Posted by mike osborn on October 10, 1997 at 14:22:09:
I'm loking for an efficient FORTRAN routine to
integrate the volume under a multi-dimensional
gaussian surface with arbitrary covariance
over definite (sometimes small) limits. I've
found the algorithm referenced below, but it does the
job from -infinity to a set of limits. For an n-D
calculation I think I have to do 2**n calls to this
routine to get the right answer (for example: to
integrate from X1 to X2 and Y1 to Y2, you have to call
DMV for X2,Y2 + X1,Y1 - X1Y2 - X2Y1).
C ALGORITHM 725, COLLECTED ALGORITHMS FROM ACM.
C THIS WORK PUBLISHED IN TRANSACTIONS ON MATHEMATICAL SOFTWARE,
C VOL. 19, NO. 4, DECEMBER, 1993, P. 546.
IMPLICIT DOUBLE PRECISION (A-H,O-Z)
C DMV CALCULATES THE MULTIVARIATE NORMAL INTEGRAL.
C THE INTEGRAL LOWER LIMITS ARE -INFINITY FOR ALL VARIABLES.
C THE UPPER LIMITS ARE GIVEN BY THE VECTOR H (INPUT).
C THE CORRELATION MATRIX IS R (INPUT).