// SolveC solves the linear Complex system A.x = b
// NOTES:
// 1) sum_b_to_root is a flag for MUMPS; it tells Solve to sum the values in 'b' arrays to the root processor
func (o *LinSolMumps) SolveC(xR, xC, bR, bC []float64, sum_b_to_root bool) (err error) {
// check
if !o.cmplx {
return chk.Err(_linsol_mumps_err11)
}
// start time
if o.ton {
o.tini = time.Now()
}
// message
if o.verb {
io.Pfgreen("\n . . . . . . . . . . . . . . LinSolMumps.SolveC . . . . . . . . . . . . . . . \n\n")
}
// MUMPS: set RHS in processor # 0
if sum_b_to_root {
mpi.SumToRoot(xR, bR)
mpi.SumToRoot(xC, bC)
// join complex values
if mpi.Rank() == 0 {
for i := 0; i < len(xR); i++ {
o.xRC[i*2], o.xRC[i*2+1] = xR[i], xC[i]
}
}
} else {
// join complex values
if mpi.Rank() == 0 {
for i := 0; i < len(xR); i++ {
o.xRC[i*2], o.xRC[i*2+1] = bR[i], bC[i]
}
}
}
// MUMPS: solve
o.mz.job = 3 // solution code
C.zmumps_c(&o.mz) // solve
if o.mz.info[1-1] < 0 {
return chk.Err(_linsol_mumps_err12, mumps_error(o.mz.info[1-1], o.mz.info[2-1]))
}
// MUMPS: split complex values
if mpi.Rank() == 0 {
for i := 0; i < len(xR); i++ {
xR[i], xC[i] = o.xRC[i*2], o.xRC[i*2+1]
}
}
// MUMPS: broadcast from root
mpi.BcastFromRoot(xR)
mpi.BcastFromRoot(xC)
// duration
if o.ton {
io.Pfcyan("%s: Time spent in LinSolMumps.Solve = %v\n", o.name, time.Now().Sub(o.tini))
}
return
}
func main() {
mpi.Start(false)
defer func() {
mpi.Stop(false)
}()
if mpi.Rank() == 0 {
io.PfYel("\nTest MPI 03\n")
}
if mpi.Size() != 3 {
chk.Panic("this test needs 3 processors")
}
x := []int{-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}
n := len(x)
id, sz := mpi.Rank(), mpi.Size()
start, endp1 := (id*n)/sz, ((id+1)*n)/sz
for i := start; i < endp1; i++ {
x[i] = i
}
//io.Pforan("x = %v\n", x)
// IntAllReduceMax
w := make([]int, n)
mpi.IntAllReduceMax(x, w)
var tst testing.T
chk.Ints(&tst, fmt.Sprintf("IntAllReduceMax: x @ proc # %d", id), x, []int{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10})
//io.Pfred("x = %v\n", x)
}
func main() {
// catch errors
defer func() {
if err := recover(); err != nil {
if mpi.Rank() == 0 {
chk.Verbose = true
for i := 8; i > 3; i-- {
chk.CallerInfo(i)
}
io.PfRed("ERROR: %v\n", err)
}
}
mpi.Stop(false)
}()
mpi.Start(false)
// default input parameters
// read input parameters
fnamepath, _ := io.ArgToFilename(0, "", ".sim", true)
verbose := io.ArgToBool(1, true)
erasePrev := io.ArgToBool(2, true)
saveSummary := io.ArgToBool(3, true)
allowParallel := io.ArgToBool(4, true)
alias := io.ArgToString(5, "")
// message
if mpi.Rank() == 0 && verbose {
io.PfWhite("\nGofem v3 -- Go Finite Element Method\n\n")
io.Pf("Copyright 2015 Dorival Pedroso and Raul Durand. All rights reserved.\n")
io.Pf("Use of this source code is governed by a BSD-style\n")
io.Pf("license that can be found in the LICENSE file.\n\n")
io.Pf("\n%v\n", io.ArgsTable(
"filename path", "fnamepath", fnamepath,
"show messages", "verbose", verbose,
"erase previous results", "erasePrev", erasePrev,
"save summary", "saveSummary", saveSummary,
"allow parallel run", "allowParallel", allowParallel,
"word to add to results", "alias", alias,
))
}
// profiling?
defer utl.DoProf(false)()
// analysis data
readSummary := false
analysis := fem.NewFEM(fnamepath, alias, erasePrev, saveSummary, readSummary, allowParallel, verbose, 0)
// run simulation
err := analysis.Run()
if err != nil {
chk.Panic("Run failed:\n%v", err)
}
}
func main() {
mpi.Start(false)
defer func() {
mpi.Stop(false)
}()
if mpi.Rank() == 0 {
chk.PrintTitle("Test SumToRoot 01")
}
M := [][]float64{
{1000, 1000, 1000, 1011, 1021, 1000},
{1000, 1000, 1000, 1012, 1022, 1000},
{1000, 1000, 1000, 1013, 1023, 1000},
{1011, 1012, 1013, 1000, 1000, 1000},
{1021, 1022, 1023, 1000, 1000, 1000},
{1000, 1000, 1000, 1000, 1000, 1000},
}
id, sz, m := mpi.Rank(), mpi.Size(), len(M)
start, endp1 := (id*m)/sz, ((id+1)*m)/sz
if sz > 6 {
chk.Panic("this test works with at most 6 processors")
}
var J la.Triplet
J.Init(m, m, m*m)
for i := start; i < endp1; i++ {
for j := 0; j < m; j++ {
J.Put(i, j, M[i][j])
}
}
la.PrintMat(fmt.Sprintf("J @ proc # %d", id), J.ToMatrix(nil).ToDense(), "%10.1f", false)
la.SpTriSumToRoot(&J)
var tst testing.T
if mpi.Rank() == 0 {
chk.Matrix(&tst, "J @ proc 0", 1.0e-17, J.ToMatrix(nil).ToDense(), [][]float64{
{1000, 1000, 1000, 1011, 1021, 1000},
{1000, 1000, 1000, 1012, 1022, 1000},
{1000, 1000, 1000, 1013, 1023, 1000},
{1011, 1012, 1013, 1000, 1000, 1000},
{1021, 1022, 1023, 1000, 1000, 1000},
{1000, 1000, 1000, 1000, 1000, 1000},
})
}
}
// SolveR solves the linear Real system A.x = b
// NOTES:
// 1) sum_b_to_root is a flag for MUMPS; it tells Solve to sum the values in 'b' arrays to the root processor
func (o *LinSolMumps) SolveR(xR, bR []float64, sum_b_to_root bool) (err error) {
// check
if !o.is_initialised {
return chk.Err("linear solver must be initialised first\n")
}
if o.cmplx {
return chk.Err(_linsol_mumps_err09)
}
// start time
if o.ton {
o.tini = time.Now()
}
// message
if o.verb {
io.Pfgreen("\n . . . . . . . . . . . . . . LinSolMumps.SolveR . . . . . . . . . . . . . . . \n\n")
}
// MUMPS: set RHS in processor # 0
if sum_b_to_root {
mpi.SumToRoot(xR, bR)
} else {
if mpi.Rank() == 0 {
copy(xR, bR) // x := b
}
}
// only proc # 0 needs the RHS
if mpi.Rank() == 0 {
o.m.rhs = (*C.double)(unsafe.Pointer(&xR[0]))
}
// MUMPS: solve
o.m.job = 3 // solution code
C.dmumps_c(&o.m) // solve
if o.m.info[1-1] < 0 {
return chk.Err(_linsol_mumps_err10, mumps_error(o.m.info[1-1], o.m.info[2-1]))
}
mpi.BcastFromRoot(xR) // broadcast from root
// duration
if o.ton {
io.Pfcyan("%s: Time spent in LinSolMumps.Solve = %v\n", o.name, time.Now().Sub(o.tini))
}
return
}
func main() {
mpi.Start(false)
defer func() {
mpi.Stop(false)
}()
if mpi.Rank() == 0 {
chk.PrintTitle("TestJacobian 02b (MPI)")
}
if mpi.Size() > 6 {
io.Pf("this tests works with 6 or less MPI processors\n")
return
}
ffcn := func(fx, x []float64) error {
fx[0] = 2.0*x[0] - x[1] + sin(x[2]) - cos(x[3]) - x[5]*x[5] - 1.0 // 0
fx[1] = -x[0] + 2.0*x[1] + cos(x[2]) - sin(x[3]) + x[5] - 1.0 // 1
fx[2] = x[0] + 3.0*x[1] + sin(x[3]) - cos(x[4]) - x[5]*x[5] - 1.0 // 2
fx[3] = 2.0*x[0] + 4.0*x[1] + cos(x[3]) - cos(x[4]) + x[5] - 1.0 // 3
fx[4] = x[0] + 5.0*x[1] - sin(x[2]) + sin(x[4]) - x[5]*x[5]*x[5] - 1.0 // 4
fx[5] = x[0] + 6.0*x[1] - cos(x[2]) + cos(x[4]) + x[5] - 1.0 // 5
return nil
}
Jfcn := func(dfdx *la.Triplet, x []float64) error {
dfdx.Start()
J := [][]float64{
{2.0, -1.0, cos(x[2]), sin(x[3]), 0.0, -2.0 * x[5]},
{-1.0, 2.0, -sin(x[2]), -cos(x[3]), 0.0, 1.0},
{1.0, 3.0, 0.0, cos(x[3]), sin(x[4]), -2.0 * x[5]},
{2.0, 4.0, 0.0, -sin(x[3]), sin(x[4]), 1.0},
{1.0, 5.0, -cos(x[2]), 0.0, cos(x[4]), -3.0 * x[5] * x[5]},
{1.0, 6.0, sin(x[2]), 0.0, -sin(x[4]), 1.0},
}
id, sz, ndim := mpi.Rank(), mpi.Size(), 6
start, endp1 := (id*ndim)/sz, ((id+1)*ndim)/sz
for col := 0; col < 6; col++ {
for row := start; row < endp1; row++ {
dfdx.Put(row, col, J[row][col])
}
}
//la.PrintMat(fmt.Sprintf("J @ %d",mpi.Rank()), dfdx.ToMatrix(nil).ToDense(), "%12.6f", false)
return nil
}
x := []float64{5.0, 5.0, pi, pi, pi, 5.0}
var tst testing.T
num.CompareJac(&tst, ffcn, Jfcn, x, 1e-6, true)
}
func main() {
mpi.Start(false)
defer func() {
mpi.Stop(false)
}()
myrank := mpi.Rank()
if myrank == 0 {
chk.PrintTitle("Test MUMPS Sol 05")
}
ndim := 10
id, sz := mpi.Rank(), mpi.Size()
start, endp1 := (id*ndim)/sz, ((id+1)*ndim)/sz
if mpi.Size() > ndim {
chk.Panic("the number of processors must be smaller than or equal to %d", ndim)
}
n := 10
b := make([]complex128, n)
x_correct := make([]complex128, n)
// Let exact solution = 1 + 0.5i
for i := 0; i < ndim; i++ {
x_correct[i] = complex(float64(i+1), float64(i+1)/10.0)
}
var t la.TripletC
t.Init(ndim, ndim, ndim, true)
// assemble a and b
for i := start; i < endp1; i++ {
// Some very fake diagonals. Should take exactly 20 GMRES steps
ar := 10.0 + float64(i)/(float64(ndim)/10.0)
ac := 10.0 - float64(i)/(float64(ndim)/10.0)
t.Put(i, i, ar, ac)
// Generate RHS to match exact solution
b[i] = complex(ar*real(x_correct[i])-ac*imag(x_correct[i]),
ar*imag(x_correct[i])+ac*real(x_correct[i]))
}
sum_b_to_root := true
la.RunMumpsTestC(&t, 1e-14, b, x_correct, sum_b_to_root)
}
func main() {
// catch errors
var tst testing.T
defer func() {
if mpi.Rank() == 0 {
if err := recover(); err != nil {
io.PfRed("ERROR: %v\n", err)
}
if tst.Failed() {
io.PfRed("test failed\n")
}
}
mpi.Stop(false)
}()
mpi.Start(false)
// start global variables and log
analysis := fem.NewFEM("data/bh16.sim", "", true, true, false, true, true, 0)
// run simulation
err := analysis.Run()
if err != nil {
tst.Error("Run failed\n")
return
}
// check
skipK := true
tolK := 1e-12
tolu := 1e-15
tols := 1e-12
fem.TestingCompareResultsU(&tst, "data/bh16.sim", "cmp/bh16.cmp", "", tolK, tolu, tols, skipK, true)
}
func main() {
// catch errors
var tst testing.T
defer func() {
if mpi.Rank() == 0 {
if err := recover(); err != nil {
io.PfRed("ERROR: %v\n", err)
}
if tst.Failed() {
io.PfRed("test failed\n")
}
}
mpi.Stop(false)
}()
mpi.Start(false)
// start global variables and log
analysis := fem.NewFEM("data/p01.sim", "", true, true, false, true, true, 0)
// run simulation
err := analysis.Run()
if err != nil {
tst.Error("Run failed\n")
return
}
}
func main() {
// catch errors
var tst testing.T
defer func() {
if mpi.Rank() == 0 {
if err := recover(); err != nil {
io.PfRed("ERROR: %v\n", err)
}
if tst.Failed() {
io.PfRed("test failed\n")
}
}
mpi.Stop(false)
}()
mpi.Start(false)
// start global variables and log
if !fem.Start("data/p01.sim", true, true) {
tst.Error("Start failed\n")
return
}
// make sure to flush log
defer fem.End()
// run simulation
if !fem.Run() {
tst.Error("Run failed\n")
return
}
}
func (o *Solver) init_mpi() {
if mpi.IsOn() {
o.root = (mpi.Rank() == 0)
if mpi.Size() > 1 {
o.Distr = true
}
}
}
func main() {
mpi.Start(false)
defer func() {
mpi.Stop(false)
}()
if mpi.Rank() == 0 {
chk.PrintTitle("TestJacobian 01b (MPI)")
}
if mpi.Size() != 2 {
io.Pf("this tests needs MPI 2 processors\n")
return
}
ffcn := func(fx, x []float64) error {
fx[0] = math.Pow(x[0], 3.0) + x[1] - 1.0
fx[1] = -x[0] + math.Pow(x[1], 3.0) + 1.0
return nil
}
Jfcn := func(dfdx *la.Triplet, x []float64) error {
dfdx.Start()
if false {
if mpi.Rank() == 0 {
dfdx.Put(0, 0, 3.0*x[0]*x[0])
dfdx.Put(1, 0, -1.0)
} else {
dfdx.Put(0, 1, 1.0)
dfdx.Put(1, 1, 3.0*x[1]*x[1])
}
} else {
if mpi.Rank() == 0 {
dfdx.Put(0, 0, 3.0*x[0]*x[0])
dfdx.Put(0, 1, 1.0)
} else {
dfdx.Put(1, 0, -1.0)
dfdx.Put(1, 1, 3.0*x[1]*x[1])
}
}
return nil
}
x := []float64{0.5, 0.5}
var tst testing.T
num.CompareJacMpi(&tst, ffcn, Jfcn, x, 1e-8, true)
}
func main() {
mpi.Start(false)
defer func() {
mpi.Stop(false)
}()
myrank := mpi.Rank()
if myrank == 0 {
chk.PrintTitle("Test MUMPS Sol 01a")
}
var t la.Triplet
switch mpi.Size() {
case 1:
t.Init(5, 5, 13)
t.Put(0, 0, 1.0)
t.Put(0, 0, 1.0)
t.Put(1, 0, 3.0)
t.Put(0, 1, 3.0)
t.Put(2, 1, -1.0)
t.Put(4, 1, 4.0)
t.Put(1, 2, 4.0)
t.Put(2, 2, -3.0)
t.Put(3, 2, 1.0)
t.Put(4, 2, 2.0)
t.Put(2, 3, 2.0)
t.Put(1, 4, 6.0)
t.Put(4, 4, 1.0)
case 2:
if myrank == 0 {
t.Init(5, 5, 6)
t.Put(0, 0, 1.0)
t.Put(0, 0, 1.0)
t.Put(1, 0, 3.0)
t.Put(0, 1, 3.0)
t.Put(2, 1, -1.0)
t.Put(4, 1, 4.0)
} else {
t.Init(5, 5, 7)
t.Put(1, 2, 4.0)
t.Put(2, 2, -3.0)
t.Put(3, 2, 1.0)
t.Put(4, 2, 2.0)
t.Put(2, 3, 2.0)
t.Put(1, 4, 6.0)
t.Put(4, 4, 1.0)
}
default:
chk.Panic("this test needs 1 or 2 procs")
}
b := []float64{8.0, 45.0, -3.0, 3.0, 19.0}
x_correct := []float64{1, 2, 3, 4, 5}
sum_b_to_root := false
la.RunMumpsTestR(&t, 1e-14, b, x_correct, sum_b_to_root)
}
func setslice(x []float64) {
switch mpi.Rank() {
case 0:
copy(x, []float64{0, 0, 0, 1, 1, 1, 2, 2, 2, 3, 3})
case 1:
copy(x, []float64{10, 10, 10, 20, 20, 20, 30, 30, 30, 40, 40})
case 2:
copy(x, []float64{100, 100, 100, 1000, 1000, 1000, 2000, 2000, 2000, 3000, 3000})
}
}
func main() {
mpi.Start(false)
defer func() {
mpi.Stop(false)
}()
myrank := mpi.Rank()
if myrank == 0 {
chk.PrintTitle("Test MUMPS Sol 04")
}
ndim := 10
id, sz := mpi.Rank(), mpi.Size()
start, endp1 := (id*ndim)/sz, ((id+1)*ndim)/sz
if mpi.Size() > ndim {
chk.Panic("the number of processors must be smaller than or equal to %d", ndim)
}
b := make([]complex128, ndim)
var t la.TripletC
t.Init(ndim, ndim, ndim*ndim, true)
for i := start; i < endp1; i++ {
j := i
if i > 0 {
j = i - 1
}
for ; j < 10; j++ {
val := 10.0 - float64(j)
if i > j {
val -= 1.0
}
t.Put(i, j, val, 0)
}
b[i] = complex(float64(i+1), 0.0)
}
x_correct := []complex128{-1, 8, -65, 454, -2725, 13624, -54497, 163490, -326981, 326991}
sum_b_to_root := true
la.RunMumpsTestC(&t, 1e-4, b, x_correct, sum_b_to_root)
}
func RunMumpsTestC(t *TripletC, tol_cmp float64, b, x_correct []complex128, sum_b_to_root bool) {
// info
symmetric := false
verbose := false
timing := false
// allocate solver
lis := GetSolver("mumps")
defer lis.Clean()
// initialise solver
err := lis.InitC(t, symmetric, verbose, timing)
if err != nil {
chk.Panic("%v", err.Error())
}
// factorise
err = lis.Fact()
if err != nil {
chk.Panic("%v", err.Error())
}
// solve
bR, bC := ComplexToRC(b)
xR := make([]float64, len(b))
xC := make([]float64, len(b))
err = lis.SolveC(xR, xC, bR, bC, sum_b_to_root) // x := inv(A) * b
if err != nil {
chk.Panic("%v", err.Error())
}
x := RCtoComplex(xR, xC)
if mpi.Rank() == 0 {
// output
A := t.ToMatrix(nil)
io.Pforan("A.x = b\n")
PrintMatC("A", A.ToDense(), "(%g+", "%gi) ", false)
PrintVecC("x", x, "(%g+", "%gi) ", false)
PrintVecC("b", b, "(%g+", "%gi) ", false)
// check
xR_correct, xC_correct := ComplexToRC(x_correct)
errR := VecMaxDiff(xR, xR_correct)
if errR > tol_cmp {
chk.Panic("test failed: errR = %g", errR)
}
errC := VecMaxDiff(xC, xC_correct)
if errC > tol_cmp {
chk.Panic("test failed: errC = %g", errC)
}
io.Pf("err(xR) = %g [1;32mOK[0m\n", errR)
io.Pf("err(xC) = %g [1;32mOK[0m\n", errC)
}
}
func main() {
mpi.Start(false)
defer func() {
mpi.Stop(false)
}()
if mpi.Rank() == 0 {
io.PfYel("\nTest MPI 04\n")
}
for i := 0; i < 60; i++ {
time.Sleep(1e9)
io.Pf("hello from %v\n", mpi.Rank())
if mpi.Rank() == 2 && i == 3 {
io.PfGreen("rank = 3 wants to abort (the following error is OK)\n")
mpi.Abort()
}
}
}
// Start initialises 'global' and starts logging
func Start(simfilepath string, erasefiles, verbose bool) (startisok bool) {
// multiprocessing data
Global.Rank = 0
Global.Nproc = 1
Global.Root = true
Global.Distr = false
if mpi.IsOn() {
Global.Rank = mpi.Rank()
Global.Nproc = mpi.Size()
Global.Root = Global.Rank == 0
Global.Distr = Global.Nproc > 1
}
Global.Verbose = verbose
if !Global.Root {
Global.Verbose = false
}
Global.WspcStop = make([]int, Global.Nproc)
Global.WspcInum = make([]int, Global.Nproc)
// simulation and convenience variables
dir := filepath.Dir(simfilepath)
fn := filepath.Base(simfilepath)
Global.Sim = inp.ReadSim(dir, fn, Global.LogPrefix, erasefiles)
LogErrCond(Global.Sim == nil, "ReadSim failed\n")
if Stop() {
return
}
Global.Ndim = Global.Sim.Ndim
Global.Dirout = Global.Sim.Data.DirOut
Global.Fnkey = Global.Sim.Data.FnameKey
Global.Enc = Global.Sim.Data.Encoder
Global.Stat = Global.Sim.Data.Stat
Global.LogBcs = Global.Sim.Data.LogBcs
Global.Debug = Global.Sim.Data.Debug
// fix show residual flag
if !Global.Root {
Global.Sim.Data.ShowR = false
}
// auxiliar structures
Global.DynCoefs = new(DynCoefs)
if !Global.DynCoefs.Init(&Global.Sim.Solver) {
return
}
Global.HydroSt = new(HydroStatic)
Global.HydroSt.Init()
// success
return true
}
/* Jacobian
========
Calculates (with N=n-1):
df0dx0, df0dx1, df0dx2, ... df0dxN
df1dx0, df1dx1, df1dx2, ... df1dxN
. . . . . . . . . . . . .
dfNdx0, dfNdx1, dfNdx2, ... dfNdxN
INPUT:
ffcn : f(x) function
x : station where dfdx has to be calculated
fx : f @ x
w : workspace with size == n == len(x)
RETURNS:
J : dfdx @ x [must be pre-allocated] */
func Jacobian(J *la.Triplet, ffcn Cb_f, x, fx, w []float64, distr bool) (err error) {
ndim := len(x)
start, endp1 := 0, ndim
if distr {
id, sz := mpi.Rank(), mpi.Size()
start, endp1 = (id*ndim)/sz, ((id+1)*ndim)/sz
if J.Max() == 0 {
J.Init(ndim, ndim, (endp1-start)*ndim)
}
} else {
if J.Max() == 0 {
J.Init(ndim, ndim, ndim*ndim)
}
}
J.Start()
// NOTE: cannot split calculation by columns unless the f function is
// independently calculated by each MPI processor.
// Otherwise, the AllReduce in f calculation would
// join pieces of f from different processors calculated for
// different x values (δx[col] from different columns).
/*
for col := start; col < endp1; col++ {
xsafe := x[col]
delta := math.Sqrt(EPS * max(CTE1, math.Abs(xsafe)))
x[col] = xsafe + delta
ffcn(w, x) // fnew
io.Pforan("x = %v, f = %v\n", x, w)
for row := 0; row < ndim; row++ {
J.Put(row, col, (w[row]-fx[row])/delta)
}
x[col] = xsafe
}
*/
var df float64
for col := 0; col < ndim; col++ {
xsafe := x[col]
delta := math.Sqrt(EPS * max(CTE1, math.Abs(xsafe)))
x[col] = xsafe + delta
err = ffcn(w, x) // w := f(x+δx[col])
if err != nil {
return
}
for row := start; row < endp1; row++ {
df = w[row] - fx[row]
//if math.Abs(df) > EPS {
J.Put(row, col, df/delta)
//}
}
x[col] = xsafe
}
return
}
// InitLogFile initialises logger
func InitLogFile(dirout, fnamekey string) (err error) {
// create log file
var rank int
if mpi.IsOn() {
rank = mpi.Rank()
}
LogFile, err = os.Create(io.Sf("%s/%s_p%d.log", dirout, fnamekey, rank))
if err != nil {
return
}
// connect logger to output file
log.SetOutput(LogFile)
return
}
func RunMumpsTestR(t *Triplet, tol_cmp float64, b, x_correct []float64, sum_b_to_root bool) {
// info
symmetric := false
verbose := false
timing := false
// allocate solver
lis := GetSolver("mumps")
defer lis.Clean()
// initialise solver
err := lis.InitR(t, symmetric, verbose, timing)
if err != nil {
chk.Panic("%v", err.Error())
}
// factorise
err = lis.Fact()
if err != nil {
chk.Panic("%v", err.Error())
}
// solve
x := make([]float64, len(b))
err = lis.SolveR(x, b, sum_b_to_root) // x := inv(A) * b
if err != nil {
chk.Panic("%v", err.Error())
}
if mpi.Rank() == 0 {
// output
A := t.ToMatrix(nil)
io.Pforan("A.x = b\n")
PrintMat("A", A.ToDense(), "%5g", false)
PrintVec("x", x, "%g ", false)
PrintVec("b", b, "%g ", false)
// check
err := VecMaxDiff(x, x_correct)
if err > tol_cmp {
chk.Panic("test failed: err = %g", err)
}
io.Pf("err(x) = %g [1;32mOK[0m\n", err)
}
}
// SpTriSumToRoot join (MPI) parallel triplets to root (Rank == 0) processor.
// NOTE: J in root is also joined into Jroot
func SpTriSumToRoot(J *Triplet) {
if mpi.Rank() == 0 {
for proc := 1; proc < mpi.Size(); proc++ {
nnz := mpi.SingleIntRecv(proc)
irec := make([]int, nnz)
drec := make([]float64, nnz)
mpi.IntRecv(irec, proc)
J.i = append(J.i, irec...)
mpi.IntRecv(irec, proc)
J.j = append(J.j, irec...)
mpi.DblRecv(drec, proc)
J.x = append(J.x, drec...)
}
J.pos = len(J.x)
J.max = J.pos
} else {
mpi.SingleIntSend(J.max, 0)
mpi.IntSend(J.i, 0)
mpi.IntSend(J.j, 0)
mpi.DblSend(J.x, 0)
}
}
func main() {
// catch errors
var tst testing.T
defer func() {
if mpi.Rank() == 0 {
if err := recover(); err != nil {
io.PfRed("ERROR: %v\n", err)
}
if tst.Failed() {
io.PfRed("test failed\n")
}
}
mpi.Stop(false)
}()
mpi.Start(false)
// start global variables and log
if !fem.Start("data/spo751.sim", true, true) {
tst.Error("Start failed\n")
return
}
// make sure to flush log
defer fem.End()
// run simulation
if !fem.Run() {
tst.Error("Run failed\n")
return
}
// check
skipK := true
tolK := 1e-17
tolu := 1e-12
tols := 1e-14
fem.TestingCompareResultsU(&tst, "data/spo751.sim", "cmp/spo751.cmp", tolK, tolu, tols, skipK, true)
}
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 main() {
// catch errors
defer func() {
if err := recover(); err != nil {
if mpi.Rank() == 0 {
chk.Verbose = true
for i := 8; i > 3; i-- {
chk.CallerInfo(i)
}
io.PfRed("ERROR: %v\n", err)
}
}
mpi.Stop(false)
}()
mpi.Start(false)
// message
if mpi.Rank() == 0 {
io.PfWhite("\nGofem v3 -- Go Finite Element Method\n\n")
io.Pf("Copyright 2015 Dorival Pedroso and Raul Durand. All rights reserved.\n")
io.Pf("Use of this source code is governed by a BSD-style\n")
io.Pf("license that can be found in the LICENSE file.\n\n")
}
// simulation filenamepath
flag.Parse()
var fnamepath string
if len(flag.Args()) > 0 {
fnamepath = flag.Arg(0)
} else {
chk.Panic("Please, provide a filename. Ex.: cylinder.sim")
}
// check extension
if io.FnExt(fnamepath) == "" {
fnamepath += ".sim"
}
// other options
erasefiles := true
verbose := true
if len(flag.Args()) > 1 {
erasefiles = io.Atob(flag.Arg(1))
}
if len(flag.Args()) > 2 {
verbose = io.Atob(flag.Arg(2))
}
// profiling?
defer utl.DoProf(false)()
// start global variables and log
if !fem.Start(fnamepath, erasefiles, verbose) {
chk.Panic("Start failed\n")
return
}
// make sure to flush log
defer fem.End()
// run simulation
if !fem.Run() {
io.PfRed("ERROR: cannot run simulation\n")
}
}
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))
}
}
// Init initialises ODE structure with default values and allocate slices
func (o *ODE) Init(method string, ndim int, fcn Cb_fcn, jac Cb_jac, M *la.Triplet, out Cb_out, silent bool) {
// primary variables
o.method = method
o.ndim = ndim
o.fcn = fcn
o.jac = jac
o.out = out
o.silent = silent
o.ZeroTrial = false
o.Atol = 1.0e-4
o.Rtol = 1.0e-4
o.IniH = 1.0e-4
o.NmaxIt = 7
o.NmaxSS = 1000
o.Mmin = 0.125
o.Mmax = 5.0
o.Mfac = 0.9
o.PredCtrl = true
o.ϵ = 1.0e-16
o.θmax = 1.0e-3
o.C1h = 1.0
o.C2h = 1.2
o.LerrStrat = 3
o.Pll = true
o.UseRmsNorm = true
o.SetTol(o.Atol, o.Rtol)
// derived variables
o.root = true
if mpi.IsOn() {
o.root = (mpi.Rank() == 0)
if mpi.Size() > 1 {
o.Distr = true
}
}
// M matrix
if M != nil {
o.mTri = M
o.mMat = o.mTri.ToMatrix(nil)
o.hasM = true
} else {
if o.method == "BwEuler" {
M = new(la.Triplet)
la.SpTriSetDiag(M, o.ndim, 1)
o.mTri = M
o.mMat = o.mTri.ToMatrix(nil)
o.hasM = true
}
}
// method
switch method {
case "FwEuler":
o.step = fweuler_step
o.accept = fweuler_accept
o.nstg = 1
case "BwEuler":
o.step = bweuler_step
o.accept = bweuler_accept
o.nstg = 1
case "MoEuler":
o.step = erk_step
o.accept = erk_accept
o.nstg = 2
o.erkdat = ERKdat{true, ME2_a, ME2_b, ME2_be, ME2_c}
case "Dopri5":
o.step = erk_step
o.accept = erk_accept
o.nstg = 7
o.erkdat = ERKdat{true, DP5_a, DP5_b, DP5_be, DP5_c}
case "Radau5":
o.step = radau5_step
o.accept = radau5_accept
o.nstg = 3
default:
chk.Panic(_ode_err1, method)
}
// allocate step variables
o.f0 = make([]float64, o.ndim)
o.scal = make([]float64, o.ndim)
// allocate rk variables
o.u = make([]float64, o.nstg)
o.v = make([][]float64, o.nstg)
o.w = make([][]float64, o.nstg)
o.δw = make([][]float64, o.nstg)
o.f = make([][]float64, o.nstg)
if method == "Radau5" {
o.z = make([][]float64, o.nstg)
o.ycol = make([][]float64, o.nstg)
o.ez = make([]float64, o.ndim)
o.lerr = make([]float64, o.ndim)
o.rhs = make([]float64, o.ndim)
}
for i := 0; i < o.nstg; i++ {
o.v[i] = make([]float64, o.ndim)
o.w[i] = make([]float64, o.ndim)
o.δw[i] = make([]float64, o.ndim)
o.f[i] = make([]float64, o.ndim)
if method == "Radau5" {
o.z[i] = make([]float64, o.ndim)
o.ycol[i] = make([]float64, o.ndim)
}
}
}
func main() {
mpi.Start(false)
defer func() {
mpi.Stop(false)
}()
myrank := mpi.Rank()
if myrank == 0 {
chk.PrintTitle("Test MUMPS Sol 01b")
}
var t la.Triplet
b := []float64{8.0, 45.0, -3.0, 3.0, 19.0}
switch mpi.Size() {
case 1:
t.Init(5, 5, 13)
t.Put(0, 0, 1.0)
t.Put(0, 0, 1.0)
t.Put(1, 0, 3.0)
t.Put(0, 1, 3.0)
t.Put(2, 1, -1.0)
t.Put(4, 1, 4.0)
t.Put(1, 2, 4.0)
t.Put(2, 2, -3.0)
t.Put(3, 2, 1.0)
t.Put(4, 2, 2.0)
t.Put(2, 3, 2.0)
t.Put(1, 4, 6.0)
t.Put(4, 4, 1.0)
case 2:
la.VecFill(b, 0)
if myrank == 0 {
t.Init(5, 5, 8)
t.Put(0, 0, 1.0)
t.Put(0, 0, 1.0)
t.Put(1, 0, 3.0)
t.Put(0, 1, 3.0)
t.Put(2, 1, -1.0)
t.Put(4, 1, 1.0)
t.Put(4, 1, 1.5)
t.Put(4, 1, 1.5)
b[0] = 8.0
b[1] = 40.0
b[2] = 1.5
} else {
t.Init(5, 5, 8)
t.Put(1, 2, 4.0)
t.Put(2, 2, -3.0)
t.Put(3, 2, 1.0)
t.Put(4, 2, 2.0)
t.Put(2, 3, 2.0)
t.Put(1, 4, 6.0)
t.Put(4, 4, 0.5)
t.Put(4, 4, 0.5)
b[1] = 5.0
b[2] = -4.5
b[3] = 3.0
b[4] = 19.0
}
default:
chk.Panic("this test needs 1 or 2 procs")
}
x_correct := []float64{1, 2, 3, 4, 5}
sum_b_to_root := true
la.RunMumpsTestR(&t, 1e-14, b, x_correct, sum_b_to_root)
}
func main() {
mpi.Start(false)
defer func() {
mpi.Stop(false)
}()
if mpi.Rank() == 0 {
io.PfYel("\nTest MPI 01\n")
}
if mpi.Size() != 3 {
chk.Panic("this test needs 3 processors")
}
n := 11
x := make([]float64, n)
id, sz := mpi.Rank(), mpi.Size()
start, endp1 := (id*n)/sz, ((id+1)*n)/sz
for i := start; i < endp1; i++ {
x[i] = float64(i)
}
// Barrier
mpi.Barrier()
io.Pfgrey("x @ proc # %d = %v\n", id, x)
// SumToRoot
r := make([]float64, n)
mpi.SumToRoot(r, x)
var tst testing.T
if id == 0 {
chk.Vector(&tst, fmt.Sprintf("SumToRoot: r @ proc # %d", id), 1e-17, r, []float64{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10})
} else {
chk.Vector(&tst, fmt.Sprintf("SumToRoot: r @ proc # %d", id), 1e-17, r, make([]float64, n))
}
// BcastFromRoot
r[0] = 666
mpi.BcastFromRoot(r)
chk.Vector(&tst, fmt.Sprintf("BcastFromRoot: r @ proc # %d", id), 1e-17, r, []float64{666, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10})
// AllReduceSum
setslice(x)
w := make([]float64, n)
mpi.AllReduceSum(x, w)
chk.Vector(&tst, fmt.Sprintf("AllReduceSum: w @ proc # %d", id), 1e-17, w, []float64{110, 110, 110, 1021, 1021, 1021, 2032, 2032, 2032, 3043, 3043})
// AllReduceSumAdd
setslice(x)
y := []float64{-1000, -1000, -1000, -1000, -1000, -1000, -1000, -1000, -1000, -1000, -1000}
mpi.AllReduceSumAdd(y, x, w)
chk.Vector(&tst, fmt.Sprintf("AllReduceSumAdd: y @ proc # %d", id), 1e-17, y, []float64{-890, -890, -890, 21, 21, 21, 1032, 1032, 1032, 2043, 2043})
// AllReduceMin
setslice(x)
mpi.AllReduceMin(x, w)
chk.Vector(&tst, fmt.Sprintf("AllReduceMin: x @ proc # %d", id), 1e-17, x, []float64{0, 0, 0, 1, 1, 1, 2, 2, 2, 3, 3})
// AllReduceMax
setslice(x)
mpi.AllReduceMax(x, w)
chk.Vector(&tst, fmt.Sprintf("AllReduceMax: x @ proc # %d", id), 1e-17, x, []float64{100, 100, 100, 1000, 1000, 1000, 2000, 2000, 2000, 3000, 3000})
}
// Radau5 step function
func radau5_step_mpi(o *Solver, y0 []float64, x0 float64, args ...interface{}) (rerr float64, err error) {
// factors
α := r5.α_ / o.h
β := r5.β_ / o.h
γ := r5.γ_ / o.h
// Jacobian and decomposition
if o.reuseJdec {
o.reuseJdec = false
} else {
// calculate only first Jacobian for all iterations (simple/modified Newton's method)
if o.reuseJ {
o.reuseJ = false
} else if !o.jacIsOK {
// Jacobian triplet
if o.jac == nil { // numerical
//if x0 == 0.0 { io.Pfgrey(" > > > > > > > > . . . numerical Jacobian . . . < < < < < < < < <\n") }
err = num.JacobianMpi(&o.dfdyT, func(fy, y []float64) (e error) {
e = o.fcn(fy, o.h, x0, y, args...)
return
}, y0, o.f0, o.w[0], o.Distr) // w works here as workspace variable
} else { // analytical
//if x0 == 0.0 { io.Pfgrey(" > > > > > > > > . . . analytical Jacobian . . . < < < < < < < < <\n") }
err = o.jac(&o.dfdyT, o.h, x0, y0, args...)
}
if err != nil {
return
}
// create M matrix
if o.doinit && !o.hasM {
o.mTri = new(la.Triplet)
if o.Distr {
id, sz := mpi.Rank(), mpi.Size()
start, endp1 := (id*o.ndim)/sz, ((id+1)*o.ndim)/sz
o.mTri.Init(o.ndim, o.ndim, endp1-start)
for i := start; i < endp1; i++ {
o.mTri.Put(i, i, 1.0)
}
} else {
o.mTri.Init(o.ndim, o.ndim, o.ndim)
for i := 0; i < o.ndim; i++ {
o.mTri.Put(i, i, 1.0)
}
}
}
o.njeval += 1
o.jacIsOK = true
}
// initialise triplets
if o.doinit {
o.rctriR = new(la.Triplet)
o.rctriC = new(la.TripletC)
o.rctriR.Init(o.ndim, o.ndim, o.mTri.Len()+o.dfdyT.Len())
xzmono := o.Distr
o.rctriC.Init(o.ndim, o.ndim, o.mTri.Len()+o.dfdyT.Len(), xzmono)
}
// update triplets
la.SpTriAdd(o.rctriR, γ, o.mTri, -1, &o.dfdyT) // rctriR := γ*M - dfdy
la.SpTriAddR2C(o.rctriC, α, β, o.mTri, -1, &o.dfdyT) // rctriC := (α+βi)*M - dfdy
// initialise solver
if o.doinit {
err = o.lsolR.InitR(o.rctriR, false, false, false)
if err != nil {
return
}
err = o.lsolC.InitC(o.rctriC, false, false, false)
if err != nil {
return
}
}
// perform factorisation
o.lsolR.Fact()
o.lsolC.Fact()
o.ndecomp += 1
}
// updated u[i]
o.u[0] = x0 + r5.c[0]*o.h
o.u[1] = x0 + r5.c[1]*o.h
o.u[2] = x0 + r5.c[2]*o.h
// (trial/initial) updated z[i] and w[i]
if o.first || o.ZeroTrial {
for m := 0; m < o.ndim; m++ {
o.z[0][m], o.w[0][m] = 0.0, 0.0
o.z[1][m], o.w[1][m] = 0.0, 0.0
o.z[2][m], o.w[2][m] = 0.0, 0.0
}
} else {
c3q := o.h / o.hprev
c1q := r5.μ1 * c3q
c2q := r5.μ2 * c3q
for m := 0; m < o.ndim; m++ {
o.z[0][m] = c1q * (o.ycol[0][m] + (c1q-r5.μ4)*(o.ycol[1][m]+(c1q-r5.μ3)*o.ycol[2][m]))
o.z[1][m] = c2q * (o.ycol[0][m] + (c2q-r5.μ4)*(o.ycol[1][m]+(c2q-r5.μ3)*o.ycol[2][m]))
o.z[2][m] = c3q * (o.ycol[0][m] + (c3q-r5.μ4)*(o.ycol[1][m]+(c3q-r5.μ3)*o.ycol[2][m]))
o.w[0][m] = r5.Ti[0][0]*o.z[0][m] + r5.Ti[0][1]*o.z[1][m] + r5.Ti[0][2]*o.z[2][m]
o.w[1][m] = r5.Ti[1][0]*o.z[0][m] + r5.Ti[1][1]*o.z[1][m] + r5.Ti[1][2]*o.z[2][m]
o.w[2][m] = r5.Ti[2][0]*o.z[0][m] + r5.Ti[2][1]*o.z[1][m] + r5.Ti[2][2]*o.z[2][m]
}
}
// iterations
o.nit = 0
o.η = math.Pow(max(o.η, o.ϵ), 0.8)
o.θ = o.θmax
o.diverg = false
var Lδw, oLδw, thq, othq, iterr, itRerr, qnewt float64
var it int
for it = 0; it < o.NmaxIt; it++ {
// max iterations ?
o.nit = it + 1
if o.nit > o.nitmax {
o.nitmax = o.nit
}
// evaluate f(x,y) at (u[i],v[i]=y0+z[i])
for i := 0; i < 3; i++ {
for m := 0; m < o.ndim; m++ {
o.v[i][m] = y0[m] + o.z[i][m]
}
o.nfeval += 1
err = o.fcn(o.f[i], o.h, o.u[i], o.v[i], args...)
if err != nil {
return
}
}
// calc rhs
if o.hasM {
// using δw as workspace here
la.SpMatVecMul(o.δw[0], 1, o.mMat, o.w[0]) // δw0 := M * w0
la.SpMatVecMul(o.δw[1], 1, o.mMat, o.w[1]) // δw1 := M * w1
la.SpMatVecMul(o.δw[2], 1, o.mMat, o.w[2]) // δw2 := M * w2
if o.Distr {
mpi.AllReduceSum(o.δw[0], o.v[0]) // v is used as workspace here
mpi.AllReduceSum(o.δw[1], o.v[1]) // v is used as workspace here
mpi.AllReduceSum(o.δw[2], o.v[2]) // v is used as workspace here
}
for m := 0; m < o.ndim; m++ {
o.v[0][m] = r5.Ti[0][0]*o.f[0][m] + r5.Ti[0][1]*o.f[1][m] + r5.Ti[0][2]*o.f[2][m] - γ*o.δw[0][m]
o.v[1][m] = r5.Ti[1][0]*o.f[0][m] + r5.Ti[1][1]*o.f[1][m] + r5.Ti[1][2]*o.f[2][m] - α*o.δw[1][m] + β*o.δw[2][m]
o.v[2][m] = r5.Ti[2][0]*o.f[0][m] + r5.Ti[2][1]*o.f[1][m] + r5.Ti[2][2]*o.f[2][m] - β*o.δw[1][m] - α*o.δw[2][m]
}
} else {
for m := 0; m < o.ndim; m++ {
o.v[0][m] = r5.Ti[0][0]*o.f[0][m] + r5.Ti[0][1]*o.f[1][m] + r5.Ti[0][2]*o.f[2][m] - γ*o.w[0][m]
o.v[1][m] = r5.Ti[1][0]*o.f[0][m] + r5.Ti[1][1]*o.f[1][m] + r5.Ti[1][2]*o.f[2][m] - α*o.w[1][m] + β*o.w[2][m]
o.v[2][m] = r5.Ti[2][0]*o.f[0][m] + r5.Ti[2][1]*o.f[1][m] + r5.Ti[2][2]*o.f[2][m] - β*o.w[1][m] - α*o.w[2][m]
}
}
// solve linear system
o.nlinsol += 1
var errR, errC error
if !o.Distr && o.Pll {
wg := new(sync.WaitGroup)
wg.Add(2)
go func() {
errR = o.lsolR.SolveR(o.δw[0], o.v[0], false)
wg.Done()
}()
go func() {
errC = o.lsolC.SolveC(o.δw[1], o.δw[2], o.v[1], o.v[2], false)
wg.Done()
}()
wg.Wait()
} else {
errR = o.lsolR.SolveR(o.δw[0], o.v[0], false)
errC = o.lsolC.SolveC(o.δw[1], o.δw[2], o.v[1], o.v[2], false)
}
// check for errors from linear solution
if errR != nil || errC != nil {
var errmsg string
if errR != nil {
errmsg += errR.Error()
}
if errC != nil {
if errR != nil {
errmsg += "\n"
}
errmsg += errC.Error()
}
err = errors.New(errmsg)
return
}
// update w and z
for m := 0; m < o.ndim; m++ {
o.w[0][m] += o.δw[0][m]
o.w[1][m] += o.δw[1][m]
o.w[2][m] += o.δw[2][m]
o.z[0][m] = r5.T[0][0]*o.w[0][m] + r5.T[0][1]*o.w[1][m] + r5.T[0][2]*o.w[2][m]
o.z[1][m] = r5.T[1][0]*o.w[0][m] + r5.T[1][1]*o.w[1][m] + r5.T[1][2]*o.w[2][m]
o.z[2][m] = r5.T[2][0]*o.w[0][m] + r5.T[2][1]*o.w[1][m] + r5.T[2][2]*o.w[2][m]
}
// rms norm of δw
Lδw = 0.0
for m := 0; m < o.ndim; m++ {
Lδw += math.Pow(o.δw[0][m]/o.scal[m], 2.0) + math.Pow(o.δw[1][m]/o.scal[m], 2.0) + math.Pow(o.δw[2][m]/o.scal[m], 2.0)
}
Lδw = math.Sqrt(Lδw / float64(3*o.ndim))
// check convergence
if it > 0 {
thq = Lδw / oLδw
if it == 1 {
o.θ = thq
} else {
o.θ = math.Sqrt(thq * othq)
}
othq = thq
if o.θ < 0.99 {
o.η = o.θ / (1.0 - o.θ)
iterr = Lδw * math.Pow(o.θ, float64(o.NmaxIt-o.nit)) / (1.0 - o.θ)
itRerr = iterr / o.fnewt
if itRerr >= 1.0 { // diverging
qnewt = max(1.0e-4, min(20.0, itRerr))
o.dvfac = 0.8 * math.Pow(qnewt, -1.0/(4.0+float64(o.NmaxIt)-1.0-float64(o.nit)))
o.diverg = true
break
}
} else { // diverging badly (unexpected step-rejection)
o.dvfac = 0.5
o.diverg = true
break
}
}
// save old norm
oLδw = Lδw
// converged
if o.η*Lδw < o.fnewt {
break
}
}
// did not converge
if it == o.NmaxIt-1 {
chk.Panic("radau5_step failed with it=%d", it)
}
// diverging => stop
if o.diverg {
rerr = 2.0 // must leave state intact, any rerr is OK
return
}
// error estimate
if o.LerrStrat == 1 {
// simple strategy => HW-VII p123 Eq.(8.17) (not good for stiff problems)
for m := 0; m < o.ndim; m++ {
o.ez[m] = r5.e0*o.z[0][m] + r5.e1*o.z[1][m] + r5.e2*o.z[2][m]
o.lerr[m] = r5.γ0*o.h*o.f0[m] + o.ez[m]
rerr += math.Pow(o.lerr[m]/o.scal[m], 2.0)
}
rerr = max(math.Sqrt(rerr/float64(o.ndim)), 1.0e-10)
} else {
// common
if o.hasM {
for m := 0; m < o.ndim; m++ {
o.ez[m] = r5.e0*o.z[0][m] + r5.e1*o.z[1][m] + r5.e2*o.z[2][m]
o.rhs[m] = o.f0[m]
}
if o.Distr {
la.SpMatVecMul(o.δw[0], γ, o.mMat, o.ez) // δw[0] = γ * M * ez (δw[0] is workspace)
mpi.AllReduceSumAdd(o.rhs, o.δw[0], o.δw[1]) // rhs += join_with_sum(δw[0]) (δw[1] is workspace)
} else {
la.SpMatVecMulAdd(o.rhs, γ, o.mMat, o.ez) // rhs += γ * M * ez
}
} else {
for m := 0; m < o.ndim; m++ {
o.ez[m] = r5.e0*o.z[0][m] + r5.e1*o.z[1][m] + r5.e2*o.z[2][m]
o.rhs[m] = o.f0[m] + γ*o.ez[m]
}
}
// HW-VII p123 Eq.(8.19)
if o.LerrStrat == 2 {
o.lsolR.SolveR(o.lerr, o.rhs, false)
rerr = o.rms_norm(o.lerr)
// HW-VII p123 Eq.(8.20)
} else {
o.lsolR.SolveR(o.lerr, o.rhs, false)
rerr = o.rms_norm(o.lerr)
if !(rerr < 1.0) {
if o.first || o.reject {
for m := 0; m < o.ndim; m++ {
o.v[0][m] = y0[m] + o.lerr[m] // y0perr
}
o.nfeval += 1
err = o.fcn(o.f[0], o.h, x0, o.v[0], args...) // f0perr
if err != nil {
return
}
if o.hasM {
la.VecCopy(o.rhs, 1, o.f[0]) // rhs := f0perr
if o.Distr {
la.SpMatVecMul(o.δw[0], γ, o.mMat, o.ez) // δw[0] = γ * M * ez (δw[0] is workspace)
mpi.AllReduceSumAdd(o.rhs, o.δw[0], o.δw[1]) // rhs += join_with_sum(δw[0]) (δw[1] is workspace)
} else {
la.SpMatVecMulAdd(o.rhs, γ, o.mMat, o.ez) // rhs += γ * M * ez
}
} else {
la.VecAdd2(o.rhs, 1, o.f[0], γ, o.ez) // rhs = f0perr + γ * ez
}
o.lsolR.SolveR(o.lerr, o.rhs, false)
rerr = o.rms_norm(o.lerr)
}
}
}
}
return
}