by func (%ld) does not match "
            "the size of y0 (%d).",
            PyArray_Size((PyObject *)result_array), *n);
        *n = -1;
        Py_DECREF(result_array);
        return;
    }

    memcpy(ydot, PyArray_DATA(result_array), (*n)*sizeof(double));
    Py_DECREF(result_array);
    return;
}


/*
 *  Copy a contiguous matrix at `c` to a Fortran-ordered matrix at `f`.
 *  `ldf` is the leading dimension of the Fortran array at `f`.
 *  `nrows` and `ncols` are the number of rows and columns of the matrix, resp.
 *  If `transposed` is 0, c[i, j] is *(c + ncols*i + j).
 *  If `transposed` is nonzero, c[i, j] is *(c + i + nrows*j)  (i.e. `c` is
 *  stored in F-contiguous order).
 */

static void
copy_array_to_fortran(double *f, int ldf, int nrows, int ncols,
                      double *c, int transposed)
{
    int i, j;
    int row_stride, col_stride;

    /* The strides count multiples of sizeof(double), not bytes. */
    if (transposed) {
        row_stride = 1;
        col_stride = nrows;
    }
    else {
        row_stride = ncols;
        col_stride = 1;
    }
    for (i = 0; i < nrows; ++i) {
        for (j = 0; j < ncols; ++j) {
            double value;
            /* value = c[i,j] */
            value = *(c + row_stride*i + col_stride*j);
            /* f[i,j] = value */
            *(f + ldf*j + i) = value;
        }
    }
}


int
ode_jacobian_function(int *n, double *t, double *y, int *ml, int *mu,
                      double *pd, int *nrowpd)
{
    /*
        This is the function called from the Fortran code. It should
            -- use call_odeint_user_function to get a multiarrayobject result
            -- check for errors and return -1 if any (though this is ignored
                           by calling program).
            -- otherwise place result of calculation in pd
    */

    PyArrayObject *result_array;
    int ndim, nrows, ncols, dim_error;
    npy_intp *dims;

    result_array = (PyArrayObject *)
                   call_odeint_user_function(global_params.python_jacobian,
                                             *n, y, *t, global_params.tfirst,
                                             global_params.extra_arguments,
                                             odepack_error);
    if (result_array == NULL) {
        *n = -1;
        return -1;
    }

    ncols = *n;
    if (global_params.jac_type == 4) {
        nrows = *ml + *mu + 1;
    }
    else {
        nrows = *n;
    }

    if (!global_params.jac_transpose) {
        int tmp;
        tmp = nrows;
        nrows = ncols;
        ncols = tmp;
    }

    ndim = PyArray_NDIM(result_array);
    if (ndim > 2) {
        PyErr_Format(PyExc_RuntimeError,
            "The Jacobian array must be two dimensional, but got ndim=%d.",
            ndim);
        *n = -1;
        Py_DECREF(result_array);
        return -1;
    }

    dims = PyArray_DIMS(result_array);
    dim_error = 0;
    if (ndim == 0) {
        if ((nrows != 1) || (ncols != 1)) {
            dim_error = 1;
        }
    }
    if (ndim == 1) {
        if ((nrows != 1) || (dims[0] != ncols)) {
            dim_error = 1;
        }
    }
    if (ndim == 2) {
        if ((dims[0] != nrows) || (dims[1] != ncols)) {
            dim_error = 1;
        }
    }
    if (dim_error) {
        char *b = "";
        if (global_params.jac_type == 4) {
            b = "banded ";
        }
        PyErr_Format(PyExc_RuntimeError,
            "Expected a %sJacobian array with shape (%d, %d)",
            b, nrows, ncols);
        *n = -1;
        Py_DECREF(result_array);
        return -1;
    }

    /*
     *  global_params.jac_type is either 1 (full Jacobian) or 4 (banded Jacobian).
     *  global_params.jac_transpose is !col_deriv, so if global_params.jac_transpose
     *  is 0, the array created by the user is already in Fortran order, and
     *  a transpose is not needed when it is copied to pd.
     */

    if ((global_params.jac_type == 1) && !global_params.jac_transpose) {
        /* Full Jacobian, no transpose needed, so we can use memcpy. */
        memcpy(pd, PyArray_DATA(result_array), (*n)*(*nrowpd)*sizeof(double));
    }
    else {
        /*
         *  global_params.jac_type == 4 (banded Jacobian), or
         *  global_params.jac_type == 1 and global_params.jac_transpose == 1.
         *
         *  We can't use memcpy when global_params.jac_type is 4 because the leading
         *  dimension of pd doesn't necessarily equal the number of rows of the
         *  matrix.
         */
        int m;  /* Number of rows in the (full or packed banded) Jacobian. */
        if (global_params.jac_type == 4) {
            m = *ml + *mu + 1;
        }
        else {
            m = *n;
        }
        copy_array_to_fortran(pd, *nrowpd, m, *n,
            (double *) PyArray_DATA(result_array),
            !global_params.jac_transpose);
    }

    Py_DECREF(result_array);
    return 0;
}


int
setup_extra_inputs(PyArrayObject **ap_rtol, PyObject *o_rtol,
                   PyArrayObject **ap_atol, PyObject *o_atol,
                   PyArrayObject **ap_tcrit, PyObject *o_tcrit,
                   int *numcrit, int neq)
{
    int itol = 0;
    double tol = 1.49012e-8;
    npy_intp one = 1;

    /* Setup tolerances */
    if (o_rtol == NULL) {
        *ap_rtol = (PyArrayObject *) PyArray_SimpleNew(1, &one, NPY_DOUBLE);
        if (*ap_rtol == NULL) {
            PYERR2(odepack_error,"Error constructing relative tolerance.");
        }
        *(double *) PyArray_DATA(*ap_rtol) = tol;                /* Default */
    }
    else {
        *ap_rtol = (PyArrayObject *) PyArray_ContiguousFromObject(o_rtol,
                                                            NPY_DOUBLE, 0, 1);
        if (*ap_rtol == NULL) {
            PYERR2(odepack_error,"Error converting relative tolerance.");
        }
        /* XXX Fix the following. */
        if (PyArray_NDIM(*ap_rtol) == 0); /* rtol is scalar */
        else if (PyArray_DIMS(*ap_rtol)[0] == neq) {
            itol |= 2;      /* Set rtol array flag */
        }
        else {
            PYERR(odepack_error, "Tolerances must be an array of the same length as the\n     number of equations or a scalar.");
        }
    }

    if (o_atol == NULL) {
        *ap_atol = (PyArrayObject *) PyArray_SimpleNew(1, &one, NPY_DOUBLE);
        if (*ap_atol == NULL) {
            PYERR2(odepack_error,"Error constructing absolute tolerance");
        }
        *(double *)PyArray_DATA(*ap_atol) = tol;
    }
    else {
        *ap_atol = (PyArrayObject *) PyArray_ContiguousFromObject(o_atol, NPY_DOUBLE, 0, 1);
        if (*ap_atol == NULL) {
            PYERR2(odepack_error,"Error converting absolute tolerance.");
        }
        /* XXX Fix the following. */
        if (PyArray_NDIM(*ap_atol) == 0); /* atol is scalar */
        else if (PyArray_DIMS(*ap_atol)[0] == neq) {
            itol |= 1;        /* Set atol array flag */
        }
        else {
            PYERR(odepack_error,"Tolerances must be an array of the same length as the\n     number of equations or a scalar.");
        }
    }
    itol++;             /* increment to get correct value */

    /* Setup t-critical */
    if (o_tcrit != NULL) {
        *ap_tcrit = (PyArrayObject *) PyArray_ContiguousFromObject(o_tcrit, NPY_DOUBLE, 0, 1);
        if (*ap_tcrit == NULL) {
            PYERR2(odepack_error,"Error constructing critical times.");
        }
        *numcrit = PyArray_Size((PyObject *) (*ap_tcrit));
    }
    return itol;

fail:       /* Needed for use of PYERR */
    return -1;
}


int
compute_lrw_liw(int *lrw, int *liw, int neq, int jt, int ml, int mu,
                int mxordn, int mxords)
{
    int lrn, lrs, nyh, lmat;

    if (jt == 1 || jt == 2) {
        lmat = neq*neq + 2;
    }
    else if (jt == 4 || jt == 5) {
        lmat = (2*ml + mu + 1)*neq + 2;
    }
    else {
        PYERR(odepack_error,"Incorrect value for jt");
    }

    if (mxordn < 0) {
        PYERR(odepack_error,"Incorrect value for mxordn");
    }
    if (mxords < 0) {
        PYERR(odepack_error,"Incorrect value for mxords");
    }
    nyh = neq;

    lrn = 20 + nyh*(mxordn+1) + 3*neq;
    lrs = 20 + nyh*(mxords+1) + 3*neq + lmat;

    *lrw = PyArray_MAX(lrn,lrs);
    *liw = 20 + neq;
    return 0;

fail:
    return -1;
}

static char doc_odeint[] =
    "[y,{infodict,}istate] = odeint(fun, y0, t, args=(), Dfun=None, "
    "col_deriv=0, ml=, mu=, full_output=0, rtol=, atol=, tcrit=, h0=0.0, "
    "hmax=0.0, hmin=0.0, ixpr=0.0, mxstep=0.0, mxhnil=0, mxordn=0, "
    "mxords=0)\n  yprime = fun(y,t,...)";


static PyObject *
odepack_odeint(PyObject *dummy, PyObject *args, PyObject *kwdict)
{
    PyObject *fcn, *y0, *p_tout, *o_rtol = NULL, *o_atol = NULL;
    PyArrayObject *ap_y = NULL, *ap_yout = NULL;
    PyArrayObject *ap_rtol = NULL, *ap_atol = NULL;
    PyArrayObject *ap_tout = NULL;
    PyObject *extra_args = NULL;
    PyObject *Dfun = Py_None;
    int neq, itol = 1, itask = 1, istate = 1, iopt = 0, lrw, *iwork, liw, jt = 4;
    double *y, t, *tout, *rtol, *atol, *rwork;
    double h0 = 0.0, hmax = 0.0, hmin = 0.0;
    int ixpr = 0, mxstep = 0, mxhnil = 0, mxordn = 12, mxords = 5, ml = -1, mu = -1;
    int tfirst;
    PyObject *o_tcrit = NULL;
    PyArrayObject *ap_tcrit = NULL;
    PyArrayObject *ap_hu = NULL, *ap_tcur = NULL, *ap_tolsf = NULL, *ap_tsw = NULL;
    PyArrayObject *ap_nst = NULL, *ap_nfe = NULL, *ap_nje = NULL, *ap_nqu = NULL;
    PyArrayObject *ap_mused = NULL;
    int imxer = 0, lenrw = 0, leniw = 0, col_deriv = 0;
    npy_intp out_sz = 0, dims[2];
    int k, ntimes, crit_ind = 0;
    int allocated = 0, full_output = 0, numcrit = 0;
    int t0count;
    double *yout, *yout_ptr, *tout_ptr, *tcrit;
    double *wa;
    static char *kwlist[] = {"fun", "y0", "t", "args", "Dfun", "col_deriv",
                             "ml", "mu", "full_output", "rtol", "atol", "tcrit",
                             "h0", "hmax", "hmin", "ixpr", "mxstep", "mxhnil",
                             "mxordn", "mxords", "tfirst", NULL};
    odepack_params save_params;

    if (!PyArg_ParseTupleAndKeywords(args, kwdict, "OOO|OOiiiiOOOdddiiiiii", kwlist,
                                     &fcn, &y0, &p_tout, &extra_args, &Dfun,
                                     &col_deriv, &ml, &mu, &full_output, &o_rtol, &o_atol,
                                     &o_tcrit, &h0, &hmax, &hmin, &ixpr, &mxstep, &mxhnil,
                                     &mxordn, &mxords, &tfirst)) {
        return NULL;
    }

    if (o_tcrit == Py_None) {
        o_tcrit = NULL;
    }
    if (o_rtol == Py_None) {
        o_rtol = NULL;
    }
    if (o_atol == Py_None) {
        o_atol = NULL;
    }

    /* Set up jt, ml, and mu */
    if (Dfun == Py_None) {
        /* set jt for internally generated */
        jt++;
    }
    if (ml < 0 && mu < 0) {
        /* neither ml nor mu given, mark jt for full jacobian */
        jt -= 3;
    }
    if (ml < 0) {
        /* if one but not both are given */
        ml = 0;
    }
    if (mu < 0) {
        mu = 0;
    }

    /* Stash the current global_params in save_params. */
    memcpy(&save_params, &global_params, sizeof(save_params));

    if (extra_args == NULL) {
        if ((extra_args = PyTuple_New(0)) == NULL) {
            goto fail;
        }
    }
    else {
        Py_INCREF(extra_args);   /* We decrement on exit. */
    }
    if (!PyTuple_Check(extra_args)) {
        PYERR(odepack_error, "Extra arguments must be in a tuple");
    }
    if (!PyCallable_Check(fcn) || (Dfun != Py_None && !PyCallable_Check(Dfun))) {
        PYERR(odepack_error, "The function and its Jacobian must be callable functions.");
    }

    /* Set global_params from the function arguments. */
    global_params.python_function = fcn;
    global_params.extra_arguments = extra_args;
    global_params.python_jacobian = Dfun;
    global_params.jac_transpose = !(col_deriv);
    global_params.jac_type = jt;
    global_params.tfirst = tfirst;

    /* Initial input vector */
    ap_y = (PyArrayObject *) PyArray_ContiguousFromObject(y0, NPY_DOUBLE, 0, 0);
    if (ap_y == NULL) {
        goto fail;
    }
    if (PyArray_NDIM(ap_y) > 1) {
        PyErr_SetString(PyExc_ValueError, "Initial condition y0 must be one-dimensional.");
        goto fail;
    }
    y = (double *) PyArray_DATA(ap_y);
    neq = PyArray_Size((PyObject *) ap_y);
    dims[1] = neq;

    /* Set of output times for integration */
    ap_tout = (PyArrayObject *) PyArray_ContiguousFromObject(p_tout, NPY_DOUBLE, 0, 0);
    if (ap_tout == NULL) {
        goto fail;
    }
    if (PyArray_NDIM(ap_tout) > 1) {
        PyErr_SetString(PyExc_ValueError, "Output times t must be one-dimensional.");
        goto fail;
    }
    tout = (double *) PyArray_DATA(ap_tout);
    ntimes = PyArray_Size((PyObject *)ap_tout);
    dims[0] = ntimes;

    t0count = 0;
    if (ntimes > 0) {
        /* Copy tout[0] to t, and count how many times it occurs. */
        t = tout[0];
        t0count = 1;
        while ((t0count < ntimes) && (tout[t0count] == t)) {
            ++t0count;
        }
    }

    /* Setup array to hold the output evaluations*/
    ap_yout= (PyArrayObject *) PyArray_SimpleNew(2,dims,NPY_DOUBLE);
    if (ap_yout== NULL) {
        goto fail;
    }
    yout = (double *) PyArray_DATA(ap_yout);

    /* Copy initial vector into first row(s) of output */
    yout_ptr = yout;
    for (k = 0; k < t0count; ++k) {
        memcpy(yout_ptr, y, neq*sizeof(double));
        yout_ptr += neq;
    }

    itol = setup_extra_inputs(&ap_rtol, o_rtol, &ap_atol, o_atol, &ap_tcrit,
                              o_tcrit, &numcrit, neq);
    if (itol < 0 ) {
        goto fail;  /* Something didn't work */
    }
    rtol = (double *) PyArray_DATA(ap_rtol);
    atol = (double *) PyArray_DATA(ap_atol);
    if (o_tcrit != NULL) {
        tcrit = (double *)(PyArray_DATA(ap_tcrit));
    }

    /* Find size of working arrays*/
    if (compute_lrw_liw(&lrw, &liw, neq, jt, ml, mu, mxordn, mxords) < 0) {
        goto fail;
    }

    if ((wa = (double *)malloc(lrw*sizeof(double) + liw*sizeof(int)))==NULL) {
        PyErr_NoMemory();
        goto fail;
    }
    allocated = 1;
    rwork = wa;
    iwork = (int *)(wa + lrw);

    iwork[0] = ml;
    iwork[1] = mu;

    if (h0 != 0.0 || hmax != 0.0 || hmin != 0.0 || ixpr != 0 || mxstep != 0 ||
            mxhnil != 0 || mxordn != 0 || mxords != 0) {
        rwork[4] = h0;
        rwork[5] = hmax;
        rwork[6] = hmin;
        iwork[4] = ixpr;
        iwork[5] = mxstep;
        iwork[6] = mxhnil;
        iwork[7] = mxordn;
        iwork[8] = mxords;
        iopt = 1;
    }
    istate = 1;
    k = t0count;

    /* If full output make some useful output arrays */
    if (full_output) {
        out_sz = ntimes-1;
        ap_hu = (PyArrayObject *) PyArray_SimpleNew(1, &out_sz, NPY_DOUBLE);
        ap_tcur = (PyArrayObject *) PyArray_SimpleNew(1, &out_sz, NPY_DOUBLE);
        ap_tolsf = (PyArrayObject *) PyArray_SimpleNew(1, &out_sz, NPY_DOUBLE);
        ap_tsw = (PyArrayObject *) PyArray_SimpleNew(1, &out_sz, NPY_DOUBLE);
        ap_nst = (PyArrayObject *) PyArray_SimpleNew(1, &out_sz, NPY_INT);
        ap_nfe = (PyArrayObject *) PyArray_SimpleNew(1, &out_sz, NPY_INT);
        ap_nje = (PyArrayObject *) PyArray_SimpleNew(1, &out_sz, NPY_INT);
        ap_nqu = (PyArrayObject *) PyArray_SimpleNew(1, &out_sz, NPY_INT);
        ap_mused = (PyArrayObject *) PyArray_SimpleNew(1, &out_sz, NPY_INT);
        if (ap_hu == NULL || ap_tcur == NULL || ap_tolsf == NULL ||
                ap_tsw == NULL || ap_nst == NULL || ap_nfe == NULL ||
                ap_nje == NULL || ap_nqu == NULL || ap_mused == NULL) {
            goto fail;
        }
    }

    if (o_tcrit != NULL) {
        /* There are critical points */
        itask = 4;
        rwork[0] = *tcrit;
    }
    while (k < ntimes && istate > 0) {    /* loop over desired times */

        tout_ptr = tout + k;
        /* Use tcrit if relevant */
        if (itask == 4 && *tout_ptr > *(tcrit + crit_ind)) {
            crit_ind++;
            rwork[0] = *(tcrit+crit_ind);
        }
        if (crit_ind >= numcrit) {
            itask = 1;  /* No more critical values */
        }

        LSODA(ode_function, &neq, y, &t, tout_ptr, &itol, rtol, atol, &itask,
              &istate, &iopt, rwork, &lrw, iwork, &liw,
              ode_jacobian_function, &jt);
        if (full_output) {
            *((double *)PyArray_DATA(ap_hu) + (k-1)) = rwork[10];
            *((double *)PyArray_DATA(ap_tcur) + (k-1)) = rwork[12];
            *((double *)PyArray_DATA(ap_tolsf) + (k-1)) = rwork[13];
            *((double *)PyArray_DATA(ap_tsw) + (k-1)) = rwork[14];
            *((int *)PyArray_DATA(ap_nst) + (k-1)) = iwork[10];
            *((int *)PyArray_DATA(ap_nfe) + (k-1)) = iwork[11];
            *((int *)PyArray_DATA(ap_nje) + (k-1)) = iwork[12];
            *((int *)PyArray_DATA(ap_nqu) + (k-1)) = iwork[13];
            if (istate == -5 || istate == -4) {
                imxer = iwork[15];
            }
            else {
                imxer = -1;
            }
            lenrw = iwork[16];
            leniw = iwork[17];
            *((int *)PyArray_DATA(ap_mused) + (k-1)) = iwork[18];
        }
        if (PyErr_Occurred()) {
            goto fail;
        }
        memcpy(yout_ptr, y, neq*sizeof(double));  /* copy integration result to output*/
        yout_ptr += neq;
        k++;
    }

    /* Restore global_params from the previously stashed save_params. */
    memcpy(&global_params, &save_params, sizeof(save_params));

    Py_DECREF(extra_args);
    Py_DECREF(ap_atol);
    Py_DECREF(ap_rtol);
    Py_XDECREF(ap_tcrit);
    Py_DECREF(ap_y);
    Py_DECREF(ap_tout);
    free(wa);

    /* Do Full output */
    if (full_output) {
        return Py_BuildValue("N{s:N,s:N,s:N,s:N,s:N,s:N,s:N,s:N,s:i,s:i,s:i,s:N}i",
                    PyArray_Return(ap_yout),
                    "hu", PyArray_Return(ap_hu),
                    "tcur", PyArray_Return(ap_tcur),
                    "tolsf", PyArray_Return(ap_tolsf),
                    "tsw", PyArray_Return(ap_tsw),
                    "nst", PyArray_Return(ap_nst),
                    "nfe", PyArray_Return(ap_nfe),
                    "nje", PyArray_Return(ap_nje),
                    "nqu", PyArray_Return(ap_nqu),
                    "imxer", imxer,
                    "lenrw", lenrw,
                    "leniw", leniw,
                    "mused", PyArray_Return(ap_mused),
                    istate);
    }
    else {
        return Py_BuildValue("Ni", PyArray_Return(ap_yout), istate);
    }

fail:
    /* Restore global_params from the previously stashed save_params. */
    memcpy(&global_params, &save_params, sizeof(save_params));

    Py_XDECREF(extra_args);
    Py_XDECREF(ap_y);
    Py_XDECREF(ap_rtol);
    Py_XDECREF(ap_atol);
    Py_XDECREF(ap_tcrit);
    Py_XDECREF(ap_tout);
    Py_XDECREF(ap_yout);
    if (allocated) {
        free(wa);
    }
    if (full_output) {
        Py_XDECREF(ap_hu);
        Py_XDECREF(ap_tcur);
        Py_XDECREF(ap_tolsf);
        Py_XDECREF(ap_tsw);
        Py_XDECREF(ap_nst);
        Py_XDECREF(ap_nfe);
        Py_XDECREF(ap_nje);
        Py_XDECREF(ap_nqu);
        Py_XDECREF(ap_mused);
    }
    return NULL;
}


static struct PyMethodDef odepack_module_methods[] = {
    {"odeint", (PyCFunction) odepack_odeint, METH_VARARGS|METH_KEYWORDS, doc_odeint},
    {NULL, NULL, 0, NULL}
};

#if PY_VERSION_HEX >= 0x03000000
static struct PyModuleDef moduledef = {
    PyModuleDef_HEAD_INIT,
    "_odepack",
    NULL,
    -1,
    odepack_module_methods,
    NULL,
    NULL,
    NULL,
    NULL
};

PyObject *
PyInit__odepack(void)
{
    PyObject *m, *d, *s;

    m = PyModule_Create(&moduledef);
    import_array();
    d = PyModule_GetDict(m);

    s = PyUString_FromString(" 1.9 ");
    PyDict_SetItemString(d, "__version__", s);
    odepack_error = PyErr_NewException ("odepack.error", NULL, NULL);
    Py_DECREF(s);
    PyDict_SetItemString(d, "error", odepack_error);
    if (PyErr_Occurred()) {
        Py_FatalError("can't initialize module odepack");
    }
    return m;
}
#else
PyMODINIT_FUNC init_odepack(void)
{
    PyObject *m, *d, *s;
    m = Py_InitModule("_odepack", odepack_module_methods);
    import_array();
    d = PyModule_GetDict(m);

    s = PyUString_FromString(" 1.9 ");
    PyDict_SetItemString(d, "__version__", s);
    odepack_error = PyErr_NewException ("odepack.error", NULL, NULL);
    Py_DECREF(s);
    if (PyErr_Occurred()) {
        Py_FatalError("can't initialize module odepack");
    }
}
#endif