Commit 6ac82e990ee0ab81340d03178f3bd7aec3d7de43
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| 1 | - | |
| 2 | -module fvn | |
| 3 | -!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! | |
| 4 | -! | |
| 5 | -! fvn : a f95 module replacement for some imsl routines | |
| 6 | -! it uses lapack for linear algebra | |
| 7 | -! it uses modified quadpack for integration | |
| 8 | -! | |
| 9 | -! William Daniau 2007 | |
| 10 | -! william.daniau@femto-st.fr | |
| 11 | -! | |
| 12 | -! Routines naming scheme : | |
| 13 | -! | |
| 14 | -! fvn_x_name | |
| 15 | -! where x can be s : real | |
| 16 | -! d : real double precision | |
| 17 | -! c : complex | |
| 18 | -! z : double complex | |
| 19 | -! | |
| 20 | -! | |
| 21 | -! This piece of code is totally free! Do whatever you want with it. However | |
| 22 | -! if you find it usefull it would be kind to give credits ;-) Nevertheless, you | |
| 23 | -! may give credits to quadpack authors. | |
| 24 | -! | |
| 25 | -! Version 1.1 | |
| 26 | -! | |
| 27 | -! TO DO LIST : | |
| 28 | -! + Order eigenvalues and vectors in decreasing eigenvalue's modulus order -> atm | |
| 29 | -! eigenvalues are given with no particular order. | |
| 30 | -! + Generic interface for fvn_x_name family -> fvn_name | |
| 31 | -! + Make some parameters optional, status for example | |
| 32 | -! + use f95 kinds "double complex" -> complex(kind=8) | |
| 33 | -! + unify quadpack routines | |
| 34 | -! + ... | |
| 35 | -! | |
| 36 | -!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! | |
| 37 | - | |
| 38 | -implicit none | |
| 39 | -! All quadpack routines are private to the module | |
| 40 | -private :: d1mach,dqag,dqag_2d_inner,dqag_2d_outer,dqage,dqage_2d_inner, & | |
| 41 | - dqage_2d_outer,dqk15,dqk15_2d_inner,dqk15_2d_outer,dqk21,dqk21_2d_inner,dqk21_2d_outer, & | |
| 42 | - dqk31,dqk31_2d_inner,dqk31_2d_outer,dqk41,dqk41_2d_inner,dqk41_2d_outer, & | |
| 43 | - dqk51,dqk51_2d_inner,dqk51_2d_outer,dqk61,dqk61_2d_inner,dqk61_2d_outer,dqpsrt | |
| 44 | - | |
| 45 | - | |
| 46 | -contains | |
| 47 | - | |
| 48 | -!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! | |
| 49 | -! | |
| 50 | -! Matrix inversion subroutines | |
| 51 | -! | |
| 52 | -!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! | |
| 53 | -subroutine fvn_s_matinv(d,a,inva,status) | |
| 54 | - ! | |
| 55 | - ! Matrix inversion of a real matrix using BLAS and LAPACK | |
| 56 | - ! | |
| 57 | - ! d (in) : matrix rank | |
| 58 | - ! a (in) : input matrix | |
| 59 | - ! inva (out) : inversed matrix | |
| 60 | - ! status (ou) : =0 if something failed | |
| 61 | - ! | |
| 62 | - integer, intent(in) :: d | |
| 63 | - real, intent(in) :: a(d,d) | |
| 64 | - real, intent(out) :: inva(d,d) | |
| 65 | - integer, intent(out) :: status | |
| 66 | - | |
| 67 | - integer, allocatable :: ipiv(:) | |
| 68 | - real, allocatable :: work(:) | |
| 69 | - real twork(1) | |
| 70 | - integer :: info | |
| 71 | - integer :: lwork | |
| 72 | - | |
| 73 | - status=1 | |
| 74 | - | |
| 75 | - allocate(ipiv(d)) | |
| 76 | - ! copy a into inva using BLAS | |
| 77 | - !call scopy(d*d,a,1,inva,1) | |
| 78 | - inva(:,:)=a(:,:) | |
| 79 | - ! LU factorization using LAPACK | |
| 80 | - call sgetrf(d,d,inva,d,ipiv,info) | |
| 81 | - ! if info is not equal to 0, something went wrong we exit setting status to 0 | |
| 82 | - if (info /= 0) then | |
| 83 | - status=0 | |
| 84 | - deallocate(ipiv) | |
| 85 | - return | |
| 86 | - end if | |
| 87 | - ! we use the query fonction of xxxtri to obtain the optimal workspace size | |
| 88 | - call sgetri(d,inva,d,ipiv,twork,-1,info) | |
| 89 | - lwork=int(twork(1)) | |
| 90 | - allocate(work(lwork)) | |
| 91 | - ! Matrix inversion using LAPACK | |
| 92 | - call sgetri(d,inva,d,ipiv,work,lwork,info) | |
| 93 | - ! again if info is not equal to 0, we exit setting status to 0 | |
| 94 | - if (info /= 0) then | |
| 95 | - status=0 | |
| 96 | - end if | |
| 97 | - deallocate(work) | |
| 98 | - deallocate(ipiv) | |
| 99 | -end subroutine | |
| 100 | - | |
| 101 | -subroutine fvn_d_matinv(d,a,inva,status) | |
| 102 | - ! | |
| 103 | - ! Matrix inversion of a double precision matrix using BLAS and LAPACK | |
| 104 | - ! | |
| 105 | - ! d (in) : matrix rank | |
| 106 | - ! a (in) : input matrix | |
| 107 | - ! inva (out) : inversed matrix | |
| 108 | - ! status (ou) : =0 if something failed | |
| 109 | - ! | |
| 110 | - integer, intent(in) :: d | |
| 111 | - double precision, intent(in) :: a(d,d) | |
| 112 | - double precision, intent(out) :: inva(d,d) | |
| 113 | - integer, intent(out) :: status | |
| 114 | - | |
| 115 | - integer, allocatable :: ipiv(:) | |
| 116 | - double precision, allocatable :: work(:) | |
| 117 | - double precision :: twork(1) | |
| 118 | - integer :: info | |
| 119 | - integer :: lwork | |
| 120 | - | |
| 121 | - status=1 | |
| 122 | - | |
| 123 | - allocate(ipiv(d)) | |
| 124 | - ! copy a into inva using BLAS | |
| 125 | - !call dcopy(d*d,a,1,inva,1) | |
| 126 | - inva(:,:)=a(:,:) | |
| 127 | - ! LU factorization using LAPACK | |
| 128 | - call dgetrf(d,d,inva,d,ipiv,info) | |
| 129 | - ! if info is not equal to 0, something went wrong we exit setting status to 0 | |
| 130 | - if (info /= 0) then | |
| 131 | - status=0 | |
| 132 | - deallocate(ipiv) | |
| 133 | - return | |
| 134 | - end if | |
| 135 | - ! we use the query fonction of xxxtri to obtain the optimal workspace size | |
| 136 | - call dgetri(d,inva,d,ipiv,twork,-1,info) | |
| 137 | - lwork=int(twork(1)) | |
| 138 | - allocate(work(lwork)) | |
| 139 | - ! Matrix inversion using LAPACK | |
| 140 | - call dgetri(d,inva,d,ipiv,work,lwork,info) | |
| 141 | - ! again if info is not equal to 0, we exit setting status to 0 | |
| 142 | - if (info /= 0) then | |
| 143 | - status=0 | |
| 144 | - end if | |
| 145 | - deallocate(work) | |
| 146 | - deallocate(ipiv) | |
| 147 | -end subroutine | |
| 148 | - | |
| 149 | -subroutine fvn_c_matinv(d,a,inva,status) | |
| 150 | - ! | |
| 151 | - ! Matrix inversion of a complex matrix using BLAS and LAPACK | |
| 152 | - ! | |
| 153 | - ! d (in) : matrix rank | |
| 154 | - ! a (in) : input matrix | |
| 155 | - ! inva (out) : inversed matrix | |
| 156 | - ! status (ou) : =0 if something failed | |
| 157 | - ! | |
| 158 | - integer, intent(in) :: d | |
| 159 | - complex, intent(in) :: a(d,d) | |
| 160 | - complex, intent(out) :: inva(d,d) | |
| 161 | - integer, intent(out) :: status | |
| 162 | - | |
| 163 | - integer, allocatable :: ipiv(:) | |
| 164 | - complex, allocatable :: work(:) | |
| 165 | - complex :: twork(1) | |
| 166 | - integer :: info | |
| 167 | - integer :: lwork | |
| 168 | - | |
| 169 | - status=1 | |
| 170 | - | |
| 171 | - allocate(ipiv(d)) | |
| 172 | - ! copy a into inva using BLAS | |
| 173 | - !call ccopy(d*d,a,1,inva,1) | |
| 174 | - inva(:,:)=a(:,:) | |
| 175 | - | |
| 176 | - ! LU factorization using LAPACK | |
| 177 | - call cgetrf(d,d,inva,d,ipiv,info) | |
| 178 | - ! if info is not equal to 0, something went wrong we exit setting status to 0 | |
| 179 | - if (info /= 0) then | |
| 180 | - status=0 | |
| 181 | - deallocate(ipiv) | |
| 182 | - return | |
| 183 | - end if | |
| 184 | - ! we use the query fonction of xxxtri to obtain the optimal workspace size | |
| 185 | - call cgetri(d,inva,d,ipiv,twork,-1,info) | |
| 186 | - lwork=int(twork(1)) | |
| 187 | - allocate(work(lwork)) | |
| 188 | - ! Matrix inversion using LAPACK | |
| 189 | - call cgetri(d,inva,d,ipiv,work,lwork,info) | |
| 190 | - ! again if info is not equal to 0, we exit setting status to 0 | |
| 191 | - if (info /= 0) then | |
| 192 | - status=0 | |
| 193 | - end if | |
| 194 | - deallocate(work) | |
| 195 | - deallocate(ipiv) | |
| 196 | -end subroutine | |
| 197 | - | |
| 198 | -subroutine fvn_z_matinv(d,a,inva,status) | |
| 199 | - ! | |
| 200 | - ! Matrix inversion of a double complex matrix using BLAS and LAPACK | |
| 201 | - ! | |
| 202 | - ! d (in) : matrix rank | |
| 203 | - ! a (in) : input matrix | |
| 204 | - ! inva (out) : inversed matrix | |
| 205 | - ! status (ou) : =0 if something failed | |
| 206 | - ! | |
| 207 | - integer, intent(in) :: d | |
| 208 | - double complex, intent(in) :: a(d,d) | |
| 209 | - double complex, intent(out) :: inva(d,d) | |
| 210 | - integer, intent(out) :: status | |
| 211 | - | |
| 212 | - integer, allocatable :: ipiv(:) | |
| 213 | - double complex, allocatable :: work(:) | |
| 214 | - double complex :: twork(1) | |
| 215 | - integer :: info | |
| 216 | - integer :: lwork | |
| 217 | - | |
| 218 | - status=1 | |
| 219 | - | |
| 220 | - allocate(ipiv(d)) | |
| 221 | - ! copy a into inva using BLAS | |
| 222 | - !call zcopy(d*d,a,1,inva,1) | |
| 223 | - inva(:,:)=a(:,:) | |
| 224 | - | |
| 225 | - ! LU factorization using LAPACK | |
| 226 | - call zgetrf(d,d,inva,d,ipiv,info) | |
| 227 | - ! if info is not equal to 0, something went wrong we exit setting status to 0 | |
| 228 | - if (info /= 0) then | |
| 229 | - status=0 | |
| 230 | - deallocate(ipiv) | |
| 231 | - return | |
| 232 | - end if | |
| 233 | - ! we use the query fonction of xxxtri to obtain the optimal workspace size | |
| 234 | - call zgetri(d,inva,d,ipiv,twork,-1,info) | |
| 235 | - lwork=int(twork(1)) | |
| 236 | - allocate(work(lwork)) | |
| 237 | - ! Matrix inversion using LAPACK | |
| 238 | - call zgetri(d,inva,d,ipiv,work,lwork,info) | |
| 239 | - ! again if info is not equal to 0, we exit setting status to 0 | |
| 240 | - if (info /= 0) then | |
| 241 | - status=0 | |
| 242 | - end if | |
| 243 | - deallocate(work) | |
| 244 | - deallocate(ipiv) | |
| 245 | -end subroutine | |
| 246 | - | |
| 247 | - | |
| 248 | -!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! | |
| 249 | -! | |
| 250 | -! Determinants | |
| 251 | -! | |
| 252 | -!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! | |
| 253 | -function fvn_s_det(d,a,status) | |
| 254 | - ! | |
| 255 | - ! Evaluate the determinant of a square matrix using lapack LU factorization | |
| 256 | - ! | |
| 257 | - ! d (in) : matrix rank | |
| 258 | - ! a (in) : The Matrix | |
| 259 | - ! status (out) : =0 if LU factorization failed | |
| 260 | - ! | |
| 261 | - integer, intent(in) :: d | |
| 262 | - real, intent(in) :: a(d,d) | |
| 263 | - integer, intent(out) :: status | |
| 264 | - real :: fvn_s_det | |
| 265 | - | |
| 266 | - real, allocatable :: wc_a(:,:) | |
| 267 | - integer, allocatable :: ipiv(:) | |
| 268 | - integer :: info,i | |
| 269 | - | |
| 270 | - status=1 | |
| 271 | - allocate(wc_a(d,d)) | |
| 272 | - allocate(ipiv(d)) | |
| 273 | - wc_a(:,:)=a(:,:) | |
| 274 | - call sgetrf(d,d,wc_a,d,ipiv,info) | |
| 275 | - if (info/= 0) then | |
| 276 | - status=0 | |
| 277 | - fvn_s_det=0.e0 | |
| 278 | - deallocate(ipiv) | |
| 279 | - deallocate(wc_a) | |
| 280 | - return | |
| 281 | - end if | |
| 282 | - fvn_s_det=1.e0 | |
| 283 | - do i=1,d | |
| 284 | - if (ipiv(i)==i) then | |
| 285 | - fvn_s_det=fvn_s_det*wc_a(i,i) | |
| 286 | - else | |
| 287 | - fvn_s_det=-fvn_s_det*wc_a(i,i) | |
| 288 | - end if | |
| 289 | - end do | |
| 290 | - deallocate(ipiv) | |
| 291 | - deallocate(wc_a) | |
| 292 | - | |
| 293 | -end function | |
| 294 | - | |
| 295 | -function fvn_d_det(d,a,status) | |
| 296 | - ! | |
| 297 | - ! Evaluate the determinant of a square matrix using lapack LU factorization | |
| 298 | - ! | |
| 299 | - ! d (in) : matrix rank | |
| 300 | - ! a (in) : The Matrix | |
| 301 | - ! status (out) : =0 if LU factorization failed | |
| 302 | - ! | |
| 303 | - integer, intent(in) :: d | |
| 304 | - double precision, intent(in) :: a(d,d) | |
| 305 | - integer, intent(out) :: status | |
| 306 | - double precision :: fvn_d_det | |
| 307 | - | |
| 308 | - double precision, allocatable :: wc_a(:,:) | |
| 309 | - integer, allocatable :: ipiv(:) | |
| 310 | - integer :: info,i | |
| 311 | - | |
| 312 | - status=1 | |
| 313 | - allocate(wc_a(d,d)) | |
| 314 | - allocate(ipiv(d)) | |
| 315 | - wc_a(:,:)=a(:,:) | |
| 316 | - call dgetrf(d,d,wc_a,d,ipiv,info) | |
| 317 | - if (info/= 0) then | |
| 318 | - status=0 | |
| 319 | - fvn_d_det=0.d0 | |
| 320 | - deallocate(ipiv) | |
| 321 | - deallocate(wc_a) | |
| 322 | - return | |
| 323 | - end if | |
| 324 | - fvn_d_det=1.d0 | |
| 325 | - do i=1,d | |
| 326 | - if (ipiv(i)==i) then | |
| 327 | - fvn_d_det=fvn_d_det*wc_a(i,i) | |
| 328 | - else | |
| 329 | - fvn_d_det=-fvn_d_det*wc_a(i,i) | |
| 330 | - end if | |
| 331 | - end do | |
| 332 | - deallocate(ipiv) | |
| 333 | - deallocate(wc_a) | |
| 334 | - | |
| 335 | -end function | |
| 336 | - | |
| 337 | -function fvn_c_det(d,a,status) ! | |
| 338 | - ! Evaluate the determinant of a square matrix using lapack LU factorization | |
| 339 | - ! | |
| 340 | - ! d (in) : matrix rank | |
| 341 | - ! a (in) : The Matrix | |
| 342 | - ! status (out) : =0 if LU factorization failed | |
| 343 | - ! | |
| 344 | - integer, intent(in) :: d | |
| 345 | - complex, intent(in) :: a(d,d) | |
| 346 | - integer, intent(out) :: status | |
| 347 | - complex :: fvn_c_det | |
| 348 | - | |
| 349 | - complex, allocatable :: wc_a(:,:) | |
| 350 | - integer, allocatable :: ipiv(:) | |
| 351 | - integer :: info,i | |
| 352 | - | |
| 353 | - status=1 | |
| 354 | - allocate(wc_a(d,d)) | |
| 355 | - allocate(ipiv(d)) | |
| 356 | - wc_a(:,:)=a(:,:) | |
| 357 | - call cgetrf(d,d,wc_a,d,ipiv,info) | |
| 358 | - if (info/= 0) then | |
| 359 | - status=0 | |
| 360 | - fvn_c_det=(0.e0,0.e0) | |
| 361 | - deallocate(ipiv) | |
| 362 | - deallocate(wc_a) | |
| 363 | - return | |
| 364 | - end if | |
| 365 | - fvn_c_det=(1.e0,0.e0) | |
| 366 | - do i=1,d | |
| 367 | - if (ipiv(i)==i) then | |
| 368 | - fvn_c_det=fvn_c_det*wc_a(i,i) | |
| 369 | - else | |
| 370 | - fvn_c_det=-fvn_c_det*wc_a(i,i) | |
| 371 | - end if | |
| 372 | - end do | |
| 373 | - deallocate(ipiv) | |
| 374 | - deallocate(wc_a) | |
| 375 | - | |
| 376 | -end function | |
| 377 | - | |
| 378 | -function fvn_z_det(d,a,status) | |
| 379 | - ! | |
| 380 | - ! Evaluate the determinant of a square matrix using lapack LU factorization | |
| 381 | - ! | |
| 382 | - ! d (in) : matrix rank | |
| 383 | - ! a (in) : The Matrix | |
| 384 | - ! det (out) : determinant | |
| 385 | - ! status (out) : =0 if LU factorization failed | |
| 386 | - ! | |
| 387 | - integer, intent(in) :: d | |
| 388 | - double complex, intent(in) :: a(d,d) | |
| 389 | - integer, intent(out) :: status | |
| 390 | - double complex :: fvn_z_det | |
| 391 | - | |
| 392 | - double complex, allocatable :: wc_a(:,:) | |
| 393 | - integer, allocatable :: ipiv(:) | |
| 394 | - integer :: info,i | |
| 395 | - | |
| 396 | - status=1 | |
| 397 | - allocate(wc_a(d,d)) | |
| 398 | - allocate(ipiv(d)) | |
| 399 | - wc_a(:,:)=a(:,:) | |
| 400 | - call zgetrf(d,d,wc_a,d,ipiv,info) | |
| 401 | - if (info/= 0) then | |
| 402 | - status=0 | |
| 403 | - fvn_z_det=(0.d0,0.d0) | |
| 404 | - deallocate(ipiv) | |
| 405 | - deallocate(wc_a) | |
| 406 | - return | |
| 407 | - end if | |
| 408 | - fvn_z_det=(1.d0,0.d0) | |
| 409 | - do i=1,d | |
| 410 | - if (ipiv(i)==i) then | |
| 411 | - fvn_z_det=fvn_z_det*wc_a(i,i) | |
| 412 | - else | |
| 413 | - fvn_z_det=-fvn_z_det*wc_a(i,i) | |
| 414 | - end if | |
| 415 | - end do | |
| 416 | - deallocate(ipiv) | |
| 417 | - deallocate(wc_a) | |
| 418 | - | |
| 419 | -end function | |
| 420 | - | |
| 421 | -!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! | |
| 422 | -! | |
| 423 | -! Condition test | |
| 424 | -! | |
| 425 | -!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! | |
| 426 | -! 1-norm | |
| 427 | -! fonction lapack slange,dlange,clange,zlange pour obtenir la 1-norm | |
| 428 | -! fonction lapack sgecon,dgecon,cgecon,zgecon pour calculer la rcond | |
| 429 | -! | |
| 430 | -subroutine fvn_s_matcon(d,a,rcond,status) | |
| 431 | - ! Matrix condition (reciprocal of condition number) | |
| 432 | - ! | |
| 433 | - ! d (in) : matrix rank | |
| 434 | - ! a (in) : The Matrix | |
| 435 | - ! rcond (out) : guess what | |
| 436 | - ! status (out) : =0 if something went wrong | |
| 437 | - ! | |
| 438 | - integer, intent(in) :: d | |
| 439 | - real, intent(in) :: a(d,d) | |
| 440 | - real, intent(out) :: rcond | |
| 441 | - integer, intent(out) :: status | |
| 442 | - | |
| 443 | - real, allocatable :: work(:) | |
| 444 | - integer, allocatable :: iwork(:) | |
| 445 | - real :: anorm | |
| 446 | - real, allocatable :: wc_a(:,:) ! working copy of a | |
| 447 | - integer :: info | |
| 448 | - integer, allocatable :: ipiv(:) | |
| 449 | - | |
| 450 | - real, external :: slange | |
| 451 | - | |
| 452 | - | |
| 453 | - status=1 | |
| 454 | - | |
| 455 | - anorm=slange('1',d,d,a,d,work) ! work is unallocated as it is only used when computing infinity norm | |
| 456 | - | |
| 457 | - allocate(wc_a(d,d)) | |
| 458 | - !call scopy(d*d,a,1,wc_a,1) | |
| 459 | - wc_a(:,:)=a(:,:) | |
| 460 | - | |
| 461 | - allocate(ipiv(d)) | |
| 462 | - call sgetrf(d,d,wc_a,d,ipiv,info) | |
| 463 | - if (info /= 0) then | |
| 464 | - status=0 | |
| 465 | - deallocate(ipiv) | |
| 466 | - deallocate(wc_a) | |
| 467 | - return | |
| 468 | - end if | |
| 469 | - allocate(work(4*d)) | |
| 470 | - allocate(iwork(d)) | |
| 471 | - call sgecon('1',d,wc_a,d,anorm,rcond,work,iwork,info) | |
| 472 | - if (info /= 0) then | |
| 473 | - status=0 | |
| 474 | - end if | |
| 475 | - deallocate(iwork) | |
| 476 | - deallocate(work) | |
| 477 | - deallocate(ipiv) | |
| 478 | - deallocate(wc_a) | |
| 479 | - | |
| 480 | -end subroutine | |
| 481 | - | |
| 482 | -subroutine fvn_d_matcon(d,a,rcond,status) | |
| 483 | - ! Matrix condition (reciprocal of condition number) | |
| 484 | - ! | |
| 485 | - ! d (in) : matrix rank | |
| 486 | - ! a (in) : The Matrix | |
| 487 | - ! rcond (out) : guess what | |
| 488 | - ! status (out) : =0 if something went wrong | |
| 489 | - ! | |
| 490 | - integer, intent(in) :: d | |
| 491 | - double precision, intent(in) :: a(d,d) | |
| 492 | - double precision, intent(out) :: rcond | |
| 493 | - integer, intent(out) :: status | |
| 494 | - | |
| 495 | - double precision, allocatable :: work(:) | |
| 496 | - integer, allocatable :: iwork(:) | |
| 497 | - double precision :: anorm | |
| 498 | - double precision, allocatable :: wc_a(:,:) ! working copy of a | |
| 499 | - integer :: info | |
| 500 | - integer, allocatable :: ipiv(:) | |
| 501 | - | |
| 502 | - double precision, external :: dlange | |
| 503 | - | |
| 504 | - | |
| 505 | - status=1 | |
| 506 | - | |
| 507 | - anorm=dlange('1',d,d,a,d,work) ! work is unallocated as it is only used when computing infinity norm | |
| 508 | - | |
| 509 | - allocate(wc_a(d,d)) | |
| 510 | - !call dcopy(d*d,a,1,wc_a,1) | |
| 511 | - wc_a(:,:)=a(:,:) | |
| 512 | - | |
| 513 | - allocate(ipiv(d)) | |
| 514 | - call dgetrf(d,d,wc_a,d,ipiv,info) | |
| 515 | - if (info /= 0) then | |
| 516 | - status=0 | |
| 517 | - deallocate(ipiv) | |
| 518 | - deallocate(wc_a) | |
| 519 | - return | |
| 520 | - end if | |
| 521 | - | |
| 522 | - allocate(work(4*d)) | |
| 523 | - allocate(iwork(d)) | |
| 524 | - call dgecon('1',d,wc_a,d,anorm,rcond,work,iwork,info) | |
| 525 | - if (info /= 0) then | |
| 526 | - status=0 | |
| 527 | - end if | |
| 528 | - deallocate(iwork) | |
| 529 | - deallocate(work) | |
| 530 | - deallocate(ipiv) | |
| 531 | - deallocate(wc_a) | |
| 532 | - | |
| 533 | -end subroutine | |
| 534 | - | |
| 535 | -subroutine fvn_c_matcon(d,a,rcond,status) | |
| 536 | - ! Matrix condition (reciprocal of condition number) | |
| 537 | - ! | |
| 538 | - ! d (in) : matrix rank | |
| 539 | - ! a (in) : The Matrix | |
| 540 | - ! rcond (out) : guess what | |
| 541 | - ! status (out) : =0 if something went wrong | |
| 542 | - ! | |
| 543 | - integer, intent(in) :: d | |
| 544 | - complex, intent(in) :: a(d,d) | |
| 545 | - real, intent(out) :: rcond | |
| 546 | - integer, intent(out) :: status | |
| 547 | - | |
| 548 | - real, allocatable :: rwork(:) | |
| 549 | - complex, allocatable :: work(:) | |
| 550 | - integer, allocatable :: iwork(:) | |
| 551 | - real :: anorm | |
| 552 | - complex, allocatable :: wc_a(:,:) ! working copy of a | |
| 553 | - integer :: info | |
| 554 | - integer, allocatable :: ipiv(:) | |
| 555 | - | |
| 556 | - real, external :: clange | |
| 557 | - | |
| 558 | - | |
| 559 | - status=1 | |
| 560 | - | |
| 561 | - anorm=clange('1',d,d,a,d,rwork) ! rwork is unallocated as it is only used when computing infinity norm | |
| 562 | - | |
| 563 | - allocate(wc_a(d,d)) | |
| 564 | - !call ccopy(d*d,a,1,wc_a,1) | |
| 565 | - wc_a(:,:)=a(:,:) | |
| 566 | - | |
| 567 | - allocate(ipiv(d)) | |
| 568 | - call cgetrf(d,d,wc_a,d,ipiv,info) | |
| 569 | - if (info /= 0) then | |
| 570 | - status=0 | |
| 571 | - deallocate(ipiv) | |
| 572 | - deallocate(wc_a) | |
| 573 | - return | |
| 574 | - end if | |
| 575 | - allocate(work(2*d)) | |
| 576 | - allocate(rwork(2*d)) | |
| 577 | - call cgecon('1',d,wc_a,d,anorm,rcond,work,rwork,info) | |
| 578 | - if (info /= 0) then | |
| 579 | - status=0 | |
| 580 | - end if | |
| 581 | - deallocate(rwork) | |
| 582 | - deallocate(work) | |
| 583 | - deallocate(ipiv) | |
| 584 | - deallocate(wc_a) | |
| 585 | -end subroutine | |
| 586 | - | |
| 587 | -subroutine fvn_z_matcon(d,a,rcond,status) | |
| 588 | - ! Matrix condition (reciprocal of condition number) | |
| 589 | - ! | |
| 590 | - ! d (in) : matrix rank | |
| 591 | - ! a (in) : The Matrix | |
| 592 | - ! rcond (out) : guess what | |
| 593 | - ! status (out) : =0 if something went wrong | |
| 594 | - ! | |
| 595 | - integer, intent(in) :: d | |
| 596 | - double complex, intent(in) :: a(d,d) | |
| 597 | - double precision, intent(out) :: rcond | |
| 598 | - integer, intent(out) :: status | |
| 599 | - | |
| 600 | - double complex, allocatable :: work(:) | |
| 601 | - double precision, allocatable :: rwork(:) | |
| 602 | - double precision :: anorm | |
| 603 | - double complex, allocatable :: wc_a(:,:) ! working copy of a | |
| 604 | - integer :: info | |
| 605 | - integer, allocatable :: ipiv(:) | |
| 606 | - | |
| 607 | - double precision, external :: zlange | |
| 608 | - | |
| 609 | - | |
| 610 | - status=1 | |
| 611 | - | |
| 612 | - anorm=zlange('1',d,d,a,d,rwork) ! rwork is unallocated as it is only used when computing infinity norm | |
| 613 | - | |
| 614 | - allocate(wc_a(d,d)) | |
| 615 | - !call zcopy(d*d,a,1,wc_a,1) | |
| 616 | - wc_a(:,:)=a(:,:) | |
| 617 | - | |
| 618 | - allocate(ipiv(d)) | |
| 619 | - call zgetrf(d,d,wc_a,d,ipiv,info) | |
| 620 | - if (info /= 0) then | |
| 621 | - status=0 | |
| 622 | - deallocate(ipiv) | |
| 623 | - deallocate(wc_a) | |
| 624 | - return | |
| 625 | - end if | |
| 626 | - | |
| 627 | - allocate(work(2*d)) | |
| 628 | - allocate(rwork(2*d)) | |
| 629 | - call zgecon('1',d,wc_a,d,anorm,rcond,work,rwork,info) | |
| 630 | - if (info /= 0) then | |
| 631 | - status=0 | |
| 632 | - end if | |
| 633 | - deallocate(rwork) | |
| 634 | - deallocate(work) | |
| 635 | - deallocate(ipiv) | |
| 636 | - deallocate(wc_a) | |
| 637 | -end subroutine | |
| 638 | - | |
| 639 | -!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! | |
| 640 | -! | |
| 641 | -! Valeurs propres/ Vecteurs propre | |
| 642 | -! | |
| 643 | -!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! | |
| 644 | - | |
| 645 | -subroutine fvn_s_matev(d,a,evala,eveca,status) | |
| 646 | - ! | |
| 647 | - ! integer d (in) : matrice rank | |
| 648 | - ! real a(d,d) (in) : The Matrix | |
| 649 | - ! complex evala(d) (out) : eigenvalues | |
| 650 | - ! complex eveca(d,d) (out) : eveca(:,j) = jth eigenvector | |
| 651 | - ! integer (out) : status =0 if something went wrong | |
| 652 | - ! | |
| 653 | - ! interfacing Lapack routine SGEEV | |
| 654 | - | |
| 655 | - integer, intent(in) :: d | |
| 656 | - real, intent(in) :: a(d,d) | |
| 657 | - complex, intent(out) :: evala(d) | |
| 658 | - complex, intent(out) :: eveca(d,d) | |
| 659 | - integer, intent(out) :: status | |
| 660 | - | |
| 661 | - real, allocatable :: wc_a(:,:) ! a working copy of a | |
| 662 | - integer :: info | |
| 663 | - integer :: lwork | |
| 664 | - real, allocatable :: wr(:),wi(:) | |
| 665 | - real :: vl ! unused but necessary for the call | |
| 666 | - real, allocatable :: vr(:,:) | |
| 667 | - real, allocatable :: work(:) | |
| 668 | - real :: twork(1) | |
| 669 | - integer i | |
| 670 | - integer j | |
| 671 | - | |
| 672 | - ! making a working copy of a | |
| 673 | - allocate(wc_a(d,d)) | |
| 674 | - !call scopy(d*d,a,1,wc_a,1) | |
| 675 | - wc_a(:,:)=a(:,:) | |
| 676 | - | |
| 677 | - allocate(wr(d)) | |
| 678 | - allocate(wi(d)) | |
| 679 | - allocate(vr(d,d)) | |
| 680 | - ! query optimal work size | |
| 681 | - call sgeev('N','V',d,wc_a,d,wr,wi,vl,1,vr,d,twork,-1,info) | |
| 682 | - lwork=int(twork(1)) | |
| 683 | - allocate(work(lwork)) | |
| 684 | - call sgeev('N','V',d,wc_a,d,wr,wi,vl,1,vr,d,work,lwork,info) | |
| 685 | - | |
| 686 | - if (info /= 0) then | |
| 687 | - status=0 | |
| 688 | - deallocate(work) | |
| 689 | - deallocate(vr) | |
| 690 | - deallocate(wi) | |
| 691 | - deallocate(wr) | |
| 692 | - deallocate(wc_a) | |
| 693 | - return | |
| 694 | - end if | |
| 695 | - | |
| 696 | - ! now fill in the results | |
| 697 | - i=1 | |
| 698 | - do while(i<=d) | |
| 699 | - evala(i)=cmplx(wr(i),wi(i)) | |
| 700 | - if (wi(i) == 0.) then ! eigenvalue is real | |
| 701 | - eveca(:,i)=cmplx(vr(:,i),0.) | |
| 702 | - else ! eigenvalue is complex | |
| 703 | - evala(i+1)=cmplx(wr(i+1),wi(i+1)) | |
| 704 | - eveca(:,i)=cmplx(vr(:,i),vr(:,i+1)) | |
| 705 | - eveca(:,i+1)=cmplx(vr(:,i),-vr(:,i+1)) | |
| 706 | - i=i+1 | |
| 707 | - end if | |
| 708 | - i=i+1 | |
| 709 | - enddo | |
| 710 | - deallocate(work) | |
| 711 | - deallocate(vr) | |
| 712 | - deallocate(wi) | |
| 713 | - deallocate(wr) | |
| 714 | - deallocate(wc_a) | |
| 715 | - | |
| 716 | -end subroutine | |
| 717 | - | |
| 718 | -subroutine fvn_d_matev(d,a,evala,eveca,status) | |
| 719 | - ! | |
| 720 | - ! integer d (in) : matrice rank | |
| 721 | - ! double precision a(d,d) (in) : The Matrix | |
| 722 | - ! double complex evala(d) (out) : eigenvalues | |
| 723 | - ! double complex eveca(d,d) (out) : eveca(:,j) = jth eigenvector | |
| 724 | - ! integer (out) : status =0 if something went wrong | |
| 725 | - ! | |
| 726 | - ! interfacing Lapack routine DGEEV | |
| 727 | - integer, intent(in) :: d | |
| 728 | - double precision, intent(in) :: a(d,d) | |
| 729 | - double complex, intent(out) :: evala(d) | |
| 730 | - double complex, intent(out) :: eveca(d,d) | |
| 731 | - integer, intent(out) :: status | |
| 732 | - | |
| 733 | - double precision, allocatable :: wc_a(:,:) ! a working copy of a | |
| 734 | - integer :: info | |
| 735 | - integer :: lwork | |
| 736 | - double precision, allocatable :: wr(:),wi(:) | |
| 737 | - double precision :: vl ! unused but necessary for the call | |
| 738 | - double precision, allocatable :: vr(:,:) | |
| 739 | - double precision, allocatable :: work(:) | |
| 740 | - double precision :: twork(1) | |
| 741 | - integer i | |
| 742 | - integer j | |
| 743 | - | |
| 744 | - ! making a working copy of a | |
| 745 | - allocate(wc_a(d,d)) | |
| 746 | - !call dcopy(d*d,a,1,wc_a,1) | |
| 747 | - wc_a(:,:)=a(:,:) | |
| 748 | - | |
| 749 | - allocate(wr(d)) | |
| 750 | - allocate(wi(d)) | |
| 751 | - allocate(vr(d,d)) | |
| 752 | - ! query optimal work size | |
| 753 | - call dgeev('N','V',d,wc_a,d,wr,wi,vl,1,vr,d,twork,-1,info) | |
| 754 | - lwork=int(twork(1)) | |
| 755 | - allocate(work(lwork)) | |
| 756 | - call dgeev('N','V',d,wc_a,d,wr,wi,vl,1,vr,d,work,lwork,info) | |
| 757 | - | |
| 758 | - if (info /= 0) then | |
| 759 | - status=0 | |
| 760 | - deallocate(work) | |
| 761 | - deallocate(vr) | |
| 762 | - deallocate(wi) | |
| 763 | - deallocate(wr) | |
| 764 | - deallocate(wc_a) | |
| 765 | - return | |
| 766 | - end if | |
| 767 | - | |
| 768 | - ! now fill in the results | |
| 769 | - i=1 | |
| 770 | - do while(i<=d) | |
| 771 | - evala(i)=dcmplx(wr(i),wi(i)) | |
| 772 | - if (wi(i) == 0.) then ! eigenvalue is real | |
| 773 | - eveca(:,i)=dcmplx(vr(:,i),0.) | |
| 774 | - else ! eigenvalue is complex | |
| 775 | - evala(i+1)=dcmplx(wr(i+1),wi(i+1)) | |
| 776 | - eveca(:,i)=dcmplx(vr(:,i),vr(:,i+1)) | |
| 777 | - eveca(:,i+1)=dcmplx(vr(:,i),-vr(:,i+1)) | |
| 778 | - i=i+1 | |
| 779 | - end if | |
| 780 | - i=i+1 | |
| 781 | - enddo | |
| 782 | - | |
| 783 | - deallocate(work) | |
| 784 | - deallocate(vr) | |
| 785 | - deallocate(wi) | |
| 786 | - deallocate(wr) | |
| 787 | - deallocate(wc_a) | |
| 788 | - | |
| 789 | -end subroutine | |
| 790 | - | |
| 791 | -subroutine fvn_c_matev(d,a,evala,eveca,status) | |
| 792 | - ! | |
| 793 | - ! integer d (in) : matrice rank | |
| 794 | - ! complex a(d,d) (in) : The Matrix | |
| 795 | - ! complex evala(d) (out) : eigenvalues | |
| 796 | - ! complex eveca(d,d) (out) : eveca(:,j) = jth eigenvector | |
| 797 | - ! integer (out) : status =0 if something went wrong | |
| 798 | - ! | |
| 799 | - ! interfacing Lapack routine CGEEV | |
| 800 | - | |
| 801 | - integer, intent(in) :: d | |
| 802 | - complex, intent(in) :: a(d,d) | |
| 803 | - complex, intent(out) :: evala(d) | |
| 804 | - complex, intent(out) :: eveca(d,d) | |
| 805 | - integer, intent(out) :: status | |
| 806 | - | |
| 807 | - complex, allocatable :: wc_a(:,:) ! a working copy of a | |
| 808 | - integer :: info | |
| 809 | - integer :: lwork | |
| 810 | - complex, allocatable :: work(:) | |
| 811 | - complex :: twork(1) | |
| 812 | - real, allocatable :: rwork(:) | |
| 813 | - complex :: vl ! unused but necessary for the call | |
| 814 | - | |
| 815 | - status=1 | |
| 816 | - | |
| 817 | - ! making a working copy of a | |
| 818 | - allocate(wc_a(d,d)) | |
| 819 | - !call ccopy(d*d,a,1,wc_a,1) | |
| 820 | - wc_a(:,:)=a(:,:) | |
| 821 | - | |
| 822 | - | |
| 823 | - ! query optimal work size | |
| 824 | - call cgeev('N','V',d,wc_a,d,evala,vl,1,eveca,d,twork,-1,rwork,info) | |
| 825 | - lwork=int(twork(1)) | |
| 826 | - allocate(work(lwork)) | |
| 827 | - allocate(rwork(2*d)) | |
| 828 | - call cgeev('N','V',d,wc_a,d,evala,vl,1,eveca,d,work,lwork,rwork,info) | |
| 829 | - | |
| 830 | - if (info /= 0) then | |
| 831 | - status=0 | |
| 832 | - end if | |
| 833 | - deallocate(rwork) | |
| 834 | - deallocate(work) | |
| 835 | - deallocate(wc_a) | |
| 836 | - | |
| 837 | -end subroutine | |
| 838 | - | |
| 839 | -subroutine fvn_z_matev(d,a,evala,eveca,status) | |
| 840 | - ! | |
| 841 | - ! integer d (in) : matrice rank | |
| 842 | - ! double complex a(d,d) (in) : The Matrix | |
| 843 | - ! double complex evala(d) (out) : eigenvalues | |
| 844 | - ! double complex eveca(d,d) (out) : eveca(:,j) = jth eigenvector | |
| 845 | - ! integer (out) : status =0 if something went wrong | |
| 846 | - ! | |
| 847 | - ! interfacing Lapack routine ZGEEV | |
| 848 | - | |
| 849 | - integer, intent(in) :: d | |
| 850 | - double complex, intent(in) :: a(d,d) | |
| 851 | - double complex, intent(out) :: evala(d) | |
| 852 | - double complex, intent(out) :: eveca(d,d) | |
| 853 | - integer, intent(out) :: status | |
| 854 | - | |
| 855 | - double complex, allocatable :: wc_a(:,:) ! a working copy of a | |
| 856 | - integer :: info | |
| 857 | - integer :: lwork | |
| 858 | - double complex, allocatable :: work(:) | |
| 859 | - double complex :: twork(1) | |
| 860 | - double precision, allocatable :: rwork(:) | |
| 861 | - double complex :: vl ! unused but necessary for the call | |
| 862 | - | |
| 863 | - status=1 | |
| 864 | - | |
| 865 | - ! making a working copy of a | |
| 866 | - allocate(wc_a(d,d)) | |
| 867 | - !call zcopy(d*d,a,1,wc_a,1) | |
| 868 | - wc_a(:,:)=a(:,:) | |
| 869 | - | |
| 870 | - ! query optimal work size | |
| 871 | - call zgeev('N','V',d,wc_a,d,evala,vl,1,eveca,d,twork,-1,rwork,info) | |
| 872 | - lwork=int(twork(1)) | |
| 873 | - allocate(work(lwork)) | |
| 874 | - allocate(rwork(2*d)) | |
| 875 | - call zgeev('N','V',d,wc_a,d,evala,vl,1,eveca,d,work,lwork,rwork,info) | |
| 876 | - | |
| 877 | - if (info /= 0) then | |
| 878 | - status=0 | |
| 879 | - end if | |
| 880 | - deallocate(rwork) | |
| 881 | - deallocate(work) | |
| 882 | - deallocate(wc_a) | |
| 883 | - | |
| 884 | -end subroutine | |
| 885 | - | |
| 886 | -!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! | |
| 887 | -! | |
| 888 | -! Akima spline interpolation and spline evaluation | |
| 889 | -! | |
| 890 | -!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! | |
| 891 | - | |
| 892 | -! Single precision | |
| 893 | -subroutine fvn_s_akima(n,x,y,br,co) | |
| 894 | - implicit none | |
| 895 | - integer, intent(in) :: n | |
| 896 | - real, intent(in) :: x(n) | |
| 897 | - real, intent(in) :: y(n) | |
| 898 | - real, intent(out) :: br(n) | |
| 899 | - real, intent(out) :: co(4,n) | |
| 900 | - | |
| 901 | - real, allocatable :: var(:),z(:) | |
| 902 | - real :: wi_1,wi | |
| 903 | - integer :: i | |
| 904 | - real :: dx,a,b | |
| 905 | - | |
| 906 | - ! br is just a copy of x | |
| 907 | - br(:)=x(:) | |
| 908 | - | |
| 909 | - allocate(var(n)) | |
| 910 | - allocate(z(n)) | |
| 911 | - ! evaluate the variations | |
| 912 | - do i=1, n-1 | |
| 913 | - var(i+2)=(y(i+1)-y(i))/(x(i+1)-x(i)) | |
| 914 | - end do | |
| 915 | - var(n+2)=2.e0*var(n+1)-var(n) | |
| 916 | - var(n+3)=2.e0*var(n+2)-var(n+1) | |
| 917 | - var(2)=2.e0*var(3)-var(4) | |
| 918 | - var(1)=2.e0*var(2)-var(3) | |
| 919 | - | |
| 920 | - do i = 1, n | |
| 921 | - wi_1=abs(var(i+3)-var(i+2)) | |
| 922 | - wi=abs(var(i+1)-var(i)) | |
| 923 | - if ((wi_1+wi).eq.0.e0) then | |
| 924 | - z(i)=(var(i+2)+var(i+1))/2.e0 | |
| 925 | - else | |
| 926 | - z(i)=(wi_1*var(i+1)+wi*var(i+2))/(wi_1+wi) | |
| 927 | - end if | |
| 928 | - end do | |
| 929 | - | |
| 930 | - do i=1, n-1 | |
| 931 | - dx=x(i+1)-x(i) | |
| 932 | - a=(z(i+1)-z(i))*dx ! coeff intermediaires pour calcul wd | |
| 933 | - b=y(i+1)-y(i)-z(i)*dx ! coeff intermediaires pour calcul wd | |
| 934 | - co(1,i)=y(i) | |
| 935 | - co(2,i)=z(i) | |
| 936 | - !co(3,i)=-(a-3.*b)/dx**2 ! mรฉthode wd | |
| 937 | - !co(4,i)=(a-2.*b)/dx**3 ! mรฉthode wd | |
| 938 | - co(3,i)=(3.e0*var(i+2)-2.e0*z(i)-z(i+1))/dx ! mรฉthode JP Moreau | |
| 939 | - co(4,i)=(z(i)+z(i+1)-2.e0*var(i+2))/dx**2 ! | |
| 940 | - ! les coefficients donnรฉs par imsl sont co(3,i)*2 et co(4,i)*6 | |
| 941 | - ! etrangement la fonction csval corrige et donne la bonne valeur ... | |
| 942 | - end do | |
| 943 | - co(1,n)=y(n) | |
| 944 | - co(2,n)=z(n) | |
| 945 | - co(3,n)=0.e0 | |
| 946 | - co(4,n)=0.e0 | |
| 947 | - | |
| 948 | - deallocate(z) | |
| 949 | - deallocate(var) | |
| 950 | - | |
| 951 | -end subroutine | |
| 952 | - | |
| 953 | -! Double precision | |
| 954 | -subroutine fvn_d_akima(n,x,y,br,co) | |
| 955 | - | |
| 956 | - implicit none | |
| 957 | - integer, intent(in) :: n | |
| 958 | - double precision, intent(in) :: x(n) | |
| 959 | - double precision, intent(in) :: y(n) | |
| 960 | - double precision, intent(out) :: br(n) | |
| 961 | - double precision, intent(out) :: co(4,n) | |
| 962 | - | |
| 963 | - double precision, allocatable :: var(:),z(:) | |
| 964 | - double precision :: wi_1,wi | |
| 965 | - integer :: i | |
| 966 | - double precision :: dx,a,b | |
| 967 | - | |
| 968 | - ! br is just a copy of x | |
| 969 | - br(:)=x(:) | |
| 970 | - | |
| 971 | - allocate(var(n)) | |
| 972 | - allocate(z(n)) | |
| 973 | - ! evaluate the variations | |
| 974 | - do i=1, n-1 | |
| 975 | - var(i+2)=(y(i+1)-y(i))/(x(i+1)-x(i)) | |
| 976 | - end do | |
| 977 | - var(n+2)=2.d0*var(n+1)-var(n) | |
| 978 | - var(n+3)=2.d0*var(n+2)-var(n+1) | |
| 979 | - var(2)=2.d0*var(3)-var(4) | |
| 980 | - var(1)=2.d0*var(2)-var(3) | |
| 981 | - | |
| 982 | - do i = 1, n | |
| 983 | - wi_1=dabs(var(i+3)-var(i+2)) | |
| 984 | - wi=dabs(var(i+1)-var(i)) | |
| 985 | - if ((wi_1+wi).eq.0.d0) then | |
| 986 | - z(i)=(var(i+2)+var(i+1))/2.d0 | |
| 987 | - else | |
| 988 | - z(i)=(wi_1*var(i+1)+wi*var(i+2))/(wi_1+wi) | |
| 989 | - end if | |
| 990 | - end do | |
| 991 | - | |
| 992 | - do i=1, n-1 | |
| 993 | - dx=x(i+1)-x(i) | |
| 994 | - a=(z(i+1)-z(i))*dx ! coeff intermediaires pour calcul wd | |
| 995 | - b=y(i+1)-y(i)-z(i)*dx ! coeff intermediaires pour calcul wd | |
| 996 | - co(1,i)=y(i) | |
| 997 | - co(2,i)=z(i) | |
| 998 | - !co(3,i)=-(a-3.*b)/dx**2 ! mรฉthode wd | |
| 999 | - !co(4,i)=(a-2.*b)/dx**3 ! mรฉthode wd | |
| 1000 | - co(3,i)=(3.d0*var(i+2)-2.d0*z(i)-z(i+1))/dx ! mรฉthode JP Moreau | |
| 1001 | - co(4,i)=(z(i)+z(i+1)-2.d0*var(i+2))/dx**2 ! | |
| 1002 | - ! les coefficients donnรฉs par imsl sont co(3,i)*2 et co(4,i)*6 | |
| 1003 | - ! etrangement la fonction csval corrige et donne la bonne valeur ... | |
| 1004 | - end do | |
| 1005 | - co(1,n)=y(n) | |
| 1006 | - co(2,n)=z(n) | |
| 1007 | - co(3,n)=0.d0 | |
| 1008 | - co(4,n)=0.d0 | |
| 1009 | - | |
| 1010 | - deallocate(z) | |
| 1011 | - deallocate(var) | |
| 1012 | - | |
| 1013 | -end subroutine | |
| 1014 | - | |
| 1015 | -! | |
| 1016 | -! Single precision spline evaluation | |
| 1017 | -! | |
| 1018 | -function fvn_s_spline_eval(x,n,br,co) | |
| 1019 | - implicit none | |
| 1020 | - real, intent(in) :: x ! x must be br(1)<= x <= br(n+1) otherwise value is extrapolated | |
| 1021 | - integer, intent(in) :: n ! number of intervals | |
| 1022 | - real, intent(in) :: br(n+1) ! breakpoints | |
| 1023 | - real, intent(in) :: co(4,n+1) ! spline coeeficients | |
| 1024 | - real :: fvn_s_spline_eval | |
| 1025 | - | |
| 1026 | - integer :: i | |
| 1027 | - real :: dx | |
| 1028 | - | |
| 1029 | - if (x<=br(1)) then | |
| 1030 | - i=1 | |
| 1031 | - else if (x>=br(n+1)) then | |
| 1032 | - i=n | |
| 1033 | - else | |
| 1034 | - i=1 | |
| 1035 | - do while(x>=br(i)) | |
| 1036 | - i=i+1 | |
| 1037 | - end do | |
| 1038 | - i=i-1 | |
| 1039 | - end if | |
| 1040 | - dx=x-br(i) | |
| 1041 | - fvn_s_spline_eval=co(1,i)+co(2,i)*dx+co(3,i)*dx**2+co(4,i)*dx**3 | |
| 1042 | - | |
| 1043 | -end function | |
| 1044 | - | |
| 1045 | -! Double precision spline evaluation | |
| 1046 | -function fvn_d_spline_eval(x,n,br,co) | |
| 1047 | - implicit none | |
| 1048 | - double precision, intent(in) :: x ! x must be br(1)<= x <= br(n+1) otherwise value is extrapolated | |
| 1049 | - integer, intent(in) :: n ! number of intervals | |
| 1050 | - double precision, intent(in) :: br(n+1) ! breakpoints | |
| 1051 | - double precision, intent(in) :: co(4,n+1) ! spline coeeficients | |
| 1052 | - double precision :: fvn_d_spline_eval | |
| 1053 | - | |
| 1054 | - integer :: i | |
| 1055 | - double precision :: dx | |
| 1056 | - | |
| 1057 | - | |
| 1058 | - if (x<=br(1)) then | |
| 1059 | - i=1 | |
| 1060 | - else if (x>=br(n+1)) then | |
| 1061 | - i=n | |
| 1062 | - else | |
| 1063 | - i=1 | |
| 1064 | - do while(x>=br(i)) | |
| 1065 | - i=i+1 | |
| 1066 | - end do | |
| 1067 | - i=i-1 | |
| 1068 | - end if | |
| 1069 | - | |
| 1070 | - dx=x-br(i) | |
| 1071 | - fvn_d_spline_eval=co(1,i)+co(2,i)*dx+co(3,i)*dx**2+co(4,i)*dx**3 | |
| 1072 | - | |
| 1073 | -end function | |
| 1074 | - | |
| 1075 | - | |
| 1076 | -! | |
| 1077 | -! Muller | |
| 1078 | -! | |
| 1079 | -! | |
| 1080 | -! | |
| 1081 | -! William Daniau 2007 | |
| 1082 | -! | |
| 1083 | -! This routine is a fortran 90 port of Hans D. Mittelmann's routine muller.f | |
| 1084 | -! http://plato.asu.edu/ftp/other_software/muller.f | |
| 1085 | -! | |
| 1086 | -! it can be used as a replacement for imsl routine dzanly with minor changes | |
| 1087 | -! | |
| 1088 | -!----------------------------------------------------------------------- | |
| 1089 | -! | |
| 1090 | -! purpose - zeros of an analytic complex function | |
| 1091 | -! using the muller method with deflation | |
| 1092 | -! | |
| 1093 | -! usage - call fvn_z_muller (f,eps,eps1,kn,n,nguess,x,itmax, | |
| 1094 | -! infer,ier) | |
| 1095 | -! | |
| 1096 | -! arguments f - a complex function subprogram, f(z), written | |
| 1097 | -! by the user specifying the equation whose | |
| 1098 | -! roots are to be found. f must appear in | |
| 1099 | -! an external statement in the calling pro- | |
| 1100 | -! gram. | |
| 1101 | -! eps - 1st stopping criterion. let fp(z)=f(z)/p | |
| 1102 | -! where p = (z-z(1))*(z-z(2))*,,,*(z-z(k-1)) | |
| 1103 | -! and z(1),...,z(k-1) are previously found | |
| 1104 | -! roots. if ((cdabs(f(z)).le.eps) .and. | |
| 1105 | -! (cdabs(fp(z)).le.eps)), then z is accepted | |
| 1106 | -! as a root. (input) | |
| 1107 | -! eps1 - 2nd stopping criterion. a root is accepted | |
| 1108 | -! if two successive approximations to a given | |
| 1109 | -! root agree within eps1. (input) | |
| 1110 | -! note. if either or both of the stopping | |
| 1111 | -! criteria are fulfilled, the root is | |
| 1112 | -! accepted. | |
| 1113 | -! kn - the number of known roots which must be stored | |
| 1114 | -! in x(1),...,x(kn), prior to entry to muller | |
| 1115 | -! nguess - the number of initial guesses provided. these | |
| 1116 | -! guesses must be stored in x(kn+1),..., | |
| 1117 | -! x(kn+nguess). nguess must be set equal | |
| 1118 | -! to zero if no guesses are provided. (input) | |
| 1119 | -! n - the number of new roots to be found by | |
| 1120 | -! muller (input) | |
| 1121 | -! x - a complex vector of length kn+n. x(1),..., | |
| 1122 | -! x(kn) on input must contain any known | |
| 1123 | -! roots. x(kn+1),..., x(kn+n) on input may, | |
| 1124 | -! on user option, contain initial guesses for | |
| 1125 | -! the n new roots which are to be computed. | |
| 1126 | -! if the user does not provide an initial | |
| 1127 | -! guess, zero is used. | |
| 1128 | -! on output, x(kn+1),...,x(kn+n) contain the | |
| 1129 | -! approximate roots found by muller. | |
| 1130 | -! itmax - the maximum allowable number of iterations | |
| 1131 | -! per root (input) | |
| 1132 | -! infer - an integer vector of length kn+n. on | |
| 1133 | -! output infer(j) contains the number of | |
| 1134 | -! iterations used in finding the j-th root | |
| 1135 | -! when convergence was achieved. if | |
| 1136 | -! convergence was not obtained in itmax | |
| 1137 | -! iterations, infer(j) will be greater than | |
| 1138 | -! itmax (output). | |
| 1139 | -! ier - error parameter (output) | |
| 1140 | -! warning error | |
| 1141 | -! ier = 33 indicates failure to converge with- | |
| 1142 | -! in itmax iterations for at least one of | |
| 1143 | -! the (n) new roots. | |
| 1144 | -! | |
| 1145 | -! | |
| 1146 | -! remarks muller always returns the last approximation for root j | |
| 1147 | -! in x(j). if the convergence criterion is satisfied, | |
| 1148 | -! then infer(j) is less than or equal to itmax. if the | |
| 1149 | -! convergence criterion is not satisified, then infer(j) | |
| 1150 | -! is set to either itmax+1 or itmax+k, with k greater | |
| 1151 | -! than 1. infer(j) = itmax+1 indicates that muller did | |
| 1152 | -! not obtain convergence in the allowed number of iter- | |
| 1153 | -! ations. in this case, the user may wish to set itmax | |
| 1154 | -! to a larger value. infer(j) = itmax+k means that con- | |
| 1155 | -! vergence was obtained (on iteration k) for the defla- | |
| 1156 | -! ted function | |
| 1157 | -! fp(z) = f(z)/((z-z(1)...(z-z(j-1))) | |
| 1158 | -! | |
| 1159 | -! but failed for f(z). in this case, better initial | |
| 1160 | -! guesses might help or, it might be necessary to relax | |
| 1161 | -! the convergence criterion. | |
| 1162 | -! | |
| 1163 | -!----------------------------------------------------------------------- | |
| 1164 | -! | |
| 1165 | -subroutine fvn_z_muller (f,eps,eps1,kn,nguess,n,x,itmax,infer,ier) | |
| 1166 | - implicit none | |
| 1167 | - double precision :: rzero,rten,rhun,rp01,ax,eps1,qz,eps,tpq | |
| 1168 | - double complex :: d,dd,den,fprt,frt,h,rt,t1,t2,t3, & | |
| 1169 | - tem,z0,z1,z2,bi,xx,xl,y0,y1,y2,x0, & | |
| 1170 | - zero,p1,one,four,p5 | |
| 1171 | - | |
| 1172 | - double complex, external :: f | |
| 1173 | - integer :: ickmax,kn,nguess,n,itmax,ier,knp1,knpn,i,l,ic, & | |
| 1174 | - knpng,jk,ick,nn,lm1,errcode | |
| 1175 | - double complex :: x(kn+n) | |
| 1176 | - integer :: infer(kn+n) | |
| 1177 | - | |
| 1178 | - | |
| 1179 | - data zero/(0.0,0.0)/,p1/(0.1,0.0)/, & | |
| 1180 | - one/(1.0,0.0)/,four/(4.0,0.0)/, & | |
| 1181 | - p5/(0.5,0.0)/, & | |
| 1182 | - rzero/0.0/,rten/10.0/,rhun/100.0/, & | |
| 1183 | - ax/0.1/,ickmax/3/,rp01/0.01/ | |
| 1184 | - | |
| 1185 | - ier = 0 | |
| 1186 | - if (n .lt. 1) then ! What the hell are doing here then ... | |
| 1187 | - return | |
| 1188 | - end if | |
| 1189 | - !eps1 = rten **(-nsig) | |
| 1190 | - eps1 = min(eps1,rp01) | |
| 1191 | - | |
| 1192 | - knp1 = kn+1 | |
| 1193 | - knpn = kn+n | |
| 1194 | - knpng = kn+nguess | |
| 1195 | - do i=1,knpn | |
| 1196 | - infer(i) = 0 | |
| 1197 | - if (i .gt. knpng) x(i) = zero | |
| 1198 | - end do | |
| 1199 | - l= knp1 | |
| 1200 | - | |
| 1201 | - ic=0 | |
| 1202 | -rloop: do while (l<=knpn) ! Main loop over new roots | |
| 1203 | - jk = 0 | |
| 1204 | - ick = 0 | |
| 1205 | - xl = x(l) | |
| 1206 | -icloop: do | |
| 1207 | - ic = 0 | |
| 1208 | - h = ax | |
| 1209 | - h = p1*h | |
| 1210 | - if (cdabs(xl) .gt. ax) h = p1*xl | |
| 1211 | -! first three points are | |
| 1212 | -! xl+h, xl-h, xl | |
| 1213 | - rt = xl+h | |
| 1214 | - call deflated_work(errcode) | |
| 1215 | - if (errcode == 1) then | |
| 1216 | - exit icloop | |
| 1217 | - end if | |
| 1218 | - | |
| 1219 | - z0 = fprt | |
| 1220 | - y0 = frt | |
| 1221 | - x0 = rt | |
| 1222 | - rt = xl-h | |
| 1223 | - call deflated_work(errcode) | |
| 1224 | - if (errcode == 1) then | |
| 1225 | - exit icloop | |
| 1226 | - end if | |
| 1227 | - | |
| 1228 | - z1 = fprt | |
| 1229 | - y1 = frt | |
| 1230 | - h = xl-rt | |
| 1231 | - d = h/(rt-x0) | |
| 1232 | - rt = xl | |
| 1233 | - | |
| 1234 | - call deflated_work(errcode) | |
| 1235 | - if (errcode == 1) then | |
| 1236 | - exit icloop | |
| 1237 | - end if | |
| 1238 | - | |
| 1239 | - | |
| 1240 | - z2 = fprt | |
| 1241 | - y2 = frt | |
| 1242 | -! begin main algorithm | |
| 1243 | - iloop: do | |
| 1244 | - dd = one + d | |
| 1245 | - t1 = z0*d*d | |
| 1246 | - t2 = z1*dd*dd | |
| 1247 | - xx = z2*dd | |
| 1248 | - t3 = z2*d | |
| 1249 | - bi = t1-t2+xx+t3 | |
| 1250 | - den = bi*bi-four*(xx*t1-t3*(t2-xx)) | |
| 1251 | -! use denominator of maximum amplitude | |
| 1252 | - t1 = cdsqrt(den) | |
| 1253 | - qz = rhun*max(cdabs(bi),cdabs(t1)) | |
| 1254 | - t2 = bi + t1 | |
| 1255 | - tpq = cdabs(t2)+qz | |
| 1256 | - if (tpq .eq. qz) t2 = zero | |
| 1257 | - t3 = bi - t1 | |
| 1258 | - tpq = cdabs(t3) + qz | |
| 1259 | - if (tpq .eq. qz) t3 = zero | |
| 1260 | - den = t2 | |
| 1261 | - qz = cdabs(t3)-cdabs(t2) | |
| 1262 | - if (qz .gt. rzero) den = t3 | |
| 1263 | -! test for zero denominator | |
| 1264 | - if (cdabs(den) .eq. rzero) then | |
| 1265 | - call trans_rt() | |
| 1266 | - call deflated_work(errcode) | |
| 1267 | - if (errcode == 1) then | |
| 1268 | - exit icloop | |
| 1269 | - end if | |
| 1270 | - z2 = fprt | |
| 1271 | - y2 = frt | |
| 1272 | - cycle iloop | |
| 1273 | - end if | |
| 1274 | - | |
| 1275 | - | |
| 1276 | - d = -xx/den | |
| 1277 | - d = d+d | |
| 1278 | - h = d*h | |
| 1279 | - rt = rt + h | |
| 1280 | -! check convergence of the first kind | |
| 1281 | - if (cdabs(h) .le. eps1*max(cdabs(rt),ax)) then | |
| 1282 | - if (ic .ne. 0) then | |
| 1283 | - exit icloop | |
| 1284 | - end if | |
| 1285 | - ic = 1 | |
| 1286 | - z0 = y1 | |
| 1287 | - z1 = y2 | |
| 1288 | - z2 = f(rt) | |
| 1289 | - xl = rt | |
| 1290 | - ick = ick+1 | |
| 1291 | - if (ick .le. ickmax) then | |
| 1292 | - cycle iloop | |
| 1293 | - end if | |
| 1294 | -! warning error, itmax = maximum | |
| 1295 | - jk = itmax + jk | |
| 1296 | - ier = 33 | |
| 1297 | - end if | |
| 1298 | - if (ic .ne. 0) then | |
| 1299 | - cycle icloop | |
| 1300 | - end if | |
| 1301 | - call deflated_work(errcode) | |
| 1302 | - if (errcode == 1) then | |
| 1303 | - exit icloop | |
| 1304 | - end if | |
| 1305 | - | |
| 1306 | - do while ( (cdabs(fprt)-cdabs(z2)*rten) .ge. rzero) | |
| 1307 | - ! take remedial action to induce | |
| 1308 | - ! convergence | |
| 1309 | - d = d*p5 | |
| 1310 | - h = h*p5 | |
| 1311 | - rt = rt-h | |
| 1312 | - call deflated_work(errcode) | |
| 1313 | - if (errcode == 1) then | |
| 1314 | - exit icloop | |
| 1315 | - end if | |
| 1316 | - end do | |
| 1317 | - z0 = z1 | |
| 1318 | - z1 = z2 | |
| 1319 | - z2 = fprt | |
| 1320 | - y0 = y1 | |
| 1321 | - y1 = y2 | |
| 1322 | - y2 = frt | |
| 1323 | - end do iloop | |
| 1324 | - end do icloop | |
| 1325 | - x(l) = rt | |
| 1326 | - infer(l) = jk | |
| 1327 | - l = l+1 | |
| 1328 | - end do rloop | |
| 1329 | - | |
| 1330 | - contains | |
| 1331 | - subroutine trans_rt() | |
| 1332 | - tem = rten*eps1 | |
| 1333 | - if (cdabs(rt) .gt. ax) tem = tem*rt | |
| 1334 | - rt = rt+tem | |
| 1335 | - d = (h+tem)*d/h | |
| 1336 | - h = h+tem | |
| 1337 | - end subroutine trans_rt | |
| 1338 | - | |
| 1339 | - subroutine deflated_work(errcode) | |
| 1340 | - ! errcode=0 => no errors | |
| 1341 | - ! errcode=1 => jk>itmax or convergence of second kind achieved | |
| 1342 | - integer :: errcode,flag | |
| 1343 | - | |
| 1344 | - flag=1 | |
| 1345 | - loop1: do while(flag==1) | |
| 1346 | - errcode=0 | |
| 1347 | - jk = jk+1 | |
| 1348 | - if (jk .gt. itmax) then | |
| 1349 | - ier=33 | |
| 1350 | - errcode=1 | |
| 1351 | - return | |
| 1352 | - end if | |
| 1353 | - frt = f(rt) | |
| 1354 | - fprt = frt | |
| 1355 | - if (l /= 1) then | |
| 1356 | - lm1 = l-1 | |
| 1357 | - do i=1,lm1 | |
| 1358 | - tem = rt - x(i) | |
| 1359 | - if (cdabs(tem) .eq. rzero) then | |
| 1360 | - !if (ic .ne. 0) go to 15 !! ?? possible? | |
| 1361 | - call trans_rt() | |
| 1362 | - cycle loop1 | |
| 1363 | - end if | |
| 1364 | - fprt = fprt/tem | |
| 1365 | - end do | |
| 1366 | - end if | |
| 1367 | - flag=0 | |
| 1368 | - end do loop1 | |
| 1369 | - | |
| 1370 | - if (cdabs(fprt) .le. eps .and. cdabs(frt) .le. eps) then | |
| 1371 | - errcode=1 | |
| 1372 | - return | |
| 1373 | - end if | |
| 1374 | - | |
| 1375 | - end subroutine deflated_work | |
| 1376 | - | |
| 1377 | - end subroutine | |
| 1378 | - | |
| 1379 | - | |
| 1380 | -!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! | |
| 1381 | -! | |
| 1382 | -! Integration | |
| 1383 | -! | |
| 1384 | -! Only double precision coded atm | |
| 1385 | -! | |
| 1386 | -!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! | |
| 1387 | - | |
| 1388 | - | |
| 1389 | -subroutine fvn_d_gauss_legendre(n,qx,qw) | |
| 1390 | -! | |
| 1391 | -! This routine compute the n Gauss Legendre abscissas and weights | |
| 1392 | -! Adapted from Numerical Recipes routine gauleg | |
| 1393 | -! | |
| 1394 | -! n (in) : number of points | |
| 1395 | -! qx(out) : abscissas | |
| 1396 | -! qw(out) : weights | |
| 1397 | -! | |
| 1398 | -implicit none | |
| 1399 | -double precision,parameter :: pi=3.141592653589793d0 | |
| 1400 | -integer, intent(in) :: n | |
| 1401 | -double precision, intent(out) :: qx(n),qw(n) | |
| 1402 | - | |
| 1403 | -integer :: m,i,j | |
| 1404 | -double precision :: z,z1,p1,p2,p3,pp | |
| 1405 | -m=(n+1)/2 | |
| 1406 | -do i=1,m | |
| 1407 | - z=cos(pi*(dble(i)-0.25d0)/(dble(n)+0.5d0)) | |
| 1408 | -iloop: do | |
| 1409 | - p1=1.d0 | |
| 1410 | - p2=0.d0 | |
| 1411 | - do j=1,n | |
| 1412 | - p3=p2 | |
| 1413 | - p2=p1 | |
| 1414 | - p1=((2.d0*dble(j)-1.d0)*z*p2-(dble(j)-1.d0)*p3)/dble(j) | |
| 1415 | - end do | |
| 1416 | - pp=dble(n)*(z*p1-p2)/(z*z-1.d0) | |
| 1417 | - z1=z | |
| 1418 | - z=z1-p1/pp | |
| 1419 | - if (dabs(z-z1)<=epsilon(z)) then | |
| 1420 | - exit iloop | |
| 1421 | - end if | |
| 1422 | - end do iloop | |
| 1423 | - qx(i)=-z | |
| 1424 | - qx(n+1-i)=z | |
| 1425 | - qw(i)=2.d0/((1.d0-z*z)*pp*pp) | |
| 1426 | - qw(n+1-i)=qw(i) | |
| 1427 | -end do | |
| 1428 | -end subroutine | |
| 1429 | - | |
| 1430 | - | |
| 1431 | - | |
| 1432 | -subroutine fvn_d_gl_integ(f,a,b,n,res) | |
| 1433 | -! | |
| 1434 | -! This is a simple non adaptative integration routine | |
| 1435 | -! using n gauss legendre abscissas and weights | |
| 1436 | -! | |
| 1437 | -! f(in) : the function to integrate | |
| 1438 | -! a(in) : lower bound | |
| 1439 | -! b(in) : higher bound | |
| 1440 | -! n(in) : number of gauss legendre pairs | |
| 1441 | -! res(out): the evaluation of the integral | |
| 1442 | -! | |
| 1443 | -double precision,external :: f | |
| 1444 | -double precision, intent(in) :: a,b | |
| 1445 | -integer, intent(in):: n | |
| 1446 | -double precision, intent(out) :: res | |
| 1447 | - | |
| 1448 | -double precision, allocatable :: qx(:),qw(:) | |
| 1449 | -double precision :: xm,xr | |
| 1450 | -integer :: i | |
| 1451 | - | |
| 1452 | -! First compute n gauss legendre abs and weight | |
| 1453 | -allocate(qx(n)) | |
| 1454 | -allocate(qw(n)) | |
| 1455 | -call fvn_d_gauss_legendre(n,qx,qw) | |
| 1456 | - | |
| 1457 | -xm=0.5d0*(b+a) | |
| 1458 | -xr=0.5d0*(b-a) | |
| 1459 | - | |
| 1460 | -res=0.d0 | |
| 1461 | - | |
| 1462 | -do i=1,n | |
| 1463 | - res=res+qw(i)*f(xm+xr*qx(i)) | |
| 1464 | -end do | |
| 1465 | - | |
| 1466 | -res=xr*res | |
| 1467 | - | |
| 1468 | -deallocate(qw) | |
| 1469 | -deallocate(qx) | |
| 1470 | - | |
| 1471 | -end subroutine | |
| 1472 | - | |
| 1473 | -!!!!!!!!!!!!!!!!!!!!!!!! | |
| 1474 | -! | |
| 1475 | -! Simple and double adaptative Gauss Kronrod integration based on | |
| 1476 | -! a modified version of quadpack ( http://www.netlib.org/quadpack | |
| 1477 | -! | |
| 1478 | -! Common parameters : | |
| 1479 | -! | |
| 1480 | -! key (in) | |
| 1481 | -! epsabs | |
| 1482 | -! epsrel | |
| 1483 | -! | |
| 1484 | -! | |
| 1485 | -!!!!!!!!!!!!!!!!!!!!!!!! | |
| 1486 | - | |
| 1487 | -subroutine fvn_d_integ_1_gk(f,a,b,epsabs,epsrel,key,res,abserr,ier,limit) | |
| 1488 | -! | |
| 1489 | -! Evaluate the integral of function f(x) between a and b | |
| 1490 | -! | |
| 1491 | -! f(in) : the function | |
| 1492 | -! a(in) : lower bound | |
| 1493 | -! b(in) : higher bound | |
| 1494 | -! epsabs(in) : desired absolute error | |
| 1495 | -! epsrel(in) : desired relative error | |
| 1496 | -! key(in) : gauss kronrod rule | |
| 1497 | -! 1: 7 - 15 points | |
| 1498 | -! 2: 10 - 21 points | |
| 1499 | -! 3: 15 - 31 points | |
| 1500 | -! 4: 20 - 41 points | |
| 1501 | -! 5: 25 - 51 points | |
| 1502 | -! 6: 30 - 61 points | |
| 1503 | -! | |
| 1504 | -! limit(in) : maximum number of subintervals in the partition of the | |
| 1505 | -! given integration interval (a,b). A value of 500 will give the same | |
| 1506 | -! behaviour as the imsl routine dqdag | |
| 1507 | -! | |
| 1508 | -! res(out) : estimated integral value | |
| 1509 | -! abserr(out) : estimated absolute error | |
| 1510 | -! ier(out) : error flag from quadpack routines | |
| 1511 | -! 0 : no error | |
| 1512 | -! 1 : maximum number of subdivisions allowed | |
| 1513 | -! has been achieved. one can allow more | |
| 1514 | -! subdivisions by increasing the value of | |
| 1515 | -! limit (and taking the according dimension | |
| 1516 | -! adjustments into account). however, if | |
| 1517 | -! this yield no improvement it is advised | |
| 1518 | -! to analyze the integrand in order to | |
| 1519 | -! determine the integration difficulaties. | |
| 1520 | -! if the position of a local difficulty can | |
| 1521 | -! be determined (i.e.singularity, | |
| 1522 | -! discontinuity within the interval) one | |
| 1523 | -! will probably gain from splitting up the | |
| 1524 | -! interval at this point and calling the | |
| 1525 | -! integrator on the subranges. if possible, | |
| 1526 | -! an appropriate special-purpose integrator | |
| 1527 | -! should be used which is designed for | |
| 1528 | -! handling the type of difficulty involved. | |
| 1529 | -! 2 : the occurrence of roundoff error is | |
| 1530 | -! detected, which prevents the requested | |
| 1531 | -! tolerance from being achieved. | |
| 1532 | -! 3 : extremely bad integrand behaviour occurs | |
| 1533 | -! at some points of the integration | |
| 1534 | -! interval. | |
| 1535 | -! 6 : the input is invalid, because | |
| 1536 | -! (epsabs.le.0 and | |
| 1537 | -! epsrel.lt.max(50*rel.mach.acc.,0.5d-28)) | |
| 1538 | -! or limit.lt.1 or lenw.lt.limit*4. | |
| 1539 | -! result, abserr, neval, last are set | |
| 1540 | -! to zero. | |
| 1541 | -! except when lenw is invalid, iwork(1), | |
| 1542 | -! work(limit*2+1) and work(limit*3+1) are | |
| 1543 | -! set to zero, work(1) is set to a and | |
| 1544 | -! work(limit+1) to b. | |
| 1545 | - | |
| 1546 | -implicit none | |
| 1547 | -double precision, external :: f | |
| 1548 | -double precision, intent(in) :: a,b,epsabs,epsrel | |
| 1549 | -integer, intent(in) :: key | |
| 1550 | -integer, intent(in) :: limit | |
| 1551 | -double precision, intent(out) :: res,abserr | |
| 1552 | -integer, intent(out) :: ier | |
| 1553 | - | |
| 1554 | -double precision, allocatable :: work(:) | |
| 1555 | -integer, allocatable :: iwork(:) | |
| 1556 | -integer :: lenw,neval,last | |
| 1557 | - | |
| 1558 | -! imsl value for limit is 500 | |
| 1559 | -lenw=limit*4 | |
| 1560 | - | |
| 1561 | -allocate(iwork(limit)) | |
| 1562 | -allocate(work(lenw)) | |
| 1563 | - | |
| 1564 | -call dqag(f,a,b,epsabs,epsrel,key,res,abserr,neval,ier,limit,lenw,last,iwork,work) | |
| 1565 | - | |
| 1566 | -deallocate(work) | |
| 1567 | -deallocate(iwork) | |
| 1568 | - | |
| 1569 | -end subroutine | |
| 1570 | - | |
| 1571 | - | |
| 1572 | - | |
| 1573 | -subroutine fvn_d_integ_2_gk(f,a,b,g,h,epsabs,epsrel,key,res,abserr,ier,limit) | |
| 1574 | -! | |
| 1575 | -! Evaluate the double integral of function f(x,y) for x between a and b and y between g(x) and h(x) | |
| 1576 | -! | |
| 1577 | -! f(in) : the function | |
| 1578 | -! a(in) : lower bound | |
| 1579 | -! b(in) : higher bound | |
| 1580 | -! g(in) : external function describing lower bound for y | |
| 1581 | -! h(in) : external function describing higher bound for y | |
| 1582 | -! epsabs(in) : desired absolute error | |
| 1583 | -! epsrel(in) : desired relative error | |
| 1584 | -! key(in) : gauss kronrod rule | |
| 1585 | -! 1: 7 - 15 points | |
| 1586 | -! 2: 10 - 21 points | |
| 1587 | -! 3: 15 - 31 points | |
| 1588 | -! 4: 20 - 41 points | |
| 1589 | -! 5: 25 - 51 points | |
| 1590 | -! 6: 30 - 61 points | |
| 1591 | -! | |
| 1592 | -! limit(in) : maximum number of subintervals in the partition of the | |
| 1593 | -! given integration interval (a,b). A value of 500 will give the same | |
| 1594 | -! behaviour as the imsl routine dqdag | |
| 1595 | -! | |
| 1596 | -! res(out) : estimated integral value | |
| 1597 | -! abserr(out) : estimated absolute error | |
| 1598 | -! ier(out) : error flag from quadpack routines | |
| 1599 | -! 0 : no error | |
| 1600 | -! 1 : maximum number of subdivisions allowed | |
| 1601 | -! has been achieved. one can allow more | |
| 1602 | -! subdivisions by increasing the value of | |
| 1603 | -! limit (and taking the according dimension | |
| 1604 | -! adjustments into account). however, if | |
| 1605 | -! this yield no improvement it is advised | |
| 1606 | -! to analyze the integrand in order to | |
| 1607 | -! determine the integration difficulaties. | |
| 1608 | -! if the position of a local difficulty can | |
| 1609 | -! be determined (i.e.singularity, | |
| 1610 | -! discontinuity within the interval) one | |
| 1611 | -! will probably gain from splitting up the | |
| 1612 | -! interval at this point and calling the | |
| 1613 | -! integrator on the subranges. if possible, | |
| 1614 | -! an appropriate special-purpose integrator | |
| 1615 | -! should be used which is designed for | |
| 1616 | -! handling the type of difficulty involved. | |
| 1617 | -! 2 : the occurrence of roundoff error is | |
| 1618 | -! detected, which prevents the requested | |
| 1619 | -! tolerance from being achieved. | |
| 1620 | -! 3 : extremely bad integrand behaviour occurs | |
| 1621 | -! at some points of the integration | |
| 1622 | -! interval. | |
| 1623 | -! 6 : the input is invalid, because | |
| 1624 | -! (epsabs.le.0 and | |
| 1625 | -! epsrel.lt.max(50*rel.mach.acc.,0.5d-28)) | |
| 1626 | -! or limit.lt.1 or lenw.lt.limit*4. | |
| 1627 | -! result, abserr, neval, last are set | |
| 1628 | -! to zero. | |
| 1629 | -! except when lenw is invalid, iwork(1), | |
| 1630 | -! work(limit*2+1) and work(limit*3+1) are | |
| 1631 | -! set to zero, work(1) is set to a and | |
| 1632 | -! work(limit+1) to b. | |
| 1633 | - | |
| 1634 | -implicit none | |
| 1635 | -double precision, external:: f,g,h | |
| 1636 | -double precision, intent(in) :: a,b,epsabs,epsrel | |
| 1637 | -integer, intent(in) :: key,limit | |
| 1638 | -integer, intent(out) :: ier | |
| 1639 | -double precision, intent(out) :: res,abserr | |
| 1640 | - | |
| 1641 | - | |
| 1642 | -double precision, allocatable :: work(:) | |
| 1643 | -integer, allocatable :: iwork(:) | |
| 1644 | -integer :: lenw,neval,last | |
| 1645 | - | |
| 1646 | -! imsl value for limit is 500 | |
| 1647 | -lenw=limit*4 | |
| 1648 | -allocate(work(lenw)) | |
| 1649 | -allocate(iwork(limit)) | |
| 1650 | - | |
| 1651 | -call dqag_2d_outer(f,a,b,g,h,epsabs,epsrel,key,res,abserr,neval,ier,limit,lenw,last,iwork,work) | |
| 1652 | - | |
| 1653 | -deallocate(iwork) | |
| 1654 | -deallocate(work) | |
| 1655 | -end subroutine | |
| 1656 | - | |
| 1657 | - | |
| 1658 | - | |
| 1659 | -subroutine fvn_d_integ_2_inner_gk(f,x,a,b,epsabs,epsrel,key,res,abserr,ier,limit) | |
| 1660 | -! | |
| 1661 | -! Evaluate the single integral of function f(x,y) for y between a and b with a | |
| 1662 | -! given x value | |
| 1663 | -! | |
| 1664 | -! This function is used for the evaluation of the double integral fvn_d_integ_2_gk | |
| 1665 | -! | |
| 1666 | -! f(in) : the function | |
| 1667 | -! x(in) : x | |
| 1668 | -! a(in) : lower bound | |
| 1669 | -! b(in) : higher bound | |
| 1670 | -! epsabs(in) : desired absolute error | |
| 1671 | -! epsrel(in) : desired relative error | |
| 1672 | -! key(in) : gauss kronrod rule | |
| 1673 | -! 1: 7 - 15 points | |
| 1674 | -! 2: 10 - 21 points | |
| 1675 | -! 3: 15 - 31 points | |
| 1676 | -! 4: 20 - 41 points | |
| 1677 | -! 5: 25 - 51 points | |
| 1678 | -! 6: 30 - 61 points | |
| 1679 | -! | |
| 1680 | -! limit(in) : maximum number of subintervals in the partition of the | |
| 1681 | -! given integration interval (a,b). A value of 500 will give the same | |
| 1682 | -! behaviour as the imsl routine dqdag | |
| 1683 | -! | |
| 1684 | -! res(out) : estimated integral value | |
| 1685 | -! abserr(out) : estimated absolute error | |
| 1686 | -! ier(out) : error flag from quadpack routines | |
| 1687 | -! 0 : no error | |
| 1688 | -! 1 : maximum number of subdivisions allowed | |
| 1689 | -! has been achieved. one can allow more | |
| 1690 | -! subdivisions by increasing the value of | |
| 1691 | -! limit (and taking the according dimension | |
| 1692 | -! adjustments into account). however, if | |
| 1693 | -! this yield no improvement it is advised | |
| 1694 | -! to analyze the integrand in order to | |
| 1695 | -! determine the integration difficulaties. | |
| 1696 | -! if the position of a local difficulty can | |
| 1697 | -! be determined (i.e.singularity, | |
| 1698 | -! discontinuity within the interval) one | |
| 1699 | -! will probably gain from splitting up the | |
| 1700 | -! interval at this point and calling the | |
| 1701 | -! integrator on the subranges. if possible, | |
| 1702 | -! an appropriate special-purpose integrator | |
| 1703 | -! should be used which is designed for | |
| 1704 | -! handling the type of difficulty involved. | |
| 1705 | -! 2 : the occurrence of roundoff error is | |
| 1706 | -! detected, which prevents the requested | |
| 1707 | -! tolerance from being achieved. | |
| 1708 | -! 3 : extremely bad integrand behaviour occurs | |
| 1709 | -! at some points of the integration | |
| 1710 | -! interval. | |
| 1711 | -! 6 : the input is invalid, because | |
| 1712 | -! (epsabs.le.0 and | |
| 1713 | -! epsrel.lt.max(50*rel.mach.acc.,0.5d-28)) | |
| 1714 | -! or limit.lt.1 or lenw.lt.limit*4. | |
| 1715 | -! result, abserr, neval, last are set | |
| 1716 | -! to zero. | |
| 1717 | -! except when lenw is invalid, iwork(1), | |
| 1718 | -! work(limit*2+1) and work(limit*3+1) are | |
| 1719 | -! set to zero, work(1) is set to a and | |
| 1720 | -! work(limit+1) to b. | |
| 1721 | - | |
| 1722 | -implicit none | |
| 1723 | -double precision, external:: f | |
| 1724 | -double precision, intent(in) :: x,a,b,epsabs,epsrel | |
| 1725 | -integer, intent(in) :: key,limit | |
| 1726 | -integer, intent(out) :: ier | |
| 1727 | -double precision, intent(out) :: res,abserr | |
| 1728 | - | |
| 1729 | - | |
| 1730 | -double precision, allocatable :: work(:) | |
| 1731 | -integer, allocatable :: iwork(:) | |
| 1732 | -integer :: lenw,neval,last | |
| 1733 | - | |
| 1734 | -! imsl value for limit is 500 | |
| 1735 | -lenw=limit*4 | |
| 1736 | -allocate(work(lenw)) | |
| 1737 | -allocate(iwork(limit)) | |
| 1738 | - | |
| 1739 | -call dqag_2d_inner(f,x,a,b,epsabs,epsrel,key,res,abserr,neval,ier,limit,lenw,last,iwork,work) | |
| 1740 | - | |
| 1741 | -deallocate(iwork) | |
| 1742 | -deallocate(work) | |
| 1743 | -end subroutine | |
| 1744 | - | |
| 1745 | -!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! | |
| 1746 | -! Include the modified quadpack files | |
| 1747 | -!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! | |
| 1748 | -include "fvn_quadpack/dqag_2d_inner.f" | |
| 1749 | -include "fvn_quadpack/dqk15_2d_inner.f" | |
| 1750 | -include "fvn_quadpack/dqk31_2d_outer.f" | |
| 1751 | -include "fvn_quadpack/d1mach.f" | |
| 1752 | -include "fvn_quadpack/dqk31_2d_inner.f" | |
| 1753 | -include "fvn_quadpack/dqage.f" | |
| 1754 | -include "fvn_quadpack/dqk15.f" | |
| 1755 | -include "fvn_quadpack/dqk21.f" | |
| 1756 | -include "fvn_quadpack/dqk31.f" | |
| 1757 | -include "fvn_quadpack/dqk41.f" | |
| 1758 | -include "fvn_quadpack/dqk51.f" | |
| 1759 | -include "fvn_quadpack/dqk61.f" | |
| 1760 | -include "fvn_quadpack/dqk41_2d_outer.f" | |
| 1761 | -include "fvn_quadpack/dqk41_2d_inner.f" | |
| 1762 | -include "fvn_quadpack/dqag_2d_outer.f" | |
| 1763 | -include "fvn_quadpack/dqpsrt.f" | |
| 1764 | -include "fvn_quadpack/dqag.f" | |
| 1765 | -include "fvn_quadpack/dqage_2d_outer.f" | |
| 1766 | -include "fvn_quadpack/dqage_2d_inner.f" | |
| 1767 | -include "fvn_quadpack/dqk51_2d_outer.f" | |
| 1768 | -include "fvn_quadpack/dqk51_2d_inner.f" | |
| 1769 | -include "fvn_quadpack/dqk61_2d_outer.f" | |
| 1770 | -include "fvn_quadpack/dqk21_2d_outer.f" | |
| 1771 | -include "fvn_quadpack/dqk61_2d_inner.f" | |
| 1772 | -include "fvn_quadpack/dqk21_2d_inner.f" | |
| 1773 | -include "fvn_quadpack/dqk15_2d_outer.f" | |
| 1774 | - | |
| 1775 | - | |
| 1776 | - | |
| 1777 | - | |
| 1778 | - | |
| 1779 | -end module fvn |