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Diffstat (limited to 'src/gram_schmidt.F90')
-rw-r--r-- | src/gram_schmidt.F90 | 121 |
1 files changed, 121 insertions, 0 deletions
diff --git a/src/gram_schmidt.F90 b/src/gram_schmidt.F90 new file mode 100644 index 0000000..61e865a --- /dev/null +++ b/src/gram_schmidt.F90 @@ -0,0 +1,121 @@ +! $Header$ + +#include "cctk.h" + +module gram_schmidt + implicit none + private + public gram_schmidt_project4 + public gram_schmidt_normalise4 + +contains + + subroutine gram_schmidt_project4 (g, y, dy, ddy, y2, x, dx, ddx) + CCTK_REAL, intent(in) :: g(0:3,0:3) + CCTK_REAL, intent(in) :: y(0:3), dy(0:3,0:3), ddy(0:3,0:3,0:3), y2 + CCTK_REAL, intent(inout) :: x(0:3), dx(0:3,0:3), ddx(0:3,0:3,0:3) + CCTK_REAL :: z(0:3), dz(0:3,0:3), ddz(0:3,0:3,0:3) + + integer :: a, b, c, d, e + + do a=0,3 + z(a) = x(a) + do d=0,3 + do e=0,3 + z(a) = z(a) - g(d,e) * x(d) * y(e) * y(a) / y2 + end do + end do + end do + + do a=0,3 + do b=0,3 + dz(a,b) = dx(a,b) + do d=0,3 + do e=0,3 + dz(a,b) = dz(a,b) - g(d,e) * ((dx(d,b) * y(e) + x(d) * dy(e,b)) * y(a) + x(d) * y(e) * dy(a,b)) / y2 + end do + end do + end do + end do + + do a=0,3 + do b=0,3 + do c=0,3 + ddz(a,b,c) = ddx(a,b,c) + do d=0,3 + do e=0,3 + ddz(a,b,c) = ddz(a,b,c) - g(d,e) * ( (ddx(d,b,c) * y(e) + dx(d,b) * dy(e,c) + dx(d,c) * dy(e,b) + x(d) * ddy(e,b,c)) * y(a) + (dx(d,b) * y(e) + x(d) * dy(e,b)) * dy(a,c) & + & + dx(d,c) * y(e) * dy(a,b) + x(d) * dy(e,c) * dy(a,b) + x(d) * y(e) * ddy(a,b,c)) / y2 + end do + end do + end do + end do + end do + + x = z + dx = dz + ddx = ddz + end subroutine gram_schmidt_project4 + + subroutine gram_schmidt_normalise4 (g, x, dx, ddx, x2) + CCTK_REAL, intent(in) :: g(0:3,0:3) + CCTK_REAL, intent(inout) :: x(0:3), dx(0:3,0:3), ddx(0:3,0:3,0:3) + CCTK_REAL, intent(in) :: x2 + CCTK_REAL, parameter :: two=2, half=1/two + CCTK_REAL :: z2, dz2(0:3), ddz2(0:3,0:3) + CCTK_REAL :: z(0:3), dz(0:3,0:3), ddz(0:3,0:3,0:3) + + integer :: a, b, c, d, e + + z2 = 0 + do d=0,3 + do e=0,3 + z2 = z2 + g(d,e) * x(d) * x(e) + end do + end do + + do a=0,3 + dz2(a) = 0 + do d=0,3 + do e=0,3 + dz2(a) = dz2(a) + 2 * g(d,e) * dx(d,a) * x(e) + end do + end do + end do + + do a=0,3 + do b=0,3 + ddz2(a,b) = 0 + do d=0,3 + do e=0,3 + ddz2(a,b) = ddz2(a,b) + 2 * g(d,e) * ddx(d,a,b) * x(e) + 2 * g(d,e) * dx(d,a) * dx(e,b) + end do + end do + end do + end do + + do a=0,3 + z(a) = x(a) / sqrt(z2 / x2) + end do + + do a=0,3 + do b=0,3 + dz(a,b) = (dx(a,b) * z2 - half * x(a) * dz2(b) / x2) / sqrt(z2 / x2)**3 + end do + end do + + do a=0,3 + do b=0,3 + do c=0,3 + ddz(a,b,c) = ((ddx(a,b,c) * z2 + dx(a,b) * dz2(c) / x2 - half * (dx(a,c) * dz2(b) / x2 + x(a) * ddz2(b,c) / x2**2)) * z2 & + & - 3*half * (dx(a,b) * z2 - half * x(a) * dz2(b) / x2) * dz2(c) / x2) / sqrt(z2 / x2)**5 + end do + end do + end do + + x = z + dx = dz + ddx = ddz + end subroutine gram_schmidt_normalise4 + +end module gram_schmidt |