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jmc |
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C $Header: $ |
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C $Name: $ |
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# include "GAD_OPTIONS.h" |
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C-- File gad_pqm_fun.F: Routines to form PQM grid-cell polynomial. |
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C-- Contents |
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C-- o QUADROOT |
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C-- o GAD_PPM_FUN_NULL |
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C-- o GAD_PPM_FUN_MONO |
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C---+----1----+----2----+----3----+----4----+----5----+----6----+----7-|--+----| |
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LOGICAL FUNCTION QUADROOT(aa,bb,cc,xx) |
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C |================================================================| |
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C | QUADROOT: find roots of quadratic ax**2 + bx + c = 0. | |
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C |================================================================| |
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implicit none |
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C ====================================================== arguments |
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_RL aa,bb,cc |
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_RL xx(1:2) |
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C ====================================================== variables |
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_RL sq,a0,b0 |
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a0 = abs(aa) |
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b0 = abs(bb) |
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sq = bb * bb - 4. _d 0 * aa * cc |
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if (a0 .gt. 0. _d 0) then |
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if (sq .ge. 0. _d 0) then |
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QUADROOT = .TRUE. |
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sq = sqrt(sq) |
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xx(1) = - bb + sq |
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xx(2) = - bb - sq |
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aa = 0.5 _d 0 / aa |
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xx(1) = xx(1) * aa |
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xx(2) = xx(2) * aa |
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else |
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QUADROOT = .FALSE. |
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end if |
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else |
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if (b0 .gt. 0. _d 0) then |
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QUADROOT = .TRUE. |
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xx(1) = - cc / bb |
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xx(2) = - cc / bb |
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else |
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QUADROOT = .FALSE. |
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end if |
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end if |
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return |
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c end function QUADROOT |
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end |
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C---+----1----+----2----+----3----+----4----+----5----+----6----+----7-|--+----| |
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SUBROUTINE GAD_PQM_FUN_NULL( |
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I ff00, |
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I fell,ferr, |
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I dell,derr, |
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O fhat,mono) |
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C |================================================================| |
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C | PQM_FUN_NULL: form PQM grid-cell polynomial. | |
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C | Piecewise Quartic Method (PQM) - unlimited variant. | |
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C |================================================================| |
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implicit none |
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C ====================================================== arguments |
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_RL ff00 |
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_RL fell,ferr |
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_RL dell,derr |
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_RL fhat(+1:+5) |
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integer mono |
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mono = +0 |
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C ============================================== unlimited profile |
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fhat(1) = |
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& + (30. _d 0 / 16. _d 0) * ff00 |
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& - ( 7. _d 0 / 16. _d 0) *(ferr+fell) |
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& + ( 1. _d 0 / 16. _d 0) *(derr-dell) |
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fhat(2) = |
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& + ( 3. _d 0 / 4. _d 0) *(ferr-fell) |
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& - ( 1. _d 0 / 4. _d 0) *(derr+dell) |
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fhat(3) = |
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& - (30. _d 0 / 8. _d 0) * ff00 |
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& + (15. _d 0 / 8. _d 0) *(ferr+fell) |
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& - ( 3. _d 0 / 8. _d 0) *(derr-dell) |
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fhat(4) = |
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& - ( 1. _d 0 / 4. _d 0) *(ferr-fell-derr-dell) |
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fhat(5) = |
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& + (30. _d 0 / 16. _d 0) * ff00 |
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& - (15. _d 0 / 16. _d 0) *(ferr+fell) |
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& + ( 5. _d 0 / 16. _d 0) *(derr-dell) |
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return |
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c end subroutine GAD_PQM_FUN_NULL |
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end |
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C---+----1----+----2----+----3----+----4----+----5----+----6----+----7-|--+----| |
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SUBROUTINE GAD_PQM_FUN_MONO( |
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I ff00, |
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I ffll,ffrr, |
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I fell,ferr, |
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I dell,derr, |
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I dfds, |
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O fhat,mono) |
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C |================================================================| |
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C | PQM_FUN_MONO: form PQM grid-cell polynomial. | |
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C | Piecewise Quartic Method (PQM) - monotonic variant. | |
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C |================================================================| |
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implicit none |
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C ====================================================== arguments |
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_RL ff00,ffll,ffrr |
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_RL fell,ferr |
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_RL dell,derr |
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_RL dfds(-1:+1) |
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_RL fhat(+1:+5) |
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integer mono |
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C ====================================================== functions |
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logical QUADROOT |
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C ====================================================== variables |
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integer bind |
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_RL aval,bval,cval |
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_RL iflx(+1:+2) |
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_RL dflx(+1:+2) |
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mono = +0 |
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C ============================================== "flatten" extrema |
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if((ffrr-ff00) * |
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& (ff00-ffll) .le. 0. _d 0) then |
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mono = +1 |
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fhat(1) = ff00 |
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fhat(2) = 0. _d 0 |
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fhat(3) = 0. _d 0 |
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fhat(4) = 0. _d 0 |
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fhat(5) = 0. _d 0 |
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return |
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end if |
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C ============================================== limit edge values |
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if((ffll - fell) * |
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& (fell - ff00) .le. 0. _d 0) then |
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mono = +1 |
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fell = ff00 - dfds(0) |
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end if |
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if((ffrr - ferr) * |
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& (ferr - ff00) .le. 0. _d 0) then |
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mono = +1 |
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ferr = ff00 + dfds(0) |
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end if |
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C ============================================== limit edge slopes |
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if((dell * dfds(-1)) .lt. 0. _d 0) then |
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mono = +1 |
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dell = dfds(-1) |
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end if |
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if((derr * dfds(+1)) .lt. 0. _d 0) then |
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mono = +1 |
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derr = dfds(+1) |
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end if |
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C ============================================== limit cell values |
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fhat(1) = |
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& + (30. _d 0 / 16. _d 0) * ff00 |
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& - ( 7. _d 0 / 16. _d 0) *(ferr+fell) |
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& + ( 1. _d 0 / 16. _d 0) *(derr-dell) |
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fhat(2) = |
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& + ( 3. _d 0 / 4. _d 0) *(ferr-fell) |
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& - ( 1. _d 0 / 4. _d 0) *(derr+dell) |
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fhat(3) = |
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& - (30. _d 0 / 8. _d 0) * ff00 |
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& + (15. _d 0 / 8. _d 0) *(ferr+fell) |
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& - ( 3. _d 0 / 8. _d 0) *(derr-dell) |
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fhat(4) = |
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& - ( 1. _d 0 / 4. _d 0) *(ferr-fell-derr-dell) |
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fhat(5) = |
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& + (30. _d 0 / 16. _d 0) * ff00 |
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& - (15. _d 0 / 16. _d 0) *(ferr+fell) |
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& + ( 5. _d 0 / 16. _d 0) *(derr-dell) |
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C ============================= calc. inflexion via 2nd-derivative |
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aval = 12. _d 0 * fhat(5) |
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bval = 6. _d 0 * fhat(4) |
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cval = 2. _d 0 * fhat(3) |
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if ( QUADROOT(aval,bval,cval,iflx) ) then |
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bind = +0 |
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if ( ( iflx(1) .gt. -1. _d 0 ) |
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& .and. ( iflx(1) .lt. +1. _d 0 ) ) then |
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C ============================= check for non-monotonic inflection |
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dflx(1) = fhat(2) |
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& + iflx(1) * fhat(3) * 2. _d 0 |
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& +(iflx(1) ** 2) * fhat(4) * 3. _d 0 |
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& +(iflx(1) ** 3) * fhat(5) * 4. _d 0 |
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if (dflx(1)*dfds(+0) .lt. 0. _d 0) then |
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if (abs(dell) |
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& .lt. abs(derr) ) then |
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bind = -1 |
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else |
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bind = +1 |
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end if |
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end if |
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end if |
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if ( ( iflx(2) .gt. -1. _d 0 ) |
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& .and. ( iflx(2) .lt. +1. _d 0 ) ) then |
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C ============================= check for non-monotonic inflection |
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dflx(2) = fhat(2) |
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& + iflx(2) * fhat(3) * 2. _d 0 |
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& +(iflx(2) ** 2) * fhat(4) * 3. _d 0 |
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& +(iflx(2) ** 3) * fhat(5) * 4. _d 0 |
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if (dflx(2)*dfds(+0) .lt. 0. _d 0) then |
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if (abs(dell) |
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& .lt. abs(derr) ) then |
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bind = -1 |
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else |
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bind = +1 |
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end if |
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end if |
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end if |
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C ============================= pop non-monotone inflexion to edge |
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if (bind .eq. -1) then |
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C ============================= pop inflection points onto -1 edge |
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mono = +2 |
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derr = |
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& -( 5. _d 0 / 1. _d 0) * ff00 |
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& +( 3. _d 0 / 1. _d 0) * ferr |
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& +( 2. _d 0 / 1. _d 0) * fell |
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dell = |
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& +( 5. _d 0 / 3. _d 0) * ff00 |
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& -( 1. _d 0 / 3. _d 0) * ferr |
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& -( 4. _d 0 / 3. _d 0) * fell |
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if (dell*dfds(-1) .lt. 0. _d 0) then |
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dell = 0. _d 0 |
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ferr = |
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& +( 5. _d 0 / 1. _d 0) * ff00 |
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& -( 4. _d 0 / 1. _d 0) * fell |
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derr = |
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& +(10. _d 0 / 1. _d 0) * ff00 |
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& -(10. _d 0 / 1. _d 0) * fell |
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end if |
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if (derr*dfds(+1) .lt. 0. _d 0) then |
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derr = 0. _d 0 |
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fell = |
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& +( 5. _d 0 / 2. _d 0) * ff00 |
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& -( 3. _d 0 / 2. _d 0) * ferr |
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dell = |
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& -( 5. _d 0 / 3. _d 0) * ff00 |
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& +( 5. _d 0 / 3. _d 0) * ferr |
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end if |
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end if |
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if (bind .eq. +1) then |
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C ============================= pop inflection points onto +1 edge |
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mono = +2 |
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derr = |
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& -( 5. _d 0 / 3. _d 0) * ff00 |
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& +( 4. _d 0 / 3. _d 0) * ferr |
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& +( 1. _d 0 / 3. _d 0) * fell |
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dell = |
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& +( 5. _d 0 / 1. _d 0) * ff00 |
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& -( 2. _d 0 / 1. _d 0) * ferr |
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& -( 3. _d 0 / 1. _d 0) * fell |
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if (dell*dfds(-1) .lt. 0. _d 0) then |
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dell = 0. _d 0 |
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ferr = |
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& +( 5. _d 0 / 2. _d 0) * ff00 |
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& -( 3. _d 0 / 2. _d 0) * fell |
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derr = |
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& +( 5. _d 0 / 3. _d 0) * ff00 |
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& -( 5. _d 0 / 3. _d 0) * fell |
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end if |
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if (derr*dfds(+1) .lt. 0. _d 0) then |
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derr = 0. _d 0 |
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fell = |
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& +( 5. _d 0 / 1. _d 0) * ff00 |
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& -( 4. _d 0 / 1. _d 0) * ferr |
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dell = |
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& -(10. _d 0 / 1. _d 0) * ff00 |
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& +(10. _d 0 / 1. _d 0) * ferr |
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end if |
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end if |
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end if |
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C ============================= re-assemble coefficients on demand |
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if (mono .eq. +2) then |
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fhat(1) = |
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|
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& + (30. _d 0 / 16. _d 0) * ff00 |
| 385 |
|
|
& - ( 7. _d 0 / 16. _d 0) *(ferr+fell) |
| 386 |
|
|
& + ( 1. _d 0 / 16. _d 0) *(derr-dell) |
| 387 |
|
|
fhat(2) = |
| 388 |
|
|
& + ( 3. _d 0 / 4. _d 0) *(ferr-fell) |
| 389 |
|
|
& - ( 1. _d 0 / 4. _d 0) *(derr+dell) |
| 390 |
|
|
fhat(3) = |
| 391 |
|
|
& - (30. _d 0 / 8. _d 0) * ff00 |
| 392 |
|
|
& + (15. _d 0 / 8. _d 0) *(ferr+fell) |
| 393 |
|
|
& - ( 3. _d 0 / 8. _d 0) *(derr-dell) |
| 394 |
|
|
fhat(4) = |
| 395 |
|
|
& - ( 1. _d 0 / 4. _d 0) *(ferr-fell-derr-dell) |
| 396 |
|
|
fhat(5) = |
| 397 |
|
|
& + (30. _d 0 / 16. _d 0) * ff00 |
| 398 |
|
|
& - (15. _d 0 / 16. _d 0) *(ferr+fell) |
| 399 |
|
|
& + ( 5. _d 0 / 16. _d 0) *(derr-dell) |
| 400 |
|
|
|
| 401 |
|
|
end if |
| 402 |
|
|
|
| 403 |
|
|
return |
| 404 |
|
|
|
| 405 |
|
|
c end subroutine GAD_PQM_FUN_MONO |
| 406 |
|
|
end |
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