func main() {
mpi.Start(false)
defer func() {
mpi.Stop(false)
}()
if mpi.Rank() == 0 {
chk.PrintTitle("ode02: Hairer-Wanner VII-p5 Eq.(1.5) Van der Pol's Equation")
}
if mpi.Size() != 2 {
chk.Panic(">> error: this test requires 2 MPI processors\n")
return
}
eps := 1.0e-6
w := make([]float64, 2) // workspace
fcn := func(f []float64, dx, x float64, y []float64, args ...interface{}) error {
f[0], f[1] = 0, 0
switch mpi.Rank() {
case 0:
f[0] = y[1]
case 1:
f[1] = ((1.0-y[0]*y[0])*y[1] - y[0]) / eps
}
// join all f
mpi.AllReduceSum(f, w)
return nil
}
jac := func(dfdy *la.Triplet, dx, x float64, y []float64, args ...interface{}) error {
if dfdy.Max() == 0 {
dfdy.Init(2, 2, 4)
}
dfdy.Start()
if false { // per column
switch mpi.Rank() {
case 0:
dfdy.Put(0, 0, 0.0)
dfdy.Put(1, 0, (-2.0*y[0]*y[1]-1.0)/eps)
case 1:
dfdy.Put(0, 1, 1.0)
dfdy.Put(1, 1, (1.0-y[0]*y[0])/eps)
}
} else { // per row
switch mpi.Rank() {
case 0:
dfdy.Put(0, 0, 0.0)
dfdy.Put(0, 1, 1.0)
case 1:
dfdy.Put(1, 0, (-2.0*y[0]*y[1]-1.0)/eps)
dfdy.Put(1, 1, (1.0-y[0]*y[0])/eps)
}
}
return nil
}
// method and flags
silent := false
fixstp := false
//method := "Dopri5"
method := "Radau5"
numjac := false
xa, xb := 0.0, 2.0
ya := []float64{2.0, -0.6}
ndim := len(ya)
// structure to hold numerical results
res := ode.Results{Method: method}
// allocate ODE object
var o ode.Solver
o.Distr = true
if numjac {
o.Init(method, ndim, fcn, nil, nil, ode.SimpleOutput, silent)
} else {
o.Init(method, ndim, fcn, jac, nil, ode.SimpleOutput, silent)
}
// tolerances and initial step size
rtol := 1e-4
atol := rtol
o.IniH = 1.0e-4
o.SetTol(atol, rtol)
//o.NmaxSS = 2
// solve problem
y := make([]float64, ndim)
copy(y, ya)
t0 := time.Now()
if fixstp {
o.Solve(y, xa, xb, 0.05, fixstp, &res)
} else {
o.Solve(y, xa, xb, xb-xa, fixstp, &res)
}
// plot
if mpi.Rank() == 0 {
io.Pfmag("elapsed time = %v\n", time.Now().Sub(t0))
plt.SetForEps(1.5, 400)
args := "'b-', marker='.', lw=1, ms=4, clip_on=0"
ode.Plot("/tmp/gosl/ode", "vdpolA_mpi.eps", &res, nil, xa, xb, "", args, func() {
_, T, err := io.ReadTable("data/vdpol_radau5_for.dat")
if err != nil {
chk.Panic("%v", err)
}
plt.Subplot(3, 1, 1)
plt.Plot(T["x"], T["y0"], "'k+',label='reference',ms=7")
plt.Subplot(3, 1, 2)
plt.Plot(T["x"], T["y1"], "'k+',label='reference',ms=7")
})
}
}
