not needed anymore
This commit is contained in:
Martin Diehl
parent
dc57f6aba0
commit
c81a90350c
245
src/math.f90
245
src/math.f90
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@ -128,7 +128,6 @@ module math
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math_EulerToR, &
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math_axisAngleToR, &
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math_qToRodrig, &
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math_EulerMisorientation, &
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math_sampleGaussVar, &
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math_eigenvectorBasisSym33, &
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math_eigenvectorBasisSym33_log, &
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@ -148,8 +147,7 @@ module math
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math_rotate_forward3333, &
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math_clip
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private :: &
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math_check, &
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halton
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math_check
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contains
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@ -1390,23 +1388,6 @@ pure function math_qToRodrig(Q)
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end function math_qToRodrig
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!--------------------------------------------------------------------------------------------------
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!> @brief misorientation angle between two sets of Euler angles
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!--------------------------------------------------------------------------------------------------
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real(pReal) pure function math_EulerMisorientation(EulerA,EulerB)
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implicit none
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real(pReal), dimension(3), intent(in) :: EulerA,EulerB
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real(pReal) :: cosTheta
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cosTheta = (math_trace33(matmul(math_EulerToR(EulerB), &
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transpose(math_EulerToR(EulerA)))) - 1.0_pReal) * 0.5_pReal
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math_EulerMisorientation = acos(math_clip(cosTheta,-1.0_pReal,1.0_pReal))
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end function math_EulerMisorientation
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!--------------------------------------------------------------------------------------------------
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!> @brief draw a random sample from Gauss variable
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!--------------------------------------------------------------------------------------------------
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@ -1778,230 +1759,6 @@ pure function math_invariantsSym33(m)
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end function math_invariantsSym33
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!-------------------------------------------------------------------------------------------------
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!> @brief computes an element of a Halton sequence.
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!> @author John Burkardt
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!> @author Martin Diehl
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!> @details Incrementally increasing elements of the Halton sequence for given bases (> 0)
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!> @details Reference:
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!> @details J.H. Halton: On the efficiency of certain quasi-random sequences of points in evaluating
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!> @details multi-dimensional integrals, Numerische Mathematik, Volume 2, pages 84-90, 1960.
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!> @details Reference for prime numbers:
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!> @details Milton Abramowitz and Irene Stegun: Handbook of Mathematical Functions,
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!> @details US Department of Commerce, 1964, pages 870-873.
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!> @details Daniel Zwillinger: CRC Standard Mathematical Tables and Formulae,
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!> @details 30th Edition, CRC Press, 1996, pages 95-98.
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!-------------------------------------------------------------------------------------------------
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function halton(bases)
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implicit none
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integer, intent(in), dimension(:):: &
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bases !< bases (prime number ID)
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real(pReal), dimension(size(bases)) :: &
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halton
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integer, save :: &
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current = 1
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real(pReal), dimension(size(bases)) :: &
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base_inv
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integer, dimension(size(bases)) :: &
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base, &
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t
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integer, dimension(0:1600), parameter :: &
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prime = [&
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1, &
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2, 3, 5, 7, 11, 13, 17, 19, 23, 29, &
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31, 37, 41, 43, 47, 53, 59, 61, 67, 71, &
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73, 79, 83, 89, 97, 101, 103, 107, 109, 113, &
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127, 131, 137, 139, 149, 151, 157, 163, 167, 173, &
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179, 181, 191, 193, 197, 199, 211, 223, 227, 229, &
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233, 239, 241, 251, 257, 263, 269, 271, 277, 281, &
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283, 293, 307, 311, 313, 317, 331, 337, 347, 349, &
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353, 359, 367, 373, 379, 383, 389, 397, 401, 409, &
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419, 421, 431, 433, 439, 443, 449, 457, 461, 463, &
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467, 479, 487, 491, 499, 503, 509, 521, 523, 541, &
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! 101:200
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547, 557, 563, 569, 571, 577, 587, 593, 599, 601, &
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607, 613, 617, 619, 631, 641, 643, 647, 653, 659, &
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661, 673, 677, 683, 691, 701, 709, 719, 727, 733, &
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739, 743, 751, 757, 761, 769, 773, 787, 797, 809, &
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811, 821, 823, 827, 829, 839, 853, 857, 859, 863, &
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877, 881, 883, 887, 907, 911, 919, 929, 937, 941, &
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947, 953, 967, 971, 977, 983, 991, 997, 1009, 1013, &
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1019, 1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069, &
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1087, 1091, 1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151, &
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1153, 1163, 1171, 1181, 1187, 1193, 1201, 1213, 1217, 1223, &
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! 201:300
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1229, 1231, 1237, 1249, 1259, 1277, 1279, 1283, 1289, 1291, &
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1297, 1301, 1303, 1307, 1319, 1321, 1327, 1361, 1367, 1373, &
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1381, 1399, 1409, 1423, 1427, 1429, 1433, 1439, 1447, 1451, &
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1453, 1459, 1471, 1481, 1483, 1487, 1489, 1493, 1499, 1511, &
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1523, 1531, 1543, 1549, 1553, 1559, 1567, 1571, 1579, 1583, &
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1597, 1601, 1607, 1609, 1613, 1619, 1621, 1627, 1637, 1657, &
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1663, 1667, 1669, 1693, 1697, 1699, 1709, 1721, 1723, 1733, &
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1741, 1747, 1753, 1759, 1777, 1783, 1787, 1789, 1801, 1811, &
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1823, 1831, 1847, 1861, 1867, 1871, 1873, 1877, 1879, 1889, &
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1901, 1907, 1913, 1931, 1933, 1949, 1951, 1973, 1979, 1987, &
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! 301:400
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1993, 1997, 1999, 2003, 2011, 2017, 2027, 2029, 2039, 2053, &
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2063, 2069, 2081, 2083, 2087, 2089, 2099, 2111, 2113, 2129, &
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2131, 2137, 2141, 2143, 2153, 2161, 2179, 2203, 2207, 2213, &
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2221, 2237, 2239, 2243, 2251, 2267, 2269, 2273, 2281, 2287, &
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2293, 2297, 2309, 2311, 2333, 2339, 2341, 2347, 2351, 2357, &
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2371, 2377, 2381, 2383, 2389, 2393, 2399, 2411, 2417, 2423, &
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2437, 2441, 2447, 2459, 2467, 2473, 2477, 2503, 2521, 2531, &
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2539, 2543, 2549, 2551, 2557, 2579, 2591, 2593, 2609, 2617, &
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2621, 2633, 2647, 2657, 2659, 2663, 2671, 2677, 2683, 2687, &
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2689, 2693, 2699, 2707, 2711, 2713, 2719, 2729, 2731, 2741, &
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! 401:500
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2749, 2753, 2767, 2777, 2789, 2791, 2797, 2801, 2803, 2819, &
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2833, 2837, 2843, 2851, 2857, 2861, 2879, 2887, 2897, 2903, &
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2909, 2917, 2927, 2939, 2953, 2957, 2963, 2969, 2971, 2999, &
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3001, 3011, 3019, 3023, 3037, 3041, 3049, 3061, 3067, 3079, &
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3083, 3089, 3109, 3119, 3121, 3137, 3163, 3167, 3169, 3181, &
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3187, 3191, 3203, 3209, 3217, 3221, 3229, 3251, 3253, 3257, &
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3259, 3271, 3299, 3301, 3307, 3313, 3319, 3323, 3329, 3331, &
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3343, 3347, 3359, 3361, 3371, 3373, 3389, 3391, 3407, 3413, &
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3433, 3449, 3457, 3461, 3463, 3467, 3469, 3491, 3499, 3511, &
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3517, 3527, 3529, 3533, 3539, 3541, 3547, 3557, 3559, 3571, &
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! 501:600
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3581, 3583, 3593, 3607, 3613, 3617, 3623, 3631, 3637, 3643, &
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3659, 3671, 3673, 3677, 3691, 3697, 3701, 3709, 3719, 3727, &
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3733, 3739, 3761, 3767, 3769, 3779, 3793, 3797, 3803, 3821, &
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3823, 3833, 3847, 3851, 3853, 3863, 3877, 3881, 3889, 3907, &
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3911, 3917, 3919, 3923, 3929, 3931, 3943, 3947, 3967, 3989, &
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4001, 4003, 4007, 4013, 4019, 4021, 4027, 4049, 4051, 4057, &
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4073, 4079, 4091, 4093, 4099, 4111, 4127, 4129, 4133, 4139, &
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4153, 4157, 4159, 4177, 4201, 4211, 4217, 4219, 4229, 4231, &
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4241, 4243, 4253, 4259, 4261, 4271, 4273, 4283, 4289, 4297, &
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4327, 4337, 4339, 4349, 4357, 4363, 4373, 4391, 4397, 4409, &
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! 601:700
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4421, 4423, 4441, 4447, 4451, 4457, 4463, 4481, 4483, 4493, &
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4507, 4513, 4517, 4519, 4523, 4547, 4549, 4561, 4567, 4583, &
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4591, 4597, 4603, 4621, 4637, 4639, 4643, 4649, 4651, 4657, &
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4663, 4673, 4679, 4691, 4703, 4721, 4723, 4729, 4733, 4751, &
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4759, 4783, 4787, 4789, 4793, 4799, 4801, 4813, 4817, 4831, &
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4861, 4871, 4877, 4889, 4903, 4909, 4919, 4931, 4933, 4937, &
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4943, 4951, 4957, 4967, 4969, 4973, 4987, 4993, 4999, 5003, &
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5009, 5011, 5021, 5023, 5039, 5051, 5059, 5077, 5081, 5087, &
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5099, 5101, 5107, 5113, 5119, 5147, 5153, 5167, 5171, 5179, &
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5189, 5197, 5209, 5227, 5231, 5233, 5237, 5261, 5273, 5279, &
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! 701:800
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5281, 5297, 5303, 5309, 5323, 5333, 5347, 5351, 5381, 5387, &
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5393, 5399, 5407, 5413, 5417, 5419, 5431, 5437, 5441, 5443, &
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5449, 5471, 5477, 5479, 5483, 5501, 5503, 5507, 5519, 5521, &
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5527, 5531, 5557, 5563, 5569, 5573, 5581, 5591, 5623, 5639, &
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5641, 5647, 5651, 5653, 5657, 5659, 5669, 5683, 5689, 5693, &
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5701, 5711, 5717, 5737, 5741, 5743, 5749, 5779, 5783, 5791, &
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5801, 5807, 5813, 5821, 5827, 5839, 5843, 5849, 5851, 5857, &
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5861, 5867, 5869, 5879, 5881, 5897, 5903, 5923, 5927, 5939, &
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5953, 5981, 5987, 6007, 6011, 6029, 6037, 6043, 6047, 6053, &
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6067, 6073, 6079, 6089, 6091, 6101, 6113, 6121, 6131, 6133, &
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! 801:900
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6143, 6151, 6163, 6173, 6197, 6199, 6203, 6211, 6217, 6221, &
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6229, 6247, 6257, 6263, 6269, 6271, 6277, 6287, 6299, 6301, &
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6311, 6317, 6323, 6329, 6337, 6343, 6353, 6359, 6361, 6367, &
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6373, 6379, 6389, 6397, 6421, 6427, 6449, 6451, 6469, 6473, &
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6481, 6491, 6521, 6529, 6547, 6551, 6553, 6563, 6569, 6571, &
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6577, 6581, 6599, 6607, 6619, 6637, 6653, 6659, 6661, 6673, &
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6679, 6689, 6691, 6701, 6703, 6709, 6719, 6733, 6737, 6761, &
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6763, 6779, 6781, 6791, 6793, 6803, 6823, 6827, 6829, 6833, &
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6841, 6857, 6863, 6869, 6871, 6883, 6899, 6907, 6911, 6917, &
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6947, 6949, 6959, 6961, 6967, 6971, 6977, 6983, 6991, 6997, &
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! 901:1000
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7001, 7013, 7019, 7027, 7039, 7043, 7057, 7069, 7079, 7103, &
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7109, 7121, 7127, 7129, 7151, 7159, 7177, 7187, 7193, 7207, &
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7211, 7213, 7219, 7229, 7237, 7243, 7247, 7253, 7283, 7297, &
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7307, 7309, 7321, 7331, 7333, 7349, 7351, 7369, 7393, 7411, &
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7417, 7433, 7451, 7457, 7459, 7477, 7481, 7487, 7489, 7499, &
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7507, 7517, 7523, 7529, 7537, 7541, 7547, 7549, 7559, 7561, &
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7573, 7577, 7583, 7589, 7591, 7603, 7607, 7621, 7639, 7643, &
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7649, 7669, 7673, 7681, 7687, 7691, 7699, 7703, 7717, 7723, &
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7727, 7741, 7753, 7757, 7759, 7789, 7793, 7817, 7823, 7829, &
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7841, 7853, 7867, 7873, 7877, 7879, 7883, 7901, 7907, 7919, &
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! 1001:1100
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7927, 7933, 7937, 7949, 7951, 7963, 7993, 8009, 8011, 8017, &
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8039, 8053, 8059, 8069, 8081, 8087, 8089, 8093, 8101, 8111, &
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8117, 8123, 8147, 8161, 8167, 8171, 8179, 8191, 8209, 8219, &
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8221, 8231, 8233, 8237, 8243, 8263, 8269, 8273, 8287, 8291, &
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8293, 8297, 8311, 8317, 8329, 8353, 8363, 8369, 8377, 8387, &
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8389, 8419, 8423, 8429, 8431, 8443, 8447, 8461, 8467, 8501, &
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8513, 8521, 8527, 8537, 8539, 8543, 8563, 8573, 8581, 8597, &
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8599, 8609, 8623, 8627, 8629, 8641, 8647, 8663, 8669, 8677, &
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8681, 8689, 8693, 8699, 8707, 8713, 8719, 8731, 8737, 8741, &
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8747, 8753, 8761, 8779, 8783, 8803, 8807, 8819, 8821, 8831, &
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! 1101:1200
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8837, 8839, 8849, 8861, 8863, 8867, 8887, 8893, 8923, 8929, &
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8933, 8941, 8951, 8963, 8969, 8971, 8999, 9001, 9007, 9011, &
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9013, 9029, 9041, 9043, 9049, 9059, 9067, 9091, 9103, 9109, &
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9127, 9133, 9137, 9151, 9157, 9161, 9173, 9181, 9187, 9199, &
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9203, 9209, 9221, 9227, 9239, 9241, 9257, 9277, 9281, 9283, &
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9293, 9311, 9319, 9323, 9337, 9341, 9343, 9349, 9371, 9377, &
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9391, 9397, 9403, 9413, 9419, 9421, 9431, 9433, 9437, 9439, &
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9461, 9463, 9467, 9473, 9479, 9491, 9497, 9511, 9521, 9533, &
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9539, 9547, 9551, 9587, 9601, 9613, 9619, 9623, 9629, 9631, &
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9643, 9649, 9661, 9677, 9679, 9689, 9697, 9719, 9721, 9733, &
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! 1201:1300
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9739, 9743, 9749, 9767, 9769, 9781, 9787, 9791, 9803, 9811, &
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9817, 9829, 9833, 9839, 9851, 9857, 9859, 9871, 9883, 9887, &
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9901, 9907, 9923, 9929, 9931, 9941, 9949, 9967, 9973, 10007, &
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10009, 10037, 10039, 10061, 10067, 10069, 10079, 10091, 10093, 10099, &
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10103, 10111, 10133, 10139, 10141, 10151, 10159, 10163, 10169, 10177, &
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10181, 10193, 10211, 10223, 10243, 10247, 10253, 10259, 10267, 10271, &
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10273, 10289, 10301, 10303, 10313, 10321, 10331, 10333, 10337, 10343, &
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10357, 10369, 10391, 10399, 10427, 10429, 10433, 10453, 10457, 10459, &
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10463, 10477, 10487, 10499, 10501, 10513, 10529, 10531, 10559, 10567, &
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10589, 10597, 10601, 10607, 10613, 10627, 10631, 10639, 10651, 10657, &
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! 1301:1400
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10663, 10667, 10687, 10691, 10709, 10711, 10723, 10729, 10733, 10739, &
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10753, 10771, 10781, 10789, 10799, 10831, 10837, 10847, 10853, 10859, &
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10861, 10867, 10883, 10889, 10891, 10903, 10909, 10937, 10939, 10949, &
|
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10957, 10973, 10979, 10987, 10993, 11003, 11027, 11047, 11057, 11059, &
|
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11069, 11071, 11083, 11087, 11093, 11113, 11117, 11119, 11131, 11149, &
|
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11159, 11161, 11171, 11173, 11177, 11197, 11213, 11239, 11243, 11251, &
|
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11257, 11261, 11273, 11279, 11287, 11299, 11311, 11317, 11321, 11329, &
|
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11351, 11353, 11369, 11383, 11393, 11399, 11411, 11423, 11437, 11443, &
|
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11447, 11467, 11471, 11483, 11489, 11491, 11497, 11503, 11519, 11527, &
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11549, 11551, 11579, 11587, 11593, 11597, 11617, 11621, 11633, 11657, &
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! 1401:1500
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11677, 11681, 11689, 11699, 11701, 11717, 11719, 11731, 11743, 11777, &
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11779, 11783, 11789, 11801, 11807, 11813, 11821, 11827, 11831, 11833, &
|
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11839, 11863, 11867, 11887, 11897, 11903, 11909, 11923, 11927, 11933, &
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||||
11939, 11941, 11953, 11959, 11969, 11971, 11981, 11987, 12007, 12011, &
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12037, 12041, 12043, 12049, 12071, 12073, 12097, 12101, 12107, 12109, &
|
||||
12113, 12119, 12143, 12149, 12157, 12161, 12163, 12197, 12203, 12211, &
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||||
12227, 12239, 12241, 12251, 12253, 12263, 12269, 12277, 12281, 12289, &
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12301, 12323, 12329, 12343, 12347, 12373, 12377, 12379, 12391, 12401, &
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12409, 12413, 12421, 12433, 12437, 12451, 12457, 12473, 12479, 12487, &
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12491, 12497, 12503, 12511, 12517, 12527, 12539, 12541, 12547, 12553, &
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! 1501:1600
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12569, 12577, 12583, 12589, 12601, 12611, 12613, 12619, 12637, 12641, &
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12647, 12653, 12659, 12671, 12689, 12697, 12703, 12713, 12721, 12739, &
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12743, 12757, 12763, 12781, 12791, 12799, 12809, 12821, 12823, 12829, &
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12841, 12853, 12889, 12893, 12899, 12907, 12911, 12917, 12919, 12923, &
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12941, 12953, 12959, 12967, 12973, 12979, 12983, 13001, 13003, 13007, &
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||||
13009, 13033, 13037, 13043, 13049, 13063, 13093, 13099, 13103, 13109, &
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13121, 13127, 13147, 13151, 13159, 13163, 13171, 13177, 13183, 13187, &
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13217, 13219, 13229, 13241, 13249, 13259, 13267, 13291, 13297, 13309, &
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13313, 13327, 13331, 13337, 13339, 13367, 13381, 13397, 13399, 13411, &
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13417, 13421, 13441, 13451, 13457, 13463, 13469, 13477, 13487, 13499]
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current = current + 1
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base = prime(bases)
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base_inv = 1.0_pReal/real(base,pReal)
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|
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halton = 0.0_pReal
|
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t = current
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do while (any( t /= 0) )
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halton = halton + real(mod(t,base), pReal) * base_inv
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base_inv = base_inv / real(base, pReal)
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t = t / base
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enddo
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end function halton
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!--------------------------------------------------------------------------------------------------
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!> @brief factorial
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!--------------------------------------------------------------------------------------------------
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|||
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