initds.f

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*DECK INITDS
      FUNCTION initds (OS, NOS, ETA)
C***BEGIN PROLOGUE  INITDS
C***PURPOSE  Determine the number of terms needed in an orthogonal
C            polynomial series so that it meets a specified accuracy.
C***LIBRARY   SLATEC (FNLIB)
C***CATEGORY  C3A2
C***TYPE      DOUBLE PRECISION (INITS-S, INITDS-D)
C***KEYWORDS  CHEBYSHEV, FNLIB, INITIALIZE, ORTHOGONAL POLYNOMIAL,
C             ORTHOGONAL SERIES, SPECIAL FUNCTIONS
C***AUTHOR  Fullerton, W., (LANL)
C***DESCRIPTION
C
C  Initialize the orthogonal series, represented by the array OS, so
C  that INITDS is the number of terms needed to insure the error is no
C  larger than ETA.  Ordinarily, ETA will be chosen to be one-tenth
C  machine precision.
C
C             Input Arguments --
C   OS     double precision array of NOS coefficients in an orthogonal
C          series.
C   NOS    number of coefficients in OS.
C   ETA    single precision scalar containing requested accuracy of
C          series.
C
C***REFERENCES  (NONE)
C***ROUTINES CALLED  XERMSG
C***REVISION HISTORY  (YYMMDD)
C   770601  DATE WRITTEN
C   890531  Changed all specific intrinsics to generic.  (WRB)
C   890831  Modified array declarations.  (WRB)
C   891115  Modified error message.  (WRB)
C   891115  REVISION DATE from Version 3.2
C   891214  Prologue converted to Version 4.0 format.  (BAB)
C   900315  CALLs to XERROR changed to CALLs to XERMSG.  (THJ)
C***END PROLOGUE  INITDS
      DOUBLE PRECISION os(*)
C***FIRST EXECUTABLE STATEMENT  INITDS
      IF (nos .LT. 1) CALL xermsg ('SLATEC', 'INITDS',
     +   'Number of coefficients is less than 1', 2, 1)
C
      err = 0.
      DO 10 ii = 1,nos
        i = nos + 1 - ii
        err = err + abs(real(os(i)))
        IF (err.GT.eta) GO TO 20
   10 CONTINUE
C
   20 IF (i .EQ. nos) CALL xermsg ('SLATEC', 'INITDS',
     +   'Chebyshev series too short for specified accuracy', 1, 1)
      initds = i
C
      RETURN
      END