d1/d2a/initds_8f_source.html

 *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

to
may be zero for pure relative error test tem the relative tolerance must be greater than or equal to
Definition: Quad-opts.cc:233

initds
function initds(OS, NOS, ETA)
Definition: initds.f:2

xermsg
subroutine xermsg(LIBRAR, SUBROU, MESSG, NERR, LEVEL)
Definition: xermsg.f:2

abs
OCTAVE_EXPORT octave_value_list return the value of the option it must match the dimension of the state and the relative tolerance must also be a vector of the same length tem it must match the dimension of the state and the absolute tolerance must also be a vector of the same length The local error test applied at each integration step is xample roup abs(local error in x(i))<