func Test_invs04(tst *testing.T) {
//verbose()
chk.PrintTitle("invs04")
a := []float64{-10.0, -20.0, -30.0, 4.0 * SQ2, 5.0 * SQ2, 6.0 * SQ2}
at := Alloc2()
Man2Ten(at, a)
io.Pf("a = %v\n", a)
chk.Matrix(tst, "Man2Ten", 1e-17, at, [][]float64{
{-10, 4, 6},
{4, -20, 5},
{6, 5, -30},
})
b := []float64{-88, -77, -55, -3 * SQ2}
bt := Alloc2()
Man2Ten(bt, b)
io.Pf("b = %v\n", b)
chk.Matrix(tst, "Man2Ten", 1e-17, bt, [][]float64{
{-88, -3, 0},
{-3, -77, 0},
{0, 0, -55},
})
ver := chk.Verbose
run_invs_tests(tst, a, ver)
run_invs_tests(tst, b, ver)
}
func Test_conv06(tst *testing.T) {
//verbose()
chk.PrintTitle("conv06")
a := [][]float64{
{1, 2, 3},
{4, 5, 6},
{7, 8, 9},
{10, 11, 12},
}
a_ := MatAlloc(4, 3)
am := MatToColMaj(a)
aa := ColMajToMatNew(am, 4, 3)
ColMajToMat(a_, am)
io.Pforan("a = %v\n", a)
io.Pforan("am = %v\n", am)
io.Pforan("aa = %v\n", aa)
chk.Vector(tst, "a => am", 1e-17, am, []float64{1, 4, 7, 10, 2, 5, 8, 11, 3, 6, 9, 12})
chk.Matrix(tst, "am => a", 1e-17, aa, a)
chk.Matrix(tst, "am => a", 1e-17, a_, a)
b := [][]float64{
{1, 2, 3, 4},
{5, 6, 7, 8},
{9, 0, -1, -2},
}
bm := MatToColMaj(b)
bb := ColMajToMatNew(bm, 3, 4)
io.Pforan("b = %v\n", b)
io.Pforan("bm = %v\n", bm)
io.Pforan("bb = %v\n", bb)
chk.Vector(tst, "b => bm", 1e-15, bm, []float64{1, 5, 9, 2, 6, 0, 3, 7, -1, 4, 8, -2})
chk.Matrix(tst, "bm => b", 1e-15, bb, b)
}
func Test_matinvSmall01(tst *testing.T) {
//verbose()
chk.PrintTitle("matinvSmall01")
noise := 0.0
tol := 1.0e-16
// 1 x 1 matrix
res := MatAlloc(1, 1)
det, err := MatInv(res, [][]float64{{2.0}}, tol)
if err != nil {
chk.Panic("%v", err.Error())
}
chk.Scalar(tst, "1 x 1 matrix: det ", tol, det, 2.0)
chk.Matrix(tst, "1 x 1 matrix: ", tol, res, [][]float64{{0.5}})
// matrix: inverse
A := [][]float64{{1.0, 2.0}, {3.0, 2.0}}
Aicorr := [][]float64{{-0.5, 0.5}, {0.75, -0.25 + noise}}
Ai := MatAlloc(2, 2)
detA, err := MatInv(Ai, A, tol)
if err != nil {
chk.Panic("%v", err.Error())
}
chk.Scalar(tst, "matrix: inv (det) ", tol, detA, -4.0+noise)
chk.Matrix(tst, "matrix: inv (A) ", tol, Ai, Aicorr)
// using MatInvG
Ai_ := MatAlloc(2, 2)
err = MatInvG(Ai_, A, tol)
if err != nil {
chk.Panic("%v", err.Error())
}
chk.Matrix(tst, "matrix: inv with MatInvG", tol, Ai_, Aicorr)
// another test
B := [][]float64{{9.0, 3.0, 5.0}, {-6.0, -9.0, 7.0}, {-1.0, -8.0, 1.0}}
Bicorr := [][]float64{
{7.642276422764227e-02, -6.991869918699187e-02, 1.073170731707317e-01},
{-1.626016260162601e-03, 2.276422764227642e-02, -1.512195121951219e-01},
{6.341463414634146e-02, 1.121951219512195e-01, -1.024390243902439e-01 + noise},
}
Bi := MatAlloc(3, 3)
detB, err := MatInv(Bi, B, tol)
if err != nil {
chk.Panic("%v", err.Error())
}
chk.Scalar(tst, "matrix: det ", tol, detB, 615.0+noise)
chk.Matrix(tst, "matrix: inv ", tol, Bi, Bicorr)
// using MatInvG
Bi_ := MatAlloc(3, 3)
err = MatInvG(Bi_, B, tol)
if err != nil {
chk.Panic("%v", err.Error())
}
chk.Matrix(tst, "matrix: inv with MatInvG", tol, Bi_, Bicorr)
}
func Test_mylab01(tst *testing.T) {
//verbose()
chk.PrintTitle("mylab01")
I := make([]int, 5)
IntFill(I, 666)
J := IntVals(5, 666)
Js := StrVals(5, "666")
M := IntsAlloc(3, 4)
N := DblsAlloc(3, 4)
S := StrsAlloc(2, 3)
A := IntRange(-1)
a := IntRange2(0, 0)
b := IntRange2(0, 1)
c := IntRange2(0, 5)
C := IntRange3(0, -5, -1)
d := IntRange2(2, 5)
D := IntRange2(-2, 5)
e := IntAddScalar(D, 2)
f := DblOnes(5)
ff := DblVals(5, 666)
g := []int{1, 2, 3, 4, 3, 4, 2, 1, 1, 2, 3, 4, 4, 2, 3, 7, 8, 3, 8, 3, 9, 0, 11, 23, 1, 2, 32, 12, 4, 32, 4, 11, 37}
h := IntUnique(g)
G := []int{1, 2, 3, 38, 3, 5, 3, 1, 2, 15, 38, 1, 11}
H := IntUnique(D, C, G, []int{16, 39})
X, Y := MeshGrid2D(3, 6, 10, 20, 4, 3)
P := [][]int{
{1, 2, 3, 4, 5},
{-1, -2, -3, -4, -5},
{6, 7, 8, 9, 10},
}
Pc := IntsClone(P)
chk.Ints(tst, "I", I, []int{666, 666, 666, 666, 666})
chk.Ints(tst, "J", J, []int{666, 666, 666, 666, 666})
chk.Strings(tst, "Js", Js, []string{"666", "666", "666", "666", "666"})
chk.Ints(tst, "A", A, []int{})
chk.Ints(tst, "a", a, []int{})
chk.Ints(tst, "b", b, []int{0})
chk.Ints(tst, "c", c, []int{0, 1, 2, 3, 4})
chk.Ints(tst, "C", C, []int{0, -1, -2, -3, -4})
chk.Ints(tst, "d", d, []int{2, 3, 4})
chk.Ints(tst, "D", D, []int{-2, -1, 0, 1, 2, 3, 4})
chk.Ints(tst, "e", e, []int{0, 1, 2, 3, 4, 5, 6})
chk.Vector(tst, "f", 1e-16, f, []float64{1, 1, 1, 1, 1})
chk.Vector(tst, "ff", 1e-16, ff, []float64{666, 666, 666, 666, 666})
chk.Ints(tst, "h", h, []int{0, 1, 2, 3, 4, 7, 8, 9, 11, 12, 23, 32, 37})
chk.Ints(tst, "H", H, []int{-4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 11, 15, 16, 38, 39})
chk.IntMat(tst, "M", M, [][]int{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}})
chk.Matrix(tst, "N", 1e-17, N, [][]float64{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}})
chk.Matrix(tst, "X", 1e-17, X, [][]float64{{3, 4, 5, 6}, {3, 4, 5, 6}, {3, 4, 5, 6}})
chk.Matrix(tst, "Y", 1e-17, Y, [][]float64{{10, 10, 10, 10}, {15, 15, 15, 15}, {20, 20, 20, 20}})
chk.StrMat(tst, "S", S, [][]string{{"", "", ""}, {"", "", ""}})
chk.IntMat(tst, "Pc", Pc, P)
}
func Test_tsr02(tst *testing.T) {
//verbose()
chk.PrintTitle("tsr02")
F := [][]float64{
{2, 8.0 / 3.0, 0},
{0, 2, 0},
{0, 0.0, 1},
}
Fi := Alloc2()
C := Alloc2()
b := Alloc2()
J, err := Inv(Fi, F)
if err != nil {
chk.Panic("%v", err)
}
RightCauchyGreenDef(C, F)
LeftCauchyGreenDef(b, F)
io.Pf("F = %v\n", F)
io.Pf("C = %v\n", C)
io.Pf("b = %v\n", b)
chk.Scalar(tst, "J", 1.0e-17, J, 4.0)
chk.Matrix(tst, "C", 1.0e-17, C, [][]float64{{36.0 / 9.0, 48.0 / 9.0, 0}, {48.0 / 9.0, 100.0 / 9.0, 0}, {0, 0, 1}})
chk.Matrix(tst, "b", 1.0e-17, b, [][]float64{{100.0 / 9.0, 48.0 / 9.0, 0}, {48.0 / 9.0, 36.0 / 9.0, 0}, {0, 0, 1}})
λ, μ := 2.0, 3.0
σ := Alloc2()
for i := 0; i < 3; i++ {
for j := 0; j < 3; j++ {
σ[i][j] = (λ/J)*math.Log(J)*It[i][j] + (μ/J)*(b[i][j]-It[i][j])
}
}
P := Alloc2()
S := Alloc2()
σfromP := Alloc2()
σfromS := Alloc2()
CauchyToPK1(P, σ, F, Fi, J)
CauchyToPK2(S, σ, F, Fi, J)
PK1ToCauchy(σfromP, P, F, Fi, J)
PK2ToCauchy(σfromS, S, F, Fi, J)
io.Pf("σ = %v\n", σ)
io.Pf("P = %v\n", P)
io.Pf("S = %v\n", S)
chk.Matrix(tst, "σfromP", 1.0e-17, σfromP, σ)
chk.Matrix(tst, "σfromS", 1.0e-14, σfromS, σ)
}
func Test_conv03(tst *testing.T) {
//verbose()
chk.PrintTitle("conv03")
var K, L, A Triplet
K.Init(6, 6, 36+2*6) // 2*6 == number of nonzeros in A
L.Init(6, 6, 36+2*6) // 2*6 == number of nonzeros in A
for i := 0; i < 6; i++ {
for j := 0; j < 6; j++ {
K.Put(i, j, 1000)
L.Put(i, j, 1000)
}
}
A.Init(2, 3, 6)
for i := 0; i < 2; i++ {
for j := 0; j < 3; j++ {
A.Put(i, j, float64(10*(i+1)+j+1))
}
}
Am := A.ToMatrix(nil)
Ad := Am.ToDense()
if chk.Verbose {
Kd := K.ToMatrix(nil).ToDense()
Ld := L.ToMatrix(nil).ToDense()
PrintMat("K", Kd, "%8g", false)
PrintMat("L", Ld, "%8g", false)
PrintMat("A", Ad, "%8g", false)
}
K.PutMatAndMatT(&A)
L.PutCCMatAndMatT(Am)
Kaug := K.ToMatrix(nil).ToDense()
Laug := L.ToMatrix(nil).ToDense()
if chk.Verbose {
PrintMat("K augmented", Kaug, "%8g", false)
PrintMat("L augmented", Laug, "%8g", false)
}
Cor := [][]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},
}
chk.Matrix(tst, "Kaug", 1.0e-17, Kaug, Cor)
chk.Matrix(tst, "Laug", 1.0e-17, Laug, Cor)
}
func Test_conv01(tst *testing.T) {
//verbose()
chk.PrintTitle("conv01")
var t Triplet
t.Init(3, 3, 10)
t.Put(0, 0, 5.0)
t.Put(0, 0, 5.0)
t.Put(0, 1, 11.0)
t.Put(0, 2, 12.0)
t.Put(1, 0, 20.0)
t.Put(1, 1, 21.0)
t.Put(1, 2, 22.0)
t.Put(2, 0, 30.0)
t.Put(2, 1, 31.0)
t.Put(2, 2, 32.0)
a := t.ToMatrix(nil)
ad := a.ToDense()
if chk.Verbose {
PrintMat("a", ad, "%5g", false)
}
chk.Matrix(tst, "a", 1e-17, ad, [][]float64{
{10, 11, 12},
{20, 21, 22},
{30, 31, 32},
})
}
func Test_conv02(tst *testing.T) {
//verbose()
chk.PrintTitle("conv02")
var t Triplet
t.Init(4, 3, 4*3+2)
t.Put(0, 0, 1.0)
t.Put(0, 1, 2.0)
t.Put(0, 2, 3.0)
t.Put(1, 0, 4.0)
t.Put(1, 1, 5.0)
t.Put(1, 2, 6.0)
t.Put(2, 0, 7.0)
t.Put(2, 1, 8.0)
t.Put(2, 2, 9.0)
t.Put(3, 0, 4.0)
t.Put(3, 1, 11.0)
t.Put(3, 2, 12.0)
t.Put(3, 0, 3.0) // repeated
t.Put(3, 0, 3.0) // repeated
a := t.ToMatrix(nil)
ad := a.ToDense()
if chk.Verbose {
PrintMat("a", ad, "%5g", false)
}
chk.Matrix(tst, "a", 1e-17, ad, [][]float64{
{1, 2, 3},
{4, 5, 6},
{7, 8, 9},
{10, 11, 12},
})
}
func Test_mmMul01(tst *testing.T) {
//verbose()
chk.PrintTitle("mmMul01. MatrixMatrix multiplication")
a := [][]float64{
{1.0, 2.0, 3.0},
{0.5, 0.75, 1.5},
}
b := [][]float64{
{0.1, 0.5, 0.5, 0.75},
{0.2, 2.0, 2.0, 2.0},
{0.3, 0.5, 0.5, 0.5},
}
c := MatAlloc(2, 4)
MatMul(c, 1, a, b) // c := 1*a*b
io.Pf("a = %v\n", a)
io.Pf("b = %v\n", b)
io.Pf("c = %v\n", c)
ccor := [][]float64{
{1.4, 6.0, 6.0, 6.25},
{0.65, 2.5, 2.5, 2.625},
}
chk.Matrix(tst, "c", 1.0e-15, c, ccor)
}
func Test_jacobi01(tst *testing.T) {
//verbose()
chk.PrintTitle("jacobi01")
A := [][]float64{
{1, 2, 3},
{2, 3, 2},
{3, 2, 2},
}
Q := MatAlloc(3, 3)
v := make([]float64, 3)
nit, err := Jacobi(Q, v, A)
if err != nil {
chk.Panic("Jacobi failed:\n%v", err)
}
io.Pforan("number of iterations = %v\n", nit)
PrintMat("A", A, "%13.8f", false)
PrintMat("Q", Q, "%13.8f", false)
PrintVec("v", v, "%13.8f", false)
chk.Matrix(tst, "Q", 1e-17, Q, [][]float64{
{7.81993314738381295e-01, 5.26633230856907386e-01, 3.33382506832158143e-01},
{-7.14394870018381645e-02, 6.07084171793832561e-01, -7.91419742017035133e-01},
{-6.19179178753124115e-01, 5.95068272145819699e-01, 5.12358171676802088e-01},
})
chk.Vector(tst, "v", 1e-17, v, []float64{-1.55809924785903786e+00, 6.69537390404459476e+00, 8.62725343814443657e-01})
}
func Test_Ts(tst *testing.T) {
//verbose()
chk.PrintTitle("Ts")
nd := test_nd
for m := 0; m < len(test_nd)-3; m++ {
//for m := 0; m < 3; m++ {
A := test_AA[m]
a := M_Alloc2(nd[m])
Ten2Man(a, A)
s := M_Dev(a)
Ts := M_Alloc4(nd[m])
M_Ts(Ts, s)
s2 := M_Alloc2(nd[m])
ds2ds := M_Alloc4(nd[m])
M_Sq(s2, s)
M_SqDeriv(ds2ds, s)
Ts_ := M_Alloc4(nd[m])
for i := 0; i < len(a); i++ {
for j := 0; j < len(a); j++ {
for k := 0; k < len(a); k++ {
for l := 0; l < len(a); l++ {
Ts_[i][j] += Psd[i][k] * ds2ds[k][l] * Psd[l][j]
}
}
}
}
chk.Matrix(tst, "Ts", 1e-13, Ts, Ts_)
}
}
func Test_tsr03(tst *testing.T) {
//verbose()
chk.PrintTitle("tsr03")
a := [][]float64{
{4.0, 1.0 / SQ2, 0},
{1.0 / SQ2, 5.0, 0},
{0, 0, 6.0},
}
am := make([]float64, 4)
aa := Alloc2()
Ten2Man(am, a)
Man2Ten(aa, am)
io.Pf("a = %v\n", a)
io.Pf("am = %v\n", am)
io.Pf("aa = %v\n", aa)
chk.Matrix(tst, "aa", 1.0e-15, aa, a)
for i := 0; i < 3; i++ {
for j := 0; j < 3; j++ {
chk.Scalar(tst, fmt.Sprintf("am[%d][%d]", i, j), 1.0e-15, M2T(am, i, j), a[i][j])
}
}
b := [][]float64{
{4.0, 1.0 / SQ2, 3.0 / SQ2},
{1.0 / SQ2, 5.0, 2.0 / SQ2},
{3.0 / SQ2, 2.0 / SQ2, 6.0},
}
bm := make([]float64, 6)
bb := Alloc2()
Ten2Man(bm, b)
Man2Ten(bb, bm)
io.Pf("b = %v\n", b)
io.Pf("bm = %v\n", bm)
io.Pf("bb = %v\n", bb)
chk.Matrix(tst, "bb", 1.0e-15, bb, b)
for i := 0; i < 3; i++ {
for j := 0; j < 3; j++ {
chk.Scalar(tst, fmt.Sprintf("bm[%d][%d]", i, j), 1.0e-15, M2T(bm, i, j), b[i][j])
}
}
}
func Test_imap(tst *testing.T) {
//utl.Tsilent = false
chk.PrintTitle("Test imap")
for name, shape := range factory {
gndim := shape.Gndim
if gndim == 1 {
continue
}
io.Pfyel("--------------------------------- %-6s---------------------------------\n", name)
// check inverse mapping
tol := 1e-14
noise := 0.01
if name == "tri10" {
tol = 1e-14
}
if shape.FaceNvertsMax > 2 {
noise = 0.0
}
nverts := shape.Nverts
C := la.MatAlloc(gndim, nverts)
s := []float64{rand.Float64(), rand.Float64(), rand.Float64()} // scale factors
la.MatCopy(C, 1.0, shape.NatCoords)
_ = tol
io.Pf("nverts:%v\n", nverts)
io.Pf("gndim:%v\n", gndim)
for i := 0; i < gndim; i++ {
for j := 0; j < nverts; j++ {
C[i][j] *= s[i]
C[i][j] += noise * rand.Float64() // noise
}
}
r := make([]float64, 3)
x := make([]float64, 3)
R := la.MatAlloc(gndim, nverts)
for j := 0; j < nverts; j++ {
for i := 0; i < gndim; i++ {
x[i] = C[i][j]
}
err := shape.InvMap(r, x, C)
io.Pf("r:%v\n", r)
_ = err
for i := 0; i < gndim; i++ {
R[i][j] = r[i]
}
}
chk.Matrix(tst, "checking", tol, R, shape.NatCoords)
io.PfGreen("OK\n")
}
}
func Test_assemb01(tst *testing.T) {
chk.PrintTitle("assemb01")
// grid
var g Grid2D
g.Init(1.0, 1.0, 3, 3)
// equations numbering
var e Equations
e.Init(g.N, []int{0, 3, 6})
// K11 and K12
var K11, K12 la.Triplet
InitK11andK12(&K11, &K12, &e)
// assembly
F1 := make([]float64, e.N1)
Assemble(&K11, &K12, F1, nil, &g, &e)
// check
K11d := K11.ToMatrix(nil).ToDense()
K12d := K12.ToMatrix(nil).ToDense()
K11c := [][]float64{
{16.0, -4.0, -8.0, 0.0, 0.0, 0.0},
{-8.0, 16.0, 0.0, -8.0, 0.0, 0.0},
{-4.0, 0.0, 16.0, -4.0, -4.0, 0.0},
{0.0, -4.0, -8.0, 16.0, 0.0, -4.0},
{0.0, 0.0, -8.0, 0.0, 16.0, -4.0},
{0.0, 0.0, 0.0, -8.0, -8.0, 16.0},
}
K12c := [][]float64{
{-4.0, 0.0, 0.0},
{0.0, 0.0, 0.0},
{0.0, -4.0, 0.0},
{0.0, 0.0, 0.0},
{0.0, 0.0, -4.0},
{0.0, 0.0, 0.0},
}
chk.Matrix(tst, "K11: ", 1e-16, K11d, K11c)
chk.Matrix(tst, "K12: ", 1e-16, K12d, K12c)
}
func RunInvCheck(tst *testing.T, key string, M, CorrectInvM [][]float64, checkI bool, Tol, TolI float64) {
m, n := len(M), len(M[0])
Mi := MatAlloc(n, m)
t0 := time.Now()
err := MatInvG(Mi, M, 1e-13)
if err != nil {
chk.Panic("%v", err.Error())
}
io.Pfpink("Lapack: time elapsed = %v\n", time.Now().Sub(t0))
MMi := MatAlloc(m, m)
MMiM := MatAlloc(m, n)
MatMul(MMi, 1, M, Mi) // MMi = M * Mi
MatMul(MMiM, 1, MMi, M) // MMiM = M * Mi * M == M
chk.Matrix(tst, io.Sf("%s => Mi - CorrectInvM ", key), Tol, Mi, CorrectInvM)
chk.Matrix(tst, io.Sf("%s => M*Mi*M = M ", key), Tol, MMiM, M)
if checkI {
I := MatAlloc(m, m)
MatSetDiag(I, 1)
chk.Matrix(tst, io.Sf("%s => M*Mi = I ", key), TolI, MMi, I)
}
}
func TestCholesky01(tst *testing.T) {
chk.PrintTitle("TestCholesky 01")
a := [][]float64{
{25.0, 15.0, -5.0},
{15.0, 18.0, 0.0},
{-5.0, 0.0, 11.0},
}
L := MatAlloc(3, 3)
Cholesky(L, a) // L is such as A = L * transp(L)
PrintMat("a", a, "%6g", false)
PrintMat("L", L, "%6g", false)
LLt := calc_LLt(L)
chk.Matrix(tst, "a = LLt", 1e-17, LLt, a)
chk.Matrix(tst, "L", 1e-17, L, [][]float64{
{5, 0, -0},
{3, 3, 0},
{-1, 1, 3},
})
}
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},
})
}
}
func TestCholesky02(tst *testing.T) {
chk.PrintTitle("TestCholesky 02")
a := [][]float64{
{2, 1, 1, 3, 2},
{1, 2, 2, 1, 1},
{1, 2, 9, 1, 5},
{3, 1, 1, 7, 1},
{2, 1, 5, 1, 8},
}
L := MatAlloc(5, 5)
Cholesky(L, a)
PrintMat("a", a, "%6g", false)
PrintMat("L", L, "%10.6f", false)
chk.Matrix(tst, "a = LLt", 1e-15, calc_LLt(L), a)
chk.Matrix(tst, "L", 1e-15, L, [][]float64{
{math.Sqrt2, 0, 0, 0, 0},
{1.0 / math.Sqrt2, math.Sqrt(3.0 / 2.0), 0, 0, 0},
{1.0 / math.Sqrt2, math.Sqrt(3.0 / 2.0), math.Sqrt(7.0), 0, 0},
{3.0 / math.Sqrt2, -1.0 / math.Sqrt(6.0), 0, math.Sqrt(7.0 / 3.0), 0},
{math.Sqrt2, 0, 4.0 / math.Sqrt(7.0), -2.0 * math.Sqrt(3.0/7.0), math.Sqrt2},
})
}
func TestSparseLA09(tst *testing.T) {
chk.PrintTitle("TestSparse LA09")
var a Triplet
SpTriSetDiag(&a, 4, 666.0)
A := a.ToMatrix(nil).ToDense()
PrintMat("diag(4) with 666 =", A, "%8g", false)
chk.Matrix(tst, "a", 1e-17, A, [][]float64{
{666, 0, 0, 0},
{0, 666, 0, 0},
{0, 0, 666, 0},
{0, 0, 0, 666},
})
}
func Test_serial03(tst *testing.T) {
//verbose()
chk.PrintTitle("serial03")
a := [][]float64{
{1, 2, 3, 4},
{5, 6, 7, 8},
{9, 0, -1, -2},
}
v := DblMatToArray(a)
b := DblArrayToMat(v, 3, 4)
io.Pforan("a => v = %v\n", v)
io.Pforan("v => a = %v\n", b)
chk.Vector(tst, "a => v", 1e-15, v, []float64{1, 5, 9, 2, 6, 0, 3, 7, -1, 4, 8, -2})
chk.Matrix(tst, "v => a", 1e-15, b, a)
}
func TestSparseLA07(tst *testing.T) {
//verbose()
chk.PrintTitle("TestSparse LA07")
var ta Triplet
ta.Init(5, 6, 9)
ta.Put(0, 0, 1)
ta.Put(2, 0, 2)
ta.Put(4, 0, 3)
ta.Put(1, 2, 3)
ta.Put(3, 2, 1)
ta.Put(0, 3, 1)
ta.Put(4, 3, 5)
ta.Put(0, 5, 7)
ta.Put(2, 5, 8)
io.Pf("ta = %+v\n", ta)
var tb Triplet
tb.Init(5, 6, 12)
tb.Put(1, 1, 1)
tb.Put(3, 1, 8)
tb.Put(0, 2, 1)
tb.Put(1, 2, 2)
tb.Put(2, 2, 3)
tb.Put(3, 2, 4)
tb.Put(4, 2, 5)
tb.Put(2, 4, 5)
tb.Put(0, 5, 1)
tb.Put(1, 5, 4)
tb.Put(2, 5, 2)
tb.Put(4, 5, 1)
io.Pf("tb = %+v\n", tb)
var tc Triplet
tc.Init(5, 6, ta.Len()+tb.Len())
SpTriAdd(&tc, 0.1, &ta, 2, &tb)
io.Pf("tc = %+v\n", tc)
chk.Matrix(tst, "c", 1e-16, tc.ToMatrix(nil).ToDense(), [][]float64{
{0.1, 0, 2.0, 0.1, 0, 2.7},
{0, 2, 4.3, 0, 0, 8.0},
{0.2, 0, 6.0, 0, 10, 4.8},
{0, 16, 8.1, 0, 0, 0.0},
{0.3, 0, 10.0, 0.5, 0, 2.0},
})
}
func TestReadMatrix01(tst *testing.T) {
//verbose()
chk.PrintTitle("ReadMatrix 01")
res, err := ReadMatrix("data/mat01.dat")
if err != nil {
tst.Errorf("[1;31mfile cannot be read:[0m\n%v\n", err.Error())
}
chk.Matrix(tst, "mat", 1.0e-17, res, [][]float64{
{1, 2, 3, 4},
{10, 20, 30, 40},
{-1, -2, -3, -4},
})
Pforan("res = %v\n", res)
}
func TestSparseLA04(tst *testing.T) {
chk.PrintTitle("TestSparse LA04")
var ta Triplet
ta.Init(3, 3, 4)
ta.Put(0, 0, 1.0)
ta.Put(1, 0, 2.0)
ta.Put(2, 1, 3.0)
ta.Put(2, 2, 4.0)
a := ta.ToMatrix(nil)
io.Pf("a = %+v\n", a)
PrintMat("a", a.ToDense(), "%2g ", false)
chk.Vector(tst, "a.x", 1e-17, a.x, []float64{1, 2, 3, 4})
chk.Ints(tst, "a.i", a.i, []int{0, 1, 2, 2})
chk.Ints(tst, "a.p", a.p, []int{0, 2, 3, 4})
var tb Triplet
tb.Init(3, 3, 4)
tb.Put(1, 0, 3.0)
tb.Put(0, 1, 2.0)
tb.Put(1, 2, 1.0)
tb.Put(2, 2, 1.0)
b := tb.ToMatrix(nil)
io.Pf("b = %+v\n", b)
PrintMat("b", b.ToDense(), "%2g ", false)
chk.Vector(tst, "b.x", 1e-17, b.x, []float64{3, 2, 1, 1})
chk.Ints(tst, "b.i", b.i, []int{1, 0, 1, 2})
chk.Ints(tst, "b.p", b.p, []int{0, 1, 2, 4})
c, a2c, b2c := SpAllocMatAddMat(a, b)
SpMatAddMat(c, 1, a, 1, b, a2c, b2c)
io.Pf("c = %+v\n", c)
PrintMat("c", c.ToDense(), "%2g ", false)
chk.Vector(tst, "c.x", 1e-17, c.x, []float64{1, 5, 2, 3, 1, 5})
chk.Ints(tst, "c.i", c.i, []int{0, 1, 0, 2, 1, 2})
chk.Ints(tst, "c.p", c.p, []int{0, 2, 4, 6})
chk.Ints(tst, "a2c", a2c, []int{0, 1, 3, 5})
chk.Ints(tst, "b2c", b2c, []int{1, 2, 4, 5})
chk.Matrix(tst, "c", 1e-17, c.ToDense(), [][]float64{{1, 2, 0}, {5, 0, 1}, {0, 3, 5}})
}
func Test_elast02(tst *testing.T) {
//verbose()
chk.PrintTitle("elast02")
//K, G := 2.0, 3.0/4.0
K, G := 1116.6666666666667, 837.5
io.Pfgreen("K = %v\n", Calc_K_from_Enu(2010, 0.2))
io.Pfgreen("G = %v\n", Calc_G_from_Knu(K, 0.2))
ndim, pstress := 2, false
var ec SmallElasticity
err := ec.Init(ndim, pstress, []*fun.Prm{
&fun.Prm{N: "K", V: K},
&fun.Prm{N: "G", V: G},
})
io.Pforan("ec: %+v\n", &ec)
if err != nil {
tst.Errorf("test failed: %v\n", err)
return
}
nsig, nalp, large, nle := 2*ndim, 0, false, false
state := NewState(nsig, nalp, large, nle)
D := la.MatAlloc(nsig, nsig)
ec.CalcD(D, state)
a := K + 4.0*G/3.0
b := K - 2.0*G/3.0
c := 2.0 * G
chk.Matrix(tst, "D", 1e-12, D, [][]float64{
{a, b, b, 0},
{b, a, b, 0},
{b, b, a, 0},
{0, 0, 0, c},
})
}
func Test_spset01(tst *testing.T) {
//verbose()
chk.PrintTitle("spset01")
// ↓ ↓ ↓ ↓ ↓ ↓
// 0 1 2 3 4 5 6 7 8 9 10 11 12
Ai := []int{0, 1, 0, 2, 4, 1, 2, 3, 4, 2, 1, 4}
Ax := []float64{2, 3, 3, -1, 4, 4, -3, 1, 2, 2, 6, 1}
Ap := []int{0, 2, 5, 9, 10, 12}
var A CCMatrix
A.Set(5, 5, Ap, Ai, Ax)
Ad := A.ToDense()
PrintMat("A", Ad, "%5g", false)
chk.Matrix(tst, "A", 1e-17, Ad, [][]float64{
{2, 3, 0, 0, 0},
{3, 0, 4, 0, 6},
{0, -1, -3, 2, 0},
{0, 0, 1, 0, 0},
{0, 4, 2, 0, 1},
})
}
func RunSvdCheck(tst *testing.T, key string, A, CorU [][]float64, CorS []float64, CorVt [][]float64, Tol float64) {
m, n := len(A), len(A[0])
ns := imin(m, n)
U, S, Vt := MatAlloc(m, m), make([]float64, ns), MatAlloc(n, n)
err := MatSvd(U, S, Vt, A, 1e-14)
if err != nil {
chk.Panic("%v", err.Error())
}
// TODO: check why U and Vt do not work in some systems => probably
// the local linear solver is sorting components in a different way
//chk.Matrix(tst, io.Sf("%s => U", key), Tol, U, CorU)
chk.Vector(tst, io.Sf("%s => S", key), Tol, S, CorS)
//chk.Matrix(tst, io.Sf("%s => Vt", key), Tol, Vt, CorVt)
usvt := MatAlloc(m, n)
for i := 0; i < m; i++ {
for j := 0; j < n; j++ {
for k := 0; k < ns; k++ {
usvt[i][j] += U[i][k] * S[k] * Vt[k][j]
}
}
}
chk.Matrix(tst, io.Sf("%s => U*S*Vt", key), Tol, A, usvt)
}
func Test_cond01(tst *testing.T) {
//verbose()
chk.PrintTitle("cond01. condition number of matrix using general inverse")
a := [][]float64{
{1, 2},
{2, 3.999},
}
cIa, err := MatCondG(a, "I", 1e-10)
if err != nil {
chk.Panic("%v", err.Error())
}
ai := MatAlloc(2, 2)
_, err = MatInv(ai, a, 1e-10)
if err != nil {
chk.Panic("%v", err.Error())
}
nIa := MatNormI(a)
nIai := MatNormI(ai)
PrintMat("a", a, "%10g", false)
PrintMat("ai", ai, "%20g", false)
io.Pforan("normI(a) = %v\n", nIa)
io.Pforan("normI(ai) = %v\n", nIai)
io.Pforan("cond(a,I) = %v\n", cIa)
chk.Matrix(tst, "ai ", 1e-9, ai, [][]float64{{-3999, 2000}, {2000, -1000}})
chk.Scalar(tst, "normI(a) ", 1e-15, nIa, 5.999)
chk.Scalar(tst, "normI(ai)", 1e-9, nIai, 5999)
chk.Scalar(tst, "condI(a) ", 1e-8, cIa, 35988.001)
b := [][]float64{
{1, 2},
{2, 3},
}
bi := MatAlloc(2, 2)
_, err = MatInv(bi, b, 1e-10)
if err != nil {
chk.Panic("%v", err.Error())
}
cIb, err := MatCondG(b, "I", 1e-10)
if err != nil {
chk.Panic("%v", err.Error())
}
cIbi, err := MatCondG(bi, "I", 1e-10)
if err != nil {
chk.Panic("%v", err.Error())
}
cFb, err := MatCondG(b, "F", 1e-10)
if err != nil {
chk.Panic("%v", err.Error())
}
cFbi, err := MatCondG(bi, "F", 1e-10)
if err != nil {
chk.Panic("%v", err.Error())
}
PrintMat("\nb", b, "%10g", false)
io.Pforan("cond(b, I) = %v\n", cIb)
io.Pforan("cond(bi,I) = %v\n", cIbi)
io.Pforan("cond(b, F) = %v\n", cFb)
io.Pforan("cond(bi,F) = %v\n", cFbi)
chk.Matrix(tst, "bi ", 1e-17, bi, [][]float64{{-3, 2}, {2, -1}})
chk.Scalar(tst, "condI(b) ", 1e-17, cIb, 25.0)
chk.Scalar(tst, "condF(b) ", 1e-14, cFb, 18.0)
}
// testing_compare_results_u compares results with u-formulation
func TestingCompareResultsU(tst *testing.T, simfname, cmpfname string, tolK, tolu, tols float64, skipK, verbose bool) {
// only root can run this test
if !Global.Root {
return
}
// read summary
sum := ReadSum(Global.Dirout, Global.Fnkey)
if sum == nil {
tst.Error("cannot read summary file for simulation=%q\n", simfname)
return
}
// allocate domain
distr := false
d := NewDomain(Global.Sim.Regions[0], distr)
if !d.SetStage(0, Global.Sim.Stages[0], distr) {
tst.Errorf("TestingCompareResultsU: SetStage failed\n")
return
}
// read file
buf, err := io.ReadFile(cmpfname)
if err != nil {
tst.Errorf("TestingCompareResultsU: ReadFile failed\n")
return
}
// unmarshal json
var cmp_set T_results_set
err = json.Unmarshal(buf, &cmp_set)
if err != nil {
tst.Errorf("TestingCompareResultsU: Unmarshal failed\n")
return
}
// run comparisons
dmult := 1.0
for idx, cmp := range cmp_set {
// displacements multiplier
if idx == 0 && math.Abs(cmp.DispMult) > 1e-10 {
dmult = cmp.DispMult
}
// time index
tidx := idx + 1
if verbose {
io.PfYel("\n\ntidx = %d . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .\n", tidx)
}
// load gofem results
if !d.In(sum, tidx, true) {
tst.Errorf("TestingCompareResultsU: reading of results failed\n")
return
}
if verbose {
io.Pfyel("time = %v\n", d.Sol.T)
}
// check K matrices
if !skipK {
if verbose {
io.Pfgreen(". . . checking K matrices . . .\n")
}
for eid, Ksg := range cmp.Kmats {
if e, ok := d.Elems[eid].(*ElemU); ok {
if !e.AddToKb(d.Kb, d.Sol, true) {
tst.Errorf("TestingCompareResultsU: AddToKb failed\n")
return
}
chk.Matrix(tst, io.Sf("K%d", eid), tolK, e.K, Ksg)
}
}
}
// check displacements
if verbose {
io.Pfgreen(". . . checking displacements . . .\n")
}
for nid, usg := range cmp.Disp {
ix := d.Vid2node[nid].Dofs[0].Eq
iy := d.Vid2node[nid].Dofs[1].Eq
chk.AnaNum(tst, "ux", tolu, d.Sol.Y[ix], usg[0]*dmult, verbose)
chk.AnaNum(tst, "uy", tolu, d.Sol.Y[iy], usg[1]*dmult, verbose)
if len(usg) == 3 {
iz := d.Vid2node[nid].Dofs[2].Eq
chk.AnaNum(tst, "uz", tolu, d.Sol.Y[iz], usg[2]*dmult, verbose)
}
}
// check stresses
if true {
if verbose {
io.Pfgreen(". . . checking stresses . . .\n")
}
for eid, sig := range cmp.Sigmas {
if verbose {
io.Pforan("eid = %d\n", eid)
}
if e, ok := d.Cid2elem[eid].(*ElemU); ok {
for ip, val := range sig {
if verbose {
io.Pfgrey2("ip = %d\n", ip)
}
σ := e.States[ip].Sig
if len(val) == 6 {
chk.AnaNum(tst, "sx ", tols, σ[0], val[0], verbose)
chk.AnaNum(tst, "sy ", tols, σ[1], val[1], verbose)
} else {
chk.AnaNum(tst, "sx ", tols, σ[0], val[0], verbose)
chk.AnaNum(tst, "sy ", tols, σ[1], val[1], verbose)
chk.AnaNum(tst, "sxy", tols, σ[3]/SQ2, val[2], verbose)
if len(val) > 3 { // sx, sy, sxy, sz
chk.AnaNum(tst, "sz ", tols, σ[2], val[3], verbose)
}
}
}
}
}
}
}
}
func Test_mylab01(tst *testing.T) {
//verbose()
chk.PrintTitle("mylab01")
I := make([]int, 5)
IntFill(I, 666)
J := IntVals(5, 666)
Js := StrVals(5, "666")
M := IntsAlloc(3, 4)
N := DblsAlloc(3, 4)
A := IntRange(-1)
a := IntRange2(0, 0)
b := IntRange2(0, 1)
c := IntRange2(0, 5)
C := IntRange3(0, -5, -1)
d := IntRange2(2, 5)
D := IntRange2(-2, 5)
e := IntAddScalar(D, 2)
f := DblOnes(5)
ff := DblVals(5, 666)
g := []int{1, 2, 3, 4, 3, 4, 2, 1, 1, 2, 3, 4, 4, 2, 3, 7, 8, 3, 8, 3, 9, 0, 11, 23, 1, 2, 32, 12, 4, 32, 4, 11, 37}
h := IntUnique(g)
G := []int{1, 2, 3, 38, 3, 5, 3, 1, 2, 15, 38, 1, 11}
H := IntUnique(D, C, G, []int{16, 39})
X, Y := MeshGrid2D(3, 6, 10, 20, 4, 3)
io.Pf("I = %v\n", I)
io.Pf("Js = %v\n", Js)
io.Pf("J = %v\n", J)
io.Pf("A = %v\n", A)
io.Pf("a = %v\n", a)
io.Pf("b = %v\n", b)
io.Pf("c = %v\n", c)
io.Pf("C = %v\n", C)
io.Pf("d = %v\n", d)
io.Pf("D = %v\n", D)
io.Pf("e = %v\n", e)
io.Pf("f = %v\n", f)
io.Pf("G = %v\n", G)
io.Pf("H = %v\n", H)
io.Pf("g = %v\n", g)
io.Pf("h = %v\n", h)
io.Pf("M = %v\n", M)
io.Pf("N = %v\n", N)
io.Pf("X = %v\n", X)
io.Pf("Y = %v\n", Y)
chk.Ints(tst, "I", I, []int{666, 666, 666, 666, 666})
chk.Ints(tst, "J", J, []int{666, 666, 666, 666, 666})
chk.Strings(tst, "Js", Js, []string{"666", "666", "666", "666", "666"})
chk.Ints(tst, "A", A, []int{})
chk.Ints(tst, "a", a, []int{})
chk.Ints(tst, "b", b, []int{0})
chk.Ints(tst, "c", c, []int{0, 1, 2, 3, 4})
chk.Ints(tst, "C", C, []int{0, -1, -2, -3, -4})
chk.Ints(tst, "d", d, []int{2, 3, 4})
chk.Ints(tst, "D", D, []int{-2, -1, 0, 1, 2, 3, 4})
chk.Ints(tst, "e", e, []int{0, 1, 2, 3, 4, 5, 6})
chk.Vector(tst, "f", 1e-16, f, []float64{1, 1, 1, 1, 1})
chk.Vector(tst, "ff", 1e-16, ff, []float64{666, 666, 666, 666, 666})
chk.Ints(tst, "h", h, []int{0, 1, 2, 3, 4, 7, 8, 9, 11, 12, 23, 32, 37})
chk.Ints(tst, "H", H, []int{-4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 11, 15, 16, 38, 39})
chk.IntMat(tst, "M", M, [][]int{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}})
chk.Matrix(tst, "N", 1e-17, N, [][]float64{{0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}})
chk.Matrix(tst, "X", 1e-17, X, [][]float64{{3, 4, 5, 6}, {3, 4, 5, 6}, {3, 4, 5, 6}})
chk.Matrix(tst, "Y", 1e-17, Y, [][]float64{{10, 10, 10, 10}, {15, 15, 15, 15}, {20, 20, 20, 20}})
}
func Test_ops03(tst *testing.T) {
//verbose()
chk.PrintTitle("ops03")
nonsymTol := 1e-15
dtol := 1e-9
dver := chk.Verbose
nd := test_nd
for idxA := 0; idxA < len(test_nd)-3; idxA++ {
//for idxA := 0; idxA < 1; idxA++ {
// tensor and eigenvalues
A := test_AA[idxA]
a := M_Alloc2(nd[idxA])
Ten2Man(a, A)
io.PfYel("\n\ntst # %d ###################################################################################\n", idxA)
io.Pfblue2("a = %v\n", a)
// inverse
Ai := Alloc2()
ai := M_Alloc2(nd[idxA])
detA, err := Inv(Ai, A)
if err != nil {
chk.Panic("%v", err)
}
deta_ := M_Det(a)
deta, err := M_Inv(ai, a, MINDET)
if err != nil {
chk.Panic("%v", err)
}
Ai_ := Alloc2()
Man2Ten(Ai_, ai)
aia := M_Alloc2(nd[idxA])
err = M_Dot(aia, ai, a, nonsymTol)
if err != nil {
chk.Panic("%v", err)
}
chk.Scalar(tst, "detA", 1e-14, detA, deta)
chk.Scalar(tst, "deta", 1e-14, deta, deta_)
chk.Matrix(tst, "Ai", 1e-14, Ai, Ai_)
chk.Vector(tst, "ai*a", 1e-15, aia, Im[:2*nd[idxA]])
io.Pforan("ai*a = %v\n", aia)
// derivative of inverse
dtol_tmp := dtol
if idxA == 5 {
dtol = 1e-8
}
var tmp float64
ai_tmp := M_Alloc2(nd[idxA])
daida := M_Alloc4(nd[idxA])
M_InvDeriv(daida, ai)
io.Pforan("ai = %v\n", ai)
for i := 0; i < len(a); i++ {
for j := 0; j < len(a); j++ {
//dnum, _ := num.DerivForward(func(x float64, args ...interface{}) (res float64) {
dnum, _ := num.DerivCentral(func(x float64, args ...interface{}) (res float64) {
tmp, a[j] = a[j], x
_, err := M_Inv(ai_tmp, a, MINDET)
a[j] = tmp
if err != nil {
chk.Panic("daida failed:\n%v", err)
}
return ai_tmp[i]
}, a[j], 1e-6)
chk.AnaNum(tst, io.Sf("dai/da[%d][%d]", i, j), dtol, daida[i][j], dnum, dver)
}
}
dtol = dtol_tmp
}
}