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Diffstat (limited to 'math/curfit/doc')
| -rw-r--r-- | math/curfit/doc/curfit.hd | 24 | ||||
| -rw-r--r-- | math/curfit/doc/curfit.hlp | 163 | ||||
| -rw-r--r-- | math/curfit/doc/curfit.men | 20 | ||||
| -rw-r--r-- | math/curfit/doc/curfit.spc | 479 | ||||
| -rw-r--r-- | math/curfit/doc/cvaccum.hlp | 51 | ||||
| -rw-r--r-- | math/curfit/doc/cvacpts.hlp | 54 | ||||
| -rw-r--r-- | math/curfit/doc/cvcoeff.hlp | 36 | ||||
| -rw-r--r-- | math/curfit/doc/cvepower.hlp | 55 | ||||
| -rw-r--r-- | math/curfit/doc/cverrors.hlp | 53 | ||||
| -rw-r--r-- | math/curfit/doc/cveval.hlp | 33 | ||||
| -rw-r--r-- | math/curfit/doc/cvfit.hlp | 62 | ||||
| -rw-r--r-- | math/curfit/doc/cvfree.hlp | 26 | ||||
| -rw-r--r-- | math/curfit/doc/cvinit.hlp | 55 | ||||
| -rw-r--r-- | math/curfit/doc/cvpower.hlp | 40 | ||||
| -rw-r--r-- | math/curfit/doc/cvrefit.hlp | 52 | ||||
| -rw-r--r-- | math/curfit/doc/cvreject.hlp | 41 | ||||
| -rw-r--r-- | math/curfit/doc/cvrestore.hlp | 32 | ||||
| -rw-r--r-- | math/curfit/doc/cvsave.hlp | 35 | ||||
| -rw-r--r-- | math/curfit/doc/cvset.hlp | 56 | ||||
| -rw-r--r-- | math/curfit/doc/cvsolve.hlp | 39 | ||||
| -rw-r--r-- | math/curfit/doc/cvstati.hlp | 47 | ||||
| -rw-r--r-- | math/curfit/doc/cvstatr.hlp | 44 | ||||
| -rw-r--r-- | math/curfit/doc/cvvector.hlp | 41 | ||||
| -rw-r--r-- | math/curfit/doc/cvzero.hlp | 26 |
24 files changed, 1564 insertions, 0 deletions
diff --git a/math/curfit/doc/curfit.hd b/math/curfit/doc/curfit.hd new file mode 100644 index 00000000..b8a00640 --- /dev/null +++ b/math/curfit/doc/curfit.hd @@ -0,0 +1,24 @@ +# Help directory for the CURFIT (curve fitting) package. + +$curfit = "math$curfit/" + +cvaccum hlp = cvaccum.hlp, src = curfit$cvaccum.gx +cvacpts hlp = cvacpts.hlp, src = curfit$cvacpts.gx +cvcoeff hlp = cvcoeff.hlp, src = curfit$cvcoeff.gx +cvepower hlp = cvepower.hlp, src = curfit$cvepower.gx +cverrors hlp = cverrors.hlp, src = curfit$cverrors.gx +cveval hlp = cveval.hlp, src = curfit$cveval.gx +cvinit hlp = cvinit.hlp, src = curfit$cvinit.gx +cvfit hlp = cvfit.hlp, src = curfit$cvfit.gx +cvfree hlp = cvfree.hlp, src = curfit$cvfree.gx +cvpower hlp = cvpower.hlp, src = curfit$cvpower.gx +cvrefit hlp = cvrefit.hlp, src = curfit$cvrefit.gx +cvreject hlp = cvreject.hlp, src = curfit$cvreject.gx +cvrestore hlp = cvrestore.hlp, src = curfit$cvrestore.gx +cvsave hlp = cvsave.hlp, src = curfit$cvsave.gx +cvsolve hlp = cvsolve.hlp, src = curfit$cvsolve.gx +cvstati hlp = cvstati.hlp, src = curfit$cvstat.gx +cvstatr hlp = cvstatr.hlp, src = curfit$cvstat.gx +cvvector hlp = cvvector.hlp, src = curfit$cvvector.gx +cvzero hlp = cvzero.hlp, src = curfit$cvzero.gx +cvset hlp = cvset.hlp, src = curfit$cvset.gx diff --git a/math/curfit/doc/curfit.hlp b/math/curfit/doc/curfit.hlp new file mode 100644 index 00000000..35950c08 --- /dev/null +++ b/math/curfit/doc/curfit.hlp @@ -0,0 +1,163 @@ +.help curfit Jul84 "Math Package" +.ih +NAME +curfit -- curve fitting package +.ih +SYNOPSIS + +.nf + cvinit (cv, curve_type, order, xmin, xmax) + cvzero (cv) + cvaccum (cv, x, y, weight, wtflag) + cvreject (cv, x, y, weight) + cvsolve (cv, ier) + cvfit (cv, x, y, weight, npts, wtflag, ier) + cvrefit (cv, x, y, weight, ier) + y = cveval (cv, x) + cvvector (cv, x, yfit, npts) + cvcoeff (cv, coeff, ncoeff) + cverrors (cv, y, weight, yfit, rms, errors) + cvsave (cv, fit) + cvstati (cv, parameter, ival) + cvstatr (cv, parameter, ival) + cvrestore (cv, fit) + cvset (cv, curve_type, xmin, xmax, coeff, ncoeff) + cvfree (cv) +.fi +.ih +DESCRIPTION +The curfit package provides a set of routines for fitting data to functions +linear in their coefficients using least squares techniques. The numerical +technique employed is the solution of the normal equations by the +Cholesky method. +.ih +NOTES +The fitting function curve_type is chosen at run time from the following +list. + +.nf + LEGENDRE # Legendre polynomials + CHEBYSHEV # Chebyshev polynomials + SPLINE3 # cubic spline with uniformly spaced break points + SPLINE1 # linear spline with uniformly spaced break points +.fi + + +The CURFIT package performs a weighted fit. +The weighting options are WTS_USR, WTS_UNIFORM and WTS_SPACING. +The user must supply a weight array. In WTS_UNIFORM mode the curfit +routines set the weights to 1. In WTS_USER mode the user must supply an +array of weight values. +In WTS_SPACING mode +the weights are set to the difference between adjacent data points. +The data must be sorted in x in order to use the WTS_SPACING mode. +In WTS_UNIFORM mode the reduced chi-squared returned by CVERRORS +is the variance of the fit and the errors in the coefficients are scaled +by the square root of this variance. Otherwise the weights are +interpreted as one over the variance of the data and the true reduced +chi-squared is returned. + +The routines assume that all the x values of interest lie in the region +xmin <= x <= xmax. Checking for out of bounds x values is the responsibility +of the calling program. The package routines assume that INDEF values +have been removed from the data set prior to entering the package +routines. + +In order to make the package definitions available to the calling program +an include <curfit.h> statement must be included in the user program. +CVINIT must be called before each fit. CVFREE frees space used by the +CURFIT package. +.ih +EXAMPLES +.nf +Example 1: Fit curve to data, unifrom weighting + + include <math/curfit.h> + + ... + + call cvinit (cv, CHEBYSHEV, 4, 1., 512.) + + call cvfit (cv, x, y, weight, 512, WTS_UNIFORM, ier) + if (ier != OK) + call error (...) + + do i = 1, 512 { + x = i + call printf ("%g %g\n") + call pargr (x) + call pargr (cveval (cv, x)) + } + + call cvfree (cv) + + +Example 2: Fit curve using accumulate mode, weight based on spacing + + include <math/curfit.h> + + ... + + old_x = x + do i = 1, 512 { + x = real (i) + if (y[i] != INDEF) { + call cvaccum (cv, x, y, weight, x - old_x, WTS_USER) + old_x = x + } + } + + call cvsolve (cv, ier) + if (ier != OK) + call error (...) + + ... + + call cvfree (cv) + + +Example 3: Fit and subtract smooth curve from image lines + + include <math/curfit.h> + + ... + + call cvinit (cv, CHEBYSHEV, order, 1., 512.) + + do line = 1, nlines { + inpix = imgl2r (im, line) + outpix = impl2r (im, line) + if (line == 1) + call cvfit (cv, x, Memr[inpix], weight, 512, WTS_UNIFORM, ier) + else + call cvrefit (cv, x, Memr[inpix], weight, ier) + if (ier != OK) + ... + call cvvector (cv, x, y, 512) + call asubr (Memr[inpix], y, Memr[outpix], 512) + } + + call cvfree (cv) + + +Example 4: Fit curve, save fit for later use by CVEVAL. LEN_FIT must be a least + order + 7 elements long. + + include <math/curfit.h> + + real fit[LEN_FIT] + + ... + call cvinit (cv, CHEBYSHEV, order, xmin, xmax) + call cvfit (cv, x, y, w, npts, WTS_UNIFORM, ier) + if (ier != OK) + ... + call cvsave (cv, fit) + call cvfree (cv) + ... + call cvrestore (cv, fit) + do i = 1, npts + yfit[i] = cveval (cv, x[i]) + call cvfree (cv) + ... +.fi diff --git a/math/curfit/doc/curfit.men b/math/curfit/doc/curfit.men new file mode 100644 index 00000000..b061badc --- /dev/null +++ b/math/curfit/doc/curfit.men @@ -0,0 +1,20 @@ + cvaccum - Accumulate point into data set + cvacpts - Accumulate points into a data set + cvcoeff - Get coefficients + cvepower - Convert errors to power series equivalents + cverrors - Calculate chi-squared and errors in coefficients + cveval - Evaluate curve at x + cvfit - Fit curve + cvfree - Free space allocated by cvinit + cvinit - Make ready to fit a curve; set up parameters of fit + cvpower - Convert coefficients to power series coefficients + cvrefit - Refit curve, same x and weight, different y + cvreject - Reject point from data set + cvrestore - Restore curve parameters and coefficients + cvsave - Save curve parameters and coefficients + cvset - Input coefficients derived external to the CURFIT package + cvsolve - Solve matrix for coefficients + cvstati - Get integer parameter + cvstatr - Get real parameter + cvvector - Evaluate curve at an array of x + cvzero - Zero arrays for new fit diff --git a/math/curfit/doc/curfit.spc b/math/curfit/doc/curfit.spc new file mode 100644 index 00000000..f5e555a3 --- /dev/null +++ b/math/curfit/doc/curfit.spc @@ -0,0 +1,479 @@ +.help curfit May84 "Math Package" +.ce +Specifications for the Curfit Package +.ce +Lindsey Davis +.ce +July 1984 + +.sh +1. Introduction + +The CURFIT package provides a set of routines for fitting data to +functions linear in their coefficients using least +squares techniques. The basic numerical technique employed +is the solution of the normal equations by the Cholesky method. +This document presents the formal requirements for the package +and describes the algorithms used. + +.sh +2. Requirements + +.ls 4 +.ls (1) +The package shall take as input a set of x and y values and their +corresponding weights. The package routines asssume that data values +equal to INDEF have been rejected from the data set or replaced with +appropriate interpolated values prior to entering the package +routines. The input data may be arbitrarily spaced in x. No assumptions +are made about the ordering of the x values, but see (3) below. +.le +.ls (2) +The package shall perform the following operations: +.ls o +Determine the coefficients of the fitting function by solving the normal +equations. The fitting function is selected at run time from the following +list: (1) LEGENDRE, Legendre polynomials, (2) CHEBYSHEV, +Chebyshev polynomials, (3) SPLINE3, Cubic spline +with uniformly spaced break points, SPLINE1, Linear spline with evenly +spaced break points. The calling sequence must be +invariant to the form of the fitting function. +.le +.ls o +Set an error code if the numerical routines are unable to fit the +specified function. +.le +.ls o +Output the values of the coefficients. +The coefficients are stored internal to the CURFIT package. +However in some applications it is the coefficients which are of primary +interest. A package routine shall exist to extract the +the coefficients from the curve descriptor structure. +.le +.ls o +Evaluate the fitting function at arbitrary value(s) of x. The evaluating +routines shall use the coefficients calculated and +the user supplied x value(s). +.le +.ls o +Calculate the standard deviation of the coefficients and the standard deviation +of the fit. +.le +.le +.ls (3) +The program shall perform a weighted fit using a user supplied weight +array and weight flag. The weighting options are WTS_USER, WTS_UNIFORM and +WTS_SPACING. In WTS_USER mode the package routines apply user supplied +weights to the individual data points, otherwise the package routines +calculate the weights. In WTS_SPACING mode the program assumes that the data +are sorted in x, and sets the individual weights to the difference between +adjacent x values. In WTS_UNIFORM mode the weights are set to 1. +.le +.ls (4) +The input data set and output coefficent, error, and fitted y arrays are single +precision real quantities. All package arithmetic shall be done in single +precision. The package shall however be designed with +conversion to double precision arithmetic in mind. +.le +.le + +.sh +3. Specifications + +.sh +3.1. List of Routines + +The package prefix will be cv for curve fit. +The following procedures shall be part of the package. +Detailed documentation for each procedure can be found by invoking +the help facility. + +.nf + cvinit (cv, curvetype, order, xmin, xmax) + cvzero (cv) + cvaccum (cv, x, y, w, wtflag) + cvreject (cv, x, y, w) + cvsolve (cv, ier) + cvfit (cv, x, y, w, npts, wtflag, ier) + cvrefit (cv, x, y, w, ier) + y = cveval (cv, x) + cvvector (cv, x, yfit, npts) + cvcoeff (cv, coeff, ncoeff) + cverrors (cv, y, w, yfit, rms, errors) + cvsave (cv, fit) + cvrestore (cv, fit) + cvset (cv, curve_type, xmin, xmax, coeff, ncoeff) + cvfree (cv) +.fi + +.sh +3.2. Algorithms + +.sh +3.2.1. Polynomial Basis Functions + +The approximating function is assumed to be of the form + +.nf + f(x) = a(1)*F(1,x) + a(2)*F(2,x) + ... + a(ncoeff)*F(ncoeff,x) +.fi + +where the F(n,x) are polynomial basis functions containing terms +of order x**(n-1), and the a(n) are the coefficients. +In order to avoid a very ill-conditioned linear system for moderate or large n +the Legendre and Chebyshev polynomials were chosen for the basis functions. +The Chebyshev and Legendre polynomials are +orthogonal over -1. <= x <= 1. The data x values are normalized to +this regime using minimum and maximum x values supplied by the user. +For each data point the ncoeff basis functions are calculated using the +following recursion relations. + +.nf + Legendre series + F(1,x) = 1. + F(2,x) = x + F(n,x) = [(2*n-3)*x*F(n-1,x)-(n-2)*F(n-2,x)]/(n-1) + + Chebyshev series + F(1,x) = 1. + F(2,x) = x + F(n,x) = 2*x*F(n-1,x)-F(n-2,x) +.fi + +.sh +3.2.2. Cubic Cardinal B-Spline + +The approximating function is assumed to be of the form + +.nf + f(x) = a(1)*F(1,x) + a(2)*F(2,x) + ... a(ncoeff)*F(ncoeff,x) +.fi + +where the basis functions, F(n, x), are the cubic cardinal B-splines +(Prenter 1975). +The user supplies minimum and maximum x values and the number of polynomial +pieces, npieces, to be fit to the data set. The number of cubic spline +coefficents, ncoeff, will be + +.nf + ncoeff = npieces + 3 +.fi + +The cardinal B-spline is stored in a lookup table. For each x the appropriate +break point is selected and the four non-zero B-splines are calculated by +nearest neighbour interpolation in the lookup table. + +.sh +3.2.3. The Normal Equations + +The coefficients, a, are determined by the solution of the normal equations + +.nf + c * a = b +.fi + +where + +.nf + c[i,j] = (F(i,x), F(j,x)) + b[j] = (F(j,x), f(x)) +.fi + +F(i,x) is the ith basis function at x, f(x) is the function to be +approximated and the inner product of two functions G and H, (G,H), +is given by + +.nf + (G, H) = sum (G(x[i]) * H(x[i]) * weight[i]) i=1,...npts +.fi + +The resulting matrix is symmetric and positive semi-definite. +Therefore it is necessary to store the ncoeff bands at or below the +diagonal. Storage is particularly efficient for the cubic spline +as only the diagonal and three adjacent lower bands are non-zero +(deBoor 1978). + +.sh +3.2.4. Method of Solution + +Since the matrix is symmetric, positive semi-definite and banded +it may be solved by the Cholesky method. The data matrix c may be +written as + +.nf + c = l * d * l-transpose +.fi + +where l is a unit lower triangular matrix and d is the diagonal of c +(deBoor 1978). Near zero pivots are handled in the following way. +At the nth elimination step the current value of the nth diagonal +element is compared with the original nth diagonal element. If the diagonal +element has been reduced by one computer word length, the entire nth +row is declared linearly dependent on the previous n-1 rows and +a(n) = 0. + +The triangular system + +.nf + l * w = b +.fi + +is solved for w (forward substitution), the vector d ** (-1) * w +is computed and the triangular system + +.nf + l-transpose * a = d ** (-1) * w +.fi + +solved for the coefficients, a (backward substitution). + +.sh +3.2.5. Errors + +The reduced ch-squared of the fit is defined as the weighted sum of +the squares of the residuals divided by the number of degrees of +freedom. + +.nf + rms = sqrt (sum (weight * (y - yfit) ** 2) / nfree) + nfree = npts - ncoeff +.fi + +The error of the j-th coefficient, error[j], is equal to the square root +of the j-th diagonal element of inverse data matrix times a scale factor. + +.nf + error[j] = sqrt (c[j,j]-inverse) * scale +.fi + +The scale factor is the square root of the variance of the data when +all the weights are equal, otherwise scale is one. + +.sh +4. Usage + +.sh +4.1. User Notes + +The following series of steps illustrates the use of the package. + +.ls 4 +.ls (1) +Insert an include <curfit.h> statement in the calling program to +make the CURFIT package definitions available to the user program. +.le +.ls (2) +Call CVINIT to initialize the curve fitting parameters. +.le +.ls (3) +Call CVACCUM to select a weighting function +and accumulate data points into the appropriate arrays and vectors. +.le +.ls (4) +Call CVSOLVE to solve the normal equations and calculate the coefficients +of the fitting function. Test for an error condition. +.le +.ls (5) +Call CVEVAL or CVVECTOR to evaluated the fitted function at the +x value(s) of interest. +.le +.ls (6) +Call CVCOEFF to fetch the number and value of the coefficients of the fitting +function. +.le +.ls (7) +Call CVERRORS to calculate the standard deviations in the +coefficients and the standard deviation of the fit. +.le +.ls (8) +Call CVFREE to release the space allocated for the fit. +.le +.le + +Steps (2) and (3) may be combined in a single step by calling CVFIT +and inputting an array of x, y and weight values. Individual points may +be rejected from the fit by calling CVREJECT and CVSOLVE to determine +a new set of coefficients. If the x and weight values remain the same +and only the y values change from fit to fit, CVREFIT can be called. + + +.sh +4.2. Examples + +.nf +Example 1: Fit curve to data, no weighting + + include <curfit.h> + ... + call cvinit (cv, CHEBYSHEV, 4, 1., 512.) + + call cvfit (cv, x, y, w, 512, WTS_UNIFORM, ier) + if (ier != OK) + call error (...) + + do i = 1, 512 { + x = i + call printf ("%g %g\n") + call pargr (x) + call pargr (cveval (cv, x)) + } + + call cvfree (cv) + +Example 2: Fit curve using accumulate mode, weight based on spacing + + include <curfit.h> + ... + call cvinit (cv, SPLINE3, npolypieces, 1., 512.) + + old_x = 0.0 + do i =1, 512 { + x = real (i) + if (y[i] != INDEF) { + call cvaccum (cv, x, y, x - old_x, WTS_USER) + old_x = x + } + } + + call cvsolve (cv, ier) + if (ier != OK) + call error (...) + ... + call cvfree (cv) + +Example 3: Fit and subtract smooth curve from image lines + + include <curfit.h> + ... + call cvinit (cv, CHEBYSHEV, order, 1., 512.) + + do line = 1, nlines { + inpix = imgl2r (im, line) + outpix = impl2r (im, line) + if (line == 1) + call cvfit (cv, x, Memr[inpix], w, 512, WTS_USER, ier) + else + call cvrefit (cv, x, Memr[inpix], w, WTS_USER, ier) + if (ier != OK) + ... + call cvvector (cv, x, y, 512) + call asubr (Memr[inpix], y, Memr[outpix], 512) + } + + call cvfree (cv) + +Example 4: Fit curve and save parameters for later use by CVEVAL + Fit must be at least order + 7 elements long. + + include <curfit.h> + + real fit[LEN_FIT) + ... + call cvinit (cv, LEGENDRE, order, xmin, xmax) + call cvfit (cv, x, y, w, npts, WTS_UNIFORM, ier) + if (ier != OK) + ... + call cvsave (cv, fit) + call cvfree (cv) + ... + call cvrestore (cv, fit) + do i = 1, npts + yfit[i] = cveval (cv, x[i]) + call cvfree (cv) + ... + +.fi + +.sh +5. Detailed Design + +.sh +5.1. Curve Descriptor Structure + +The CURFIT parameters, and the +size and location of the arrays and vectors used in the fitting procedure +are stored in the curve descriptor structure. The structure is referenced +by the pointer cv returned by the CVINIT routine. The curve +descriptor structure is defined in the package +header file curfit.h. The structure is listed below. + +.nf +define LEN_CVSTRUCT 17 + +# CURFIT parameters + +define CV_TYPE Memi[$1] # Type of curve to be fitted +define CV_ORDER Memi[$1+1] # Order of the fit +define CV_NPIECES Memi[$1+2] # Number of polynomial pieces (spline) +define CV_NCOEFF Memi[$1+3] # Number of coefficients +define CV_XMAX Memr[$1+4] # Maximum x value +define CV_XMIN Memr[$1+5] # Minimum x value +define CV_RANGE Memr[$1+6] # Xmax minus xmin +define CV_MAXMIN Memr[$1+7] # Xmax plus xmin +define CV_SPACING Memr[$1+8] # Break point spacing (spline) +define CV_NPTS Memi[$1+9] # Number of data points + +# Pointers to storage arrays and vectors + +define CV_XBASIS Memi[$1+10] # Basis functions single x +define CV_MATRIX Memi[$1+11] # Pointer to matrix +define CV_CHOFAC Memi[$1+12] # Pointer to Cholesky factorization +define CV_VECTOR Memi[$1+13] # Pointer to vector +define CV_COEFF Memi[$1+14] # Pointer to coefficient vector + +# Used only by CVREFIT + +define CV_BASIS Memi[$1+15] # Pointer to basis functions all x +define CV_LEFT Memi[$1+16] # Pointer to index array (spline) +.fi + +.sh +5.2. Storage Requirements + +The storage requirements are listed below. + +.ls 4 +.ls real MATRIX[order,ncoeff] +The real array, matrix, stores the original accumulated data. Storage of this +array is required by the CURFIT routines CVACCUM and CVREJECT which accumulate +and reject individual points from the data set respectively. If the fitting +function is SPLINE3 then order = 4, otherwise order = ncoeff. +.le +.ls real CHOFAC[order, ncoeff] +The real array chofac stores the Cholesky factorization of matrix. +Storage of CHOFAC is required by the CURFIT routines CVERRORS and +CVREFIT. +.le +.ls real VECTOR[ncoeff] +Ncoeff real storage units must be allocated for the vector containing +the right side of the matrix equation. VECTOR is stored for use by the +CVREJECT and CVACCUM routines. Vector is zeroed before every CVREFIT call. +.le +.ls real COEFF[ncoeff] +The coefficients of the fitted function must be stored for use by +the CVEVAL, CVVECTOR, and CVCOEFF routines. +.le +.ls real BASIS[order,npts] +Space is allocated for the basis functions only if the routine CVREFIT is +called. The first call to CVREFIT generates an array of basis functions and +subsequent calls reference the array. +.le +.ls int LEFT[npts] +Space for the array left is allocated only if +CVREFIT is called. The array indicates to which element of +the matrix a given spline function should be accumulated. +.le +.le + +.sh +6. References + +.ls (1) +Carl de Boor, "A Practical Guide to Splines", 1978, Springer-Verlag New +York Inc. +.le +.ls (2) +P.M. Prenter, "Splines and Variational Methods", 1975, John Wiley and Sons +Inc. +.le +.endhelp diff --git a/math/curfit/doc/cvaccum.hlp b/math/curfit/doc/cvaccum.hlp new file mode 100644 index 00000000..4fc3a37b --- /dev/null +++ b/math/curfit/doc/cvaccum.hlp @@ -0,0 +1,51 @@ +.help cvaccum Jun84 "Curfit Package" +.ih +NAME +cvaccum -- accumulate a single data point into the matrix +.ih +SYNOPSIS +include <math/curfit.h> + +cvaccum (cv, x, y, weight, wtflag) + +.nf +pointer cv # curve descriptor +real x # x value +real y # y value +real weight # weight +int wtflag # type of weighting +.fi +.ih +ARGUMENTS +.ls cv +Pointer to the curve descriptor structure. +.le +.ls x +X value. Checking for out of bounds x values is the responsibility of the +user. +.le +.ls y +Y value. +.le +.ls weight +Weight assigned to the data point. +.le +.ls wtflag +Type of weighting. The options are WTS_USER, WTS_UNIFORM or WTS_SPACING. +If wtflag equals WTS_USER the weight for each point is supplied by the user. +If wtflag is either WTS_UNIFORM or WTS_SPACING the routine sets weight +to one. +.le +.ih +DESCRIPTION +Calculate the non-zero basis functions for the given value of x. +Compute the contribution of the data point to the normal equations and +sum into the appropriate arrays and vectors. +.ih +NOTES +The WTS_SPACING option cannot be used with CVACCUM. Weights will be set +to 1. +.ih +SEE ALSO +cvfit, cvrefit +.endhelp diff --git a/math/curfit/doc/cvacpts.hlp b/math/curfit/doc/cvacpts.hlp new file mode 100644 index 00000000..c5a6cffd --- /dev/null +++ b/math/curfit/doc/cvacpts.hlp @@ -0,0 +1,54 @@ +.help cvacpts Jun84 "Curfit Package" +.ih +NAME +include <math/curfit.h> + +cvacpts -- fit a curve to a set of data values +.ih +SYNOPSIS +cvacpts (cv, x, y, weight, npts, wtflag) + +.nf +pointer cv # curve descriptor +real x[] # array of x values +real y[] # array of y values +real weight[] # array of weights +int npts # number of data points +int wtflag # type of weighting +.fi +.ih +ARGUMENTS +.ls cv +Pointer to the curve descriptor structure. +.le +.ls x +Array of x values. +.le +.ls y +Array of y values +.le +.ls weight +Array of weights +.le +.ls wtflag +Type of weighting. The options are WTS_USER, WTS_SPACING and +WTS_UNIFORM. If wtflag = WTS_USER individual weights for each data point +are supplied by the calling program and points with zero-valued weights are +not included in the fit. If wtflag = WTS_UNIFORM, all weights are assigned +values of 1. If wtflag = WTS_SPACING, the weights are set equal to the +difference between adjacent data points. In order to correctly use the +WTS_SPACING option the data must be sorted in x. +.le +.ih +DESCRIPTION +CVACPTS zeroes the matrix and vectors, calculates the non-zero basis functions, +calculates the contribution +of each data point to the normal equations and accumulates it into the +appropriate array and vector elements. +.ih +NOTES +Checking for out of bounds x values is the responsibility of the user. +.ih +SEE ALSO +cvaccum +.endhelp diff --git a/math/curfit/doc/cvcoeff.hlp b/math/curfit/doc/cvcoeff.hlp new file mode 100644 index 00000000..6467cd60 --- /dev/null +++ b/math/curfit/doc/cvcoeff.hlp @@ -0,0 +1,36 @@ +.help cvcoeff Jun84 "Curfit Package" +.ih +NAME +cvcoeff -- get the number and values of the coefficients +.ih +SYNOPSIS +cvcoeff (cv, coeff, ncoeff) + +.nf +pointer cv # curve descriptor +real coeff[] # the coefficient array +int ncoeff # the number of coefficients +.fi +.ih +ARGUMENTS +.ls pointer +Pointer to the curve descriptor. +.le +.ls coeff +Array of coefficients. +.le +.ls ncoeff +The number of coefficients. +.le +.ih +DESCRIPTION +CVCOEFF fetches the coefficient array and the number of coefficients from the +curve descriptor structure. +.ih +NOTES +The variable ncoeff is only equal to the order specified in CVINIT if the +curve_type is LEGENDRE or CHEBYSHEV. If curve_type is SPLINE3 then +ncoeff = order + 3. If curve_type is SPLINE1 then ncoeff = order + 1. +.ih +SEE ALSO +.endhelp diff --git a/math/curfit/doc/cvepower.hlp b/math/curfit/doc/cvepower.hlp new file mode 100644 index 00000000..58e78dae --- /dev/null +++ b/math/curfit/doc/cvepower.hlp @@ -0,0 +1,55 @@ +.help cvepower Jun95 "Curfit Package" +.ih +NAME +cvepower -- compute the errors of the equivalent power series +.ih +SYNOPSIS +cvepower (cv, y, weight, yfit, npts, chisqr, errors) + +.nf +pointer cv # curve descriptor +real y[] # array of y data points +weight weight[] # array of weights +real yfit[] # array of fitted data points +int npts # number of points +real chisqr # the standard deviation of the fit +real errors[] # standard deviations of the power series coefficients +.fi +.ih +ARGUMENTS +.ls cv +Pointer to the curve descriptor structure +.le +.ls y +Array of y data points +.le +.ls yfit +Array of fitted y values +.le +.ls npts +The number of points +.le +.ls chisqr +Reduced chi-squared of the fit. +.le +.ls errors +Array of standard deviations of the equivalent power series coefficients. +.le +.ih +DESCRIPTION +Calculate the reduced chi-squared of the fit and the standard deviation +of the equivalent power series coefficients for fitted Legendre and +Chebyshev polynomials. The errors are rescaled to the equivalent power +series and to the original data range. +.ih +NOTES +The standard deviation of the fit is the square root of the sum of the +weighted squares of the residuals divided by the number of degrees of freedom. +If the weights are equal, then the reduced chi-squared is the +variance of the fit +The error of the j-th coefficient is the square root of the j-th diagonal +element of the inverse of the data matrix. If the weights are equal to one, +then the errors are scaled by the square root of the variance of the data. +.ih +SEE ALSO +.endhelp diff --git a/math/curfit/doc/cverrors.hlp b/math/curfit/doc/cverrors.hlp new file mode 100644 index 00000000..a0a0fbb2 --- /dev/null +++ b/math/curfit/doc/cverrors.hlp @@ -0,0 +1,53 @@ +.help cverrors Jun84 "Curfit Package" +.ih +NAME +cverrors -- calculate the standard deviation of the fit and errors +.ih +SYNOPSIS +cverrors (cv, y, weight, yfit, npts, chisqr, errors) + +.nf +pointer cv # curve descriptor +real y[] # array of y data points +weight weight[] # array of weights +real yfit[] # array of fitted data points +int npts # number of points +real chisqr # the standard deviation of the fit +real errors[] # standard deviations of the coefficients +.fi +.ih +ARGUMENTS +.ls cv +Pointer to the curve descriptor structure +.le +.ls y +Array of y data points +.le +.ls yfit +Array of fitted y values +.le +.ls npts +The number of points +.le +.ls chisqr +Reduced chi-squared of the fit. +.le +.ls errors +Array of standard deviations of the coefficients. +.le +.ih +DESCRIPTION +Calculate the reduced chi-squared of the fit and the standard deviation +of the coefficients. +.ih +NOTES +The standard deviation of the fit is the square root of the sum of the +weighted squares of the residuals divided by the number of degrees of freedom. +If the weights are equal, then the reduced chi-squared is the +variance of the fit +The error of the j-th coefficient is the square root of the j-th diagonal +element of the inverse of the data matrix. If the weights are equal to one, +then the errors are scaled by the square root of the variance of the data. +.ih +SEE ALSO +.endhelp diff --git a/math/curfit/doc/cveval.hlp b/math/curfit/doc/cveval.hlp new file mode 100644 index 00000000..48cd7f10 --- /dev/null +++ b/math/curfit/doc/cveval.hlp @@ -0,0 +1,33 @@ +.help cveval Jun84 "Curfit Package" +.ih +NAME +cveval -- evaluate the fitted function at a single x value +.ih +SYNOPSIS +y = cveval (cv, x) + +.nf +pointer cv # curve descriptor +real x # x value +.fi +.ih +ARGUMENTS +.ls cv +Pointer to the curve descriptor structure. +.le +.ls x +X value at which the curve is to be evaluated. +.le +.ih +DESCRIPTION +Evaluate the curve at the specified value of x. CVEVAL is a real +function which returns the fitted y value. +.ih +NOTES +It uses the coefficient array stored in the curve descriptor structure. +The x values are assumed to lie in the region xmin <= x <= xmax. Checking +for out of bounds x values is the responsibility of the user. +.ih +SEE ALSO +cvvector +.endhelp diff --git a/math/curfit/doc/cvfit.hlp b/math/curfit/doc/cvfit.hlp new file mode 100644 index 00000000..cb6beb24 --- /dev/null +++ b/math/curfit/doc/cvfit.hlp @@ -0,0 +1,62 @@ +.help cvfit Jun84 "Curfit Package" +.ih +NAME +cvfit -- fit a curve to a set of data values +.ih +SYNOPSIS +cvfit (cv, x, y, weight, npts, wtflag, ier) + +.nf +pointer cv # curve descriptor +real x[] # array of x values +real y[] # array of y values +real weight[] # array of weights +int npts # number of data points +int wtflag # type of weighting +int ier # error code +.fi +.ih +ARGUMENTS +.ls cv +Pointer to the curve descriptor structure. +.le +.ls x +Array of x values. +.le +.ls y +Array of y values +.le +.ls weight +Array of weights +.le +.ls wtflag +Type of weighting. The options are WTS_USER, WTS_SPACING and +WTS_UNIFORM. If wtflag = WTS_USER individual weights for each data point +are supplied by the calling program and points with zero-valued weights are +not included in the fit. If wtflag = WTS_UNIFORM, all weights are assigned +values of 1. If wtflag = WTS_SPACING, the weights are set equal to the +difference between adjacent data points. In order to correctly use the +WTS_SPACING option the data must be sorted in x. +.le +.ls ier +Error code for the fit. The options are OK, SINGULAR and +NO_DEG_FREEDON. If ier = SINGULAR, the numerical routines will compute a +solution but one or more of the coefficients will be +zero. If ier = NO_DEG_FREEDOM, there were too few data points to solve the +matrix equations and the routine returns without fitting the data. +.le +.ih +DESCRIPTION +CVFIT zeroes the matrix and vectors, calculates the non-zero basis functions, +calculates the contribution +of each data point to the normal equations and accumulates it into the +appropriate array and vector elements. The Cholesky factorization of the +data array is computed and the coefficients of the fitting function are +calculated. +.ih +NOTES +Checking for out of bounds x values is the responsibility of the user. +.ih +SEE ALSO +cvrefit, cvaccum, cvsolve, cvchofac, cvcholsv +.endhelp diff --git a/math/curfit/doc/cvfree.hlp b/math/curfit/doc/cvfree.hlp new file mode 100644 index 00000000..c486b306 --- /dev/null +++ b/math/curfit/doc/cvfree.hlp @@ -0,0 +1,26 @@ +.help cvfree Jun84 "Curfit Package" +.ih +NAME +cvfree -- free the curve descriptor structure +.ih +SYNOPSIS +cvfree (cv) + +.nf +pointer cv # curve descriptor +.fi +.ih +ARGUMENTS +.ls cv +Pointer to the curve descriptor structure. +.le +.ih +DESCRIPTION +Frees the curve descriptor structure. +.ih +NOTES +CVFREE should be called after each curve fit. +.ih +SEE ALSO +cvinit +.endhelp diff --git a/math/curfit/doc/cvinit.hlp b/math/curfit/doc/cvinit.hlp new file mode 100644 index 00000000..dc891ed2 --- /dev/null +++ b/math/curfit/doc/cvinit.hlp @@ -0,0 +1,55 @@ +.help cvinit Jun84 "Curfit Package" +.ih +NAME +cvinit -- initialise curve descriptor +.ih +SYNOPSIS +include <math/curfit.h> + +cvinit (cv, curve_type, order, xmin, xmax) + +.nf +pointer cv # curve descriptor +int curve_type # the fitting function +int order # order of the fit +real xmin # minimum x value +real xmax # maximum x value +.fi +.ih +ARGUMENTS +.ls cv +Pointer to the curve descriptor structure. +.le +.ls curve_type +Fitting function. +Permitted values are LEGENDRE and CHEBYSHEV, for Legendre and +Chebyshev polynomials and SPLINE3 and SPLINE1 for a cubic spline +and linear spline with uniformly spaced +break points. +.le +.ls order +Order of the polynomial to be fit or the number of polynomial pieces +to be fit by a cubic spline. Order must be greater than or equal to one. +If curve_type is set to LEGENDRE or CHEBYSHEV and order equals one, a constant +term is fit to the data. +.le +.ls xmax, xmin +Minimum and maximum x values. All x values of interest +including the data x values and the x values of any curve to be evaluated +must fall in the range xmin <= x <= xmax. Checking for out of bounds x +values is the responsibility of user. +.le +.ih +DESCRIPTION +Allocate space for the curve descriptor structure and the arrays and +vectors used by the numerical routines. Initialize all arrays and vectors +to zero. Return the +curve descriptor to the calling routine. +.ih +NOTES +CVINIT must be the first CURFIT routine called. CVINIT returns if an +illegal curve type is requested. +.ih +SEE ALSO +cvfree +.endhelp diff --git a/math/curfit/doc/cvpower.hlp b/math/curfit/doc/cvpower.hlp new file mode 100644 index 00000000..386558ce --- /dev/null +++ b/math/curfit/doc/cvpower.hlp @@ -0,0 +1,40 @@ +.help cvpower Jan86 "Curfit Package" +.ih +NAME +cvpower -- convert coefficients to power series coefficients. +.ih +SYNOPSIS +.nf +include <math/curfit.h> +include "curfitdef.h" + +cvpower (cv, ps_coeff, ncoeff) + +pointer cv # Curve descriptor +real ps_coeff[ncoeff] # Power series coefficients +int ncoeff # Number of coefficients in fit +.fi +.ih +ARGUMENTS +.ls cv +Pointer to the curve descriptor structure. +.le +.ls ps_coeff +The output array of power series coefficients. +.le +.ls ncoeff +The output number of coefficients in the fit. +.le +.ih +DESCRIPTION +This routine routines the equivlalent power series fit coefficients +and the number of coefficients. + +The coefficients of either a legendre or chebyshev solution can be converted +to power series coefficients of the form y = a0 + a1*x + a2*x**2 + a3*x**3... +The output coefficients are scaled to the original data range. +.ih +NOTES +Only legendre and chebyshev coefficients are converted. An error is +reported for other curve types. +.endhelp diff --git a/math/curfit/doc/cvrefit.hlp b/math/curfit/doc/cvrefit.hlp new file mode 100644 index 00000000..4612b4c6 --- /dev/null +++ b/math/curfit/doc/cvrefit.hlp @@ -0,0 +1,52 @@ +.help cvrefit Jun84 "Curfit Package" +.ih +NAME +cvrefit -- refit new y vector using old x vector and weights +.ih +SYNOPSIS +cvrefit (cv, x, y, w, ier) + +.nf +pointer cv # curve descriptor +real x[] # array of x values +real y[] # array of y values +real weight[] # array of weights +int ier # error code +.fi +.ih +ARGUMENTS +.ls cv +Pointer to the curve descriptor +.le +.ls x +Array of x values. +.le +.ls y +Array of y values. +.le +.ls weight +Array of weights. +.le +.ls ier +Error code. The options are OK, SINGULAR and NO_DEG_FREEDOM. If ier equals +singular a solution is computed but one or more of the coefficients may +be zero. If ier equals NO_DEG_FREEDOM, there are insufficient data points +to compute a solution and CVREFIT returns without solving for the coefficients. +.le +.ih +DESCRIPTION +In some application the x and weight values remain unchanged from fit to fit +and only the y values vary. In this case it is redundant to reaccumulate +the matrix and perform the Cholesky factorization. CVREFIT zeros and +reaccumulates the vector on the right hand side of the matrix equation +and performs the forward and back substitution phase to fit for a new +coefficient vector. +.ih +NOTES +In the first call to CVREFIT space is allocated for the non-zero basis +functions. Subsequent call to CVREFIT reference this array to avoid +recaculating basis functions at every call. +.ih +SEE ALSO +cvfit, cvaccum, cvsolve, cvchoslv +.endhelp diff --git a/math/curfit/doc/cvreject.hlp b/math/curfit/doc/cvreject.hlp new file mode 100644 index 00000000..52e5ca4f --- /dev/null +++ b/math/curfit/doc/cvreject.hlp @@ -0,0 +1,41 @@ +.help cvreject June84 "Curfit Package" +.ih +NAME +cvreject -- reject a single data point from the data set to be fit +.ih +SYNOPSIS +cvreject (cv, x, y, weight) + +.nf +pointer cv # curve descriptor +real x # x value +real y # y value +real weight # weight value +.fi +.ih +ARGUMENTS +.ls cv +Pointer to the curve descriptor structure. +.le +.ls x +X value. +.le +.ls y +Y value. +.le +.ls weight +The weight value. +.le +.ih +DESCRIPTION +CVREJECT removes an individul data point from the data set. +The non-zero basis functions for each x are calculated. The contribution +of each x to the normal equations is computed and subtracted from the +appropriate arrays and vectors. +An array of points can be removed from the fit by repeated calls to CVREJECT +followed by a single call to CVSOLVE to calculate a new set of coefficients. +.ih +NOTES +.ih +SEE ALSO +.endhelp diff --git a/math/curfit/doc/cvrestore.hlp b/math/curfit/doc/cvrestore.hlp new file mode 100644 index 00000000..84d352ee --- /dev/null +++ b/math/curfit/doc/cvrestore.hlp @@ -0,0 +1,32 @@ +.help cvrestore Aug84 "Curfit Package" +.ih +NAME +cvrestore -- restore fit parameters +.ih +SYNOPSIS +cvrestore (cv, fit) + +.nf +pointer cv # pointer to curve descriptor +real fit[] # array containing curve parameters +.fi +.ih +ARGUMENTS +.ls cv +Pointer to curve descriptor structure. Returned by CVRESTORE. +.le +.ls fit +Array containing the curve parameters. Must have at least 7 + order +elements, where order is the parameter set in CVINIT. +.le +.ih +DESCRIPTION +CVRESTORE returns oldcv the pointer to the curve descriptor and +stores the curve parameters in fit in the structure ready for +use by cveval or cvvector. +.ih +NOTES +.ih +SEE ALSO +cvsave +.endhelp diff --git a/math/curfit/doc/cvsave.hlp b/math/curfit/doc/cvsave.hlp new file mode 100644 index 00000000..144beaff --- /dev/null +++ b/math/curfit/doc/cvsave.hlp @@ -0,0 +1,35 @@ +.help cvsave Aug84 "Curfit Package" +.ih +NAME +cvsave -- save parameters of fit +.ih +SYNOPSIS +call cvsave (cv, fit) + +.nf +pointer cv # curve descriptor +real fit[] # array containing the fit parameters +.fi +.ih +ARGUMENTS +.ls cv +The pointer to the curve descriptor structure. +.le +.ls fit +Array containing the fit parameters. +Fit must contain at least 7 + order elements, where order is the order of the +fit as set in CVINIT. +.le +.ih +DESCRIPTION +CVSAVE saves the curve parameters in the real array fit. +The first four elements of fit contain the curve_type, order, xmin and xmax. +The coefficients are stored in the remaining array elements. +.ih +NOTES +CVSAVE does not preserve the matrices and vectors used by the fitting +routines. +.ih +SEE ALSO +cvrestore +.endhelp diff --git a/math/curfit/doc/cvset.hlp b/math/curfit/doc/cvset.hlp new file mode 100644 index 00000000..5eb79f30 --- /dev/null +++ b/math/curfit/doc/cvset.hlp @@ -0,0 +1,56 @@ +.help cvset Nov84 "Curfit Package" +.ih +NAME +cvset -- input fit parameters derived external to CURFIT +.ih +SYNOPSIS +include <math/curfit.h> + +cvset (cv, curve_type, xmin, xmax, coeff, ncoeff) + +.nf +pointer cv # pointer to curve descriptor +int curve_type # functional form of the curve to be fitted +real xmin, xmax # minimum and maximum x values +real coeff[ncoeff] # coefficient array +int ncoeff # number of coefficients +.fi +.ih +ARGUMENTS +.ls cv +Pointer to curve descriptor structure. Returned by CVSET. +.le +.ls curve_type +Type of curve to be input. Must be one of LEGENDRE, CHEBYSHEV, SPLINE3 +or SPLINE1. +.le +.ls xmin, xmax +The minimum and maximum data or fitted x values. The Legendre and +Chebyshev polynomials are assumed to be normalized over this range. +For the cubic and linear spline functions, the data range (xmax - xmin) is +divided into (ncoeff - 3) and (ncoeff - 1) evenly spaced polynomial pieces +respectively. +.le +.ls coeff +Array containing the coefficients. Must have at least 7 + order +elements, where order has the same meaning as the order parameter set in CVINIT. +.le +.ls ncoeff +The number of coefficients. For polynomial functions, ncoeff +equals 1 plus the order of the polynomial, e.g. a second order +polynomial curve will have three coefficients. For the cubic +and linear spline the number of polynomial pieces fit are +(ncoeff - 3) and (ncoeff - 1) respectively. +.le +.ih +DESCRIPTION +CVSET returns cv the pointer to the curve descriptor and +stores the curve parameters in the CURFIT structure ready for +use by CVEVAL or CVVECTOR. +.ih +NOTES +The splines are assumed to have been fit in the least squares sense. +.ih +SEE ALSO +cvsave +.endhelp diff --git a/math/curfit/doc/cvsolve.hlp b/math/curfit/doc/cvsolve.hlp new file mode 100644 index 00000000..16badae2 --- /dev/null +++ b/math/curfit/doc/cvsolve.hlp @@ -0,0 +1,39 @@ +.help cvsolve Jun84 "Curfit Package" +.ih +NAME +cvsolve -- solve a linear system of eqns by the Cholesky method +.ih +SYNOPSIS +cvsolve (cv, ier) + +.nf +pointer cv # curve descriptor +int ier # error code +.fi +.ih +ARGUMENTS +.ls cv +Pointer to the curve descriptor +.le +.ls ier +Error code returned by the fitting routines. The options are +OK, SINGULAR and NO_DEG_FREEDOM. If ier is SINGULAR the matrix is singular, +CVSOLVE will compute a solution to the normal equationsbut one or more of the +coefficients will be zero. +If ier equals NO_DEG_FREEDOM, too few data points exist for a reasonable +solution to be computed. CVSOLVE returns +without fitting the data. +.le +.ih +DESCRIPTION +CVSOLVE call two routines CVCHOFAC and CVCHOSLV. CVCHOFAC computes the +Cholesky factorization of the data matrix. CVCHOSLV solves for the +coefficients of the fitting function by forward and back substitution. +An error code is returned by CVSOLVE if it is unable to solve the normal +equations as formulated. +.ih +NOTES +.ih +SEE ALSO +cvchofac, cvchoslv +.endhelp diff --git a/math/curfit/doc/cvstati.hlp b/math/curfit/doc/cvstati.hlp new file mode 100644 index 00000000..ffd05d0a --- /dev/null +++ b/math/curfit/doc/cvstati.hlp @@ -0,0 +1,47 @@ +.help cvstati May85 "Curfit Package" +.ih +NAME +cvstati -- get integer parameter +.ih +SYNOPSIS +include <math/curfit.h> + +ival = cvstati (cv, parameter) + +.nf +pointer cv # curve descriptor +int parameter # parameter to be returned +.fi +.ih +ARGUMENTS +.ls cv +The pointer to the curve descriptor structure. +.le +.ls parameter +Parameter to be return. Definitions in curfit.h are: +.nf + define CVTYPE 1 # curve type + define CVORDER 2 # order + define CVNCOEFF 3 # number of coefficients + define CVNSAVE 4 # length of save buffer +.fi +.le +.ih +DESCRIPTION +The values of integer parameters are returned. The parameters include +the curve type, the order, the number of coefficients, and the length +of the buffer required by CVSAVE (which is of TY_REAL). +.ih +EXAMPLES +.nf + include <curfit.h> + + int cvstati() + + call malloc (buf, cvstati (cv, CVNSAVE), TY_REAL) + call cvsave (cv, Memr[buf]) +.fi +.ih +SEE ALSO +cvstatr +.endhelp diff --git a/math/curfit/doc/cvstatr.hlp b/math/curfit/doc/cvstatr.hlp new file mode 100644 index 00000000..f4d959c2 --- /dev/null +++ b/math/curfit/doc/cvstatr.hlp @@ -0,0 +1,44 @@ +.help cvstatr May85 "Curfit Package" +.ih +NAME +cvstatr -- get real parameter +.ih +SYNOPSIS +include <math/curfit.h> + +rval = cvstatr (cv, parameter) + +.nf +pointer cv # curve descriptor +int parameter # parameter to be returned +.fi +.ih +ARGUMENTS +.ls cv +The pointer to the curve descriptor structure. +.le +.ls parameter +Parameter to be return. Definitions in curfit.h are: +.nf + define CVXMIN 5 # minimum ordinate + define CVORDER 6 # maximum ordinate +.fi +.le +.ih +DESCRIPTION +The values of real parameters are returned. The parameters include +the minimum and maximum ordinate values of the curve. +.ih +EXAMPLES +.nf + include <curfit.h> + + real cvstatr() + + xmin = cvstatr (cv, CVXMIN) + xmax = cvstatr (cv, CVXMAX) +.fi +.ih +SEE ALSO +cvstati +.endhelp diff --git a/math/curfit/doc/cvvector.hlp b/math/curfit/doc/cvvector.hlp new file mode 100644 index 00000000..79c0282f --- /dev/null +++ b/math/curfit/doc/cvvector.hlp @@ -0,0 +1,41 @@ +.help cvvector Jun84 "Curfit Package" +.ih +NAME +cvvector -- evaluate the fitted curve at a set of points +.ih +SYNOPSIS +cvvector (cv, x, yfit, npts) + +.nf +pointer cv # curve descriptor +real x[] # x array +real yfit[] # array of fitted y values +int npts # number of x values +.fi +.ih +ARGUMENTS +.ls cv +Pointer to the curve descriptor structure. +.le +.ls x +Array of x values +.le +.ls yfit +Array of fitted y values +.le +.ls npts +The number of x values at which the curve is to be evaluated. +.le +.ih +DESCRIPTION +Fit the curve to an array of data points. CVVECTOR uses the coefficients +stored in the curve descriptor structure. +.ih +NOTES +The x values are assumed to lie +in the region xmin <= x <= xmax. Checking for out of bounds x values is the +responsibility of the user. +.ih +SEE ALSO +cveval +.endhelp diff --git a/math/curfit/doc/cvzero.hlp b/math/curfit/doc/cvzero.hlp new file mode 100644 index 00000000..7f9e07e2 --- /dev/null +++ b/math/curfit/doc/cvzero.hlp @@ -0,0 +1,26 @@ +.help cvzero Aug84 "Curfit Package" +.ih +NAME +cvzero -- set up for a new curve fit +.ih +SYNOPSIS +cvzero (cv) + +.nf +pointer cv # curve descriptor +.fi +.ih +ARGUMENTS +.ls cv +Pointer to the curve descriptor structure. +.le +.ih +DESCRIPTION +CVZERO zeros the matrix and right side of the matrix equation. +.ih +NOTES +CVZERO can be used to reinitialize the matrix and right side of the matrix +equation to begin a new fit in accumulate mode. +.ih +SEE ALSO +cvfit, cvinit |