Merge 32ef191 into 24e2481

ranocha · Apr 13, 2020 · 573ae16 · 573ae16
2 parents 24e2481 + 32ef191
commit 573ae16
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diff --git a/Project.toml b/Project.toml
@@ -1,7 +1,7 @@
 name = "SummationByPartsOperators"
 uuid = "9f78cca6-572e-554e-b819-917d2f1cf240"
 author = ["Hendrik Ranocha"]
-version = "0.3.2"
+version = "0.3.3"
 
 [deps]
 ArgCheck = "dce04be8-c92d-5529-be00-80e4d2c0e197"

diff --git a/dev/MattssonAlmquistVanDerWeide2018Accurate_dev.jl b/dev/MattssonAlmquistVanDerWeide2018Accurate_dev.jl
@@ -0,0 +1,154 @@
+using LinearAlgebra
+
+# order 4
+h = [
+  2.1259737557798e-01,
+  1.0260290400758e+00,
+  1.0775123588954e+00,
+  9.8607273802835e-01,
+  1, 1, 1, 1
+  ]
+e = [1//1, 0, 0, 0, 0, 0, 0, 0]
+H = Diagonal(h)
+
+q1 = [0,
+  6.5605279837843e-01,
+  -1.9875859409017e-01,
+  4.2705795711740e-02,
+  0, 0, 0, 0]'
+q2 = [-q1[2], 0,
+  8.1236966439895e-01,
+  -1.5631686602052e-01,
+  0, 0, 0, 0]'
+q3 = [-q1[3], -q2[3], 0,
+  6.9694440364211e-01,
+  -1//12, 0, 0, 0]'
+q4 = [-q1[4], -q2[4], -q3[4], 0,
+  2//3, -1//12, 0, 0]'
+q5 = [-q1[5] -q2[5] -q3[5] -q4[5] 0 2//3 -1//12 0]
+q6 = [0 0 0 1//12 -2//3 0 2//3 -1//12]
+q7 = [0 0 0 0 1//12 -2//3 0 2//3]
+q8 = [0 0 0 0 0 1//12 -2//3 0]
+Q = vcat(q1, q2, q3, q4, q5, q6, q7, q8)
+
+D1 = H \ (Q - 1//2*e*e'); display(D1)
+
+
+
+# order 6
+h = [
+  1.3030223027124e-01,
+  6.8851501587715e-01,
+  9.5166202564389e-01,
+  9.9103890475697e-01,
+  1.0028757074552e+00,
+  9.9950151111941e-01,
+  1, 1, 1
+  ]
+e = [1//1, 0, 0, 0, 0, 0, 0, 0, 0]
+H = Diagonal(h)
+
+q1 = [0,
+  6.6042071945824e-01,
+  -2.2104152954203e-01,
+  7.6243679810093e-02,
+  -1.7298206716724e-02,
+  1.6753369904210e-03,
+  0, 0, 0]'
+q2 = [-q1[2], 0,
+  8.7352798702787e-01,
+  -2.6581719253084e-01,
+  5.7458484948314e-02,
+  -4.7485599871040e-03,
+  0, 0, 0]'
+q3 = [-q1[3], -q2[3], 0,
+  8.1707122038457e-01,
+  -1.8881125503769e-01,
+  2.4226492138960e-02,
+  0, 0, 0]'
+q4 = [-q1[4], -q2[4], -q3[4], 0,
+  7.6798636652679e-01,
+  -1.5715532552963e-01,
+  1//60, 0, 0]'
+q5 = [-q1[5], -q2[5], -q3[5], -q4[5], 0,
+  7.5266872305402e-01,
+  -3//20, 1//60, 0]'
+q6 = [-q1[6], -q2[6], -q3[6], -q4[6], -q5[6], 0,
+  3//4, -3//20, 1//60]'
+q7 = [0 0 0 -1//60 3//20 -3//4 0 3//4 -3//20]
+q8 = [0 0 0 0 -1//60 3//20 -3//4 0 3//4]
+q9 = [0 0 0 0 0 -1//60 3//20 -3//4 0]
+Q = vcat(q1, q2, q3, q4, q5, q6, q7, q8, q9)
+
+D1 = H \ (Q - 1//2*e*e'); display(D1)
+
+
+
+# order 8
+h = [
+  1.0758368078310e-01,
+  6.1909685107891e-01,
+  9.6971176519117e-01,
+  1.1023441350947e+00,
+  1.0244688965833e+00,
+  9.9533550116831e-01,
+  1.0008236941028e+00,
+  9.9992060631812e-01,
+  1, 1, 1, 1]
+e = [1//1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
+H = Diagonal(h)
+
+q1 = [0,
+  6.7284756079369e-01,
+  -2.5969732837062e-01,
+  1.3519390385721e-01,
+  -6.9678474730984e-02,
+  2.6434024071371e-02,
+  -5.5992311465618e-03,
+  4.9954552590464e-04,
+  0, 0, 0, 0]'
+q2 = [-q1[2], 0,
+  9.4074021172233e-01,
+  -4.0511642426516e-01,
+  1.9369192209331e-01,
+  -6.8638079843479e-02,
+  1.3146457241484e-02,
+  -9.7652615479254e-04,
+  0, 0, 0, 0]'
+q3 = [-q1[3], -q2[3], 0,
+  9.4316393361096e-01,
+  -3.5728039257451e-01,
+  1.1266686855013e-01,
+  -1.8334941452280e-02,
+  8.2741521740941e-04,
+  0, 0, 0, 0]'
+q4 = [-q1[4], -q2[4], -q3[4], 0,
+  8.7694387866575e-01,
+  -2.4698058719506e-01,
+  4.7291642094198e-02,
+  -4.0135203618880e-03,
+  0, 0, 0, 0]'
+q5 = [-q1[5], -q2[5], -q3[5], -q4[5], 0,
+  8.1123946853807e-01,
+  -2.0267150541446e-01,
+  3.8680398901392e-02,
+  -3.5714285714286e-03,
+  0, 0, 0]'
+q6 = [-q1[6], -q2[6], -q3[6], -q4[6], -q5[6], 0,
+  8.0108544742793e-01,
+  -2.0088756283071e-01,
+  3.8095238095238e-02,
+  -3.5714285714286e-03,
+  0, 0]'
+q7 = [-q1[7], -q2[7], -q3[7], -q4[7], -q5[7], -q6[7], 0,
+  8.0039405922650e-01,
+  -1//5, 4//105, -1//280, 0]'
+q8 = [-q1[8], -q2[8], -q3[8], -q4[8], -q5[8], -q6[8], -q7[8], 0,
+  4//5, -1//5, 4//105, -1//280]'
+q9 = [0 0 0 0 1//280 -4//105 1//5 -4//5 0 4//5 -1//5 4//105]
+q10 = [0 0 0 0 0 1//280 -4//105 1//5 -4//5 0 4//5 -1//5]
+q11 = [0 0 0 0 0 0 1//280 -4//105 1//5 -4//5 0 4//5]
+q12 = [0 0 0 0 0 0 0 1//280 -4//105 1//5 -4//5 0]
+Q = vcat(q1, q2, q3, q4, q5, q6, q7, q8, q9, q10, q11, q12)
+
+D1 = H \ (Q - 1//2*e*e'); display(D1)
diff --git a/dev/MattssonAlmquistVanDerWeide2018Minimal_dev.jl b/dev/MattssonAlmquistVanDerWeide2018Minimal_dev.jl
@@ -0,0 +1,127 @@
+using LinearAlgebra
+
+# order 4
+h = [
+  2.6864248295847e-01,
+  1.0094667153500e+00,
+  9.9312068011715e-01,
+  1, 1, 1, 1, 1
+  ]
+e = [1//1, 0, 0, 0, 0, 0, 0, 0]
+H = Diagonal(h)
+
+q1 = [0,
+  6.1697245625434e-01,
+  -1.1697245625434e-01,
+  0.0000000000000e+00,
+  0, 0, 0, 0]'
+q2 = [-q1[2], 0,
+  7.0030578958767e-01,
+  -8.3333333333333e-02,
+  0.0000000000000e+00,
+  0, 0, 0]'
+q3 = [-q1[3], -q2[3], 0,
+  2//3, -1//12, 0, 0, 0]'
+q4 = [-q1[4], -q2[4], -q3[4], 0,
+  2//3, -1//12, 0, 0]'
+q5 = [-q1[5] -q2[5] -q3[5] -q4[5] 0 2//3 -1//12 0]
+q6 = [0 0 0 1//12 -2//3 0 2//3 -1//12]
+q7 = [0 0 0 0 1//12 -2//3 0 2//3]
+q8 = [0 0 0 0 0 1//12 -2//3 0]
+Q = vcat(q1, q2, q3, q4, q5, q6, q7, q8)
+
+D1 = H \ (Q - 1//2*e*e'); display(D1)
+
+
+
+# order 6
+h = [
+  1.2740260779883e-01,
+  6.1820981002054e-01,
+  9.4308973897679e-01,
+  1.0093019060199e+00,
+  9.9884825610465e-01,
+  1, 1, 1, 1
+  ]
+e = [1//1, 0, 0, 0, 0, 0, 0, 0, 0]
+H = Diagonal(h)
+
+q1 = [0,
+  6.3217364546846e-01,
+  -1.6411963429825e-01,
+  3.6495407984639e-02,
+  -4.5494191548490e-03,
+  0, 0, 0, 0]'
+q2 = [-q1[2], 0,
+  8.0515625504417e-01,
+  -2.0755653563249e-01,
+  3.4573926056780e-02,
+  0, 0, 0, 0]'
+q3 = [-q1[3], -q2[3], 0,
+  7.9402676057785e-01,
+  -1.6965680649860e-01,
+  1.6666666666667e-02,
+  0, 0, 0]'
+q4 = [-q1[4], -q2[4], -q3[4], 0,
+  7.5629896626333e-01,
+  -3//20, 1//60, 0, 0]'
+q5 = [-q1[5] -q2[5] -q3[5] -q4[5] 0 3//4 -3//20 1//60 0]
+q6 = [0 0 -1//60 3//20 -3//4 0 3//4 -3//20 1//60]
+q7 = [0 0 0 -1//60 3//20 -3//4 0 3//4 -3//20]
+q8 = [0 0 0 0 -1//60 3//20 -3//4 0 3//4]
+q9 = [0 0 0 0 0 -1//60 3//20 -3//4 0]
+Q = vcat(q1, q2, q3, q4, q5, q6, q7, q8, q9)
+
+D1 = H \ (Q - 1//2*e*e'); display(D1)
+
+
+
+# order 8
+h = [
+  1.4523997892351e-01,
+  7.6864793350174e-01,
+  9.9116487068535e-01,
+  9.9992473335107e-01,
+  1.0002097054636e+00,
+  9.9996591555866e-01,
+  1, 1, 1, 1
+  ]
+e = [1//1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
+H = Diagonal(h)
+
+q1 = [0,
+  6.6697342753834e-01,
+  -2.2919342278749e-01,
+  7.4283116457276e-02,
+  -1.2020661178873e-02,
+  -4.2460029252999e-05,
+  0, 0, 0, 0]'
+q2 = [-q1[2], 0,
+  8.8241196934163e-01,
+  -2.6653314104602e-01,
+  5.5302527504316e-02,
+  -4.2079282615860e-03,
+  0, 0, 0, 0]'
+q3 = [-q1[3], -q2[3], 0,
+  8.2904844081126e-01,
+  -2.1156614214635e-01,
+  3.9307676460659e-02,
+  -3.5714285714286e-03,
+  0, 0, 0]'
+q4 = [-q1[4], -q2[4], -q3[4], 0,
+  8.0305501223679e-01,
+  -2.0078040553808e-01,
+  3.8095238095238e-02,
+  -3.5714285714286e-03,
+  0, 0]'
+q5 = [-q1[5], -q2[5], -q3[5], -q4[5], 0,
+  8.0024692689207e-01,
+  -1//5, 4//105, -1//280, 0]'
+q6 = [-q1[6] -q2[6] -q3[6] -q4[6] -q5[6] 0 4//5 -1//5 4//105 -1//280]
+q7 = [0 0 1//280 -4//105 1//5 -4//5 0 4//5 -1//5 4//105]
+q8 = [0 0 0 1//280 -4//105 1//5 -4//5 0 4//5 -1//5]
+q9 = [0 0 0 0 1//280 -4//105 1//5 -4//5 0 4//5]
+q10 = [0 0 0 0 0 1//280 -4//105 1//5 -4//5 0]
+Q = vcat(q1, q2, q3, q4, q5, q6, q7, q8, q9, q10)
+
+D1 = H \ (Q - 1//2*e*e'); display(D1)