NASA Ocean Color

ocssw V2022
       SUBROUTINE legend(N,M,X,P)
 C  VERSION OF 2/9/87
 C  PURPOSE   
 C    COMPUTES LEGENDRE AND ASSOCIATED LEGENDRE FUNCTIONS UP TO 
 C    DEGREE N AND ORDER M, N.GE.M  
 C  INPUT 
 C    N      = DEGREE OF SPHERICAL HARMONICS
 C    M      = ORDER OF SPHERICAL HARMONICS 
 C    X      = SIN (LATITUDE)   
 C  OUTPUT
 C    P      = 2-D LEGENDRE FUNCTIONS   
 C  CALLED BY SUBROUTINES 
 C    DER   
 C  CALL SUBROUTINES  
 C    NONE  
 C  REFERENCES
 C    JPL EM 312/87-153, 20 APRIL 1987
 C  ANALYSIS
 C    J. H. KWOK - JPL  
 C  PROGRAMMER
 C    J. H. KWOK - JPL  
 C  PROGRAM MODIFICATION  
 C    NONE  
 C  COMMENTS  
 C    THIS PROGRAM HAS BEEN DIMENSION FOR MAXIMUM OF 40X40 HARMONICS.   
 C    FOR HIGHER ORDER OR DEGREE, REDIMENSION P( , ). THE FUNCTIONS 
 C    ARE STORED AS PIJ=P(I+1,J+1).  INPUT N CAN BE .GE. M. 
 C   
       IMPLICIT DOUBLE PRECISION (a-h,o-z)   
       dimension p(41,41)
       DATA one/1.d0/
       p(1,1)=one
       p(2,1)=x
 C *** COMPUTE LEGENDRE FUNCTIONS UP TO DEGREE N 
       DO 100 i=2,n  
   100 p(i+1,1)=((2*i-1)*x*p(i,1)-(i-1)*p(i-1,1))/i  
       IF (m.EQ.0) RETURN
 C *** COMPUTE ASSOCIATED LEGENDRE FUNCTIONS UP TO ORDER M   
       y=dsqrt(one-x*x) 
       p(2,2)=y  
       IF (m.EQ.1) GO TO 400 
 C *** THIS IS THE SECTORIAL PART OF THE ASSOCIATED FUNCTIONS
       DO 200 i=2,m  
   200 p(i+1,i+1)=(2*i-1)*y*p(i,i)   
   400 CONTINUE  
 C *** THIS THE TESSERAL PART OF THE ASSOCIATED FUNCTIONS
       DO 500 i=2,n  
       i1=i-1
       DO 300 j=1,i1 
       IF (j.GT.m) GO TO 500 
       p(i+1,j+1)=(2*i-1)*y*p(i,j)   
       IF (i-2.GE.j) p(i+1,j+1)=p(i+1,j+1)+p(i-1,j+1)
   300 CONTINUE  
   500 CONTINUE  
       RETURN
       END
legend
subroutine legend(N, M, X, P)
Definition: legend.f:2