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m_xsolve.f90
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!***********************************************************************
! Copyright (c) 2019 D. de Vries
! Original Copyright (c) 2000 Mark Drela
!
! This file is part of XFoil.
!
! XFoil is free software: you can redistribute it and/or modify
! it under the terms of the GNU General Public License as published by
! the Free Software Foundation, either version 3 of the License, or
! (at your option) any later version.
!
! XFoil is distributed in the hope that it will be useful,
! but WITHOUT ANY WARRANTY; without even the implied warranty of
! MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
! GNU General Public License for more details.
!
! You should have received a copy of the GNU General Public License
! along with XFoil. If not, see <https://www.gnu.org/licenses/>.
!***********************************************************************
!*==GAUSS.f90 processed by SPAG 7.21DC at 11:25 on 11 Jan 2019
module m_xsolve
contains
subroutine gauss(Nsiz, Nn, Z, R, Nrhs)
implicit none
!
!*** Start of declarations rewritten by SPAG
!
! Dummy arguments
!
integer :: Nn, Nrhs, Nsiz
real, dimension(Nsiz, Nrhs) :: R
real, dimension(Nsiz, Nsiz) :: Z
intent (in) Nn, Nrhs, Nsiz
intent (inout) R, Z
!
! Local variables
!
integer :: k, l, n, np, np1, nx
real :: pivot, temp, ztmp
!
!*** End of declarations rewritten by SPAG
!
!
!*** Start of declarations rewritten by SPAG
!
! Dummy arguments
!
!
! Local variables
!
!
!*** End of declarations rewritten by SPAG
!
! *******************************************************
! * *
! * Solves general NxN system in NN unknowns *
! * with arbitrary number (NRHS) of righthand sides. *
! * Assumes system is invertible... *
! * ...if it isn't, a divide by zero will result. *
! * *
! * Z is the coefficient matrix... *
! * ...destroyed during solution process. *
! * R is the righthand side(s)... *
! * ...replaced by the solution vector(s). *
! * *
! * Mark Drela 1984 *
! *******************************************************
!
!
do np = 1, Nn - 1
np1 = np + 1
!
!------ find max pivot index NX
nx = np
do n = np1, Nn
if (abs(Z(n, np))>abs(Z(nx, np))) nx = n
enddo
!
pivot = 1.0 / Z(nx, np)
!
!------ switch pivots
Z(nx, np) = Z(np, np)
!
!------ switch rows & normalize pivot row
do l = np1, Nn
temp = Z(nx, l) * pivot
Z(nx, l) = Z(np, l)
Z(np, l) = temp
enddo
!
do l = 1, Nrhs
temp = R(nx, l) * pivot
R(nx, l) = R(np, l)
R(np, l) = temp
enddo
!
!------ forward eliminate everything
do k = np1, Nn
ztmp = Z(k, np)
!
! IF(ZTMP.EQ.0.0) GO TO 15
!
do l = np1, Nn
Z(k, l) = Z(k, l) - ztmp * Z(np, l)
enddo
do l = 1, Nrhs
R(k, l) = R(k, l) - ztmp * R(np, l)
enddo
enddo
!
enddo
!
!---- solve for last row
do l = 1, Nrhs
R(Nn, l) = R(Nn, l) / Z(Nn, Nn)
enddo
!
!---- back substitute everything
do np = Nn - 1, 1, -1
np1 = np + 1
do l = 1, Nrhs
do k = np1, Nn
R(np, l) = R(np, l) - Z(np, k) * R(k, l)
enddo
enddo
enddo
!
end subroutine gauss
!*==CGAUSS.f90 processed by SPAG 7.21DC at 11:25 on 11 Jan 2019
! GAUSS
subroutine cgauss(Nsiz, Nn, Z, R, Nrhs)
implicit none
!
!*** Start of declarations rewritten by SPAG
!
! Dummy arguments
!
integer :: Nn, Nrhs, Nsiz
complex, dimension(Nsiz, Nrhs) :: R
complex, dimension(Nsiz, Nsiz) :: Z
intent (in) Nn, Nrhs, Nsiz
intent (inout) R, Z
!
! Local variables
!
integer :: k, l, n, np, np1, nx
complex :: pivot, temp, ztmp
!
!*** End of declarations rewritten by SPAG
!
!
!*** Start of declarations rewritten by SPAG
!
! Dummy arguments
!
!
! Local variables
!
!
!*** End of declarations rewritten by SPAG
!
!********************************************
! Solves general complex linear systems.
!********************************************
!
do np = 1, Nn - 1
np1 = np + 1
!
!------ find max pivot index NX
nx = np
do n = np1, Nn
if (abs(Z(n, np))>abs(Z(nx, np))) nx = n
enddo
!
pivot = (1.0, 0.0) / Z(nx, np)
!
!------ switch pivots
Z(nx, np) = Z(np, np)
!
!------ switch rows & normalize pivot row
do l = np1, Nn
temp = Z(nx, l) * pivot
Z(nx, l) = Z(np, l)
Z(np, l) = temp
enddo
!
do l = 1, Nrhs
temp = R(nx, l) * pivot
R(nx, l) = R(np, l)
R(np, l) = temp
enddo
!
!------ forward eliminate everything
do k = np1, Nn
ztmp = Z(k, np)
!
! IF(ZTMP.EQ.0.0) GO TO 15
!
do l = np1, Nn
Z(k, l) = Z(k, l) - ztmp * Z(np, l)
enddo
do l = 1, Nrhs
R(k, l) = R(k, l) - ztmp * R(np, l)
enddo
enddo
!
enddo
!
!---- solve for last row
do l = 1, Nrhs
R(Nn, l) = R(Nn, l) / Z(Nn, Nn)
enddo
!
!---- back substitute everything
do np = Nn - 1, 1, -1
np1 = np + 1
do l = 1, Nrhs
do k = np1, Nn
R(np, l) = R(np, l) - Z(np, k) * R(k, l)
enddo
enddo
enddo
!
end subroutine cgauss
!*==LUDCMP.f90 processed by SPAG 7.21DC at 11:25 on 11 Jan 2019
! CGAUSS
subroutine ludcmp(Nsiz, N, A, Indx)
implicit none
!
!*** Start of declarations rewritten by SPAG
!
! PARAMETER definitions
!
integer, parameter :: NVX = 500
!
! Dummy arguments
!
integer :: N, Nsiz
real, dimension(Nsiz, Nsiz) :: A
integer, dimension(Nsiz) :: Indx
intent (in) N, Nsiz
intent (out) Indx
intent (inout) A
!
! Local variables
!
real :: aamax, dum, sum
integer :: i, imax, j, k
real, dimension(NVX) :: vv
!
!*** End of declarations rewritten by SPAG
!
!
!*** Start of declarations rewritten by SPAG
!
! PARAMETER definitions
!
!
! Dummy arguments
!
!
! Local variables
!
!
!*** End of declarations rewritten by SPAG
!
! *******************************************************
! * *
! * Factors a full NxN matrix into an LU form. *
! * Subr. BAKSUB can back-substitute it with some RHS.*
! * Assumes matrix is non-singular... *
! * ...if it isn't, a divide by zero will result. *
! * *
! * A is the matrix... *
! * ...replaced with its LU factors. *
! * *
! * Mark Drela 1988 *
! *******************************************************
!
!
!
if (N>NVX) stop 'LUDCMP: Array overflow. Increase NVX.'
!
do i = 1, N
aamax = 0.
do j = 1, N
aamax = max(abs(A(i, j)), aamax)
enddo
vv(i) = 1.0 / aamax
enddo
!
do j = 1, N
do i = 1, j - 1
sum = A(i, j)
do k = 1, i - 1
sum = sum - A(i, k) * A(k, j)
enddo
A(i, j) = sum
enddo
!
aamax = 0.
do i = j, N
sum = A(i, j)
do k = 1, j - 1
sum = sum - A(i, k) * A(k, j)
enddo
A(i, j) = sum
!
dum = vv(i) * abs(sum)
if (dum>=aamax) then
imax = i
aamax = dum
endif
enddo
!
if (j/=imax) then
do k = 1, N
dum = A(imax, k)
A(imax, k) = A(j, k)
A(j, k) = dum
enddo
vv(imax) = vv(j)
endif
!
Indx(j) = imax
if (j/=N) then
dum = 1.0 / A(j, j)
do i = j + 1, N
A(i, j) = A(i, j) * dum
enddo
endif
!
enddo
!
end subroutine ludcmp
!*==BAKSUB.f90 processed by SPAG 7.21DC at 11:25 on 11 Jan 2019
! LUDCMP
subroutine baksub(Nsiz, N, A, Indx, B)
implicit none
!
!*** Start of declarations rewritten by SPAG
!
! Dummy arguments
!
integer :: N, Nsiz
real, dimension(Nsiz, Nsiz) :: A
real, dimension(Nsiz) :: B
integer, dimension(Nsiz) :: Indx
intent (in) A, Indx, N, Nsiz
intent (inout) B
!
! Local variables
!
integer :: i, ii, j, ll
real :: sum
!
!*** End of declarations rewritten by SPAG
!
!
!*** Start of declarations rewritten by SPAG
!
! Dummy arguments
!
!
! Local variables
!
!
!*** End of declarations rewritten by SPAG
!
!
ii = 0
do i = 1, N
ll = Indx(i)
sum = B(ll)
B(ll) = B(i)
if (ii/=0) then
do j = ii, i - 1
sum = sum - A(i, j) * B(j)
enddo
elseif (sum/=0.0) then
ii = i
endif
B(i) = sum
enddo
!
do i = N, 1, -1
sum = B(i)
if (i<N) then
do j = i + 1, N
sum = sum - A(i, j) * B(j)
enddo
endif
B(i) = sum / A(i, i)
enddo
!
end subroutine baksub
!*==BLSOLV.f90 processed by SPAG 7.21DC at 11:25 on 11 Jan 2019
! BAKSUB
subroutine blsolv
use i_xfoil
implicit none
!
!*** Start of declarations rewritten by SPAG
!
! Local variables
!
integer :: iv, ivp, ivte1, ivz, k, kv, l
real :: pivot, vacc1, vacc2, vacc3, vtmp, vtmp1, vtmp2, vtmp3
!
!*** End of declarations rewritten by SPAG
!
!
!*** Start of declarations rewritten by SPAG
!
! Local variables
!
!
!*** End of declarations rewritten by SPAG
!
!-----------------------------------------------------------------
! Custom solver for coupled viscous-inviscid Newton system:
!
! A | | . | | . | d R S
! B A | . | | . | d R S
! | B A . | | . | d R S
! . . . . | | . | d = R - dRe S
! | | | B A | . | d R S
! | Z | | B A . | d R S
! . . . . . . . | d R S
! | | | | | | B A d R S
!
! A, B, Z 3x3 blocks containing linearized BL equation coefficients
! | 3x1 vectors containing mass defect influence
! coefficients on Ue
! d 3x1 unknown vectors (Newton deltas for Ctau, Theta, m)
! R 3x1 residual vectors
! S 3x1 Re influence vectors
!-----------------------------------------------------------------
!
ivte1 = ISYs(IBLte(1), 1)
!
vacc1 = VACcel
vacc2 = VACcel * 2.0 / (S(N) - S(1))
vacc3 = VACcel * 2.0 / (S(N) - S(1))
!
do iv = 1, NSYs
!
ivp = iv + 1
!
!====== Invert VA(IV) block
!
!------ normalize first row
pivot = 1.0 / VA(1, 1, iv)
VA(1, 2, iv) = VA(1, 2, iv) * pivot
do l = iv, NSYs
VM(1, l, iv) = VM(1, l, iv) * pivot
enddo
VDEl(1, 1, iv) = VDEl(1, 1, iv) * pivot
VDEl(1, 2, iv) = VDEl(1, 2, iv) * pivot
!
!------ eliminate lower first column in VA block
do k = 2, 3
vtmp = VA(k, 1, iv)
VA(k, 2, iv) = VA(k, 2, iv) - vtmp * VA(1, 2, iv)
do l = iv, NSYs
VM(k, l, iv) = VM(k, l, iv) - vtmp * VM(1, l, iv)
enddo
VDEl(k, 1, iv) = VDEl(k, 1, iv) - vtmp * VDEl(1, 1, iv)
VDEl(k, 2, iv) = VDEl(k, 2, iv) - vtmp * VDEl(1, 2, iv)
enddo
!
!
!------ normalize second row
pivot = 1.0 / VA(2, 2, iv)
do l = iv, NSYs
VM(2, l, iv) = VM(2, l, iv) * pivot
enddo
VDEl(2, 1, iv) = VDEl(2, 1, iv) * pivot
VDEl(2, 2, iv) = VDEl(2, 2, iv) * pivot
!
!------ eliminate lower second column in VA block
k = 3
vtmp = VA(k, 2, iv)
do l = iv, NSYs
VM(k, l, iv) = VM(k, l, iv) - vtmp * VM(2, l, iv)
enddo
VDEl(k, 1, iv) = VDEl(k, 1, iv) - vtmp * VDEl(2, 1, iv)
VDEl(k, 2, iv) = VDEl(k, 2, iv) - vtmp * VDEl(2, 2, iv)
!
!
!------ normalize third row
pivot = 1.0 / VM(3, iv, iv)
do l = ivp, NSYs
VM(3, l, iv) = VM(3, l, iv) * pivot
enddo
VDEl(3, 1, iv) = VDEl(3, 1, iv) * pivot
VDEl(3, 2, iv) = VDEl(3, 2, iv) * pivot
!
!
!------ eliminate upper third column in VA block
vtmp1 = VM(1, iv, iv)
vtmp2 = VM(2, iv, iv)
do l = ivp, NSYs
VM(1, l, iv) = VM(1, l, iv) - vtmp1 * VM(3, l, iv)
VM(2, l, iv) = VM(2, l, iv) - vtmp2 * VM(3, l, iv)
enddo
VDEl(1, 1, iv) = VDEl(1, 1, iv) - vtmp1 * VDEl(3, 1, iv)
VDEl(2, 1, iv) = VDEl(2, 1, iv) - vtmp2 * VDEl(3, 1, iv)
VDEl(1, 2, iv) = VDEl(1, 2, iv) - vtmp1 * VDEl(3, 2, iv)
VDEl(2, 2, iv) = VDEl(2, 2, iv) - vtmp2 * VDEl(3, 2, iv)
!
!------ eliminate upper second column in VA block
vtmp = VA(1, 2, iv)
do l = ivp, NSYs
VM(1, l, iv) = VM(1, l, iv) - vtmp * VM(2, l, iv)
enddo
VDEl(1, 1, iv) = VDEl(1, 1, iv) - vtmp * VDEl(2, 1, iv)
VDEl(1, 2, iv) = VDEl(1, 2, iv) - vtmp * VDEl(2, 2, iv)
!
!
if (iv/=NSYs) then
!
!====== Eliminate VB(IV+1) block, rows 1 -> 3
do k = 1, 3
vtmp1 = VB(k, 1, ivp)
vtmp2 = VB(k, 2, ivp)
vtmp3 = VM(k, iv, ivp)
do l = ivp, NSYs
VM(k, l, ivp) = VM(k, l, ivp) - (vtmp1 * VM(1, l, iv) &
+ vtmp2 * VM(2, l, iv) + vtmp3 * VM(3, l, iv))
enddo
VDEl(k, 1, ivp) = VDEl(k, 1, ivp) &
- (vtmp1 * VDEl(1, 1, iv) + vtmp2 * VDEl(2, 1, iv) + vtmp3 * VDEl(3, 1, iv))
VDEl(k, 2, ivp) = VDEl(k, 2, ivp) &
- (vtmp1 * VDEl(1, 2, iv) + vtmp2 * VDEl(2, 2, iv) + vtmp3 * VDEl(3, 2, iv))
enddo
!
if (iv==ivte1) then
!------- eliminate VZ block
ivz = ISYs(IBLte(2) + 1, 2)
!
do k = 1, 3
vtmp1 = VZ(k, 1)
vtmp2 = VZ(k, 2)
do l = ivp, NSYs
VM(k, l, ivz) = VM(k, l, ivz) - (vtmp1 * VM(1, l, iv) + vtmp2 * VM(2, l, iv))
enddo
VDEl(k, 1, ivz) = VDEl(k, 1, ivz) - (vtmp1 * VDEl(1, 1, iv) + vtmp2 * VDEl(2, 1, iv))
VDEl(k, 2, ivz) = VDEl(k, 2, ivz) - (vtmp1 * VDEl(1, 2, iv) + vtmp2 * VDEl(2, 2, iv))
enddo
endif
!
if (ivp/=NSYs) then
!
!====== Eliminate lower VM column
do kv = iv + 2, NSYs
vtmp1 = VM(1, iv, kv)
vtmp2 = VM(2, iv, kv)
vtmp3 = VM(3, iv, kv)
!
if (abs(vtmp1)>vacc1) then
do l = ivp, NSYs
VM(1, l, kv) = VM(1, l, kv) - vtmp1 * VM(3, l, iv)
enddo
VDEl(1, 1, kv) = VDEl(1, 1, kv) - vtmp1 * VDEl(3, 1, iv)
VDEl(1, 2, kv) = VDEl(1, 2, kv) - vtmp1 * VDEl(3, 2, iv)
endif
!
if (abs(vtmp2)>vacc2) then
do l = ivp, NSYs
VM(2, l, kv) = VM(2, l, kv) - vtmp2 * VM(3, l, iv)
enddo
VDEl(2, 1, kv) = VDEl(2, 1, kv) - vtmp2 * VDEl(3, 1, iv)
VDEl(2, 2, kv) = VDEl(2, 2, kv) - vtmp2 * VDEl(3, 2, iv)
endif
!
if (abs(vtmp3)>vacc3) then
do l = ivp, NSYs
VM(3, l, kv) = VM(3, l, kv) - vtmp3 * VM(3, l, iv)
enddo
VDEl(3, 1, kv) = VDEl(3, 1, kv) - vtmp3 * VDEl(3, 1, iv)
VDEl(3, 2, kv) = VDEl(3, 2, kv) - vtmp3 * VDEl(3, 2, iv)
endif
!
enddo
endif
endif
!
enddo
!
!
!
do iv = NSYs, 2, -1
!
!------ eliminate upper VM columns
vtmp = VDEl(3, 1, iv)
do kv = iv - 1, 1, -1
VDEl(1, 1, kv) = VDEl(1, 1, kv) - VM(1, iv, kv) * vtmp
VDEl(2, 1, kv) = VDEl(2, 1, kv) - VM(2, iv, kv) * vtmp
VDEl(3, 1, kv) = VDEl(3, 1, kv) - VM(3, iv, kv) * vtmp
enddo
!
vtmp = VDEl(3, 2, iv)
do kv = iv - 1, 1, -1
VDEl(1, 2, kv) = VDEl(1, 2, kv) - VM(1, iv, kv) * vtmp
VDEl(2, 2, kv) = VDEl(2, 2, kv) - VM(2, iv, kv) * vtmp
VDEl(3, 2, kv) = VDEl(3, 2, kv) - VM(3, iv, kv) * vtmp
enddo
!
enddo
!
end subroutine blsolv
end module m_xsolve