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matrix_test.go
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614 lines (601 loc) · 90.5 KB
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package tensor
import (
"fmt"
"math"
"math/cmplx"
"testing"
)
func TestEye(t *testing.T) {
t.Parallel()
tests := []struct {
n int
k int
b *Dense
}{
{n: 4, k: 0, b: T2([][]complex64{{1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}})},
{n: 4, k: 2, b: T2([][]complex64{{0, 0, 1, 0}, {0, 0, 0, 1}, {0, 0, 0, 0}, {0, 0, 0, 0}})},
{n: 4, k: -2, b: T2([][]complex64{{0, 0, 0, 0}, {0, 0, 0, 0}, {1, 0, 0, 0}, {0, 1, 0, 0}})},
}
for i, test := range tests {
t.Run(fmt.Sprintf("%d", i), func(t *testing.T) {
t.Parallel()
b := Zeros(1).Eye(test.n, test.k)
if err := b.Equal(test.b, 0); err != nil {
t.Fatalf("%#v %#v", b, test.b)
}
})
}
}
func TestInfNorm(t *testing.T) {
t.Parallel()
tests := []struct {
a *Dense
norm float32
}{
{
a: T2([][]complex64{{-3, 3 + 4i, 7}, {2, 6, 4}, {0, 2, 8}}),
norm: 15,
},
}
for i, test := range tests {
t.Run(fmt.Sprintf("%d", i), func(t *testing.T) {
t.Parallel()
if test.a.InfNorm() != test.norm {
t.Fatalf("%f %f", test.a.InfNorm(), test.norm)
}
})
}
}
func TestTriu(t *testing.T) {
t.Parallel()
tests := []struct {
a *Dense
k int
b [][]complex64
}{
{
a: T2([][]complex64{
{999, 1 + 2i, 5i, 3},
{-2, 999, 3i, 4},
{-1i, 1 - 3i, 999, 7},
{1, 0, -3, 999},
{99, 99, 99, 99},
}),
k: -3,
b: [][]complex64{
{999, 1 + 2i, 5i, 3},
{-2, 999, 3i, 4},
{-1i, 1 - 3i, 999, 7},
{1, 0, -3, 999},
{0, 99, 99, 99},
},
},
{
a: T2([][]complex64{
{999, 1 + 2i, 5i, 3},
{-2, 999, 3i, 4},
{-1i, 1 - 3i, 999, 7},
{1, 0, -3, 999},
{99, 99, 99, 99},
}),
k: -2,
b: [][]complex64{
{999, 1 + 2i, 5i, 3},
{-2, 999, 3i, 4},
{-1i, 1 - 3i, 999, 7},
{0, 0, -3, 999},
{0, 0, 99, 99},
},
},
{
a: T2([][]complex64{
{999, 1 + 2i, 5i, 3},
{-2, 999, 3i, 4},
{-1i, 1 - 3i, 999, 7},
{1, 0, -3, 999},
{99, 99, 99, 99},
}),
k: -1,
b: [][]complex64{
{999, 1 + 2i, 5i, 3},
{-2, 999, 3i, 4},
{0, 1 - 3i, 999, 7},
{0, 0, -3, 999},
{0, 0, 0, 99},
},
},
{
a: T2([][]complex64{
{999, 1 + 2i, 5i, 3},
{-2, 999, 3i, 4},
{-1i, 1 - 3i, 999, 7},
{1, 0, -3, 999},
{99, 99, 99, 99},
}),
k: 0,
b: [][]complex64{
{999, 1 + 2i, 5i, 3},
{0, 999, 3i, 4},
{0, 0, 999, 7},
{0, 0, 0, 999},
{0, 0, 0, 0},
},
},
{
a: T2([][]complex64{
{999, 1 + 2i, 5i, 3},
{-2, 999, 3i, 4},
{-1i, 1 - 3i, 999, 7},
{1, 0, -3, 999},
{99, 99, 99, 99},
}),
k: 1,
b: [][]complex64{
{0, 1 + 2i, 5i, 3},
{0, 0, 3i, 4},
{0, 0, 0, 7},
{0, 0, 0, 0},
{0, 0, 0, 0},
},
},
{
a: T2([][]complex64{
{999, 1 + 2i, 5i, 3},
{-2, 999, 3i, 4},
{-1i, 1 - 3i, 999, 7},
{1, 0, -3, 999},
{99, 99, 99, 99},
}),
k: 2,
b: [][]complex64{
{0, 0, 5i, 3},
{0, 0, 0, 4},
{0, 0, 0, 0},
{0, 0, 0, 0},
{0, 0, 0, 0},
},
},
{
a: T2([][]complex64{
{999, 1 + 2i, 5i, 3},
{-2, 999, 3i, 4},
{-1i, 1 - 3i, 999, 7},
{1, 0, -3, 999},
{99, 99, 99, 99},
}),
k: 3,
b: [][]complex64{
{0, 0, 0, 3},
{0, 0, 0, 0},
{0, 0, 0, 0},
{0, 0, 0, 0},
{0, 0, 0, 0},
},
},
{
a: T2([][]complex64{
{999, 1 + 2i, 5i, 3, 99},
{-2, 999, 3i, 4, 99},
{-1i, 1 - 3i, 999, 7, 99},
{1, 0, -3, 999, 99},
}),
k: 3,
b: [][]complex64{
{0, 0, 0, 3, 99},
{0, 0, 0, 0, 99},
{0, 0, 0, 0, 0},
{0, 0, 0, 0, 0},
},
},
}
for i, test := range tests {
t.Run(fmt.Sprintf("%d", i), func(t *testing.T) {
t.Parallel()
if err := equal2(test.a.Triu(test.k), test.b, 0); err != nil {
t.Fatalf("%+v", err)
}
})
}
}
func TestTril(t *testing.T) {
t.Parallel()
tests := []struct {
a *Dense
k int
b [][]complex64
}{
{
a: T2([][]complex64{
{999, 1 + 2i, 5i, 3},
{-2, 999, 3i, 4},
{-1i, 1 - 3i, 999, 7},
{1, 0, -3, 999},
{99, 99, 99, 99},
}),
k: 2,
b: [][]complex64{
{999, 1 + 2i, 5i, 0},
{-2, 999, 3i, 4},
{-1i, 1 - 3i, 999, 7},
{1, 0, -3, 999},
{99, 99, 99, 99},
},
},
{
a: T2([][]complex64{
{999, 1 + 2i, 5i, 3},
{-2, 999, 3i, 4},
{-1i, 1 - 3i, 999, 7},
{1, 0, -3, 999},
{99, 99, 99, 99},
}),
k: 1,
b: [][]complex64{
{999, 1 + 2i, 0, 0},
{-2, 999, 3i, 0},
{-1i, 1 - 3i, 999, 7},
{1, 0, -3, 999},
{99, 99, 99, 99},
},
},
{
a: T2([][]complex64{
{999, 1 + 2i, 5i, 3},
{-2, 999, 3i, 4},
{-1i, 1 - 3i, 999, 7},
{1, 0, -3, 999},
{99, 99, 99, 99},
}),
k: 0,
b: [][]complex64{
{999, 0, 0, 0},
{-2, 999, 0, 0},
{-1i, 1 - 3i, 999, 0},
{1, 0, -3, 999},
{99, 99, 99, 99},
},
},
{
a: T2([][]complex64{
{999, 1 + 2i, 5i, 3},
{-2, 999, 3i, 4},
{-1i, 1 - 3i, 999, 7},
{1, 0, -3, 999},
{99, 99, 99, 99},
}),
k: -3,
b: [][]complex64{
{0, 0, 0, 0},
{0, 0, 0, 0},
{0, 0, 0, 0},
{1, 0, 0, 0},
{99, 99, 0, 0},
},
},
{
a: T2([][]complex64{
{999, 1 + 2i, 5i, 3, 99},
{-2, 999, 3i, 4, 99},
{-1i, 1 - 3i, 999, 7, 99},
{1, 0, -3, 999, 99},
}),
k: 2,
b: [][]complex64{
{999, 1 + 2i, 5i, 0, 0},
{-2, 999, 3i, 4, 0},
{-1i, 1 - 3i, 999, 7, 99},
{1, 0, -3, 999, 99},
},
},
}
for i, test := range tests {
t.Run(fmt.Sprintf("%d", i), func(t *testing.T) {
t.Parallel()
if err := equal2(test.a.Tril(test.k), test.b, 0); err != nil {
t.Fatalf("%+v", err)
}
})
}
}
func TestEig22(t *testing.T) {
t.Parallel()
tests := []struct {
a *Dense
lambda0 complex64
lambda1 complex64
}{
{
a: T2([][]complex64{{2 + 1i, -3 + 2i}, {1 - 3i, -1i}}),
lambda0: -1.85847 - 2.27395i,
lambda1: 3.85847 + 2.27395i,
},
}
for i, test := range tests {
t.Run(fmt.Sprintf("%d", i), func(t *testing.T) {
t.Parallel()
lambda0, lambda1 := eig22(test.a)
if abs(lambda0-test.lambda0) > 1e-5 {
t.Fatalf("%v %v", lambda0, test.lambda0)
}
if abs(lambda1-test.lambda1) > 1e-5 {
t.Fatalf("%v %v", lambda1, test.lambda1)
}
})
}
}
func TestSVD22(t *testing.T) {
t.Parallel()
tests := []struct {
a *Dense
s [][]complex64
}{
{
a: T2([][]complex64{{4, -3}, {0, 1}}),
s: [][]complex64{{5.03679629, 0}, {0, 0.7941556}},
},
{
a: T2([][]complex64{{4, -3}, {-2, 1}}),
s: [][]complex64{{5.4649857, 0}, {0, 0.36596619}},
},
{
a: T2([][]complex64{{2 + 1i, -3 + 2i}, {0, -1i}}),
s: [][]complex64{{4.32817429, 0}, {0, 0.51663076}},
},
{
a: T2([][]complex64{{2 + 1i, -3 + 2i}, {1 - 3i, -1i}}),
s: [][]complex64{{4.53908337, 0}, {0, 2.89770982}},
},
{
a: T2([][]complex64{{-0.999931, 1e-8}, {-1e-8i, 0.9998751}}),
s: [][]complex64{{0.999931, 0}, {0, 0.9998751}},
},
{
a: T2([][]complex64{{-0.999931, 0}, {0, 0.9998751}}),
s: [][]complex64{{0.999931, 0}, {0, 0.9998751}},
},
{
a: T2([][]complex64{{0.9998751, 0}, {1e-8i, -0.999931i}}),
s: [][]complex64{{0.999931, 0}, {0, 0.9998751}},
},
{
a: T2([][]complex64{{0, -0.999931}, {0.9998751, 0}}),
s: [][]complex64{{0.999931, 0}, {0, 0.9998751}},
},
{
a: T2([][]complex64{{0, 0.9998751i}, {-0.999931, 1e-8 - 1e-8i}}),
s: [][]complex64{{0.999931, 0}, {0, 0.9998751}},
},
{
a: T2([][]complex64{{0, 0.9998751i}, {-0.999931, 1e-5 - 1e-5i}}),
s: [][]complex64{{0.99993188, 0}, {0, 0.99987422}},
},
{
a: T2([][]complex64{{0, 0}, {0.9998751, -0.999931}}),
s: [][]complex64{{1.41407645, 0}, {0, 0}},
},
}
for i, test := range tests {
t.Run(fmt.Sprintf("%d", i), func(t *testing.T) {
t.Parallel()
s := Zeros(test.a.Shape()...).Set([]int{0, 0}, test.a)
u, v := Zeros(2, 2), Zeros(2, 2)
svd22(s, u, v)
if err := equal2(s, test.s, epsilon); err != nil {
t.Fatalf("%+v %#v", err, s.ToSlice2())
}
eye := Zeros(1).Eye(2, 0).ToSlice2()
if err := equal2(gemm(u, u.H()), eye, epsilon); err != nil {
t.Fatalf("%+v", err)
}
if err := equal2(gemm(v, v.H()), eye, epsilon); err != nil {
t.Fatalf("%+v", err)
}
usv := gemm(u, s, v.H())
if err := equal2(usv, test.a.ToSlice2(), epsilon); err != nil {
t.Fatalf("%+v", err)
}
})
}
}
func TestExp(t *testing.T) {
t.Parallel()
// transient returns the transient example described in
// Nineteen Dubious Ways to Compute the Exponential of a Matrix, Twenty-Five Years Later, C.B. Moler and C.F.Van Loan (2003), SIAM Review 45, 3-49.
transient := func() *Dense {
n := 25
c := Zeros(1).Eye(n, 1)
c.SetAt([]int{n - 1, 0}, 1)
d := Zeros(n, n)
for i := range n {
v := complex64(cmplx.Exp(1i * 2 * math.Pi * complex(float64(i)/float64(n), 0)))
d.SetAt([]int{i, i}, v)
}
return c.Add(1, d).Add(-1.1, Zeros(1).Eye(n, 0))
}
tests := []struct {
a *Dense
b *Dense
tol float32
}{
{
a: T2([][]complex64{{-49, 24}, {-64, 31}}),
b: T2([][]complex64{{-0.735759, 0.551819}, {-1.471518, 1.103638}}),
tol: 1e-4,
},
{
a: T2([][]complex64{{0, 6, 0, 0}, {0, 0, 6, 0}, {0, 0, 0, 6}, {0, 0, 0, 0}}),
b: T2([][]complex64{{1, 6, 18, 36}, {0, 1, 6, 18}, {0, 0, 1, 6}, {0, 0, 0, 1}}),
tol: 1e-6,
},
{
a: T2([][]complex64{{1 + 1e-5, 1}, {0, 1 - 1e-5}}),
b: T2([][]complex64{{2.718309, 2.718282}, {0, 2.718255}}),
tol: 1e-6,
},
{
a: transient().Mul(2),
b: T2([][]complex64{
{0.818731 + 1.13847e-31i, 1.52345 + 0.382639i, 1.28844 + 0.666142i, 0.667249 + 0.547847i, 0.240877 + 0.286824i, 0.0656123 + 0.108774i, 0.0143394 + 0.0322384i, 0.00266958 + 0.00786244i, 0.000453086 + 0.00163831i, 7.52371e-05 + 0.000299963i, 1.27951e-05 + 4.92731e-05i, 2.22266e-06 + 7.371e-06i, 3.81287e-07 + 1.01458e-06i, 6.2545e-08 + 1.29344e-07i, 9.63988e-09 + 1.53285e-08i, 1.38825e-09 + 1.6908e-09i, 1.86983e-10 + 1.7343e-10i, 2.36456e-11 + 1.64867e-11i, 2.82111e-12 + 1.44299e-12i, 3.1912e-13 + 1.14948e-13i, 3.43798e-14 + 8.16806e-15i, 3.54037e-15 + 4.98885e-16i, 3.49324e-16 + 2.42114e-17i, 3.3052e-17 + 7.45117e-19i, 2.99617e-18 + 3.62075e-31i},
{2.99617e-18 + 5.56401e-31i, 0.67571 + 0.366847i, 1.04317 + 0.92095i, 0.732563 + 0.974421i, 0.313266 + 0.61809i, 0.0920897 + 0.274064i, 0.0199985 + 0.0928712i, 0.00344639 + 0.0255249i, 0.000541193 + 0.00593654i, 9.87654e-05 + 0.00120511i, 2.31286e-05 + 0.000218348i, 5.79238e-06 + 3.58669e-05i, 1.33593e-06 + 5.39762e-06i, 2.72902e-07 + 7.49073e-07i, 4.9585e-08 + 9.62153e-08i, 8.12234e-09 + 1.14538e-08i, 1.21571e-09 + 1.26275e-09i, 1.68187e-10 + 1.28528e-10i, 2.17133e-11 + 1.20022e-11i, 2.63675e-12 + 1.01677e-12i, 3.03133e-13 + 7.66066e-14i, 3.31577e-14 + 4.94726e-15i, 3.46226e-15 + 2.53194e-16i, 3.45595e-16 + 8.19629e-18i, 3.29579e-17 + 9.42935e-31i},
{3.3052e-17 - 7.45117e-19i, 2.99617e-18 + 5.21927e-32i, 0.36481 + 0.524989i, 0.442927 + 1.00676i, 0.228837 + 0.893532i, 0.0600332 + 0.502007i, 0.00438337 + 0.204928i, -0.0027104 + 0.0658935i, -0.00120341 + 0.0176024i, -0.000246279 + 0.00405266i, -1.6389e-05 + 0.000824818i, 7.84888e-06 + 0.000150952i, 3.83884e-06 + 2.5119e-05i, 1.08103e-06 + 3.82685e-06i, 2.38119e-07 + 5.35837e-07i, 4.47276e-08 + 6.90608e-08i, 7.45689e-09 + 8.18676e-09i, 1.12946e-09 + 8.89527e-10i, 1.57862e-10 + 8.79257e-11i, 2.05925e-11 + 7.79397e-12i, 2.52872e-12 + 6.0256e-13i, 2.94191e-13 + 3.82237e-14i, 3.25643e-14 + 1.65548e-15i, 3.43636e-15 - 2.62296e-29i, 3.45595e-16 - 8.19629e-18i},
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{0.240877 - 0.286824i, 0.124641 - 0.0928336i, 0.0473158 - 0.0207425i, 0.0139198 - 0.00279119i, 0.00330581 + 0i, 0.000655497 + 0.000116602i, 0.000111784 + 3.78926e-05i, 1.68436e-05 + 8.1357e-06i, 2.29877e-06 + 1.39066e-06i, 2.90519e-07 + 2.02438e-07i, 3.4634e-08 + 2.59976e-08i, 3.94886e-09 + 3.00947e-09i, 4.34369e-10 + 3.18338e-10i, 4.62885e-11 + 3.10178e-11i, 4.78377e-12 + 2.79281e-12i, 4.79221e-13 + 2.31923e-13i, 4.64967e-14 + 1.76061e-14i, 4.36772e-15 + 1.19586e-15i, 3.97318e-16 + 6.89744e-17i, 3.50282e-17 + 2.84953e-18i, 2.99617e-18 - 2.24111e-30i, -0.0380473 - 0.321323i, 0.0410402 - 0.785498i, 0.228837 - 0.893532i, 0.313266 - 0.61809i},
{0.667249 - 0.547847i, 0.396285 - 0.190764i, 0.168257 - 0.0371515i, 0.0542716 - 1.73472e-17i, 0.0139198 + 0.00279119i, 0.00294779 + 0.00115042i, 0.000532807 + 0.000304623i, 8.47418e-05 + 6.27756e-05i, 1.22006e-05 + 1.08193e-05i, 1.63101e-06 + 1.62229e-06i, 2.0671e-07 + 2.17075e-07i, 2.51976e-08 + 2.63747e-08i, 2.97649e-09 + 2.94426e-09i, 3.41341e-10 + 3.04226e-10i, 3.79474e-11 + 2.92027e-11i, 4.0798e-12 + 2.60385e-12i, 4.23369e-13 + 2.14699e-13i, 4.2369e-14 + 1.61919e-14i, 4.08989e-15 + 1.09116e-15i, 3.81186e-16 + 6.22427e-17i, 3.43486e-17 + 2.52975e-18i, 2.99617e-18 + 4.42579e-31i, 0.0953867 - 0.466478i, 0.442927 - 1.00676i, 0.732563 - 0.974421i},
{1.28844 - 0.666142i, 0.940233 - 0.223729i, 0.464405 - 2.498e-16i, 0.168257 + 0.0371515i, 0.0473158 + 0.0207425i, 0.0108002 + 0.00712948i, 0.00208029 + 0.00184398i, 0.000350517 + 0.000388349i, 5.34572e-05 + 6.96732e-05i, 7.61145e-06 + 1.09759e-05i, 1.0369e-06 + 1.55144e-06i, 1.3715e-07 + 1.99851e-07i, 1.76904e-08 + 2.3718e-08i, 2.21889e-09 + 2.61154e-09i, 2.69155e-10 + 2.67794e-10i, 3.14208e-11 + 2.55928e-11i, 3.51977e-12 + 2.27409e-12i, 3.7801e-13 + 1.86669e-13i, 3.89461e-14 + 1.39743e-14i, 3.85547e-15 + 9.30204e-16i, 3.67435e-16 + 5.20261e-17i, 3.37699e-17 + 2.05102e-18i, 2.99617e-18 + 1.51051e-30i, 0.36481 - 0.524989i, 1.04317 - 0.92095i},
{1.52345 - 0.382639i, 1.53862 - 4.996e-16i, 0.940233 + 0.223729i, 0.396285 + 0.190764i, 0.124641 + 0.0928336i, 0.0309737 + 0.0321727i, 0.0063792 + 0.00870776i, 0.00113889 + 0.00194407i, 0.000184304 + 0.000371752i, 2.81908e-05 + 6.25903e-05i, 4.20462e-06 + 9.47022e-06i, 6.19349e-07 + 1.30705e-06i, 8.96982e-08 + 1.66276e-07i, 1.26137e-08 + 1.96294e-08i, 1.70234e-09 + 2.15847e-09i, 2.18915e-10 + 2.2133e-10i, 2.67495e-11 + 2.11341e-11i, 3.10654e-12 + 1.8711e-12i, 3.43578e-13 + 1.5231e-13i, 3.62898e-14 + 1.12271e-14i, 3.67144e-15 + 7.28251e-16i, 3.56681e-16 + 3.90837e-17i, 3.33285e-17 + 1.44342e-18i, 2.99617e-18 + 7.68446e-31i, 0.67571 - 0.366847i},
}),
tol: 1e-5,
},
{
a: transient().Mul(14),
b: T2([][]complex64{
{0.247835 - 8.67362e-19i, -0.0103584 + 1.59544i, -4.67805 + 1.196i, -6.03203 - 6.94765i, 2.66025 - 12.2875i, 11.0538 - 7.3897i, 11.4561 + 0.358556i, 7.29101 + 4.10668i, 3.46981 + 4.05096i, 1.42025 + 2.69266i, 0.596458 + 1.47415i, 0.303047 + 0.713733i, 0.182544 + 0.309611i, 0.112695 + 0.115199i, 0.0640891 + 0.0308021i, 0.0314165 - 9.24193e-05i, 0.0120542 - 0.00742012i, 0.00244836 - 0.0061652i, -0.00112641 - 0.00310882i, -0.00164114 - 0.000739625i, -0.00100377 + 0.000465297i, -0.000199702 + 0.000777355i, 0.00040645 + 0.000602985i, 0.000792132 + 0.000264174i, 0.00106226 - 6.50521e-19i},
{0.00106226 - 4.33681e-19i, -0.14861 - 0.0526998i, -0.00789037 - 0.806161i, 1.71281 - 1.05018i, 3.10784 + 1.00202i, 2.0503 + 3.33141i, -0.0408562 + 3.70778i, -1.23502 + 2.64422i, -1.3216 + 1.47048i, -0.930464 + 0.736254i, -0.525238 + 0.376496i, -0.251097 + 0.208358i, -0.0994068 + 0.119832i, -0.0275185 + 0.0659963i, 0.000356155 + 0.0321653i, 0.00720184 + 0.0125031i, 0.00596139 + 0.00276956i, 0.00298492 - 0.000845256i, 0.000732084 - 0.00136737i, -0.000326492 - 0.000777744i, -0.000505022 - 0.000106493i, -0.000254734 + 0.000273083i, 0.000102909 + 0.000335693i, 0.000435736 + 0.000188696i, 0.000758759 - 6.50521e-19i},
{0.000792132 - 0.000264174i, 0.00106226 - 9.75782e-19i, 0.040005 + 0.019851i, 0.0394244 + 0.19202i, -0.228965 + 0.36734i, -0.584332 + 0.244792i, -0.691071 - 0.0576874i, -0.553007 - 0.254858i, -0.35708 - 0.273314i, -0.211459 - 0.197482i, -0.124469 - 0.111112i, -0.073451 - 0.0490321i, -0.041408 - 0.0143346i, -0.0207672 + 0.000726267i, -0.00835466 + 0.00471536i, -0.0019873 + 0.00391556i, 0.000450554 + 0.0019793i, 0.000824312 + 0.000505001i, 0.000455451 - 0.000165799i, 5.81917e-05 - 0.000255857i, -0.00012116 - 0.000101607i, -9.62994e-05 + 5.37578e-05i, 3.38882e-05 + 9.66074e-05i, 0.000200533 - 8.13152e-20i, 0.000435736 - 0.000188696i},
{0.00040645 - 0.000602985i, 0.000890154 - 0.000511749i, 0.00106226 - 7.86047e-19i, -0.00474404 - 0.00044578i, -0.0158055 - 0.0160692i, -0.0123613 - 0.0457569i, 0.00764818 - 0.0650599i, 0.0247207 - 0.0633963i, 0.0275734 - 0.0500509i, 0.0200373 - 0.035441i, 0.0100924 - 0.02342i, 0.0026183 - 0.0142095i, -0.0011926 - 0.00749032i, -0.00216526 - 0.00308412i, -0.00167047 - 0.000689627i, -0.000817564 + 0.000241865i, -0.000190703 + 0.000355218i, 7.74532e-05 + 0.000178773i, 9.71179e-05 + 1.45604e-05i, 2.94989e-05 - 4.37663e-05i, -1.86584e-05 - 2.46165e-05i, -1.70853e-05 + 7.79072e-06i, 1.13808e-05 + 5.42101e-20i, 3.38882e-05 - 9.66074e-05i, 0.000102909 - 0.000335693i},
{-0.000199702 - 0.000777355i, 0.000396695 - 0.00111359i, 0.00104667 - 0.000727169i, 0.00106226 - 7.21672e-19i, 0.000876208 + 0.000132442i, 0.00158031 - 0.000147914i, 0.00293862 - 1.78382e-05i, 0.00387097 + 0.000393647i, 0.00390564 + 0.000473702i, 0.00324128 + 9.79204e-05i, 0.00224922 - 0.000397907i, 0.00125306 - 0.000678493i, 0.000482161 - 0.000651143i, 3.62303e-05 - 0.000428685i, -0.000120324 - 0.000181749i, -0.000105339 - 2.1398e-05i, -4.01243e-05 + 3.3982e-05i, 3.9944e-06 + 2.56788e-05i, 1.27289e-05 + 3.55079e-06i, 3.82636e-06 - 5.91765e-06i, -2.92832e-06 - 2.91079e-06i, -3.44747e-06 - 1.35525e-20i, -1.70853e-05 - 7.79072e-06i, -9.62994e-05 - 5.37578e-05i, -0.000254734 - 0.000273083i},
{-0.00100377 - 0.000465297i, -0.000691325 - 0.00149555i, 0.000489411 - 0.00174067i, 0.00125183 - 0.000896899i, 0.00106226 - 1.32815e-18i, 0.000533565 + 0.000334655i, 0.000192978 + 0.000312187i, 8.47973e-05 + 0.00023151i, 8.66229e-05 + 0.000174421i, 0.000110043 + 0.000119563i, 0.000114345 + 5.60225e-05i, 8.96277e-05 - 2.18187e-07i, 4.818e-05 - 3.02552e-05i, 1.11235e-05 - 3.12683e-05i, -7.78453e-06 - 1.64258e-05i, -9.30349e-06 - 2.11441e-06i, -3.38793e-06 + 3.52703e-06i, 9.50835e-07 + 2.30229e-06i, 1.27465e-06 - 1.40027e-07i, 1.652e-08 - 6.99462e-07i, -7.35458e-07 + 6.77626e-21i, -2.92832e-06 + 2.91079e-06i, -1.86584e-05 + 2.46165e-05i, -0.00012116 + 0.000101607i, -0.000505022 + 0.000106493i},
{-0.00164114 + 0.000739625i, -0.00251017 - 0.00096615i, -0.00123059 - 0.0027127i, 0.000776088 - 0.00245095i, 0.00149277 - 0.00101027i, 0.00106226 - 9.82558e-19i, 0.000471385 + 0.00026685i, 0.000143654 + 0.000199915i, 2.92106e-05 + 9.9341e-05i, 4.05991e-06 + 4.13948e-05i, 2.55291e-06 + 1.53893e-05i, 3.18747e-06 + 4.04593e-06i, 1.95678e-06 - 6.35587e-07i, 5.00175e-08 - 1.54418e-06i, -9.01708e-07 - 6.50924e-07i, -6.36646e-07 + 2.54783e-07i, -2.49893e-08 + 3.80034e-07i, 1.86183e-07 + 7.06727e-08i, 4.73783e-08 - 9.25412e-08i, -9.27242e-08 - 8.47033e-22i, 1.652e-08 + 6.99462e-07i, 3.82636e-06 + 5.91765e-06i, 2.94989e-05 + 4.37663e-05i, 5.81917e-05 + 0.000255857i, -0.000326492 + 0.000777744i},
{-0.00112641 + 0.00310882i, -0.0046388 + 0.00174546i, -0.00491177 - 0.00253766i, -0.0014819 - 0.00458875i, 0.00132694 - 0.00315828i, 0.00175432 - 0.00106017i, 0.00106226 - 1.0842e-18i, 0.000438593 + 0.000214576i, 0.000138641 + 0.000148657i, 3.57856e-05 + 6.94321e-05i, 8.1476e-06 + 2.69309e-05i, 1.93767e-06 + 9.36567e-06i, 5.68577e-07 + 3.00875e-06i, 1.69352e-07 + 9.37184e-07i, 5.5763e-08 + 3.33779e-07i, 5.73622e-08 + 1.36557e-07i, 5.29566e-08 + 3.28719e-08i, 1.85274e-08 - 8.77275e-09i, -8.93094e-09 + 0i, 4.73783e-08 + 9.25412e-08i, 1.27465e-06 + 1.40027e-07i, 1.27289e-05 - 3.55079e-06i, 9.71179e-05 - 1.45604e-05i, 0.000455451 + 0.000165799i, 0.000732084 + 0.00136737i},
{0.00244836 + 0.0061652i, -0.00520824 + 0.00852953i, -0.0111336 + 0.00150469i, -0.00763596 - 0.00630134i, -0.000957955 - 0.00705591i, 0.00216468 - 0.00373933i, 0.00202007 - 0.00104345i, 0.00106226 - 1.0842e-18i, 0.000417056 + 0.000168398i, 0.00013724 + 0.000109831i, 4.13451e-05 + 4.94766e-05i, 1.24611e-05 + 1.87879e-05i, 4.05848e-06 + 6.45719e-06i, 1.47034e-06 + 2.06698e-06i, 5.78693e-07 + 6.14085e-07i, 2.34508e-07 + 1.58828e-07i, 9.11474e-08 + 2.89405e-08i, 3.19845e-08 - 5.29396e-23i, 1.85274e-08 + 8.77275e-09i, 1.86183e-07 - 7.06727e-08i, 9.50835e-07 - 2.30229e-06i, 3.9944e-06 - 2.56788e-05i, 7.74532e-05 - 0.000178773i, 0.000824312 - 0.000505001i, 0.00298492 + 0.000845256i},
{0.0120542 + 0.00742012i, 0.000782723 + 0.0214758i, -0.0190685 + 0.0151991i, -0.0213392 - 0.00408972i, -0.00898401 - 0.0130284i, 0.000805508 - 0.00970349i, 0.00324887 - 0.00406086i, 0.00227331 - 0.000961165i, 0.00106226 - 9.75782e-19i, 0.000402762 + 0.000126719i, 0.000137081 + 7.77618e-05i, 4.51482e-05 + 3.33197e-05i, 1.5196e-05 + 1.19674e-05i, 5.3551e-06 + 3.7719e-06i, 1.96038e-06 + 1.02084e-06i, 7.25889e-07 + 2.03186e-07i, 2.63703e-07 - 1.05879e-22i, 9.11474e-08 - 2.89405e-08i, 5.29566e-08 - 3.28719e-08i, -2.49893e-08 - 3.80034e-07i, -3.38793e-06 - 3.52703e-06i, -4.01243e-05 - 3.3982e-05i, -0.000190703 - 0.000355218i, 0.000450554 - 0.0019793i, 0.00596139 - 0.00276956i},
{0.0314165 + 9.24193e-05i, 0.0245178 + 0.0415019i, -0.023693 + 0.0499893i, -0.0485779 + 0.0114454i, -0.0309181 - 0.0200384i, -0.00646975 - 0.0220667i, 0.00400431 - 0.0118078i, 0.00447551 - 0.004012i, 0.00249813 - 0.000818488i, 0.00106226 - 1.0842e-18i, 0.000393449 + 8.83273e-05i, 0.00013729 + 4.98536e-05i, 4.74794e-05 + 1.92708e-05i, 1.66756e-05 + 5.83215e-06i, 5.94434e-06 + 1.24129e-06i, 2.11181e-06 - 1.37643e-21i, 7.25889e-07 - 2.03186e-07i, 2.34508e-07 - 1.58828e-07i, 5.73622e-08 - 1.36557e-07i, -6.36646e-07 - 2.54783e-07i, -9.30349e-06 + 2.11441e-06i, -0.000105339 + 2.1398e-05i, -0.000817564 - 0.000241865i, -0.0019873 - 0.00391556i, 0.00720184 - 0.0125031i},
{0.0640891 - 0.0308021i, 0.0890724 + 0.0655524i, -0.0101121 + 0.128262i, -0.0995126 + 0.0628916i, -0.0850171 - 0.023435i, -0.0301352 - 0.0470601i, 0.00186529 - 0.0307181i, 0.00836919 - 0.0125362i, 0.00569238 - 0.00353366i, 0.00268041 - 0.000624383i, 0.00106226 - 1.0842e-18i, 0.000387821 + 5.21499e-05i, 0.000137508 + 2.43682e-05i, 4.85852e-05 + 6.31126e-06i, 1.71444e-05 - 8.47033e-21i, 5.94434e-06 - 1.24129e-06i, 1.96038e-06 - 1.02084e-06i, 5.78693e-07 - 6.14085e-07i, 5.5763e-08 - 3.33779e-07i, -9.01708e-07 + 6.50924e-07i, -7.78453e-06 + 1.64258e-05i, -0.000120324 + 0.000181749i, -0.00167047 + 0.000689627i, -0.00835466 - 0.00471536i, 0.000356155 - 0.0321653i},
{0.112695 - 0.115199i, 0.24101 + 0.0830016i, 0.0562347 + 0.296056i, -0.195078 + 0.201095i, -0.212954 - 0.0119402i, -0.0949157 - 0.0992995i, -0.0089344 - 0.0763749i, 0.0157778 - 0.0348849i, 0.0131347 - 0.011262i, 0.00672725 - 0.00263763i, 0.00280869 - 0.000391045i, 0.00106226 - 1.51788e-18i, 0.000385165 + 1.72451e-05i, 0.000137594 - 1.0842e-19i, 4.85852e-05 - 6.31126e-06i, 1.66756e-05 - 5.83215e-06i, 5.3551e-06 - 3.7719e-06i, 1.47034e-06 - 2.06698e-06i, 1.69352e-07 - 9.37184e-07i, 5.00175e-08 + 1.54418e-06i, 1.11235e-05 + 3.12683e-05i, 3.62303e-05 + 0.000428685i, -0.00216526 + 0.00308412i, -0.0207672 - 0.000726267i, -0.0275185 - 0.0659963i},
{0.182544 - 0.309611i, 0.575004 + 0.077272i, 0.24056 + 0.656202i, -0.391967 + 0.533067i, -0.511875 + 0.0297386i, -0.254458 - 0.219516i, -0.0376887 - 0.187665i, 0.0336573 - 0.0909271i, 0.0319951 - 0.0310246i, 0.0172225 - 0.0078573i, 0.00742236 - 0.00141035i, 0.00287491 - 0.000133137i, 0.00106226 - 4.33681e-19i, 0.000385165 - 1.72451e-05i, 0.000137508 - 2.43682e-05i, 4.74794e-05 - 1.92708e-05i, 1.5196e-05 - 1.19674e-05i, 4.05848e-06 - 6.45719e-06i, 5.68577e-07 - 3.00875e-06i, 1.95678e-06 + 6.35587e-07i, 4.818e-05 + 3.02552e-05i, 0.000482161 + 0.000651143i, -0.0011926 + 0.00749032i, -0.041408 + 0.0143346i, -0.0994068 - 0.119832i},
{0.303047 - 0.713733i, 1.28105 + 0.0569611i, 0.626099 + 1.44937i, -0.865769 + 1.25621i, -1.20292 + 0.0821608i, -0.606674 - 0.529777i, -0.0834008 - 0.459823i, 0.0901092 - 0.223557i, 0.0837376 - 0.0755374i, 0.0451427 - 0.0183828i, 0.0195873 - 0.00282251i, 0.00766727 - 1.21431e-17i, 0.00287491 + 0.000133137i, 0.00106226 - 1.0842e-18i, 0.000387821 - 5.21499e-05i, 0.00013729 - 4.98536e-05i, 4.51482e-05 - 3.33197e-05i, 1.24611e-05 - 1.87879e-05i, 1.93767e-06 - 9.36567e-06i, 3.18747e-06 - 4.04593e-06i, 8.96277e-05 + 2.18187e-07i, 0.00125306 + 0.000678493i, 0.0026183 + 0.0142095i, -0.073451 + 0.0490321i, -0.251097 - 0.208358i},
{0.596458 - 1.47415i, 2.69981 + 0.18457i, 1.18005 + 3.20676i, -2.13237 + 2.62173i, -2.72839 - 0.0818579i, -1.25559 - 1.37444i, -0.0612671 - 1.10012i, 0.28539 - 0.504106i, 0.228468 - 0.155034i, 0.117867 - 0.0295104i, 0.0502061 - 1.11022e-16i, 0.0195873 + 0.00282251i, 0.00742236 + 0.00141035i, 0.00280869 + 0.000391045i, 0.00106226 - 1.0842e-18i, 0.000393449 - 8.83273e-05i, 0.000137081 - 7.77618e-05i, 4.13451e-05 - 4.94766e-05i, 8.1476e-06 - 2.69309e-05i, 2.55291e-06 - 1.53893e-05i, 0.000114345 - 5.60225e-05i, 0.00224922 + 0.000397907i, 0.0100924 + 0.02342i, -0.124469 + 0.111112i, -0.525238 - 0.376496i},
{1.42025 - 2.69266i, 5.24125 + 1.11227i, 1.25882 + 6.8511i, -5.43522 + 4.52587i, -5.68439 - 1.39571i, -2.01714 - 3.55068i, 0.435579 - 2.43069i, 0.907625 - 0.965406i, 0.604354 - 0.222507i, 0.288777 - 1.11022e-16i, 0.117867 + 0.0295104i, 0.0451427 + 0.0183828i, 0.0172225 + 0.0078573i, 0.00672725 + 0.00263763i, 0.00268041 + 0.000624383i, 0.00106226 - 8.67362e-19i, 0.000402762 - 0.000126719i, 0.00013724 - 0.000109831i, 3.57856e-05 - 6.94321e-05i, 4.05991e-06 - 4.13948e-05i, 0.000110043 - 0.000119563i, 0.00324128 - 9.79204e-05i, 0.0200373 + 0.035441i, -0.211459 + 0.197482i, -0.930464 - 0.736254i},
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{11.4561 - 0.358556i, 4.431 + 22.8791i, -29.9776 + 16.368i, -31.3927 - 22.2456i, 0.735455 - 34.9163i, 20.0952 - 17.264i, 17.2981 - 1.42109e-14i, 8.31223 + 5.49683i, 2.58662 + 4.48234i, 0.435579 + 2.43069i, -0.0612671 + 1.10012i, -0.0834008 + 0.459823i, -0.0376887 + 0.187665i, -0.0089344 + 0.0763749i, 0.00186529 + 0.0307181i, 0.00400431 + 0.0118078i, 0.00324887 + 0.00406086i, 0.00202007 + 0.00104345i, 0.00106226 - 6.50521e-19i, 0.000471385 - 0.00026685i, 0.000192978 - 0.000312187i, 0.00293862 + 1.78382e-05i, 0.00764818 + 0.0650599i, -0.691071 + 0.0576874i, -0.0408562 - 3.70778i},
{11.0538 + 7.3897i, -13.0541 + 25.8894i, -44.1773 - 8.1655i, -13.4609 - 51.2721i, 33.2834 - 37.4073i, 39.3324 - 9.23706e-14i, 20.0952 + 17.264i, 4.33319 + 15.0857i, -1.48075 + 8.22887i, -2.01714 + 3.55068i, -1.25559 + 1.37444i, -0.606674 + 0.529777i, -0.254458 + 0.219516i, -0.0949157 + 0.0992995i, -0.0301352 + 0.0470601i, -0.00646975 + 0.0220667i, 0.000805508 + 0.00970349i, 0.00216468 + 0.00373933i, 0.00175432 + 0.00106017i, 0.00106226 - 8.13152e-19i, 0.000533565 - 0.000334655i, 0.00158031 + 0.000147914i, -0.0123613 + 0.0457569i, -0.584332 - 0.244792i, 2.0503 - 3.33141i},
{2.66025 + 12.2875i, -28.617 + 8.80385i, -26.4158 - 42.0405i, 34.0307 - 51.714i, 61.2487 + 0i, 33.2834 + 37.4073i, 0.735455 + 34.9163i, -11.2216 + 18.153i, -9.85058 + 6.29103i, -5.68439 + 1.39571i, -2.72839 + 0.0818579i, -1.20292 - 0.0821608i, -0.511875 - 0.0297386i, -0.212954 + 0.0119402i, -0.0850171 + 0.023435i, -0.0309181 + 0.0200384i, -0.00898401 + 0.0130284i, -0.000957955 + 0.00705591i, 0.00132694 + 0.00315828i, 0.00149277 + 0.00101027i, 0.00106226 - 7.86047e-19i, 0.000876208 - 0.000132442i, -0.0158055 + 0.0160692i, -0.228965 - 0.36734i, 3.10784 - 1.00202i},
{-6.03203 + 6.94765i, -19.3467 - 15.1814i, 18.1381 - 40.5396i, 59.2211 - 1.42109e-13i, 34.0307 + 51.714i, -13.4609 + 51.2721i, -31.3927 + 22.2456i, -24.3076 + 1.29031i, -12.7532 - 5.12665i, -5.43522 - 4.52587i, -2.13237 - 2.62173i, -0.865769 - 1.25621i, -0.391967 - 0.533067i, -0.195078 - 0.201095i, -0.0995126 - 0.0628916i, -0.0485779 - 0.0114454i, -0.0213392 + 0.00408972i, -0.00763596 + 0.00630134i, -0.0014819 + 0.00458875i, 0.000776088 + 0.00245095i, 0.00125183 + 0.000896899i, 0.00106226 - 9.21572e-19i, -0.00474404 + 0.00044578i, 0.0394244 - 0.19202i, 1.71281 + 1.05018i},
{-4.67805 - 1.196i, 3.50009 - 14.7451i, 30.6071 - 3.55271e-14i, 18.1381 + 40.5396i, -26.4158 + 42.0405i, -44.1773 + 8.1655i, -29.9776 - 16.368i, -11.2692 - 19.4535i, -1.43265 - 13.0594i, 1.25882 - 6.8511i, 1.18005 - 3.20676i, 0.626099 - 1.44937i, 0.24056 - 0.656202i, 0.0562347 - 0.296056i, -0.0101121 - 0.128262i, -0.023693 - 0.0499893i, -0.0190685 - 0.0151991i, -0.0111336 - 0.00150469i, -0.00491177 + 0.00253766i, -0.00123059 + 0.0027127i, 0.000489411 + 0.00174067i, 0.00104667 + 0.000727169i, 0.00106226 - 8.40257e-19i, 0.040005 - 0.019851i, -0.00789037 + 0.806161i},
{-0.0103584 - 1.59544i, 6.41539 - 4.44089e-15i, 3.50009 + 14.7451i, -19.3467 + 15.1814i, -28.617 - 8.80385i, -13.0541 - 25.8894i, 4.431 - 22.8791i, 10.49 - 12.1741i, 8.7041 - 4.43555i, 5.24125 - 1.11227i, 2.69981 - 0.18457i, 1.28105 - 0.0569611i, 0.575004 - 0.077272i, 0.24101 - 0.0830016i, 0.0890724 - 0.0655524i, 0.0245178 - 0.0415019i, 0.000782723 - 0.0214758i, -0.00520824 - 0.00852953i, -0.0046388 - 0.00174546i, -0.00251017 + 0.00096615i, -0.000691325 + 0.00149555i, 0.000396695 + 0.00111359i, 0.000890154 + 0.000511749i, 0.00106226 - 1.30104e-18i, -0.14861 + 0.0526998i},
}),
tol: 2e-4,
},
{
a: transient().Mul(28),
b: T2([][]complex64{
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{9.94331e-05 + 0.000469877i, -0.00132038 - 0.000189982i, 0.000479894 - 0.00250932i, 0.00366566 + 1.73472e-18i, 0.00159927 + 0.0038643i, -0.00223771 + 0.00325633i, -0.00315553 + 0.000455434i, -0.00195169 - 0.00112962i, -0.000718332 - 0.00123661i, -0.000121798 - 0.000820924i, 4.32879e-05 - 0.000446854i, 4.8073e-05 - 0.000225254i, 2.24365e-05 - 0.000111697i, 3.57492e-06 - 5.51042e-05i, -4.92347e-06 - 2.62065e-05i, -6.80947e-06 - 1.11388e-05i, -5.62706e-06 - 3.46064e-06i, -3.52844e-06 + 7.678e-08i, -1.57234e-06 + 1.29995e-06i, -1.62689e-07 + 1.30365e-06i, 6.31854e-07 + 7.46133e-07i, 8.83701e-07 - 2.64698e-22i, 8.69822e-07 - 7.29925e-07i, -7.38002e-06 + 2.5372e-06i, 6.52508e-05 - 9.19074e-05i},
{0.000508135 + 4.22428e-05i, -0.000585132 + 0.00117413i, -0.0020668 - 0.00121835i, 0.00118789 - 0.00309502i, 0.00366566 + 1.04083e-17i, 0.00175927 + 0.00288691i, -0.000815026 + 0.00255589i, -0.00158822 + 0.00100313i, -0.00118612 + 1.6049e-05i, -0.000636029 - 0.000264469i, -0.000294651 - 0.000231081i, -0.000134435 - 0.000139613i, -6.65182e-05 - 7.07195e-05i, -3.64582e-05 - 3.09675e-05i, -2.09834e-05 - 1.07263e-05i, -1.17178e-05 - 1.47468e-06i, -5.7959e-06 + 2.00822e-06i, -2.09979e-06 + 2.63731e-06i, -1.67996e-08 + 2.0087e-06i, 9.06406e-07 + 9.83008e-07i, 1.0336e-06 - 6.35275e-22i, 6.31854e-07 - 7.46133e-07i, -6.42636e-08 - 1.47083e-06i, 1.72161e-06 + 9.92045e-06i, -7.95987e-05 - 0.000108557i},
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{-0.00143181 - 0.000254872i, 0.0018472 - 0.0025224i, 0.00368669 + 0.00378121i, -0.00451385 + 0.00533324i, -0.00690064 - 0.00288033i, -0.000637273 - 0.00670148i, 0.00383893 - 0.00360074i, 0.00366566 - 1.38778e-17i, 0.00191434 + 0.00131479i, 0.000668818 + 0.00118807i, 0.000147575 + 0.000739808i, 6.7718e-06 + 0.00039975i, -6.43551e-06 + 0.00020607i, 5.10717e-06 + 0.000104967i, 1.34576e-05 + 5.21059e-05i, 1.5374e-05 + 2.35999e-05i, 1.30689e-05 + 8.05612e-06i, 8.90349e-06 + 1.35525e-20i, 4.46069e-06 - 3.44358e-06i, 6.41572e-07 - 3.9673e-06i, -2.09979e-06 - 2.63731e-06i, -3.52844e-06 - 7.678e-08i, -3.28153e-06 + 5.31457e-06i, -2.22466e-05 - 4.18392e-05i, 0.000207286 + 0.000407292i},
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}),
tol: 5e-4,
},
{
a: transient().Mul(36),
b: T2([][]complex64{
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{-0.561402 - 0.402048i, 0.825084 - 2.17421i, 4.51313 - 7.10543e-15i, 2.82195 + 5.39003i, -2.91836 + 5.56471i, -5.12692 + 1.28783i, -3.36694 - 1.72091i, -1.14275 - 2.0826i, -0.0356059 - 1.34471i, 0.226785 - 0.664045i, 0.184366 - 0.290003i, 0.101902 - 0.124283i, 0.046573 - 0.0561208i, 0.0180545 - 0.0271437i, 0.00532079 - 0.0135699i, 0.000390789 - 0.00661411i, -0.00106484 - 0.00293478i, -0.00116129 - 0.00105025i, -0.000856019 - 0.000154573i, -0.000510348 + 0.000246087i, -0.000174257 + 0.000423967i, 0.00022477 + 0.000415874i, 0.000607517 + 8.67362e-19i, 0.000254407 - 0.000119694i, -0.0547981 + 0.0459146i},
{0.0694484 - 0.274274i, 1.10287 - 1.9984e-15i, 0.825084 + 2.17421i, -2.18905 + 2.49709i, -3.56367 - 0.374634i, -1.85513 - 2.51176i, 0.158723 - 2.29452i, 0.897586 - 1.17871i, 0.768162 - 0.381041i, 0.452665 - 0.0555272i, 0.226238 + 0.0218896i, 0.105948 + 0.0210674i, 0.0489542 + 0.00884795i, 0.0225142 + 0.00103013i, 0.00998662 - 0.00203081i, 0.00396088 - 0.00246439i, 0.00115523 - 0.00186417i, 2.92581e-06 - 0.00107594i, -0.000328125 - 0.000457371i, -0.000313795 - 9.12893e-05i, -0.000212524 + 8.73536e-05i, -0.000100001 + 0.000200875i, 0.000135259 + 0.000292674i, 0.000607517 + 1.38778e-17i, -0.0155032 - 0.0086543i},
}),
tol: 5e-5,
},
{
a: transient().Mul(59),
b: T2([][]complex64{
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{0.000213831 + 2.49366e-18i, -0.000975559 + 0.00195558i, -0.00734308 - 0.00151306i, -0.00371965 - 0.0137175i, 0.0118411 - 0.0143415i, 0.0187098 - 0.00110203i, 0.012508 + 0.00921261i, 0.00398648 + 0.0103334i, -0.000524897 + 0.00700363i, -0.00156013 + 0.00375638i, -0.00122147 + 0.00182947i, -0.000694602 + 0.000894729i, -0.000322895 + 0.000463849i, -0.000116488 + 0.000252188i, -1.82615e-05 + 0.000135436i, 1.94044e-05 + 6.5555e-05i, 2.6143e-05 + 2.37936e-05i, 1.91718e-05 + 1.37345e-06i, 8.44659e-06 - 7.35705e-06i, -3.80165e-07 - 7.14014e-06i, -4.51686e-06 - 2.43459e-06i, -3.43759e-06 + 2.54565e-06i, 1.23348e-06 + 4.14916e-06i, 5.65962e-06 + 1.63936e-07i, 6.59199e-07 + 3.86247e-19i},
{7.37711e-06 - 5.31777e-05i, 0.000213831 - 1.15874e-18i, 5.46747e-05 + 0.000383791i, -0.000472941 + 0.000152609i, -0.000301642 - 0.000458073i, 0.000274779 - 0.000473444i, 0.000476861 - 7.40487e-05i, 0.000319196 + 0.000192039i, 0.00012304 + 0.000223401i, 2.05111e-05 + 0.000156735i, -9.21262e-06 + 9.01161e-05i, -9.72503e-06 + 4.79983e-05i, -4.28401e-06 + 2.50927e-05i, -1.72561e-07 + 1.29543e-05i, 1.71736e-06 + 6.34547e-06i, 2.08041e-06 + 2.67404e-06i, 1.66913e-06 + 6.97301e-07i, 9.94851e-07 - 2.36442e-07i, 3.5147e-07 - 5.19627e-07i, -1.10798e-07 - 4.15599e-07i, -3.21886e-07 - 1.15291e-07i, -2.46773e-07 + 2.21107e-07i, 1.39007e-07 + 4.00326e-07i, 8.30976e-07 - 2.96462e-21i, 5.65962e-06 - 1.63936e-07i},
{-1.90464e-05 - 1.02956e-05i, 2.71087e-05 - 0.000103014i, 0.000213831 + 2.41235e-18i, 9.34089e-05 + 0.000265397i, -0.000204152 + 0.000199206i, -0.000235333 - 6.05386e-05i, -7.4925e-05 - 0.000167014i, 4.12132e-05 - 0.00011855i, 6.44725e-05 - 4.67933e-05i, 4.67331e-05 - 7.93086e-06i, 2.64822e-05 + 3.88356e-06i, 1.38056e-05 + 4.53228e-06i, 7.22286e-06 + 2.64142e-06i, 3.90277e-06 + 9.93438e-07i, 2.11862e-06 + 3.42706e-08i, 1.07119e-06 - 3.86225e-07i, 4.26994e-07 - 4.7169e-07i, 4.59076e-08 - 3.74272e-07i, -1.39758e-07 - 1.98286e-07i, -1.73391e-07 - 1.75742e-08i, -9.33843e-08 + 1.11006e-07i, 5.53412e-08 + 1.36667e-07i, 1.99646e-07 + 6.35275e-22i, 1.39007e-07 - 4.00326e-07i, 1.23348e-06 - 4.14916e-06i},
{-1.09765e-05 + 6.09859e-06i, -5.74502e-05 - 4.67948e-05i, 5.86142e-05 - 0.000146378i, 0.000213831 + 3.44234e-18i, 0.00010101 + 0.000194303i, -8.91893e-05 + 0.00016191i, -0.000133065 + 2.72347e-05i, -7.73937e-05 - 4.61095e-05i, -2.29287e-05 - 5.03134e-05i, 1.29845e-06 - 3.19392e-05i, 6.37973e-06 - 1.64662e-05i, 5.01633e-06 - 8.00274e-06i, 2.85158e-06 - 4.05295e-06i, 1.31042e-06 - 2.22915e-06i, 4.24593e-07 - 1.29362e-06i, -2.02582e-08 - 7.34629e-07i, -1.98588e-07 - 3.63014e-07i, -2.20876e-07 - 1.12464e-07i, -1.56535e-07 + 4.03818e-08i, -5.38194e-08 + 1.05164e-07i, 4.73881e-08 + 8.85484e-08i, 1.04874e-07 + 4.63221e-22i, 5.53412e-08 - 1.36667e-07i, -2.46773e-07 - 2.21107e-07i, -3.43759e-06 - 2.54565e-06i},
{-3.38339e-06 + 9.55294e-06i, -6.37113e-05 + 2.00674e-05i, -9.05661e-05 - 0.000117886i, 9.9914e-05 - 0.000180544i, 0.000213831 + 4.16063e-18i, 0.000103958 + 0.000148061i, -3.04308e-05 + 0.000128575i, -7.07316e-05 + 4.99043e-05i, -5.23014e-05 + 8.84973e-07i, -2.68096e-05 - 1.29365e-05i, -1.15056e-05 - 1.14314e-05i, -4.78315e-06 - 7.12612e-06i, -2.25476e-06 - 3.86035e-06i, -1.31219e-06 - 1.9176e-06i, -8.80318e-07 - 8.4801e-07i, -6.00235e-07 - 2.76649e-07i, -3.73474e-07 + 1.19658e-08i, -1.82909e-07 + 1.31479e-07i, -3.39069e-08 + 1.44261e-07i, 6.26718e-08 + 8.979e-08i, 9.44108e-08 + 4.10282e-22i, 4.73881e-08 - 8.85484e-08i, -9.33843e-08 - 1.11006e-07i, -3.21886e-07 + 1.15291e-07i, -4.51686e-06 + 2.43459e-06i},
{2.23067e-06 + 1.22533e-05i, -3.13105e-05 + 6.75374e-05i, -0.000170412 - 4.30495e-06i, -9.67236e-05 - 0.000220333i, 0.000148413 - 0.000203366i, 0.000213831 + 3.38813e-18i, 0.000105412 + 0.000114973i, 3.12168e-06 + 0.000101594i, -3.22598e-05 + 5.16719e-05i, -2.92633e-05 + 1.7969e-05i, -1.80987e-05 + 4.02384e-06i, -9.73428e-06 + 1.846e-07i, -5.03699e-06 - 2.41497e-07i, -2.61151e-06 + 4.71388e-08i, -1.34034e-06 + 2.94206e-07i, -6.34955e-07 + 3.84959e-07i, -2.26164e-07 + 3.54988e-07i, 4.93726e-09 + 2.54813e-07i, 1.12829e-07 + 1.25422e-07i, 1.2567e-07 + 4.23516e-22i, 6.26718e-08 - 8.979e-08i, -5.38194e-08 - 1.05164e-07i, -1.73391e-07 + 1.75742e-08i, -1.10798e-07 + 4.15599e-07i, -3.80165e-07 + 7.14014e-06i},
{1.39396e-05 + 1.63978e-05i, 2.44781e-05 + 9.68903e-05i, -0.000172166 + 0.000152015i, -0.000303918 - 0.000120765i, -5.77759e-05 - 0.000339344i, 0.000201064 - 0.00021341i, 0.000213831 - 2.98156e-19i, 0.00010623 + 8.95077e-05i, 2.36987e-05 + 7.93552e-05i, -7.68108e-06 + 4.57476e-05i, -1.18339e-05 + 2.18858e-05i, -8.32054e-06 + 9.97225e-06i, -4.63148e-06 + 4.83511e-06i, -2.22914e-06 + 2.64244e-06i, -8.79204e-07 + 1.58623e-06i, -1.76308e-07 + 9.65514e-07i, 1.51218e-07 + 5.36371e-07i, 2.56297e-07 + 2.21099e-07i, 2.25085e-07 + 2.11758e-22i, 1.12829e-07 - 1.25422e-07i, -3.39069e-08 - 1.44261e-07i, -1.56535e-07 - 4.03818e-08i, -1.39758e-07 + 1.98286e-07i, 3.5147e-07 + 5.19627e-07i, 8.44659e-06 + 7.35705e-06i},
{4.11055e-05 + 1.31348e-05i, 0.000113314 + 0.000110443i, -8.25648e-05 + 0.000344761i, -0.000486618 + 0.00013184i, -0.000392517 - 0.000358211i, 3.5367e-05 - 0.000451559i, 0.000254559 - 0.000210044i, 0.000213831 - 1.84314e-18i, 0.000106727 + 6.87539e-05i, 3.68436e-05 + 6.03935e-05i, 8.30929e-06 + 3.68111e-05i, 4.67803e-07 + 1.95926e-05i, -4.4997e-07 + 1.00503e-05i, 8.92043e-08 + 5.17769e-06i, 5.65635e-07 + 2.65212e-06i, 7.46322e-07 + 1.26284e-06i, 6.9579e-07 + 4.59069e-07i, 5.07356e-07 + 2.32934e-21i, 2.56297e-07 - 2.21099e-07i, 4.93726e-09 - 2.54813e-07i, -1.82909e-07 - 1.31479e-07i, -2.20876e-07 + 1.12464e-07i, 4.59076e-08 + 3.74272e-07i, 9.94851e-07 + 2.36442e-07i, 1.91718e-05 - 1.37345e-06i},
{8.96639e-05 - 1.98395e-05i, 0.000271571 + 9.27823e-05i, 0.000151667 + 0.000594283i, -0.000615444 + 0.000604195i, -0.000885736 - 0.000188871i, -0.000345654 - 0.000688379i, 0.000179313 - 0.000530455i, 0.000305536 - 0.000193481i, 0.000213831 - 1.3871e-17i, 0.000107041 + 5.10233e-05i, 4.53298e-05 + 4.36517e-05i, 1.85889e-05 + 2.66854e-05i, 8.55675e-06 + 1.42515e-05i, 4.83336e-06 + 7.02605e-06i, 3.18015e-06 + 3.121e-06i, 2.16455e-06 + 1.05418e-06i, 1.36816e-06 - 2.11758e-21i, 6.9579e-07 - 4.59069e-07i, 1.51218e-07 - 5.36371e-07i, -2.26164e-07 - 3.54988e-07i, -3.73474e-07 - 1.19658e-08i, -1.98588e-07 + 3.63014e-07i, 4.26994e-07 + 4.7169e-07i, 1.66913e-06 - 6.97301e-07i, 2.6143e-05 - 2.37936e-05i},
{0.000157674 - 0.000125366i, 0.000574226 - 1.25427e-05i, 0.000672759 + 0.000948571i, -0.000637331 + 0.00147276i, -0.00164069 + 0.000317222i, -0.0010886 - 0.000902787i, -9.94112e-05 - 0.00101902i, 0.000357791 - 0.000552825i, 0.000350792 - 0.00016476i, 0.000213831 - 1.08962e-17i, 0.000107239 + 3.52499e-05i, 5.06332e-05 + 2.83702e-05i, 2.47487e-05 + 1.61099e-05i, 1.31367e-05 + 7.42953e-06i, 7.45732e-06 + 2.49258e-06i, 4.24063e-06 - 3.81165e-21i, 2.16455e-06 - 1.05418e-06i, 7.46322e-07 - 1.26284e-06i, -1.76308e-07 - 9.65514e-07i, -6.34955e-07 - 3.84959e-07i, -6.00235e-07 + 2.76649e-07i, -2.02582e-08 + 7.34629e-07i, 1.07119e-06 + 3.86225e-07i, 2.08041e-06 - 2.67404e-06i, 1.94044e-05 - 6.5555e-05i},
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{0.000285686 - 0.000963464i, 0.00241905 - 0.00117522i, 0.00426856 + 0.00259894i, 6.49023e-05 + 0.00660073i, -0.00544117 + 0.00392584i, -0.00542513 - 0.00134354i, -0.00212746 - 0.00338289i, 0.000246221 - 0.00252932i, 0.000886405 - 0.0011837i, 0.00070832 - 0.000385578i, 0.000413306 - 7.87166e-05i, 0.000213831 - 1.10589e-17i, 0.000107412 + 6.82869e-06i, 5.44843e-05 - 1.45012e-18i, 2.76416e-05 - 5.38154e-06i, 1.31367e-05 - 7.42953e-06i, 4.83336e-06 - 7.02605e-06i, 8.92043e-08 - 5.17769e-06i, -2.22914e-06 - 2.64244e-06i, -2.61151e-06 - 4.71388e-08i, -1.31219e-06 + 1.9176e-06i, 1.31042e-06 + 2.22915e-06i, 3.90277e-06 - 9.93438e-07i, -1.72561e-07 - 1.29543e-05i, -0.000116488 - 0.000252188i},
{0.000331877 - 0.00220733i, 0.00517368 - 0.00296931i, 0.0094682 + 0.00520209i, 0.000689042 + 0.0139956i, -0.0110715 + 0.00868701i, -0.0113906 - 0.00230194i, -0.00471718 - 0.00676879i, 0.00023819 - 0.00520732i, 0.00167091 - 0.00250874i, 0.00138641 - 0.000863468i, 0.000820399 - 0.000208856i, 0.000426636 - 2.68002e-05i, 0.000213831 - 5.52943e-18i, 0.000107412 - 6.82869e-06i, 5.35518e-05 - 1.39754e-05i, 2.47487e-05 - 1.61099e-05i, 8.55675e-06 - 1.42515e-05i, -4.4997e-07 - 1.00503e-05i, -4.63148e-06 - 4.83511e-06i, -5.03699e-06 + 2.41497e-07i, -2.25476e-06 + 3.86035e-06i, 2.85158e-06 + 4.05295e-06i, 7.22286e-06 - 2.64142e-06i, -4.28401e-06 - 2.50927e-05i, -0.000322895 - 0.000463849i},
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{0.062771 - 0.0215701i, 0.135285 + 0.138432i, -0.123321 + 0.321381i, -0.430358 + 0.0564349i, -0.280586 - 0.319294i, 0.0526926 - 0.339121i, 0.189518 - 0.144633i, 0.147241 - 2.63678e-15i, 0.0713359 + 0.0425274i, 0.0251093 + 0.0358628i, 0.00660254 + 0.0210042i, 0.00124224 + 0.0106955i, 0.00023819 + 0.00520732i, 0.000246221 + 0.00252932i, 0.000341095 + 0.00122152i, 0.000357791 + 0.000552825i, 0.000305536 + 0.000193481i, 0.000213831 + 1.08149e-17i, 0.00010623 - 8.95077e-05i, 3.12168e-06 - 0.000101594i, -7.07316e-05 - 4.99043e-05i, -7.73937e-05 + 4.61095e-05i, 4.12132e-05 + 0.00011855i, 0.000319196 - 0.000192039i, 0.00398648 - 0.0103334i},
{0.0997077 + 0.0257138i, 0.0487491 + 0.304986i, -0.466405 + 0.299735i, -0.611747 - 0.34424i, -0.0500519 - 0.687004i, 0.401208 - 0.385761i, 0.386523 + 3.46945e-16i, 0.189518 + 0.144633i, 0.0499807 + 0.124481i, -0.00282461 + 0.0703992i, -0.0119732 + 0.0331723i, -0.00876298 + 0.0147415i, -0.00471718 + 0.00676879i, -0.00212746 + 0.00338289i, -0.00075722 + 0.00183196i, -9.94112e-05 + 0.00101902i, 0.000179313 + 0.000530455i, 0.000254559 + 0.000210044i, 0.000213831 + 7.15573e-18i, 0.000105412 - 0.000114973i, -3.04308e-05 - 0.000128575i, -0.000133065 - 2.72347e-05i, -7.4925e-05 + 0.000167014i, 0.000476861 + 7.40487e-05i, 0.012508 - 0.00921261i},
{0.0802919 + 0.114397i, -0.236367 + 0.362744i, -0.774221 - 0.141351i, -0.294728 - 0.958899i, 0.630282 - 0.761431i, 0.800616 - 3.66374e-15i, 0.401208 + 0.385761i, 0.0526926 + 0.339121i, -0.0717697 + 0.178922i, -0.0725452 + 0.0701906i, -0.0449913 + 0.0224921i, -0.0234144 + 0.00656883i, -0.0113906 + 0.00230194i, -0.00542513 + 0.00134354i, -0.00252982 + 0.00108758i, -0.0010886 + 0.000902787i, -0.000345654 + 0.000688379i, 3.5367e-05 + 0.000451559i, 0.000201064 + 0.00021341i, 0.000213831 + 3.57787e-18i, 0.000103958 - 0.000148061i, -8.91893e-05 - 0.00016191i, -0.000235333 + 6.05386e-05i, 0.000274779 + 0.000473444i, 0.0187098 + 0.00110203i},
{-0.0346083 + 0.156511i, -0.510809 + 0.070071i, -0.473044 - 0.826754i, 0.670387 - 1.0261i, 1.21529 + 1.11022e-16i, 0.630282 + 0.761431i, -0.0500519 + 0.687004i, -0.280586 + 0.319294i, -0.226629 + 0.0744542i, -0.123948 - 0.0124014i, -0.0568552 - 0.0241907i, -0.0246511 - 0.0165332i, -0.0110715 - 0.00868701i, -0.00544117 - 0.00392584i, -0.00292519 - 0.00147846i, -0.00164069 - 0.000317222i, -0.000885736 + 0.000188871i, -0.000392517 + 0.000358211i, -5.77759e-05 + 0.000339344i, 0.000148413 + 0.000203366i, 0.000213831 + 2.01933e-18i, 0.00010101 - 0.000194303i, -0.000204152 - 0.000199206i, -0.000301642 + 0.000458073i, 0.0118411 + 0.0143415i},
{-0.13637 + 0.0577689i, -0.332253 - 0.371488i, 0.424473 - 0.838718i, 1.22522 - 8.88178e-16i, 0.670387 + 1.0261i, -0.294728 + 0.958899i, -0.611747 + 0.34424i, -0.430358 - 0.0564349i, -0.19289 - 0.14871i, -0.0611804 - 0.111152i, -0.0128429 - 0.0612918i, -0.000680693 - 0.0298478i, 0.000689042 - 0.0139956i, 6.49023e-05 - 0.00660073i, -0.000449954 - 0.00315198i, -0.000637331 - 0.00147276i, -0.000615444 - 0.000604195i, -0.000486618 - 0.00013184i, -0.000303918 + 0.000120765i, -9.67236e-05 + 0.000220333i, 9.9914e-05 + 0.000180544i, 0.000213831 + 1.46367e-18i, 9.34089e-05 - 0.000265397i, -0.000472941 - 0.000152609i, -0.00371965 + 0.0137175i},
{-0.0802256 - 0.0639768i, 0.130704 - 0.341316i, 0.708486 - 8.32667e-17i, 0.424473 + 0.838718i, -0.473044 + 0.826754i, -0.774221 + 0.141351i, -0.466405 - 0.299735i, -0.123321 - 0.321381i, 0.0287379 - 0.191287i, 0.0524393 - 0.0858535i, 0.0365553 - 0.0332268i, 0.0197061 - 0.0124984i, 0.0094682 - 0.00520209i, 0.00426856 - 0.00259894i, 0.00180862 - 0.00151477i, 0.000672759 - 0.000948571i, 0.000151667 - 0.000594283i, -8.25648e-05 - 0.000344761i, -0.000172166 - 0.000152015i, -0.000170412 + 4.30495e-06i, -9.05661e-05 + 0.000117886i, 5.86142e-05 + 0.000146378i, 0.000213831 - 1.21973e-19i, 5.46747e-05 - 0.000383791i, -0.00734308 + 0.00151306i},
{0.0135546 - 0.0450494i, 0.181147 + 1.80411e-16i, 0.130704 + 0.341316i, -0.332253 + 0.371488i, -0.510809 - 0.070071i, -0.236367 - 0.362744i, 0.0487491 - 0.304986i, 0.135285 - 0.138432i, 0.104495 - 0.0324614i, 0.0568705 + 0.00433984i, 0.0263692 + 0.00924171i, 0.0115865 + 0.00609417i, 0.00517368 + 0.00296931i, 0.00241905 + 0.00117522i, 0.00117416 + 0.00034238i, 0.000574226 + 1.25427e-05i, 0.000271571 - 9.27823e-05i, 0.000113314 - 0.000110443i, 2.44781e-05 - 9.68903e-05i, -3.13105e-05 - 6.75374e-05i, -6.37113e-05 - 2.00674e-05i, -5.74502e-05 + 4.67948e-05i, 2.71087e-05 + 0.000103014i, 0.000213831 - 5.01444e-19i, -0.000975559 - 0.00195558i},
}),
tol: 5e-5,
},
}
for i, test := range tests {
t.Run(fmt.Sprintf("%d", i), func(t *testing.T) {
t.Parallel()
bufs := [4]*Dense{Zeros(1), Zeros(1), Zeros(1), Zeros(1)}
b := Exp(test.a, bufs)
if err := b.Equal(test.b, test.tol); err != nil {
t.Errorf("%+v", err)
}
})
}
}