Documentation for module minimax_exp_k53

Routines to calculate the minimax coefficients in order to approximate 1/x as a sum over exponential functions 1/x ~ SUM_{i}^{K} w_i EXP(-a_i * x) for x belonging to [1:Rc]. This module contains coefficients for minimax approximations with 1 <= k <= 53. Generated from data from http://www.mis.mpg.de/scicomp/EXP_SUM/1_x This module should not be modified manually and should not be used anywhere except in main minimax module. This file was created using the scripts in cp2k/tools/minimax_tools.

source: minimax_exp_k53.F
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public Subroutines/Functions:

SUBROUTINE
get_minimax_coeff_low (i, aw)
...

Parameters:

REAL(dp)
:: err_mm(N_APPROX) = 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992e-10_dp,3.719e-10_dp,4.359e-10_dp,5.451e-10_dp,6.777e-10_dp,9.820e-10_dp,1.185e-09_dp,1.338e-09_dp,1.460e-09_dp,1.650e-09_dp,1.854e-09_dp,2.246e-09_dp,2.464e-09_dp,2.609e-09_dp,2.715e-09_dp,2.863e-09_dp,2.999e-09_dp,3.179e-09_dp,3.190e-09_dp,2.010e-12_dp,6.528e-12_dp,1.195e-11_dp,1.774e-11_dp,2.368e-11_dp,2.966e-11_dp,3.561e-11_dp,4.152e-11_dp,4.735e-11_dp,5.310e-11_dp,1.057e-10_dp,1.506e-10_dp,1.899e-10_dp,2.250e-10_dp,2.567e-10_dp,2.858e-10_dp,3.126e-10_dp,3.375e-10_dp,3.609e-10_dp,5.381e-10_dp,6.595e-10_dp,7.525e-10_dp,8.280e-10_dp,8.916e-10_dp,9.465e-10_dp,9.947e-10_dp,1.038e-09_dp,1.076e-09_dp,1.333e-09_dp,1.480e-09_dp,1.581e-09_dp,1.656e-09_dp,1.763e-09_dp,1.866e-09_dp,2.028e-09_dp,2.086e-09_dp,2.094e-09_dp,1.159e-09_dp,1.284e-09_dp,1.341e-09_dp,1.371e-09_dp,1.385e-09_dp,9.203e-10_dp,9.227e-10_dp,6.020e-10_dp,6.162e-10_dp,6.188e-10_dp,3.912e-10_dp,4.053e-10_dp,4.177e-10_dp,2.536e-10_dp,2.651e-10_dp,2.814e-10_dp,2.837e-10_dp,1.642e-10_dp,1.730e-10_dp,1.870e-10_dp,1.925e-10_dp,1.938e-10_dp,1.062e-10_dp,1.128e-10_dp,1.238e-10_dp,1.289e-10_dp,1.316e-10_dp,1.329e-10_dp,1.331e-10_dp,6.860e-11_dp,7.343e-11_dp,8.181e-11_dp,8.593e-11_dp,9.004e-11_dp,9.194e-11_dp,6.365e-11_dp,6.382e-11_dp,4.353e-11_dp,4.452e-11_dp,2.962e-11_dp,3.121e-11_dp,2.011e-11_dp,2.147e-11_dp,2.197e-11_dp,1.364e-11_dp,1.476e-11_dp,1.554e-11_dp,9.246e-12_dp,1.013e-11_dp,1.055e-11_dp,1.104e-11_dp,6.262e-12_dp,6.943e-12_dp,7.635e-12_dp,7.869e-12_dp,5.591e-12_dp,5.633e-12_dp,3.938e-12_dp,4.047e-12_dp,2.766e-12_dp,2.919e-12_dp,1.940e-12_dp,2.063e-12_dp,2.113e-12_dp,1.360e-12_dp,1.534e-12_dp,9.524e-13_dp,1.035e-12_dp,1.074e-12_dp,1.118e-12_dp,6.667e-13_dp,7.317e-13_dp,7.639e-13_dp,7.969e-13_dp,8.172e-13_dp,4.429e-14_dp,5.718e-14_dp,6.780e-14_dp,7.692e-14_dp,9.218e-14_dp,1.103e-13_dp,1.515e-13_dp,1.790e-13_dp,1.998e-13_dp,2.167e-13_dp,2.309e-13_dp,2.432e-13_dp,2.724e-13_dp,3.314e-13_dp,3.911e-13_dp,3.911e-13_dp,4.100e-13_dp,4.380e-13_dp,4.664e-13_dp,5.171e-13_dp,5.430e-13_dp,5.594e-13_dp,5.708e-13_dp,5.855e-13_dp,5.983e-13_dp,5.992e-13_dp,4.321e-13_dp,4.407e-13_dp,3.120e-13_dp,3.251e-13_dp,2.025e-13_dp,2.251e-13_dp,2.371e-13_dp,2.405e-13_dp,2.405e-13_dp]
INTEGER
:: k_max = 53
INTEGER
:: k_mm(N_APPROX) = [1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,18,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,19,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,20,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,21,22,22,22,22,22,22,22,22,22,22,22,22,22,22,22,22,22,22,22,22,22,22,22,22,22,22,22,22,22,22,22,22,22,22,23,23,23,23,23,23,23,23,23,23,23,23,23,23,23,23,23,23,23,23,23,23,23,23,23,23,23,23,23,23,23,23,23,23,23,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,24,25,25,25,25,25,25,25,25,25,25,25,25,25,25,25,25,25,25,25,25,25,25,25,25,25,25,25,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,27,27,27,27,27,27,27,27,27,27,27,27,27,27,27,27,27,27,27,27,27,27,27,27,27,27,27,27,27,27,27,27,27,27,27,27,27,28,28,28,28,28,29,29,30,30,30,31,31,31,32,32,32,32,33,33,33,33,33,34,34,34,34,34,34,34,35,35,35,35,35,35,36,36,37,37,38,38,39,39,39,40,40,40,41,41,41,41,42,42,42,42,43,43,44,44,45,45,46,46,46,47,47,48,48,48,48,49,49,49,49,49,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,50,51,51,52,52,53,53,53,53,53]
INTEGER
:: k_p(N_K+1) = [1,10,23,42,64,92,121,154,177,201,227,254,282,311,342,380,419,458,497,536,575,612,646,681,717,744,789,826,831,833,836,839,843,848,855,861,863,865,867,870,873,877,881,883,885,887,890,892,896,901,927,929,931,936]
INTEGER
:: n_approx = 935
REAL(dp)
:: r_max = 4.0e+12_dp
REAL(dp)
:: r_mm(N_APPROX) = 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5.0e+09_dp,6.0e+09_dp,7.0e+09_dp,1.0e+10_dp,2.0e+10_dp,3.0e+10_dp,4.0e+10_dp,5.0e+10_dp,7.0e+10_dp,1.0e+11_dp,2.0e+11_dp,3.0e+11_dp,4.0e+11_dp,5.0e+11_dp,7.0e+11_dp,1.0e+12_dp,2.0e+12_dp,1.0e+12_dp,2.0e+12_dp,1.0e+12_dp,3.0e+12_dp,4.0e+11_dp,1.0e+12_dp,2.0e+12_dp,3.0e+12_dp,4.0e+12_dp]

SUBROUTINEget_minimax_coeff_low(i, aw)

...

Arguments:
INTEGER,
INTENT(in)
:: i ...
REAL(dp),
INTENT(inout)
:: aw(k_mm(i)*2) ...