Add some functionality:

Conversion between 4 and 3+1 dimensions
Check for nans (isnan for Fortran)
Gram-Schmidt orthonormalisation
Calculate Riemann, Ricci, and Weyl tensors in 2, 3, and 4 dimensions
Calculate time derivatives


git-svn-id: http://svn.einsteintoolkit.org/cactus/EinsteinUtils/TGRtensor/trunk@21 b716e942-a2de-43ad-8f52-f3dfe468e4e7

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