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() {
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 main() {
mpi.Start(false)
defer func() {
mpi.Stop(false)
}()
myrank := mpi.Rank()
if myrank == 0 {
chk.PrintTitle("Test MUMPS Sol 03")
}
var t la.TripletC
switch mpi.Size() {
case 1:
t.Init(5, 5, 13, true)
t.Put(0, 0, 1.0, 0)
t.Put(0, 0, 1.0, 0)
t.Put(1, 0, 3.0, 0)
t.Put(0, 1, 3.0, 0)
t.Put(2, 1, -1.0, 0)
t.Put(4, 1, 4.0, 0)
t.Put(1, 2, 4.0, 0)
t.Put(2, 2, -3.0, 0)
t.Put(3, 2, 1.0, 0)
t.Put(4, 2, 2.0, 0)
t.Put(2, 3, 2.0, 0)
t.Put(1, 4, 6.0, 0)
t.Put(4, 4, 1.0, 0)
case 2:
if myrank == 0 {
t.Init(5, 5, 6, true)
t.Put(0, 0, 1.0, 0)
t.Put(0, 0, 1.0, 0)
t.Put(1, 0, 3.0, 0)
t.Put(0, 1, 3.0, 0)
t.Put(2, 1, -1.0, 0)
t.Put(4, 1, 4.0, 0)
} else {
t.Init(5, 5, 7, true)
t.Put(1, 2, 4.0, 0)
t.Put(2, 2, -3.0, 0)
t.Put(3, 2, 1.0, 0)
t.Put(4, 2, 2.0, 0)
t.Put(2, 3, 2.0, 0)
t.Put(1, 4, 6.0, 0)
t.Put(4, 4, 1.0, 0)
}
default:
chk.Panic("this test needs 1 or 2 procs")
}
b := []complex128{8.0, 45.0, -3.0, 3.0, 19.0}
x_correct := []complex128{1, 2, 3, 4, 5}
sum_b_to_root := false
la.RunMumpsTestC(&t, 1e-14, b, x_correct, sum_b_to_root)
}
func main() {
// given the following matrix of complex numbers:
// _ _
// | 19.73 12.11-i 5i 0 0 |
// | -0.51i 32.3+7i 23.07 i 0 |
// A = | 0 -0.51i 70+7.3i 3.95 19+31.83i |
// | 0 0 1+1.1i 50.17 45.51 |
// |_ 0 0 0 -9.351i 55 _|
//
// and the following vector:
// _ _
// | 77.38+8.82i |
// | 157.48+19.8i |
// b = | 1175.62+20.69i |
// | 912.12-801.75i |
// |_ 550-1060.4i _|
//
// solve:
// A.x = b
//
// the solution is:
// _ _
// | 3.3-i |
// | 1+0.17i |
// x = | 5.5 |
// | 9 |
// |_ 10-17.75i _|
// flag indicating to store (real,complex) values in monolithic form => 1D array
xzmono := false
// input matrix in Complex Triplet format
var A la.TripletC
A.Init(5, 5, 16, xzmono) // 5 x 5 matrix with 16 non-zeros
// first column
A.Put(0, 0, 19.73, 0) // i=0, j=0, real=19.73, complex=0
A.Put(1, 0, 0, -0.51) // i=1, j=0, real=0, complex=-0.51
// second column
A.Put(0, 1, 12.11, -1) // i=0, j=1, real=12.11, complex=-1
A.Put(1, 1, 32.3, 7)
A.Put(2, 1, 0, -0.51)
// third column
A.Put(0, 2, 0, 5)
A.Put(1, 2, 23.07, 0)
A.Put(2, 2, 70, 7.3)
A.Put(3, 2, 1, 1.1)
// fourth column
A.Put(1, 3, 0, 1)
A.Put(2, 3, 3.95, 0)
A.Put(3, 3, 50.17, 0)
A.Put(4, 3, 0, -9.351)
// fifth column
A.Put(2, 4, 19, 31.83)
A.Put(3, 4, 45.51, 0)
A.Put(4, 4, 55, 0)
// right-hand-side
b := []complex128{
77.38 + 8.82i,
157.48 + 19.8i,
1175.62 + 20.69i,
912.12 - 801.75i,
550 - 1060.4i,
}
// allocate solver
lis := la.GetSolver("umfpack")
defer lis.Clean()
// info
symmetric := false
verbose := false
timing := false
// initialise solver (C)omplex
err := lis.InitC(&A, symmetric, verbose, timing)
if err != nil {
io.Pfred("solver failed:\n%v", err)
return
}
// factorise
err = lis.Fact()
if err != nil {
io.Pfred("solver failed:\n%v", err)
return
}
// auxiliary variables
bR, bC := la.ComplexToRC(b) // real and complex components of b
xR := make([]float64, len(b)) // real compoments of x
xC := make([]float64, len(b)) // complex compoments of x
// solve (C)omplex
var dummy bool
err = lis.SolveC(xR, xC, bR, bC, dummy) // x := inv(A) * b
if err != nil {
io.Pfred("solver failed:\n%v", err)
return
}
// join solution vector
x := la.RCtoComplex(xR, xC)
// output
a := A.ToMatrix(nil)
io.Pforan("A.x = b\n")
la.PrintMatC("A", a.ToDense(), "(%5g", "%+6gi) ", false)
la.PrintVecC("b", b, "(%g", "%+gi) ", false)
la.PrintVecC("x", x, "(%.3f", "%+.3fi) ", false)
}
func main() {
// given the following matrix of complex numbers:
// _ _
// | 19.73 12.11-i 5i 0 0 |
// | -0.51i 32.3+7i 23.07 i 0 |
// A = | 0 -0.51i 70+7.3i 3.95 19+31.83i |
// | 0 0 1+1.1i 50.17 45.51 |
// |_ 0 0 0 -9.351i 55 _|
//
// and the following vector:
// _ _
// | 77.38+8.82i |
// | 157.48+19.8i |
// b = | 1175.62+20.69i |
// | 912.12-801.75i |
// |_ 550-1060.4i _|
//
// solve:
// A.x = b
//
// the solution is:
// _ _
// | 3.3-i |
// | 1+0.17i |
// x = | 5.5 |
// | 9 |
// |_ 10-17.75i _|
// flag indicating to store (real,complex) values in monolithic form => 1D array
xzmono := false
// input matrix in Complex Triplet format
var A la.TripletC
A.Init(5, 5, 16, xzmono) // 5 x 5 matrix with 16 non-zeros
// first column
A.Put(0, 0, 19.73, 0) // i=0, j=0, real=19.73, complex=0
A.Put(1, 0, 0, -0.51) // i=1, j=0, real=0, complex=-0.51
// second column
A.Put(0, 1, 12.11, -1) // i=0, j=1, real=12.11, complex=-1
A.Put(1, 1, 32.3, 7)
A.Put(2, 1, 0, -0.51)
// third column
A.Put(0, 2, 0, 5)
A.Put(1, 2, 23.07, 0)
A.Put(2, 2, 70, 7.3)
A.Put(3, 2, 1, 1.1)
// fourth column
A.Put(1, 3, 0, 1)
A.Put(2, 3, 3.95, 0)
A.Put(3, 3, 50.17, 0)
A.Put(4, 3, 0, -9.351)
// fifth column
A.Put(2, 4, 19, 31.83)
A.Put(3, 4, 45.51, 0)
A.Put(4, 4, 55, 0)
// right-hand-side
b := []complex128{
77.38 + 8.82i,
157.48 + 19.8i,
1175.62 + 20.69i,
912.12 - 801.75i,
550 - 1060.4i,
}
// solve
x, err := la.SolveComplexLinSys(&A, b)
if err != nil {
io.Pfred("solver failed:\n%v", err)
return
}
// output
a := A.ToMatrix(nil)
io.Pforan("A.x = b\n")
la.PrintMatC("A", a.ToDense(), "(%5g", "%+6gi) ", false)
la.PrintVecC("b", b, "(%g", "%+gi) ", false)
la.PrintVecC("x", x, "(%.3f", "%+.3fi) ", false)
}