share/hompack/fortran/powp.f

   1       SUBROUTINE POWP(NNNN,XXXX,YYYY)
   2 C
   3 C THIS SUBROUTINE TAKES A NON-NEGATIVE POWER OF A COMPLEX NUMBER:
   4 C YYYY = XXXX**NNNN USING DE MOIVRE'S FORMULA:
   5 C
   6 C     YYYY = R**NNNN * (COS(NNNN*THETA),SIN(NNNN*THETA)),
   7 C
   8 C WHERE R=DNRM2(2,XXXX,1) AND THETA=ATAN2(XXXX(2),XXXX(1)).
   9 C
  10 C NOTE: POWP SETS 0**0 EQUAL TO 1.
  11 C
  12 C ON INPUT:
  13 C
  14 C NNNN  IS A NON-NEGATIVE INTEGER.
  15 C
  16 C XXXX  IS AN ARRAY OF LENGTH TWO REPRESENTING A COMPLEX
  17 C       NUMBER, WHERE XXXX(1) = REAL PART OF XXXX AND XXXX(2) =
  18 C       IMAGINARY PART OF XXXX.
  19 C
  20 C ON OUTPUT:
  21 C
  22 C YYYY  IS AN ARRAY OF LENGTH TWO REPRESENTING THE RESULT OF
  23 C       THE POWER, YYYY = XXXX**NNNN, WHERE YYYY(1) =
  24 C       REAL PART OF YYYY AND YYYY(2) = IMAGINARY PART OF YYYY.
  25 C
  26 C SUBROUTINES: COS, SIN, ATAN2, DNRM2
  27 C
  28 C DECLARATION OF INPUT
  29       INTEGER NNNN
  30       DOUBLE PRECISION XXXX
  31       DIMENSION XXXX(2)
  32 C
  33 C DECLARATION OF OUTPUT
  34       DOUBLE PRECISION YYYY
  35       DIMENSION YYYY(2)
  36 C
  37 C DECLARATION OF VARIABLES
  38       DOUBLE PRECISION R,RR,T,TT
  39 C
  40 C DECLARATION OF FUNCTIONS
  41       DOUBLE PRECISION  DNRM2
  42 C
  43       IF (NNNN .EQ. 0) THEN
  44           YYYY(1)=1.
  45           YYYY(2)=0.
  46           RETURN
  47       ENDIF
  48       IF (NNNN .EQ. 1) THEN
  49           YYYY(1)=XXXX(1)
  50           YYYY(2)=XXXX(2)
  51           RETURN
  52       ENDIF
  53       R = DNRM2(2,XXXX,1)
  54       IF (R .EQ. 0.0) THEN
  55           YYYY(1)=0.0
  56           YYYY(2)=0.0
  57           RETURN
  58       END IF
  59       RR= R**NNNN
  60       T = ATAN2(XXXX(2),XXXX(1))
  61       TT= NNNN*T
  62       YYYY(1) = RR*COS(TT)
  63       YYYY(2) = RR*SIN(TT)
  64       RETURN
  65       END