Blame view
fvn_integ/fvn_integ.f90
13.7 KB
b93026039
git-svn-id: https...
|
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 |
module fvn_integ
use fvn_common
implicit none
! Gauss legendre
interface fvn_gauss_legendre
module procedure fvn_d_gauss_legendre
end interface fvn_gauss_legendre
! Simple Gauss Legendre integration
interface fvn_gl_integ
module procedure fvn_d_gl_integ
end interface fvn_gl_integ
! Adaptative Gauss Kronrod integration f(x)
interface fvn_integ_1_gk
module procedure fvn_d_integ_1_gk
end interface fvn_integ_1_gk
! Adaptative Gauss Kronrod integration f(x,y)
interface fvn_integ_2_gk
module procedure fvn_d_integ_2_gk
end interface fvn_integ_2_gk
contains
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!
! Integration
!
! Only double precision coded atm
!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
subroutine fvn_d_gauss_legendre(n,qx,qw)
!
! This routine compute the n Gauss Legendre abscissas and weights
! Adapted from Numerical Recipes routine gauleg
!
! n (in) : number of points
! qx(out) : abscissas
! qw(out) : weights
!
implicit none
double precision,parameter :: pi=3.141592653589793d0
integer, intent(in) :: n
double precision, intent(out) :: qx(n),qw(n)
integer :: m,i,j
double precision :: z,z1,p1,p2,p3,pp
m=(n+1)/2
do i=1,m
z=cos(pi*(dble(i)-0.25d0)/(dble(n)+0.5d0))
iloop: do
p1=1.d0
p2=0.d0
do j=1,n
p3=p2
p2=p1
p1=((2.d0*dble(j)-1.d0)*z*p2-(dble(j)-1.d0)*p3)/dble(j)
end do
pp=dble(n)*(z*p1-p2)/(z*z-1.d0)
z1=z
z=z1-p1/pp
if (dabs(z-z1)<=epsilon(z)) then
exit iloop
end if
end do iloop
qx(i)=-z
qx(n+1-i)=z
qw(i)=2.d0/((1.d0-z*z)*pp*pp)
qw(n+1-i)=qw(i)
end do
end subroutine
subroutine fvn_d_gl_integ(f,a,b,n,res)
!
! This is a simple non adaptative integration routine
! using n gauss legendre abscissas and weights
!
! f(in) : the function to integrate
! a(in) : lower bound
! b(in) : higher bound
! n(in) : number of gauss legendre pairs
! res(out): the evaluation of the integral
!
double precision,external :: f
double precision, intent(in) :: a,b
integer, intent(in):: n
double precision, intent(out) :: res
double precision, allocatable :: qx(:),qw(:)
double precision :: xm,xr
integer :: i
! First compute n gauss legendre abs and weight
allocate(qx(n))
allocate(qw(n))
call fvn_d_gauss_legendre(n,qx,qw)
xm=0.5d0*(b+a)
xr=0.5d0*(b-a)
res=0.d0
do i=1,n
res=res+qw(i)*f(xm+xr*qx(i))
end do
res=xr*res
deallocate(qw)
deallocate(qx)
end subroutine
!!!!!!!!!!!!!!!!!!!!!!!!
!
! Simple and double adaptative Gauss Kronrod integration based on
! a modified version of quadpack ( http://www.netlib.org/quadpack
!
! Common parameters :
!
! key (in)
! epsabs
! epsrel
!
!
!!!!!!!!!!!!!!!!!!!!!!!!
subroutine fvn_d_integ_1_gk(f,a,b,epsabs,epsrel,key,res,abserr,ier,limit)
!
! Evaluate the integral of function f(x) between a and b
!
! f(in) : the function
! a(in) : lower bound
! b(in) : higher bound
! epsabs(in) : desired absolute error
! epsrel(in) : desired relative error
! key(in) : gauss kronrod rule
! 1: 7 - 15 points
! 2: 10 - 21 points
! 3: 15 - 31 points
! 4: 20 - 41 points
! 5: 25 - 51 points
! 6: 30 - 61 points
!
! limit(in) : maximum number of subintervals in the partition of the
! given integration interval (a,b). A value of 500 will give the same
! behaviour as the imsl routine dqdag
!
! res(out) : estimated integral value
! abserr(out) : estimated absolute error
! ier(out) : error flag from quadpack routines
! 0 : no error
! 1 : maximum number of subdivisions allowed
! has been achieved. one can allow more
! subdivisions by increasing the value of
! limit (and taking the according dimension
! adjustments into account). however, if
! this yield no improvement it is advised
! to analyze the integrand in order to
! determine the integration difficulaties.
! if the position of a local difficulty can
! be determined (i.e.singularity,
! discontinuity within the interval) one
! will probably gain from splitting up the
! interval at this point and calling the
! integrator on the subranges. if possible,
! an appropriate special-purpose integrator
! should be used which is designed for
! handling the type of difficulty involved.
! 2 : the occurrence of roundoff error is
! detected, which prevents the requested
! tolerance from being achieved.
! 3 : extremely bad integrand behaviour occurs
! at some points of the integration
! interval.
! 6 : the input is invalid, because
! (epsabs.le.0 and
! epsrel.lt.max(50*rel.mach.acc.,0.5d-28))
! or limit.lt.1 or lenw.lt.limit*4.
! result, abserr, neval, last are set
! to zero.
! except when lenw is invalid, iwork(1),
! work(limit*2+1) and work(limit*3+1) are
! set to zero, work(1) is set to a and
! work(limit+1) to b.
implicit none
double precision, external :: f
double precision, intent(in) :: a,b,epsabs,epsrel
integer, intent(in) :: key
integer, intent(in),optional :: limit
double precision, intent(out) :: res,abserr
integer, intent(out) :: ier
double precision, allocatable :: work(:)
integer, allocatable :: iwork(:)
integer :: lenw,neval,last
integer :: limitw
! imsl value for limit is 500
limitw=500
if (present(limit)) limitw=limit
lenw=limitw*4
allocate(iwork(limitw))
allocate(work(lenw))
call dqag(f,a,b,epsabs,epsrel,key,res,abserr,neval,ier,limitw,lenw,last,iwork,work)
deallocate(work)
deallocate(iwork)
end subroutine
subroutine fvn_d_integ_2_gk(f,a,b,g,h,epsabs,epsrel,key,res,abserr,ier,limit)
!
! Evaluate the double integral of function f(x,y) for x between a and b and y between g(x) and h(x)
!
! f(in) : the function
! a(in) : lower bound
! b(in) : higher bound
! g(in) : external function describing lower bound for y
! h(in) : external function describing higher bound for y
! epsabs(in) : desired absolute error
! epsrel(in) : desired relative error
! key(in) : gauss kronrod rule
! 1: 7 - 15 points
! 2: 10 - 21 points
! 3: 15 - 31 points
! 4: 20 - 41 points
! 5: 25 - 51 points
! 6: 30 - 61 points
!
! limit(in) : maximum number of subintervals in the partition of the
! given integration interval (a,b). A value of 500 will give the same
! behaviour as the imsl routine dqdag
!
! res(out) : estimated integral value
! abserr(out) : estimated absolute error
! ier(out) : error flag from quadpack routines
! 0 : no error
! 1 : maximum number of subdivisions allowed
! has been achieved. one can allow more
! subdivisions by increasing the value of
! limit (and taking the according dimension
! adjustments into account). however, if
! this yield no improvement it is advised
! to analyze the integrand in order to
! determine the integration difficulaties.
! if the position of a local difficulty can
! be determined (i.e.singularity,
! discontinuity within the interval) one
! will probably gain from splitting up the
! interval at this point and calling the
! integrator on the subranges. if possible,
! an appropriate special-purpose integrator
! should be used which is designed for
! handling the type of difficulty involved.
! 2 : the occurrence of roundoff error is
! detected, which prevents the requested
! tolerance from being achieved.
! 3 : extremely bad integrand behaviour occurs
! at some points of the integration
! interval.
! 6 : the input is invalid, because
! (epsabs.le.0 and
! epsrel.lt.max(50*rel.mach.acc.,0.5d-28))
! or limit.lt.1 or lenw.lt.limit*4.
! result, abserr, neval, last are set
! to zero.
! except when lenw is invalid, iwork(1),
! work(limit*2+1) and work(limit*3+1) are
! set to zero, work(1) is set to a and
! work(limit+1) to b.
implicit none
double precision, external:: f,g,h
double precision, intent(in) :: a,b,epsabs,epsrel
integer, intent(in) :: key
integer, intent(in), optional :: limit
integer, intent(out) :: ier
double precision, intent(out) :: res,abserr
double precision, allocatable :: work(:)
integer :: limitw
integer, allocatable :: iwork(:)
integer :: lenw,neval,last
! imsl value for limit is 500
limitw=500
if (present(limit)) limitw=limit
lenw=limitw*4
allocate(work(lenw))
allocate(iwork(limitw))
call dqag_2d_outer(f,a,b,g,h,epsabs,epsrel,key,res,abserr,neval,ier,limitw,lenw,last,iwork,work)
deallocate(iwork)
deallocate(work)
end subroutine
subroutine fvn_d_integ_2_inner_gk(f,x,a,b,epsabs,epsrel,key,res,abserr,ier,limit)
!
! Evaluate the single integral of function f(x,y) for y between a and b with a
! given x value
!
! This function is used for the evaluation of the double integral fvn_d_integ_2_gk
!
! f(in) : the function
! x(in) : x
! a(in) : lower bound
! b(in) : higher bound
! epsabs(in) : desired absolute error
! epsrel(in) : desired relative error
! key(in) : gauss kronrod rule
! 1: 7 - 15 points
! 2: 10 - 21 points
! 3: 15 - 31 points
! 4: 20 - 41 points
! 5: 25 - 51 points
! 6: 30 - 61 points
!
! limit(in) : maximum number of subintervals in the partition of the
! given integration interval (a,b). A value of 500 will give the same
! behaviour as the imsl routine dqdag
!
! res(out) : estimated integral value
! abserr(out) : estimated absolute error
! ier(out) : error flag from quadpack routines
! 0 : no error
! 1 : maximum number of subdivisions allowed
! has been achieved. one can allow more
! subdivisions by increasing the value of
! limit (and taking the according dimension
! adjustments into account). however, if
! this yield no improvement it is advised
! to analyze the integrand in order to
! determine the integration difficulaties.
! if the position of a local difficulty can
! be determined (i.e.singularity,
! discontinuity within the interval) one
! will probably gain from splitting up the
! interval at this point and calling the
! integrator on the subranges. if possible,
! an appropriate special-purpose integrator
! should be used which is designed for
! handling the type of difficulty involved.
! 2 : the occurrence of roundoff error is
! detected, which prevents the requested
! tolerance from being achieved.
! 3 : extremely bad integrand behaviour occurs
! at some points of the integration
! interval.
! 6 : the input is invalid, because
! (epsabs.le.0 and
! epsrel.lt.max(50*rel.mach.acc.,0.5d-28))
! or limit.lt.1 or lenw.lt.limit*4.
! result, abserr, neval, last are set
! to zero.
! except when lenw is invalid, iwork(1),
! work(limit*2+1) and work(limit*3+1) are
! set to zero, work(1) is set to a and
! work(limit+1) to b.
implicit none
double precision, external:: f
double precision, intent(in) :: x,a,b,epsabs,epsrel
integer, intent(in) :: key
integer, intent(in),optional :: limit
integer, intent(out) :: ier
double precision, intent(out) :: res,abserr
double precision, allocatable :: work(:)
integer :: limitw
integer, allocatable :: iwork(:)
integer :: lenw,neval,last
! imsl value for limit is 500
limitw=500
if (present(limit)) limitw=limit
lenw=limitw*4
allocate(work(lenw))
allocate(iwork(limitw))
call dqag_2d_inner(f,x,a,b,epsabs,epsrel,key,res,abserr,neval,ier,limitw,lenw,last,iwork,work)
deallocate(iwork)
deallocate(work)
end subroutine
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
! Include the modified quadpack files
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
include "dqag_2d_inner.f"
include "dqk15_2d_inner.f"
include "dqk31_2d_outer.f"
include "dqk31_2d_inner.f"
include "dqage.f"
include "dqk15.f"
include "dqk21.f"
include "dqk31.f"
include "dqk41.f"
include "dqk51.f"
include "dqk61.f"
include "dqk41_2d_outer.f"
include "dqk41_2d_inner.f"
include "dqag_2d_outer.f"
include "dqpsrt.f"
include "dqag.f"
include "dqage_2d_outer.f"
include "dqage_2d_inner.f"
include "dqk51_2d_outer.f"
include "dqk51_2d_inner.f"
include "dqk61_2d_outer.f"
include "dqk21_2d_outer.f"
include "dqk61_2d_inner.f"
include "dqk21_2d_inner.f"
include "dqk15_2d_outer.f"
end module fvn_integ
|