// Update updates pc and sl for given Δpc. An implicit ODE solver is used.
func Update(mdl Model, pc0, sl0, Δpc float64) (slNew float64, err error) {
// wetting flag
wet := Δpc < 0
// callback functions
// x = [0.0, 1.0]
// pc = pc0 + x * Δpc
// y[0] = sl
// f(x,y) = dy/dx = dsl/dpc * dpc/dx = Cc * Δpc
// J(x,y) = df/dy = DCcDsl * Δpc
fcn := func(f []float64, x float64, y []float64, args ...interface{}) (e error) {
f[0], e = mdl.Cc(pc0+x*Δpc, y[0], wet)
f[0] *= Δpc
return nil
}
jac := func(dfdy *la.Triplet, x float64, y []float64, args ...interface{}) (e error) {
if dfdy.Max() == 0 {
dfdy.Init(1, 1, 1)
}
J, e := mdl.J(pc0+x*Δpc, y[0], wet)
dfdy.Start()
dfdy.Put(0, 0, J)
return
}
// ode solver
var odesol ode.ODE
odesol.Init("Radau5", 1, fcn, jac, nil, nil, true)
odesol.SetTol(1e-10, 1e-7)
odesol.Distr = false // this is important to avoid problems with MPI runs
// solve
y := []float64{sl0}
err = odesol.Solve(y, 0, 1, 1, false)
slNew = y[0]
return
}
func main() {
mpi.Start(false)
defer func() {
mpi.Stop(false)
}()
if mpi.Rank() == 0 {
chk.PrintTitle("Test ODE 02b")
io.Pfcyan("Hairer-Wanner VII-p5 Eq.(1.5) Van der Pol's Equation (MPI)\n")
}
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, 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, 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
}
// data
silent := false
fixstp := false
//method := "Dopri5"
method := "Radau5"
xa, xb := 0.0, 2.0
ya := []float64{2.0, -0.6}
ndim := len(ya)
// output
var b bytes.Buffer
out := func(first bool, dx, x float64, y []float64, args ...interface{}) error {
if mpi.Rank() == 0 {
if first {
fmt.Fprintf(&b, "%23s %23s %23s %23s\n", "dx", "x", "y0", "y1")
}
fmt.Fprintf(&b, "%23.15E %23.15E %23.15E %23.15E\n", dx, x, y[0], y[1])
}
return nil
}
defer func() {
if mpi.Rank() == 0 {
extra := "d2 = Read('data/vdpol_radau5_for.dat')\n" +
"subplot(3,1,1)\n" +
"plot(d2['x'],d2['y0'],'k+',label='res',ms=10)\n" +
"subplot(3,1,2)\n" +
"plot(d2['x'],d2['y1'],'k+',label='res',ms=10)\n"
ode.Plot("/tmp/gosl", "vdpolB", method, &b, []int{0, 1}, ndim, nil, xa, xb, true, false, extra)
}
}()
// one run
var o ode.ODE
o.Distr = true
//numjac := true
numjac := false
if numjac {
o.Init(method, ndim, fcn, nil, nil, out, silent)
} else {
o.Init(method, ndim, fcn, jac, nil, out, silent)
}
// tolerances and initial step size
rtol := 1e-4
atol := rtol
o.SetTol(atol, rtol)
o.IniH = 1.0e-4
//o.NmaxSS = 2
y := make([]float64, ndim)
copy(y, ya)
t0 := time.Now()
if fixstp {
o.Solve(y, xa, xb, 0.05, fixstp)
} else {
o.Solve(y, xa, xb, xb-xa, fixstp)
}
if mpi.Rank() == 0 {
io.Pfmag("elapsed time = %v\n", time.Now().Sub(t0))
}
}