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))
}
}
func TestDiffusion1D(tst *testing.T) {
//verbose()
chk.PrintTitle("Test Diffusion 1D (cooling)")
// solution parameters
silent := false
fixstp := true
//fixstp := false
//method := "FwEuler"
method := "BwEuler"
//method := "Dopri5"
//method := "Radau5"
//numjac := true
numjac := false
rtol := 1e-4
atol := rtol
// timestep
t0, tf, dt := 0.0, 0.2, 0.03
// problem data
kx := 1.0 // conductivity
N := 6 // number of nodes
//Nb := N + 2 // augmented system dimension
xmax := 1.0 // length
dx := xmax / float64(N-1) // spatial step size
dxx := dx * dx
mol := []float64{kx / dxx, -2.0 * kx / dxx, kx / dxx}
// function
fcn := func(f []float64, t float64, y []float64, args ...interface{}) error {
for i := 0; i < N; i++ {
f[i] = 0
if i == 0 || i == N-1 {
continue // skip presc node
}
for p, j := range []int{i - 1, i, i + 1} {
if j < 0 {
j = i + 1
} // left boundary
if j == N {
j = i - 1
} // right boundary
f[i] += mol[p] * y[j]
}
}
//io.Pfgrey("y = %v\n", y)
//io.Pfcyan("f = %v\n", f)
return nil
}
// Jacobian
jac := func(dfdy *la.Triplet, t float64, y []float64, args ...interface{}) error {
//chk.Panic("jac is not available")
if dfdy.Max() == 0 {
//dfdy.Init(Nb, Nb, 3*N)
dfdy.Init(N, N, 3*N)
}
dfdy.Start()
for i := 0; i < N; i++ {
if i == 0 || i == N-1 {
dfdy.Put(i, i, 0.0)
continue
}
for p, j := range []int{i - 1, i, i + 1} {
if j < 0 {
j = i + 1
} // left boundary
if j == N {
j = i - 1
} // right boundary
dfdy.Put(i, j, mol[p])
}
}
return nil
}
// initial values
x := utl.LinSpace(0.0, xmax, N)
y := make([]float64, N)
//y := make([]float64, Nb)
for i := 0; i < N; i++ {
y[i] = 4.0*x[i] - 4.0*x[i]*x[i]
}
// debug
f0 := make([]float64, N)
//f0 := make([]float64, Nb)
fcn(f0, 0, y)
if false {
io.Pforan("y0 = %v\n", y)
io.Pforan("f0 = %v\n", f0)
var J la.Triplet
jac(&J, 0, y)
la.PrintMat("J", J.ToMatrix(nil).ToDense(), "%8.3f", false)
}
//chk.Panic("stop")
/*
// constraints
var A la.Triplet
A.Init(2, N, 2)
A.Put(0, 0, 1.0)
A.Put(1, N-1, 1.0)
io.Pfcyan("A = %+v\n", A)
Am := A.ToMatrix(nil)
c := make([]float64, 2)
la.SpMatVecMul(c, 1, Am, y) // c := Am*y
la.PrintMat("A", Am.ToDense(), "%3g", false)
io.Pfcyan("c = %v ([0, 0] => consistent)\n", c)
*/
/*
// mass matrix
var M la.Triplet
M.Init(Nb, Nb, N + 4)
for i := 0; i < N; i++ {
M.Put(i, i, 1.0)
}
M.PutMatAndMatT(&A)
Mm := M.ToMatrix(nil)
la.PrintMat("M", Mm.ToDense(), "%3g", false)
*/
// output
var b0, b1, b2 bytes.Buffer
fmt.Fprintf(&b0, "from gosl import *\n")
fmt.Fprintf(&b1, "T = array([")
fmt.Fprintf(&b2, "U = array([")
out := func(first bool, dt, t float64, y []float64, args ...interface{}) error {
fmt.Fprintf(&b1, "%23.15E,", t)
fmt.Fprintf(&b2, "[")
for i := 0; i < N; i++ {
fmt.Fprintf(&b2, "%23.15E,", y[i])
}
fmt.Fprintf(&b2, "],")
return nil
}
defer func() {
fmt.Fprintf(&b1, "])\n")
fmt.Fprintf(&b2, "])\n")
fmt.Fprintf(&b2, "X = linspace(0.0, %g, %d)\n", xmax, N)
fmt.Fprintf(&b2, "tt, xx = meshgrid(T, X)\n")
fmt.Fprintf(&b2, "ax = PlotSurf(tt, xx, vstack(transpose(U)), 't', 'x', 'u', 0.0, 1.0)\n")
fmt.Fprintf(&b2, "ax.view_init(20.0, 30.0)\n")
fmt.Fprintf(&b2, "show()\n")
io.WriteFileD("/tmp/gosl", "plot_diffusion_1d.py", &b0, &b1, &b2)
}()
// ode solver
var Jfcn Cb_jac
var osol ODE
if !numjac {
Jfcn = jac
}
osol.Init(method, N, fcn, Jfcn, nil, out, silent)
//osol.Init(method, Nb, fcn, Jfcn, &M, out, silent)
osol.SetTol(atol, rtol)
// constant Jacobian
if method == "BwEuler" {
osol.CteTg = true
osol.Verbose = true
}
// run
wallt0 := time.Now()
if !fixstp {
dt = tf - t0
}
osol.Solve(y, t0, tf, dt, fixstp)
io.Pfmag("elapsed time = %v\n", time.Now().Sub(wallt0))
}
func main() {
mpi.Start(false)
defer func() {
mpi.Stop(false)
}()
if mpi.Rank() == 0 {
chk.PrintTitle("Test ODE 04b (MPI)")
io.Pfcyan("Hairer-Wanner VII-p376 Transistor Amplifier (MPI)\n")
io.Pfcyan("(from E Hairer's website, not the system in the book)\n")
}
if mpi.Size() != 3 {
chk.Panic(">> error: this test requires 3 MPI processors\n")
return
}
// RIGHT-HAND SIDE OF THE AMPLIFIER PROBLEM
w := make([]float64, 8) // workspace
fcn := func(f []float64, x float64, y []float64, args ...interface{}) error {
d := args[0].(*HWtransData)
UET := d.UE * math.Sin(d.W*x)
FAC1 := d.BETA * (math.Exp((y[3]-y[2])/d.UF) - 1.0)
FAC2 := d.BETA * (math.Exp((y[6]-y[5])/d.UF) - 1.0)
la.VecFill(f, 0)
switch mpi.Rank() {
case 0:
f[0] = y[0] / d.R9
case 1:
f[1] = (y[1]-d.UB)/d.R8 + d.ALPHA*FAC1
f[2] = y[2]/d.R7 - FAC1
case 2:
f[3] = y[3]/d.R5 + (y[3]-d.UB)/d.R6 + (1.0-d.ALPHA)*FAC1
f[4] = (y[4]-d.UB)/d.R4 + d.ALPHA*FAC2
f[5] = y[5]/d.R3 - FAC2
f[6] = y[6]/d.R1 + (y[6]-d.UB)/d.R2 + (1.0-d.ALPHA)*FAC2
f[7] = (y[7] - UET) / d.R0
}
mpi.AllReduceSum(f, w)
return nil
}
// JACOBIAN OF THE AMPLIFIER PROBLEM
jac := func(dfdy *la.Triplet, x float64, y []float64, args ...interface{}) error {
d := args[0].(*HWtransData)
FAC14 := d.BETA * math.Exp((y[3]-y[2])/d.UF) / d.UF
FAC27 := d.BETA * math.Exp((y[6]-y[5])/d.UF) / d.UF
if dfdy.Max() == 0 {
dfdy.Init(8, 8, 16)
}
NU := 2
dfdy.Start()
switch mpi.Rank() {
case 0:
dfdy.Put(2+0-NU, 0, 1.0/d.R9)
dfdy.Put(2+1-NU, 1, 1.0/d.R8)
dfdy.Put(1+2-NU, 2, -d.ALPHA*FAC14)
dfdy.Put(0+3-NU, 3, d.ALPHA*FAC14)
dfdy.Put(2+2-NU, 2, 1.0/d.R7+FAC14)
case 1:
dfdy.Put(1+3-NU, 3, -FAC14)
dfdy.Put(2+3-NU, 3, 1.0/d.R5+1.0/d.R6+(1.0-d.ALPHA)*FAC14)
dfdy.Put(3+2-NU, 2, -(1.0-d.ALPHA)*FAC14)
dfdy.Put(2+4-NU, 4, 1.0/d.R4)
dfdy.Put(1+5-NU, 5, -d.ALPHA*FAC27)
case 2:
dfdy.Put(0+6-NU, 6, d.ALPHA*FAC27)
dfdy.Put(2+5-NU, 5, 1.0/d.R3+FAC27)
dfdy.Put(1+6-NU, 6, -FAC27)
dfdy.Put(2+6-NU, 6, 1.0/d.R1+1.0/d.R2+(1.0-d.ALPHA)*FAC27)
dfdy.Put(3+5-NU, 5, -(1.0-d.ALPHA)*FAC27)
dfdy.Put(2+7-NU, 7, 1.0/d.R0)
}
return nil
}
// MATRIX "M"
c1, c2, c3, c4, c5 := 1.0e-6, 2.0e-6, 3.0e-6, 4.0e-6, 5.0e-6
var M la.Triplet
M.Init(8, 8, 14)
M.Start()
NU := 1
switch mpi.Rank() {
case 0:
M.Put(1+0-NU, 0, -c5)
M.Put(0+1-NU, 1, c5)
M.Put(2+0-NU, 0, c5)
M.Put(1+1-NU, 1, -c5)
M.Put(1+2-NU, 2, -c4)
M.Put(1+3-NU, 3, -c3)
case 1:
M.Put(0+4-NU, 4, c3)
M.Put(2+3-NU, 3, c3)
M.Put(1+4-NU, 4, -c3)
case 2:
M.Put(1+5-NU, 5, -c2)
M.Put(1+6-NU, 6, -c1)
M.Put(0+7-NU, 7, c1)
M.Put(2+6-NU, 6, c1)
M.Put(1+7-NU, 7, -c1)
}
// WRITE FILE FUNCTION
idxstp := 1
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, "%6s%23s%23s%23s%23s%23s%23s%23s%23s%23s\n", "ns", "x", "y0", "y1", "y2", "y3", "y4", "y5", "y6", "y7")
}
fmt.Fprintf(&b, "%6d%23.15E", idxstp, x)
for j := 0; j < len(y); j++ {
fmt.Fprintf(&b, "%23.15E", y[j])
}
fmt.Fprintf(&b, "\n")
idxstp += 1
}
return nil
}
defer func() {
if mpi.Rank() == 0 {
io.WriteFileD("/tmp/gosl", "hwamplifierB.res", &b)
}
}()
// INITIAL DATA
D, xa, xb, ya := HWtransIni()
// SET ODE SOLVER
silent := false
fixstp := false
//method := "Dopri5"
method := "Radau5"
ndim := len(ya)
//numjac := true
numjac := false
var osol ode.ODE
osol.Pll = true
if numjac {
osol.Init(method, ndim, fcn, nil, &M, out, silent)
} else {
osol.Init(method, ndim, fcn, jac, &M, out, silent)
}
osol.IniH = 1.0e-6 // initial step size
// SET TOLERANCES
atol, rtol := 1e-11, 1e-5
osol.SetTol(atol, rtol)
// RUN
t0 := time.Now()
if fixstp {
osol.Solve(ya, xa, xb, 0.01, fixstp, &D)
} else {
osol.Solve(ya, xa, xb, xb-xa, fixstp, &D)
}
if mpi.Rank() == 0 {
io.Pfmag("elapsed time = %v\n", time.Now().Sub(t0))
}
}
// Hairer-Wanner VII-p5 Eq.(1.5) Van der Pol's Equation
func TestODE02a(tst *testing.T) {
//verbose()
chk.PrintTitle("Test ODE 02a")
io.Pfcyan("Hairer-Wanner VII-p5 Eq.(1.5) Van der Pol's Equation\n")
eps := 1.0e-6
fcn := func(f []float64, x float64, y []float64, args ...interface{}) error {
f[0] = y[1]
f[1] = ((1.0-y[0]*y[0])*y[1] - y[0]) / eps
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()
dfdy.Put(0, 0, 0.0)
dfdy.Put(0, 1, 1.0)
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 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() {
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"
Plot("/tmp/gosl", "vdpolA", method, &b, []int{0, 1}, ndim, nil, xa, xb, true, false, extra)
}()
// one run
var o ODE
numjac := true
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)
}
io.Pfmag("elapsed time = %v\n", time.Now().Sub(t0))
}
func main() {
mpi.Start(false)
defer func() {
mpi.Stop(false)
}()
if mpi.Rank() == 0 {
chk.PrintTitle("ode04: Hairer-Wanner VII-p376 Transistor Amplifier\n")
}
if mpi.Size() != 3 {
chk.Panic(">> error: this test requires 3 MPI processors\n")
return
}
// data
UE, UB, UF, ALPHA, BETA := 0.1, 6.0, 0.026, 0.99, 1.0e-6
R0, R1, R2, R3, R4, R5 := 1000.0, 9000.0, 9000.0, 9000.0, 9000.0, 9000.0
R6, R7, R8, R9 := 9000.0, 9000.0, 9000.0, 9000.0
W := 2.0 * 3.141592654 * 100.0
// initial values
xa := 0.0
ya := []float64{0.0,
UB,
UB / (R6/R5 + 1.0),
UB / (R6/R5 + 1.0),
UB,
UB / (R2/R1 + 1.0),
UB / (R2/R1 + 1.0),
0.0}
// endpoint of integration
xb := 0.05
//xb = 0.0123 // OK
//xb = 0.01235 // !OK
// right-hand side of the amplifier problem
w := make([]float64, 8) // workspace
fcn := func(f []float64, dx, x float64, y []float64, args ...interface{}) error {
UET := UE * math.Sin(W*x)
FAC1 := BETA * (math.Exp((y[3]-y[2])/UF) - 1.0)
FAC2 := BETA * (math.Exp((y[6]-y[5])/UF) - 1.0)
la.VecFill(f, 0)
switch mpi.Rank() {
case 0:
f[0] = y[0] / R9
case 1:
f[1] = (y[1]-UB)/R8 + ALPHA*FAC1
f[2] = y[2]/R7 - FAC1
case 2:
f[3] = y[3]/R5 + (y[3]-UB)/R6 + (1.0-ALPHA)*FAC1
f[4] = (y[4]-UB)/R4 + ALPHA*FAC2
f[5] = y[5]/R3 - FAC2
f[6] = y[6]/R1 + (y[6]-UB)/R2 + (1.0-ALPHA)*FAC2
f[7] = (y[7] - UET) / R0
}
mpi.AllReduceSum(f, w)
return nil
}
// Jacobian of the amplifier problem
jac := func(dfdy *la.Triplet, dx, x float64, y []float64, args ...interface{}) error {
FAC14 := BETA * math.Exp((y[3]-y[2])/UF) / UF
FAC27 := BETA * math.Exp((y[6]-y[5])/UF) / UF
if dfdy.Max() == 0 {
dfdy.Init(8, 8, 16)
}
NU := 2
dfdy.Start()
switch mpi.Rank() {
case 0:
dfdy.Put(2+0-NU, 0, 1.0/R9)
dfdy.Put(2+1-NU, 1, 1.0/R8)
dfdy.Put(1+2-NU, 2, -ALPHA*FAC14)
dfdy.Put(0+3-NU, 3, ALPHA*FAC14)
dfdy.Put(2+2-NU, 2, 1.0/R7+FAC14)
case 1:
dfdy.Put(1+3-NU, 3, -FAC14)
dfdy.Put(2+3-NU, 3, 1.0/R5+1.0/R6+(1.0-ALPHA)*FAC14)
dfdy.Put(3+2-NU, 2, -(1.0-ALPHA)*FAC14)
dfdy.Put(2+4-NU, 4, 1.0/R4)
dfdy.Put(1+5-NU, 5, -ALPHA*FAC27)
case 2:
dfdy.Put(0+6-NU, 6, ALPHA*FAC27)
dfdy.Put(2+5-NU, 5, 1.0/R3+FAC27)
dfdy.Put(1+6-NU, 6, -FAC27)
dfdy.Put(2+6-NU, 6, 1.0/R1+1.0/R2+(1.0-ALPHA)*FAC27)
dfdy.Put(3+5-NU, 5, -(1.0-ALPHA)*FAC27)
dfdy.Put(2+7-NU, 7, 1.0/R0)
}
return nil
}
// matrix "M"
c1, c2, c3, c4, c5 := 1.0e-6, 2.0e-6, 3.0e-6, 4.0e-6, 5.0e-6
var M la.Triplet
M.Init(8, 8, 14)
M.Start()
NU := 1
switch mpi.Rank() {
case 0:
M.Put(1+0-NU, 0, -c5)
M.Put(0+1-NU, 1, c5)
M.Put(2+0-NU, 0, c5)
M.Put(1+1-NU, 1, -c5)
M.Put(1+2-NU, 2, -c4)
M.Put(1+3-NU, 3, -c3)
case 1:
M.Put(0+4-NU, 4, c3)
M.Put(2+3-NU, 3, c3)
M.Put(1+4-NU, 4, -c3)
case 2:
M.Put(1+5-NU, 5, -c2)
M.Put(1+6-NU, 6, -c1)
M.Put(0+7-NU, 7, c1)
M.Put(2+6-NU, 6, c1)
M.Put(1+7-NU, 7, -c1)
}
// flags
silent := false
fixstp := false
//method := "Dopri5"
method := "Radau5"
ndim := len(ya)
numjac := false
// structure to hold numerical results
res := ode.Results{Method: method}
// ODE solver
var osol ode.Solver
osol.Pll = true
// solve problem
if numjac {
osol.Init(method, ndim, fcn, nil, &M, ode.SimpleOutput, silent)
} else {
osol.Init(method, ndim, fcn, jac, &M, ode.SimpleOutput, silent)
}
osol.IniH = 1.0e-6 // initial step size
// set tolerances
atol, rtol := 1e-11, 1e-5
osol.SetTol(atol, rtol)
// run
t0 := time.Now()
if fixstp {
osol.Solve(ya, xa, xb, 0.01, fixstp, &res)
} else {
osol.Solve(ya, xa, xb, xb-xa, fixstp, &res)
}
// plot
if mpi.Rank() == 0 {
io.Pfmag("elapsed time = %v\n", time.Now().Sub(t0))
plt.SetForEps(2.0, 400)
args := "'b-', marker='.', lw=1, clip_on=0"
ode.Plot("/tmp/gosl/ode", "hwamplifier_mpi.eps", &res, nil, xa, xb, "", args, func() {
_, T, err := io.ReadTable("data/radau5_hwamplifier.dat")
if err != nil {
chk.Panic("%v", err)
}
for j := 0; j < ndim; j++ {
plt.Subplot(ndim+1, 1, j+1)
plt.Plot(T["x"], T[io.Sf("y%d", j)], "'k+',label='reference',ms=10")
}
})
}
}
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")
})
}
}
// Hairer-Wanner VII-p5 Eq.(1.5) Van der Pol's Equation
func Test_ode02(tst *testing.T) {
//verbose()
chk.PrintTitle("ode02: Hairer-Wanner VII-p5 Eq.(1.5) Van der Pol's Equation")
// problem definition
eps := 1.0e-6
fcn := func(f []float64, dx, x float64, y []float64, args ...interface{}) error {
f[0] = y[1]
f[1] = ((1.0-y[0]*y[0])*y[1] - y[0]) / eps
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()
dfdy.Put(0, 0, 0.0)
dfdy.Put(0, 1, 1.0)
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 := Results{Method: method}
// allocate ODE object
var o Solver
if numjac {
o.Init(method, ndim, fcn, nil, nil, SimpleOutput, silent)
} else {
o.Init(method, ndim, fcn, jac, nil, 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)
}
io.Pfmag("elapsed time = %v\n", time.Now().Sub(t0))
// plot
if chk.Verbose {
plt.SetForEps(1.5, 400)
args := "'b-', marker='.', lw=1, ms=4, clip_on=0"
Plot("/tmp/gosl/ode", "vdpolA.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")
})
}
}