Procedures

Constructor for bspline_1d

Constructor for a bspline_1d type (auto knots). This is a wrapper for initialize_1d_auto_knots.

It returns an empty bspline_1d type. Note that INITIALIZE still needs to be called before it can be used. Not really that useful except perhaps in some OpenMP applications.

Constructor for a bspline_1d type (user-specified knots). This is a wrapper for initialize_1d_specify_knots.

Constructor for bspline_2d

Constructor for a bspline_2d type (auto knots). This is a wrapper for initialize_2d_auto_knots.

It returns an empty bspline_2d type. Note that INITIALIZE still needs to be called before it can be used. Not really that useful except perhaps in some OpenMP applications.

Constructor for a bspline_2d type (user-specified knots). This is a wrapper for initialize_2d_specify_knots.

Constructor for bspline_3d

Constructor for a bspline_3d type (auto knots). This is a wrapper for initialize_3d_auto_knots.

It returns an empty bspline_3d type. Note that INITIALIZE still needs to be called before it can be used. Not really that useful except perhaps in some OpenMP applications.

Constructor for a bspline_3d type (user-specified knots). This is a wrapper for initialize_3d_specify_knots.

Constructor for bspline_4d

Constructor for a bspline_4d type (auto knots). This is a wrapper for initialize_4d_auto_knots.

It returns an empty bspline_4d type. Note that INITIALIZE still needs to be called before it can be used. Not really that useful except perhaps in some OpenMP applications.

Constructor for a bspline_4d type (user-specified knots). This is a wrapper for initialize_4d_specify_knots.

Constructor for bspline_5d

Constructor for a bspline_5d type (auto knots). This is a wrapper for initialize_5d_auto_knots.

It returns an empty bspline_5d type. Note that INITIALIZE still needs to be called before it can be used. Not really that useful except perhaps in some OpenMP applications.

Constructor for a bspline_5d type (user-specified knots). This is a wrapper for initialize_5d_specify_knots.

Constructor for bspline_6d

Constructor for a bspline_6d type (auto knots). This is a wrapper for initialize_6d_auto_knots.

It returns an empty bspline_6d type. Note that INITIALIZE still needs to be called before it can be used. Not really that useful except perhaps in some OpenMP applications.

Constructor for a bspline_6d type (user-specified knots). This is a wrapper for initialize_6d_specify_knots.

Check the validity of the inputs to the db*ink routines. Prints warning message if there is an error, and also sets iflag and status_ok.

Error checks for the user-specified knot vector sizes.

Checks if the value is withing the range of the knot vectors. This is called by the various db*val routines.

This sets the iflag variable in the class to 0 (which indicates that everything is OK). It can be used after an error is encountered.

dasum takes the sum of the absolute values.

DAXPY constant times a vector plus a vector. uses unrolled loops for increments equal to one.

Computes the integral on (x1,x2) of a product of a function fun and the idx-th derivative of a kx-th order b-spline, using the b-representation (tx,bcoef,nx,kx), with an adaptive 8-point Legendre-Gauss algorithm. (x1,x2) must be a subinterval of t(kx) <= x <= t(nx+1).

1D initialization routines.

Alternate version of db1ink_default, where the boundary conditions can be specified.

Alternate version of db1ink_alt, where the first and last 3 knots are specified by the user.

Determines the parameters of a function that interpolates the one-dimensional gridded data $$[x(i),\mathrm{fcn}(i)] ~\mathrm{for}~ i=1,..,n_x$$ The interpolating function and its derivatives may subsequently be evaluated by the function db1val.

Computes the integral on (x1,x2) of a kx-th order b-spline. Orders kx as high as 20 are permitted by applying a 2, 6, or 10 point gauss formula on subintervals of (x1,x2) which are formed by included (distinct) knots.

1D evaluation routines.

Alternate version of db1val_default for use with db1ink_alt and db1ink_alt_2.

Evaluates the tensor product piecewise polynomial interpolant constructed by the routine db1ink or one of its derivatives at the point xval.

Determines the parameters of a function that interpolates the two-dimensional gridded data $$[x(i),y(j),\mathrm{fcn}(i,j)] ~\mathrm{for}~ i=1,..,n_x ~\mathrm{and}~ j=1,..,n_y$$ The interpolating function and its derivatives may subsequently be evaluated by the function db2val.

Evaluates the tensor product piecewise polynomial interpolant constructed by the routine db2ink or one of its derivatives at the point (xval,yval).

Determines the parameters of a function that interpolates the three-dimensional gridded data $$[x(i),y(j),z(k),\mathrm{fcn}(i,j,k)] ~\mathrm{for}~ i=1,..,n_x ~\mathrm{and}~ j=1,..,n_y, ~\mathrm{and}~ k=1,..,n_z$$ The interpolating function and its derivatives may subsequently be evaluated by the function db3val.

Evaluates the tensor product piecewise polynomial interpolant constructed by the routine db3ink or one of its derivatives at the point (xval,yval,zval).

Determines the parameters of a function that interpolates the four-dimensional gridded data $$[x(i),y(j),z(k),q(l),\mathrm{fcn}(i,j,k,l)] ~\mathrm{for}~ i=1,..,n_x ~\mathrm{and}~ j=1,..,n_y, ~\mathrm{and}~ k=1,..,n_z, ~\mathrm{and}~ l=1,..,n_q$$ The interpolating function and its derivatives may subsequently be evaluated by the function db4val.

Evaluates the tensor product piecewise polynomial interpolant constructed by the routine db4ink or one of its derivatives at the point (xval,yval,zval,qval).

Determines the parameters of a function that interpolates the five-dimensional gridded data:

Evaluates the tensor product piecewise polynomial interpolant constructed by the routine db5ink or one of its derivatives at the point (xval,yval,zval,qval,rval).

Determines the parameters of a function that interpolates the six-dimensional gridded data:

Evaluates the tensor product piecewise polynomial interpolant constructed by the routine db6ink or one of its derivatives at the point (xval,yval,zval,qval,rval,sval).

dbfqad computes the integral on (x1,x2) of a product of a function f and the id-th derivative of a k-th order b-spline, using the b-representation (t,bcoef,n,k). (x1,x2) must be a subinterval of t(k) <= x <= t(n+1). an integration routine, dbsgq8 (a modification of gaus8), integrates the product on subintervals of (x1,x2) formed by included (distinct) knots

DBINT4 computes the B representation (t,bcoef,n,k) of a cubic spline (k=4) which interpolates data (x(i),y(i)),i=1,ndata.

dbintk produces the b-spline coefficients, bcoef, of the b-spline of order k with knots t(i), i=1,...,n+k, which takes on the value y(i) at x(i), i=1,...,n. the spline or any of its derivatives can be evaluated by calls to dbvalu.

dbknot chooses a knot sequence for interpolation of order k at the data points x(i), i=1,..,n. the n+k knots are placed in the array t. k knots are placed at each endpoint and not-a-knot end conditions are used. the remaining knots are placed at data points if n is even and between data points if n is odd. the rightmost knot is shifted slightly to the right to insure proper interpolation at x(n) (see page 350 of the reference).

These subroutines solve the least squares problem Ax = b for banded matrices A using sequential accumulation of rows of the data matrix. Exactly one right-hand side vector is permitted.

These subroutines solve the least squares problem Ax = b for banded matrices A using sequential accumulation of rows of the data matrix. Exactly one right-hand side vector is permitted.

Returns in w the LU-factorization (without pivoting) of the banded matrix a of order nrow with (nbandl + 1 + nbandu) bands or diagonals in the work array w .

Companion routine to dbnfac. it returns the solution x of the linear system a*x = b in place of b, given the lu-factorization for a in the work array w from dbnfac.

DBSGQ8, a modification of gaus8, integrates the product of fun(x) by the id-th derivative of a spline dbvalu between limits a and b using an adaptive 8-point Legendre-Gauss algorithm.

DBSPVD calculates the value and all derivatives of order less than nderiv of all basis functions which do not (possibly) vanish at x. ileft is input such that t(ileft) <= x < t(ileft+1). A call to dintrv(t,n+1,x, ilo,ileft,mflag) will produce the proper ileft. The output of dbspvd is a matrix vnikx(i,j) of dimension at least (k,nderiv) whose columns contain the k nonzero basis functions and their nderiv-1 right derivatives at x, i=1,k, j=1,nderiv. These basis functions have indices ileft-k+i, i=1,k, k <= ileft <= n. The nonzero part of the i-th basis function lies in (t(i),t(i+k)), i=1,n).

Calculates the value of all (possibly) nonzero basis functions at x of order max(jhigh,(j+1)*(index-1)), where t(k) <= x <= t(n+1) and j=iwork is set inside the routine on the first call when index=1. ileft is such that t(ileft) <= x < t(ileft+1). a call to dintrv(t,n+1,x,ilo,ileft,mflag) produces the proper ileft. dbspvn calculates using the basic algorithm needed in dbspvd. if only basis functions are desired, setting jhigh=k and index=1 can be faster than calling dbspvd, but extra coding is required for derivatives (index=2) and dbspvd is set up for this purpose.

DBSQAD computes the integral on (x1,x2) of a k-th order b-spline using the b-representation (t,bcoef,n,k). orders k as high as 20 are permitted by applying a 2, 6, or 10 point gauss formula on subintervals of (x1,x2) which are formed by included (distinct) knots.

dbtpcf computes b-spline interpolation coefficients for nf sets of data stored in the columns of the array fcn. the b-spline coefficients are stored in the rows of bcoef however. each interpolation is based on the n abcissa stored in the array x, and the n+k knots stored in the array t. the order of each interpolation is k.

Evaluates the b-representation (t,a,n,k) of a b-spline at x for the function value on ideriv=0 or any of its derivatives on ideriv=1,2,...,k-1. right limiting values (right derivatives) are returned except at the right end point x=t(n+1) where left limiting values are computed. the spline is defined on t(k) $\le$ x $\le$ t(n+1). dbvalu returns a fatal error message when x is outside of this interval.

DCOPY copies a vector, x, to a vector, y. uses unrolled loops for increments equal to 1.

dcv is a companion function subprogram for dfc. The documentation for dfc has complete usage instructions.

ddot forms the dot product of two vectors. uses unrolled loops for increments equal to one.

This subprogram fits a piecewise polynomial curve to discrete data. The piecewise polynomials are represented as B-splines. The fitting is done in a weighted least squares sense.

This is a companion subprogram to DEFC. This subprogram does weighted least squares fitting of data by B-spline curves. The documentation for DEFC has complete usage instructions.

Destructor for bspline_1d class.

Destructor for bspline_2d class.

Destructor for bspline_3d class.

Destructor for bspline_4d class.

Destructor for bspline_5d class.

Destructor for bspline_6d class.

Destructor for contents of the base bspline_class class. (this routine is called by the extended classes).

This subprogram fits a piecewise polynomial curve to discrete data. The piecewise polynomials are represented as B-splines. The fitting is done in a weighted least squares sense. Equality and inequality constraints can be imposed on the fitted curve.

This is a companion subprogram to DFC. The documentation for DFC has complete usage instructions.

Calculates value and derivs of all B-splines which do not vanish at X

Calculates the value of all possibly nonzero B-splines at X of order MAX(JHIGH,(J+1)(INDEX-1)) on T.

Construction and/or application of a single Householder transformation. Q = I + U*(U**T)/B

Solve a least squares problem for banded matrices using sequential accumulation of rows of the data matrix. Exactly one right-hand side vector is permitted.

Computes the largest integer ileft in 1 $\le$ ileft $\le$ lxt such that xt(ileft) $\le$ x where xt(*) is a subdivision of the x interval. precisely,

Determine an N1-vector W, and an N2-vector Z which minimizes the Euclidean length of W subject to GW+HZ >= Y. This is the least projected distance problem, LPDP. The matrices G and H are of respective dimensions M by N1 and M by N2.

This subprogram solves a linearly constrained least squares problem with both equality and inequality constraints, and, if the user requests, obtains a covariance matrix of the solution parameters.

This is a companion subprogram to DLSEI. The documentation for DLSEI has complete usage instructions.

returns the euclidean norm of a vector

apply the modified givens transformation, H, to the 2 by n matrix

construct the modified givens transformation matrix H

DSCAL scales a vector by a constant. uses unrolled loops for increment equal to 1.

Sort an array and optionally make the same interchanges in an auxiliary array. The array may be sorted in increasing or decreasing order.

DSWAP interchanges two vectors. uses unrolled loops for increments equal to 1.

This is a companion subprogram to DWNNLS. The documentation for DWNNLS has complete usage instructions.

This is a companion subprogram to DWNNLS. The documentation for DWNNLS has complete usage instructions.

To update the column Sum Of Squares and find the pivot column. The column Sum of Squares Vector will be updated at each step. When numerically necessary, these values will be recomputed.

To test independence of incoming column.

Perform column interchange. Exchange elements of permuted index vector and perform column interchanges.

This subprogram solves a linearly constrained least squares problem. Suppose there are given matrices E and A of respective dimensions ME by N and MA by N, and vectors F and B of respective lengths ME and MA. This subroutine solves the problem

Evaluate a bspline_1d interpolate. This is a wrapper for db1val.

Evaluate a bspline_2d interpolate. This is a wrapper for db2val.

Evaluate a bspline_3d interpolate. This is a wrapper for db3val.

Evaluate a bspline_4d interpolate. This is a wrapper for db4val.

Evaluate a bspline_5d interpolate. This is a wrapper for db5val.

Evaluate a bspline_6d interpolate. This is a wrapper for db6val.

Finalizer for bspline_1d class. Just a wrapper for destroy_1d.

Finalizer for bspline_2d class. Just a wrapper for destroy_2d.

Finalizer for bspline_3d class. Just a wrapper for destroy_3d.

Finalizer for bspline_4d class. Just a wrapper for destroy_4d.

Finalizer for bspline_5d class. Just a wrapper for destroy_5d.

Finalizer for bspline_6d class. Just a wrapper for destroy_6d.

Evaluate a bspline_1d definite integral. This is a wrapper for db1fqad.

Get the status message from a bspline_class routine call.

Returns a message string associated with the status code.

Returns the value of x to use for computing the interval in t, depending on if extrapolation is allowed or not.

idamax finds the index of the first element having maximum absolute value.

Initialize a bspline_1d type (with automatically-computed knots). This is a wrapper for db1ink.

Initialize a bspline_1d type (with user-specified knots). This is a wrapper for db1ink.

Initialize a bspline_2d type (with automatically-computed knots). This is a wrapper for db2ink.

Initialize a bspline_2d type (with user-specified knots). This is a wrapper for db2ink.

Initialize a bspline_3d type (with automatically-computed knots). This is a wrapper for db3ink.

Initialize a bspline_3d type (with user-specified knots). This is a wrapper for db3ink.

Initialize a bspline_4d type (with automatically-computed knots). This is a wrapper for db4ink.

Initialize a bspline_4d type (with user-specified knots). This is a wrapper for db4ink.

Initialize a bspline_5d type (with automatically-computed knots). This is a wrapper for db5ink.

Initialize a bspline_5d type (with user-specified knots). This is a wrapper for db5ink.

Initialize a bspline_6d type (with automatically-computed knots). This is a wrapper for db6ink.

Initialize a bspline_6d type (with user-specified knots). This is a wrapper for db6ink.

Evaluate a bspline_1d definite integral. This is a wrapper for db1sqad.

Sets the extrap flag in the class.

Actual size of a bspline_1d structure in bits.

Actual size of a bspline_2d structure in bits.

Actual size of a bspline_3d structure in bits.

Actual size of a bspline_4d structure in bits.

Actual size of a bspline_5d structure in bits.

Actual size of a bspline_6d structure in bits.

Recursive quicksoft. Modified to also carry along a second array.

This routines returns true if the iflag code from the last routine called was =0. Maybe of the routines have output iflag variables, so they can be checked explicitly, or this routine can be used.