Commit d32a4703383b961c2182b5ea68585cf33b41060b
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fvnlib.f90
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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 |