pchip_module Module

derivative value at the end of an interval.

derivative value at the end of an interval.

the data slope over that interval

endpoints if interval of definition of cubic

endpoints if interval of definition of cubic

function values at the ends of the interval

function values at the ends of the interval

derivative values at the ends of the interval

derivative values at the ends of the interval

endpoints of interval of integration

endpoints of interval of integration

is the order of the desired derivative approximation. K must be at least 3 (error return if not).

contains the K values of the independent variable. X need not be ordered, but the values MUST be distinct. (Not checked here.)

contains the associated slope values: S(I) = (F(I+1)-F(I))/(X(I+1)-X(I)), I=1(1)K-1. (Note that S need only be of length K-1.) Will be destroyed on output.

will be set to -1 if K<2 .

number of data points. (Error return if N<2).

array of independent variable values. The elements of X must be strictly increasing: X(I-1) < X(I), I = 2(1)N. (Error return if not.)

array of function values. F(1+(I-1)*INCFD) is the value corresponding to X(I).

array of derivative values. D(1+(I-1)*INCFD) is the value corresponding to X(I).

increment between successive values in F and D. (Error return if INCFD<1).

logical variable which should be set to .TRUE. if the user wishes to skip checks for validity of preceding parameters, or to .FALSE. otherwise. This will save time in case these checks have already been performed (say, in dpchim or dpchic). SKIP will be set to .TRUE. on return with IERR>=0 .

the limits of integration. NOTE: There is no requirement that [A,B] be contained in [X(1),X(N)]. However, the resulting integral value will be highly suspect, if not.

the limits of integration. NOTE: There is no requirement that [A,B] be contained in [X(1),X(N)]. However, the resulting integral value will be highly suspect, if not.

error flag.

number of data points. (Error return if N<2).

array of independent variable values. The elements of X must be strictly increasing: X(I-1) < X(I), I = 2(1)N. (Error return if not.)

array of function values. F(1+(I-1)*INCFD) is the value corresponding to X(I).

array of derivative values. D(1+(I-1)*INCFD) is the value corresponding to X(I).

increment between successive values in F and D. (Error return if INCFD<1).

logical variable which should be set to .TRUE. if the user wishes to skip checks for validity of preceding parameters, or to .FALSE. otherwise. This will save time in case these checks have already been performed (say, in dpchim or dpchic). SKIP will be set to .TRUE. on return with IERR = 0 or -4.

indices in X-array for the limits of integration. both must be in the range [1,N]. (Error return if not.) No restrictions on their relative values.

indices in X-array for the limits of integration. both must be in the range [1,N]. (Error return if not.) No restrictions on their relative values.

error flag.

initial endpoint of interval of definition of cubic. (Error return if X1==X2.)

final endpoint of interval of definition of cubic. (Error return if X1==X2.)

value of function at X1.

value of function at X2.

value of derivative at X1.

value of derivative at X2.

number of evaluation points. (Error return if NE<1).

array of points at which the functions are to be evaluated. If any of the XE are outside the interval [X1,X2], a warning error is returned in NEXT.

array of values of the cubic function defined by X1,X2, F1,F2, D1,D2 at the points XE.

array of values of the first derivative of the same function at the points XE.

array indicating number of extrapolation points:

error flag.

initial endpoint of interval of definition of cubic. (Error return if X1==X2.)

final endpoint of interval of definition of cubic. (Error return if X1==X2.)

value of function at X1.

value of function at X2.

value of derivative at X1.

value of derivative at X2.

number of evaluation points. (Error return if NE<1).

array of points at which the function is to be evaluated. If any of the XE are outside the interval [X1,X2], a warning error is returned in NEXT.

array of values of the cubic function defined by X1,X2, F1,F2, D1,D2 at the points XE.

integer array indicating number of extrapolation points:

error flag.

the number of data points, N>=2 . (not checked)

array of independent variable values. The elements of X must be strictly increasing: X(I-1) < X(I), I = 2(1)N. (not checked) nmax, the dimension of X, must be >=N.

array of dependent variable values. F(1+(I-1)*INCFD) is the value corresponding to X(I). nmax, the second dimension of F, must be >=N.

array of derivative values at the data points. D(1+(I-1)*INCFD) is the value corresponding to X(I). nmax, the second dimension of D, must be >=N.

the increment between successive values in F and D. This argument is provided primarily for 2-D applications. It may have the value 1 for one-dimensional applications, in which case F and D may be singly-subscripted arrays.

a flag to control the knot sequence. The knot sequence T is normally computed from X by putting a double knot at each X and setting the end knot pairs according to the value of KNOTYP:

the number of knots.

array of 2*N+4 knots for the B-representation.

array of 2*N B-spline coefficients.

the dimension of the B-spline space. (Set to 2*N.)

the order of the B-spline. (Set to 4.)

an error flag:

array of length 2 specifying desired boundary conditions:

array of length 2 specifying desired boundary values.

number of data points. (assumes N>=2)

array of independent variable values. (the elements of X are assumed to be strictly increasing.)

array of interval lengths.

array of data slopes. If the data are (X(I),Y(I)), I=1(1)N, then these inputs are:

(input) real8 array of derivative values at the data points. The value corresponding to X(I) must be stored in D(1+(I-1)INCFD), I=1(1)N.

increment between successive values in D. This argument is provided primarily for 2-D applications.

error flag.

number of data points. If N=2, simply does linear interpolation.

array of interval lengths.

array of data slopes. If the data are (X(I),Y(I)), I=1(1)N, then these inputs are:

array of derivative values at data points. If the data are monotonic, these values will determine a a monotone cubic Hermite function. The value corresponding to X(I) is stored in D(1+(I-1)*INCFD), I=1(1)N. No other entries in D are changed.

increment between successive values in D. This argument is provided primarily for 2-D applications.

the number of data points. (Error return if N<2).

array of independent variable values. The elements of X must be strictly increasing: X(I-1) < X(I), I = 2(1)N. (Error return if not.)

array of function values. F(1+(I-1)*INCFD) is the value corresponding to X(I).

array of derivative values. D(1+(I-1)*INCFD) is is the value corresponding to X(I).

the increment between successive values in F and D. (Error return if INCFD<1).

logical variable which should be set to .TRUE. if the user wishes to skip checks for validity of preceding parameters, or to .FALSE. otherwise. This will save time in case these checks have already been performed. SKIP will be set to .TRUE. on normal return.

array indicating on which intervals the PCH function defined by N, X, F, D is monotonic. For data interval [X(I),X(I+1)]:

error flag.

indicates the amount of control desired over local excursions from data.

number of data points. (assumes N>2).

array of interval lengths.

array of data slopes. If the data are (X(I),Y(I)), I=1(1)N, then these inputs are:

(input) array of derivative values at the data points, as determined by dpchci.

increment between successive values in D. This argument is provided primarily for 2-D applications.

error flag. should be zero. If negative, trouble in dpchsw. (should never happen.)

number of data points. (Error return if N<2).

array of independent variable values. The elements of X must be strictly increasing: X(I-1) < X(I), I = 2(1)N. (Error return if not.)

array of function values. F(1+(I-1)*INCFD) is the value corresponding to X(I).

array of derivative values. D(1+(I-1)*INCFD) is the value corresponding to X(I).

increment between successive values in F and D. (Error return if INCFD<1).

logical variable which should be set to .TRUE. if the user wishes to skip checks for validity of preceding parameters, or to .FALSE. otherwise. This will save time in case these checks have already been performed (say, in dpchim or dpchic). SKIP will be set to .TRUE. on normal return.

number of evaluation points. (Error return if NE<1).

array of points at which the functions are to be evaluated. NOTES:

array of values of the cubic Hermite function defined by N, X, F, D at the points XE.

array of values of the first derivative of the same function at the points XE.

error flag.

number of data points. (Error return if N<2).

array of independent variable values. The elements of X must be strictly increasing: X(I-1) < X(I), I = 2(1)N. (Error return if not.)

array of function values. F(1+(I-1)*INCFD) is the value corresponding to X(I).

array of derivative values. D(1+(I-1)*INCFD) is the value corresponding to X(I).

increment between successive values in F and D. (Error return if INCFD<1).

logical variable which should be set to .TRUE. if the user wishes to skip checks for validity of preceding parameters, or to .FALSE. otherwise. This will save time in case these checks have already been performed (say, in dpchim or dpchic). SKIP will be set to .TRUE. on normal return.

number of evaluation points. (Error return if NE<1).

array of points at which the function is to be evaluated.

array of values of the cubic Hermite function defined by N, X, F, D at the points XE.

error flag.

array of length 2 specifying desired boundary conditions:

array of length 2 specifying desired boundary values, as indicated above.

indicates desired treatment of points where direction of monotonicity switches: Set SWITCH to zero if interpolant is required to be mono- tonic in each interval, regardless of monotonicity of data.

number of data points. (Error return if N<2).

array of independent variable values. The elements of X must be strictly increasing: X(I-1) < X(I), I = 2(1)N. (Error return if not.)

array of dependent variable values to be interpolated. F(1+(I-1)*INCFD) is value corresponding to X(I).

array of derivative values at the data points. These values will determine a monotone cubic Hermite function on each subinterval on which the data are monotonic, except possibly adjacent to switches in monotonicity. The value corresponding to X(I) is stored in D(1+(I-1)*INCFD), I=1(1)N. No other entries in D are changed.

increment between successive values in F and D. This argument is provided primarily for 2-D applications. (Error return if INCFD<1).

array of working storage. The user may wish to know that the returned values are:

length of work array. (Error return if NWK<2*(N-1)).

error flag.

number of data points. (Error return if N<2). If N=2, simply does linear interpolation.

array of independent variable values. The elements of X must be strictly increasing: X(I-1) < X(I), I = 2(1)N. (Error return if not.)

array of dependent variable values to be interpolated. F(1+(I-1)*INCFD) is value corresponding to X(I). DPCHIM is designed for monotonic data, but it will work for any F-array. It will force extrema at points where monotonicity switches direction. If some other treatment of switch points is desired, dpchic should be used instead.

array of derivative values at the data points. If the data are monotonic, these values will determine a monotone cubic Hermite function. The value corresponding to X(I) is stored in D(1+(I-1)*INCFD), I=1(1)N. No other entries in D are changed.

increment between successive values in F and D. This argument is provided primarily for 2-D applications. (Error return if INCFD<1).

error flag.

integer array of length 2 specifying desired boundary conditions:

array of length 2 specifying desired boundary values, as indicated above.

number of data points. (Error return if N<2).

array of independent variable values. The elements of X must be strictly increasing: X(I-1) < X(I), I = 2(1)N. (Error return if not.)

array of dependent variable values to be interpolated. F(1+(I-1)*INCFD) is value corresponding to X(I).

array of derivative values at the data points. These values will determine the cubic spline interpolant with the requested boundary conditions. The value corresponding to X(I) is stored in D(1+(I-1)*INCFD), I=1(1)N. No other entries in D are changed.

increment between successive values in F and D. This argument is provided primarily for 2-D applications. (Error return if INCFD<1).

array of working storage.

length of work array. (Error return if NWK<2*N).

error flag.

maximum allowed difference between F(IEXTRM) and the cubic determined by derivative values D1,D2. (assumes DFMAX>0.)

index of the extreme data value. (assumes IEXTRM = 1 or 2 . Any value /=1 is treated as 2.)

derivative values at the ends of the interval. (Assumes D1*D2 <= 0.) (output) may be modified if necessary to meet the restriction imposed by DFMAX.

derivative values at the ends of the interval. (Assumes D1*D2 <= 0.) (output) may be modified if necessary to meet the restriction imposed by DFMAX.

interval length. (Assumes H>0.)

data slope on the interval.

error flag. should be zero.

name of the library

name of the routine that detected the error

text of the error or warning message

error code

value in the range 0 to 2 that indicates the level (severity) of the error.