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factorize.f90
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factorize.f90
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! The code was developed at the Fritz Haber Institute, and
! the intellectual properties and copyright of this file
! are with the Max Planck Society. When you use it, please
! cite R. Gomez-Abal, X. Li, C. Ambrosch-Draxl, M. Scheffler,
! Extended linear tetrahedron method for the calculation of q-dependent
! dynamical response functions, to be published in Comp. Phys. Commun. (2010)
!BOP
!
! !ROUTINE: factorize
!
! !INTERFACE:
subroutine factorize(n,x,k,div)
! !DESCRIPTION:
!
! This subroutine factorizes the real coordinates of a vector x, the output is an integer vector k, such that k(i)/div=x(i)
!
! !INPUT PARAMETERS:
implicit none
integer(4), intent(in) :: n
real(8), intent(in) :: x(n)
! !OUTPUT PARAMETERS:
integer(4), intent(out) :: div
integer(4), intent(out) :: k(n)
! !DEFINDED PARAMETERS:
!!$ integer(4), parameter :: nprim=1000
integer(4), parameter :: nprim=168
! !LOCAL VARIABLES:
integer(4) :: ik
integer(4) :: ip
integer(4), dimension(nprim) :: iprim
integer(4) :: i,j
integer(4) :: d(n)
real(8) :: y,z
logical :: found
logical hec
!!$data iprim / &
!!$ 2,3,5,7,11,13,17,19,23,29,31,37,41,43, &
!!$ 47,53,59,61,67,71,73,79,83,89,97,101,103,107,&
!!$ 109,113,127,131,137,139,149,151,157,163,167,173,179,181,&
!!$ 191,193,197,199,211,223,227,229,233,239,241,251,257,263,&
!!$ 269,271,277,281,283,293,307,311,313,317,331,337,347,349,&
!!$ 353,359,367,373,379,383,389,397,401,409,419,421,431,433,&
!!$ 439,443,449,457,461,463,467,479,487,491,499,503,509,521,&
!!$ 523,541,547,557,563,569,571,577,587,593,599,601,607,613,&
!!$ 617,619,631,641,643,647,653,659,661,673,677,683,691,701,&
!!$ 709,719,727,733,739,743,751,757,761,769,773,787,797,809,&
!!$ 811,821,823,827,829,839,853,857,859,863,877,881,883,887,&
!!$ 907,911,919,929,937,941,947,953,967,971,977,983,991,997,&
!!$ 1009,1013,1019,1021,1031,1033,1039,1049,1051,1061,1063,1069,1087,1091,&
!!$ 1093,1097,1103,1109,1117,1123,1129,1151,1153,1163,1171,1181,1187,1193,&
!!$ 1201,1213,1217,1223,1229,1231,1237,1249,1259,1277,1279,1283,1289,1291,&
!!$ 1297,1301,1303,1307,1319,1321,1327,1361,1367,1373,1381,1399,1409,1423,&
!!$ 1427,1429,1433,1439,1447,1451,1453,1459,1471,1481,1483,1487,1489,1493,&
!!$ 1499,1511,1523,1531,1543,1549,1553,1559,1567,1571,1579,1583,1597,1601,&
!!$ 1607,1609,1613,1619,1621,1627,1637,1657,1663,1667,1669,1693,1697,1699,&
!!$ 1709,1721,1723,1733,1741,1747,1753,1759,1777,1783,1787,1789,1801,1811,&
!!$ 1823,1831,1847,1861,1867,1871,1873,1877,1879,1889,1901,1907,1913,1931,&
!!$ 1933,1949,1951,1973,1979,1987,1993,1997,1999,2003,2011,2017,2027,2029,&
!!$ 2039,2053,2063,2069,2081,2083,2087,2089,2099,2111,2113,2129,2131,2137,&
!!$ 2141,2143,2153,2161,2179,2203,2207,2213,2221,2237,2239,2243,2251,2267,&
!!$ 2269,2273,2281,2287,2293,2297,2309,2311,2333,2339,2341,2347,2351,2357,&
!!$ 2371,2377,2381,2383,2389,2393,2399,2411,2417,2423,2437,2441,2447,2459,&
!!$ 2467,2473,2477,2503,2521,2531,2539,2543,2549,2551,2557,2579,2591,2593,&
!!$ 2609,2617,2621,2633,2647,2657,2659,2663,2671,2677,2683,2687,2689,2693,&
!!$ 2699,2707,2711,2713,2719,2729,2731,2741,2749,2753,2767,2777,2789,2791,&
!!$ 2797,2801,2803,2819,2833,2837,2843,2851,2857,2861,2879,2887,2897,2903,&
!!$ 2909,2917,2927,2939,2953,2957,2963,2969,2971,2999,3001,3011,3019,3023,&
!!$ 3037,3041,3049,3061,3067,3079,3083,3089,3109,3119,3121,3137,3163,3167,&
!!$ 3169,3181,3187,3191,3203,3209,3217,3221,3229,3251,3253,3257,3259,3271,&
!!$ 3299,3301,3307,3313,3319,3323,3329,3331,3343,3347,3359,3361,3371,3373,&
!!$ 3389,3391,3407,3413,3433,3449,3457,3461,3463,3467,3469,3491,3499,3511,&
!!$ 3517,3527,3529,3533,3539,3541,3547,3557,3559,3571,3581,3583,3593,3607,&
!!$ 3613,3617,3623,3631,3637,3643,3659,3671,3673,3677,3691,3697,3701,3709,&
!!$ 3719,3727,3733,3739,3761,3767,3769,3779,3793,3797,3803,3821,3823,3833,&
!!$ 3847,3851,3853,3863,3877,3881,3889,3907,3911,3917,3919,3923,3929,3931,&
!!$ 3943,3947,3967,3989,4001,4003,4007,4013,4019,4021,4027,4049,4051,4057,&
!!$ 4073,4079,4091,4093,4099,4111,4127,4129,4133,4139,4153,4157,4159,4177,&
!!$ 4201,4211,4217,4219,4229,4231,4241,4243,4253,4259,4261,4271,4273,4283,&
!!$ 4289,4297,4327,4337,4339,4349,4357,4363,4373,4391,4397,4409,4421,4423,&
!!$ 4441,4447,4451,4457,4463,4481,4483,4493,4507,4513,4517,4519,4523,4547,&
!!$ 4549,4561,4567,4583,4591,4597,4603,4621,4637,4639,4643,4649,4651,4657,&
!!$ 4663,4673,4679,4691,4703,4721,4723,4729,4733,4751,4759,4783,4787,4789,&
!!$ 4793,4799,4801,4813,4817,4831,4861,4871,4877,4889,4903,4909,4919,4931,&
!!$ 4933,4937,4943,4951,4957,4967,4969,4973,4987,4993,4999,5003,5009,5011,&
!!$ 5021,5023,5039,5051,5059,5077,5081,5087,5099,5101,5107,5113,5119,5147,&
!!$ 5153,5167,5171,5179,5189,5197,5209,5227,5231,5233,5237,5261,5273,5279,&
!!$ 5281,5297,5303,5309,5323,5333,5347,5351,5381,5387,5393,5399,5407,5413,&
!!$ 5417,5419,5431,5437,5441,5443,5449,5471,5477,5479,5483,5501,5503,5507,&
!!$ 5519,5521,5527,5531,5557,5563,5569,5573,5581,5591,5623,5639,5641,5647,&
!!$ 5651,5653,5657,5659,5669,5683,5689,5693,5701,5711,5717,5737,5741,5743,&
!!$ 5749,5779,5783,5791,5801,5807,5813,5821,5827,5839,5843,5849,5851,5857,&
!!$ 5861,5867,5869,5879,5881,5897,5903,5923,5927,5939,5953,5981,5987,6007,&
!!$ 6011,6029,6037,6043,6047,6053,6067,6073,6079,6089,6091,6101,6113,6121,&
!!$ 6131,6133,6143,6151,6163,6173,6197,6199,6203,6211,6217,6221,6229,6247,&
!!$ 6257,6263,6269,6271,6277,6287,6299,6301,6311,6317,6323,6329,6337,6343,&
!!$ 6353,6359,6361,6367,6373,6379,6389,6397,6421,6427,6449,6451,6469,6473,&
!!$ 6481,6491,6521,6529,6547,6551,6553,6563,6569,6571,6577,6581,6599,6607,&
!!$ 6619,6637,6653,6659,6661,6673,6679,6689,6691,6701,6703,6709,6719,6733,&
!!$ 6737,6761,6763,6779,6781,6791,6793,6803,6823,6827,6829,6833,6841,6857,&
!!$ 6863,6869,6871,6883,6899,6907,6911,6917,6947,6949,6959,6961,6967,6971,&
!!$ 6977,6983,6991,6997,7001,7013,7019,7027,7039,7043,7057,7069,7079,7103,&
!!$ 7109,7121,7127,7129,7151,7159,7177,7187,7193,7207,7211,7213,7219,7229,&
!!$ 7237,7243,7247,7253,7283,7297,7307,7309,7321,7331,7333,7349,7351,7369,&
!!$ 7393,7411,7417,7433,7451,7457,7459,7477,7481,7487,7489,7499,7507,7517,&
!!$ 7523,7529,7537,7541,7547,7549,7559,7561,7573,7577,7583,7589,7591,7603,&
!!$ 7607,7621,7639,7643,7649,7669,7673,7681,7687,7691,7699,7703,7717,7723,&
!!$ 7727,7741,7753,7757,7759,7789,7793,7817,7823,7829,7841,7853,7867,7873,&
!!$ 7877,7879,7883,7901,7907,7919 /
data iprim / 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, &
& 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, &
& 73, 79, 83, 89, 97,101,103,107,109,113, &
& 127,131,137,139,149,151,157,163,167,173, &
& 179,181,191,193,197,199,211,223,227,229, &
& 233,239,241,251,257,263,269,271,277,281, &
& 283,293,307,311,313,317,331,337,347,349, &
& 353,359,367,373,379,383,389,397,401,409, &
& 419,421,431,433,439,443,449,457,461,463, &
& 467,479,487,491,499,503,509,521,523,541, &
& 547,557,563,569,571,577,587,593,599,601, &
& 607,613,617,619,631,641,643,647,653,659, &
& 661,673,677,683,691,701,709,719,727,733, &
& 739,743,751,757,761,769,773,787,797,809, &
& 811,821,823,827,829,839,853,857,859,863, &
& 877,881,883,887,907,911,919,929,937,941, &
& 947,953,967,971,977,983,991,997/
!INTRINSIC ROUTINES:
! !EXTERNAL ROUTINES:
! !REVISION HISTORY:
!
! Created May 2006 by RGA
!EOP
!BOC
do i=1,n
found=.false.
j=1
do while (.not.found)
j=j+1
y=x(i)*dble(j)
k(i)=int(y)
z=dble(k(i))-y
! if(abs(z).lt.1.0d-10)then ! sag commented out
if (abs(dble(int(y))-y).lt.1.0d-3)then ! sag in place
found=.true.
d(i)=j
endif
enddo ! .not.found
k(i)=int(y)!sag
enddo ! i
div=1
do i=1,n
div=div*d(i)
enddo
do i=1,n
k(i)=k(i)*div/d(i)
enddo
do ip=1,nprim
hec=div.ge.iprim(ip)
do while (hec)
hec = mod(div,iprim(ip)).eq.0
ik=0
do while((ik.lt.n).and.hec)
ik=ik+1
hec = hec.and.(mod(k(ik),iprim(ip)).eq.0)
enddo
if(hec) then
div=div/iprim(ip)
do ik=1,n
k(ik)=k(ik)/iprim(ip)
enddo
endif
enddo
enddo
if(div.eq.0) div=1
return
end subroutine factorize