odrpack_core – odrpack

Core mathematical routines, except drivers, and BLAS/LINPACK.

Uses

- odrpack_kinds
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Graph Key

Nodes of different colours represent the following:

Solid arrows point from a submodule to the (sub)module which it is descended from. Dashed arrows point from a module or program unit to modules which it uses.
Where possible, edges connecting nodes are given different colours to make them easier to distinguish in large graphs.

Abstract Interfaces

abstract interface

public subroutine fcn_t(beta, xplusd, ifixb, ifixx, ideval, f, fjacb, fjacd, istop)

User-supplied subroutine for evaluating the model.

Arguments

Type	Intent		Name
real(kind=wp),	intent(in)	::	beta(:)	Current values of parameters.
real(kind=wp),	intent(in)	::	xplusd(:,:)	Current value of explanatory variable, i.e., `x + delta`. Shape: `(n, m)`.
integer,	intent(in)	::	ifixb(:)	Indicators for "fixing" parameters (`beta`).
integer,	intent(in)	::	ifixx(:,:)	Indicators for "fixing" explanatory variable (`x`). Shape: `(ldifx, m)`.
integer,	intent(in)	::	ideval	Indicator for selecting computation to be performed.
real(kind=wp),	intent(out)	::	f(:,:)	Predicted function values. Shape: `(n, q)`.
real(kind=wp),	intent(out)	::	fjacb(:,:,:)	Jacobian with respect to `beta`. Shape: `(n, np, q)`.
real(kind=wp),	intent(out)	::	fjacd(:,:,:)	Jacobian with respect to errors `delta`. Shape: `(n, m, q)`.
integer,	intent(out)	::	istop	Stopping condition, with meaning as follows. `0`: Current `beta` and `x + delta` were acceptable and values were computed successfully. `1`: Current `beta` and `x + delta` are not acceptable; 'odrpack' should select values closer to most recently used values if possible. `-1`: Current `beta` and `x + delta` are not acceptable; 'odrpack' should stop.

Functions

public pure function derstep(itype, k, betak, ssf, stpb, neta) result(res)

Compute step size for center and forward difference calculations.

Arguments

Type	Intent		Name
integer,	intent(in)	::	itype	Finite difference method being used. `0`: Forward finite differences. `1`: Central finite differences.
integer,	intent(in)	::	k	Index into `beta` where `betak` resides.
real(kind=wp),	intent(in)	::	betak	`k`-th function parameter.
real(kind=wp),	intent(in)	::	ssf(k)	Scale used for the `beta`s.
real(kind=wp),	intent(in)	::	stpb(k)	Relative step used for computing finite difference derivatives with respect to `beta`.
integer,	intent(in)	::	neta	Number of good digits in the function results.

Return Value real(kind=wp)

public pure function hstep(itype, neta, i, j, stp, ldstp) result(res)

Set relative step size for finite difference derivatives.

Arguments

Type	Intent		Name
integer,	intent(in)	::	itype	Finite difference method being used. `0`: Forward finite differences. `1`: Central finite differences.
integer,	intent(in)	::	neta	Number of good digits in the function results.
integer,	intent(in)	::	i	Identifier for selecting user-supplied step sizes.
integer,	intent(in)	::	j	Identifier for selecting user-supplied step sizes.
real(kind=wp),	intent(in)	::	stp(ldstp,j)	Step size for the finite difference derivative.
integer,	intent(in)	::	ldstp	Leading dimension of array `stp`.

Return Value real(kind=wp)

public pure function ppf_normal(p) result(res)

Compute the percent point function value for the normal (Gaussian) distribution with mean 0 and standard deviation 1, and with probability density function:

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=wp),	intent(in)			::	p	Probability at which the percent point is to be evaluated; `0 < p < 1`.

Return Value real(kind=wp)

public pure function ppf_tstudent(p, idf) result(res)

Compute the percent point function value for the student's T distribution with idf degrees of freedom.

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=wp),	intent(in)			::	p	Probability at which the percent point is to be evaluated; `0 < p < 1`.
integer,	intent(in)			::	idf	Degrees of freedom.

Return Value real(kind=wp)

Subroutines

public subroutine trust_region(n, m, np, q, npp, f, fjacb, fjacd, wd, ldwd, ld2wd, ss, tt, ldtt, delta, alpha2, tau, epsfcn, isodr, tfjacb, omega, u, qraux, jpvt, s, t, nlms, rcond, irank, wrk1, wrk2, wrk3, wrk4, wrk5, wrk, lwrk, istopc)

Compute Levenberg-Marquardt parameter and steps s and t using analog of the trust-region Levenberg-Marquardt algorithm.

Arguments

Type	Intent		Name
integer,	intent(in)	::	n	Number of observations.
integer,	intent(in)	::	m	Number of columns of data in the explanatory variable.
integer,	intent(in)	::	np	Number of function parameters.
integer,	intent(in)	::	q	Number of responses per observation.
integer,	intent(in)	::	npp	Number of function parameters being estimated.
real(kind=wp),	intent(in)	::	f(n,q)	Weighted estimated values of `epsilon`.
real(kind=wp),	intent(in)	::	fjacb(n,np,q)	Jacobian with respect to `beta`.
real(kind=wp),	intent(in)	::	fjacd(n,m,q)	Jacobian with respect to `delta`.
real(kind=wp),	intent(in)	::	wd(ldwd,ld2wd,m)	`delta` weights.
integer,	intent(in)	::	ldwd	Leading dimension of array `wd`.
integer,	intent(in)	::	ld2wd	Second dimension of array `wd`.
real(kind=wp),	intent(in)	::	ss(np)	Scaling values used for the unfixed `beta`s.
real(kind=wp),	intent(in)	::	tt(ldtt,m)	Scale used for the `delta`s.
integer,	intent(in)	::	ldtt	Leading dimension of array `tt`.
real(kind=wp),	intent(in)	::	delta(n,m)	Estimated errors in the explanatory variables.
real(kind=wp),	intent(inout)	::	alpha2	Current Levenberg-Marquardt parameter.
real(kind=wp),	intent(inout)	::	tau	Trust region diameter.
real(kind=wp),	intent(in)	::	epsfcn	Function's precision.
logical,	intent(in)	::	isodr	Variable designating whether the solution is by ODR (`.true.`) or by OLS (`.false.`).
real(kind=wp),	intent(out)	::	tfjacb(n,q,np)	Array `omega*fjacb`.
real(kind=wp),	intent(out)	::	omega(q,q)	Array `(I-fjacdinv(p)trans(fjacd))**(-1/2)`.
real(kind=wp),	intent(out)	::	u(np)	Approximate null vector for `tfjacb`.
real(kind=wp),	intent(out)	::	qraux(np)	Array required to recover the orthogonal part of the QR decomposition.
integer,	intent(out)	::	jpvt(np)	Pivot vector.
real(kind=wp),	intent(out)	::	s(np)	Step for `beta`.
real(kind=wp),	intent(out)	::	t(n,m)	Step for `delta`.
integer,	intent(out)	::	nlms	Number of Levenberg-Marquardt steps taken.
real(kind=wp),	intent(out)	::	rcond	Approximate reciprocal condition of `tfjacb`.
integer,	intent(out)	::	irank	Aank deficiency of the Jacobian wrt `beta`.
real(kind=wp),	intent(out)	::	wrk1(n,q,m)	Work array of `(n, q, m)` elements.
real(kind=wp),	intent(out)	::	wrk2(n,q)	Work array of `(n, q)` elements.
real(kind=wp),	intent(out)	::	wrk3(np)	Work array of `(np)` elements.
real(kind=wp),	intent(out)	::	wrk4(m,m)	Work array of `(m, m)` elements.
real(kind=wp),	intent(out)	::	wrk5(m)	Work array of `(m)` elements.
real(kind=wp),	intent(out)	::	wrk(lwrk)	Work array of `(lwrk)` elements, equivalenced to `wrk1` and `wrk2`.
integer,	intent(in)	::	lwrk	Length of vector `wrk`.
integer,	intent(out)	::	istopc	Variable designating whether the computations were stopped due to some other numerical error detected within subroutine `dodstp`.

public pure subroutine access_workspace(n, m, np, q, ldwe, ld2we, rwork, lrwork, iwork, liwork, access, isodr, jpvt, omega, u, qraux, sd, vcv, wrk1, wrk2, wrk3, wrk4, wrk5, wrk6, nnzw, npp, job, partol, sstol, maxit, taufac, eta, neta, lunrpt, ipr1, ipr2, ipr2f, ipr3, wss, rvar, idf, tau, alpha, niter, nfev, njev, int2, olmavg, rcond, irank, actrs, pnorm, prers, rnorms, istop)

Access or store values in the work arrays.

Arguments

Type	Intent		Name
integer,	intent(in)	::	n	Number of observations.
integer,	intent(in)	::	m	Number of columns of data in the explanatory variable.
integer,	intent(in)	::	np	Number of function parameters.
integer,	intent(in)	::	q	Number of responses per observation.
integer,	intent(in)	::	ldwe	Leading dimension of array `we`.
integer,	intent(in)	::	ld2we	Second dimension of array `we`.
real(kind=wp),	intent(inout)	::	rwork(lrwork)	Real work space.
integer,	intent(in)	::	lrwork	Length of vector `rwork`.
integer,	intent(inout)	::	iwork(liwork)	Integer work space.
integer,	intent(in)	::	liwork	Length of vector `iwork`.
logical,	intent(in)	::	access	Variable designating whether information is to be accessed from the work arrays (`.true.`) or stored in them (`.false.`).
logical,	intent(in)	::	isodr	Variable designating whether the solution is to be found by ODR (`.true.`) or by OLS (`.false.`).
integer,	intent(out)	::	jpvt	Pivot vector.
integer,	intent(out)	::	omega	Starting location in array `rwork` of array `omega(q**2)`.
integer,	intent(out)	::	u	Starting location in array `rwork` of array `u(np)`.
integer,	intent(out)	::	qraux	Starting location in array `rwork` of array `qraux(np)`.
integer,	intent(out)	::	sd	Starting location in array `rwork` of array `sd(np)`.
integer,	intent(out)	::	vcv	Starting location in array `rwork` of array `vcv(np**2)`.
integer,	intent(out)	::	wrk1	Starting location in array `rwork` of array `wrk1(n, m, q)`.
integer,	intent(out)	::	wrk2	Starting location in array `rwork` of array `wrk2(n, q)`.
integer,	intent(out)	::	wrk3	Starting location in array `rwork` of array `wrk3(np)`.
integer,	intent(out)	::	wrk4	Starting location in array `rwork` of array `wrk4(m, m)`.
integer,	intent(out)	::	wrk5	Starting location in array `rwork` of array `wrk5(m)`.
integer,	intent(out)	::	wrk6	Starting location in array `rwork` of array `wrk6(n, np, q)`.
integer,	intent(out)	::	nnzw	Number of nonzero weighted observations.
integer,	intent(out)	::	npp	Number of function parameters actually estimated.
integer,	intent(out)	::	job	Variable controlling problem initialization and computational method.
real(kind=wp),	intent(inout)	::	partol	Parameter convergence stopping tolerance.
real(kind=wp),	intent(inout)	::	sstol	Sum-of-squares convergence stopping tolerance.
integer,	intent(out)	::	maxit	Maximum number of iterations allowed.
real(kind=wp),	intent(out)	::	taufac	Factor used to compute the initial trust region diameter.
real(kind=wp),	intent(out)	::	eta	Relative noise in the function results.
integer,	intent(out)	::	neta	Number of accurate digits in the function results.
integer,	intent(out)	::	lunrpt	Logical unit number used for computation reports.
integer,	intent(out)	::	ipr1	Value of the fourth digit (from the right) of `iprint`, which controls the initial summary report.
integer,	intent(out)	::	ipr2	Value of the third digit (from the right) of `iprint`, which controls the iteration reports.
integer,	intent(out)	::	ipr2f	Value of the second digit (from the right) of `iprint`, which controls the frequency of the iteration reports.
integer,	intent(out)	::	ipr3	Value of the first digit (from the right) of `iprint`, which controls the final summary report.
real(kind=wp),	intent(inout)	::	wss(3)	Sum of the squares of the weighted `epsilons` and `deltas`, the sum of the squares of the weighted `deltas`, and the sum of the squares of the weighted `epsilons`.
real(kind=wp),	intent(inout)	::	rvar	Residual variance, i.e. the standard deviation squared.
integer,	intent(inout)	::	idf	Degrees of freedom of the fit, equal to the number of observations with nonzero weighted derivatives minus the number of parameters being estimated.
real(kind=wp),	intent(inout)	::	tau	Trust region diameter.
real(kind=wp),	intent(inout)	::	alpha	Levenberg-Marquardt parameter.
integer,	intent(inout)	::	niter	Number of iterations taken.
integer,	intent(inout)	::	nfev	Number of function evaluations.
integer,	intent(inout)	::	njev	Number of Jacobian evaluations.
integer,	intent(inout)	::	int2	Number of internal doubling steps.
real(kind=wp),	intent(inout)	::	olmavg	Average number of Levenberg-Marquardt steps per iteration.
real(kind=wp),	intent(inout)	::	rcond	Approximate reciprocal condition of `fjacb`.
integer,	intent(inout)	::	irank	Rank deficiency of the Jacobian wrt `beta`.
real(kind=wp),	intent(inout)	::	actrs	Saved actual relative reduction in the sum-of-squares.
real(kind=wp),	intent(inout)	::	pnorm	Norm of the scaled estimated parameters.
real(kind=wp),	intent(inout)	::	prers	Saved predicted relative reduction in the sum-of-squares.
real(kind=wp),	intent(inout)	::	rnorms	Norm of the saved weighted `epsilons` and `deltas`.
integer,	intent(inout)	::	istop	Variable designating whether there are problems computing the function at the current `beta` and `delta`.

public pure subroutine esubi(n, m, wd, ldwd, ld2wd, alpha, tt, ldtt, i, e)

Compute e = wd + alpha*tt**2.

Arguments

Type	Intent		Name
integer,	intent(in)	::	n	Number of observations.
integer,	intent(in)	::	m	Number of columns of data in the independent variable.
real(kind=wp),	intent(in)	::	wd(ldwd,ld2wd,m)	Squared `delta` weights.
integer,	intent(in)	::	ldwd	Leading dimension of array `wd`.
integer,	intent(in)	::	ld2wd	Second dimension of array `wd`.
real(kind=wp),	intent(in)	::	alpha	Levenberg-Marquardt parameter.
real(kind=wp),	intent(in)	::	tt(ldtt,m)	Scaling values used for `delta`.
integer,	intent(in)	::	ldtt	Leading dimension of array `tt`.
integer,	intent(in)	::	i	Indexing variable.
real(kind=wp),	intent(out)	::	e(m,m)	Value of the array `e = wd + alphatt*2`.

public subroutine eta_fcn(fcn, n, m, np, q, xplusd, beta, epsmac, nrow, partmp, pv0, ifixb, ifixx, ldifx, istop, nfev, eta, neta, fjacd, f, fjacb, wrk7, info, lower, upper)

Compute noise and number of good digits in function results.

Arguments

Type	Intent		Name
procedure(fcn_t)		::	fcn	User-supplied subroutine for evaluating the model.
integer,	intent(in)	::	n	Number of observations.
integer,	intent(in)	::	m	Number of columns of data in the explanatory variable.
integer,	intent(in)	::	np	Number of function parameters.
integer,	intent(in)	::	q	Number of responses per observation.
real(kind=wp),	intent(in)	::	xplusd(n,m)	Values of `x + delta`.
real(kind=wp),	intent(in)	::	beta(np)	Function parameters.
real(kind=wp),	intent(in)	::	epsmac	Value of machine precision.
integer,	intent(in)	::	nrow	Row number at which the derivative is to be checked.
real(kind=wp),	intent(out)	::	partmp(np)	Model parameters.
real(kind=wp),	intent(in)	::	pv0(n,q)	Original predicted values.
integer,	intent(in)	::	ifixb(np)	Values designating whether the elements of `beta` are fixed at their input values or not.
integer,	intent(in)	::	ifixx(ldifx,m)	Values designating whether the elements of `x` are fixed at their input values or not.
integer,	intent(in)	::	ldifx	Leading dimension of array `ifixx`.
integer,	intent(out)	::	istop	Variable designating whether there are problems computing the function at the current `beta` and `delta`.
integer,	intent(inout)	::	nfev	Number of function evaluations.
real(kind=wp),	intent(out)	::	eta	Noise in the model results.
integer,	intent(out)	::	neta	Number of accurate digits in the model results.
real(kind=wp),	intent(out)	::	fjacd(n,m,q)	Jacobian wrt `delta`.
real(kind=wp),	intent(out)	::	f(n,q)	Function values.
real(kind=wp),	intent(out)	::	fjacb(n,np,q)	Jacobian wrt `beta`.
real(kind=wp),	intent(out)	::	wrk7(-2:2,q)	Work array of `(5, q)` elements.
integer,	intent(out)	::	info	Variable indicating the status of the computation.
real(kind=wp),	intent(in)	::	lower(np)	Lower bound of `beta`.
real(kind=wp),	intent(in)	::	upper(np)	Upper bound of `beta`.

public subroutine eval_jac(fcn, anajac, cdjac, n, m, np, q, betac, beta, stpb, ifixb, ifixx, ldifx, x, delta, xplusd, stpd, ldstpd, ssf, tt, ldtt, neta, fn, stp, wrk1, wrk2, wrk3, wrk6, tempret, fjacb, isodr, fjacd, we1, ldwe, ld2we, njev, nfev, istop, info, lower, upper)

Compute the weighted Jacobians wrt beta and delta.

Arguments

Type	Intent		Name
procedure(fcn_t)		::	fcn	User-supplied subroutine for evaluating the model.
logical,	intent(in)	::	anajac	Variable designating whether the Jacobians are computed by finite differences (`.false.`) or not (`.true.`).
logical,	intent(in)	::	cdjac	Variable designating whether the Jacobians are computed by central differences (`.true.`) or by forward differences (`.false.`).
integer,	intent(in)	::	n	Number of observations.
integer,	intent(in)	::	m	Number of columns of data in the independent variable.
integer,	intent(in)	::	np	Number of function parameters.
integer,	intent(in)	::	q	Number of responses per observation.
real(kind=wp),	intent(in)	::	betac(np)	Current estimated values of the unfixed `beta`s.
real(kind=wp),	intent(out)	::	beta(np)	Function parameters.
real(kind=wp),	intent(in)	::	stpb(np)	Relative step used for computing finite difference derivatives with respect to `beta`.
integer,	intent(in)	::	ifixb(np)	Values designating whether the elements of `beta` are fixed at their input values or not.
integer,	intent(in)	::	ifixx(ldifx,m)	Values designating whether the elements of `delta` are fixed at their input values or not.
integer,	intent(in)	::	ldifx	Leading dimension of array `ifixx`.
real(kind=wp),	intent(in)	::	x(n,m)	Independent variable.
real(kind=wp),	intent(in)	::	delta(n,m)	Estimated values of `delta`.
real(kind=wp),	intent(out)	::	xplusd(n,m)	Values of `x + delta`.
real(kind=wp),	intent(in)	::	stpd(ldstpd,m)	Relative step used for computing finite difference derivatives with respect to `delta`.
integer,	intent(in)	::	ldstpd	Leading dimension of array `stpd`.
real(kind=wp),	intent(in)	::	ssf(np)	Scale used for the `beta`s.
real(kind=wp),	intent(in)	::	tt(ldtt,m)	Scaling values used for `delta`.
integer,	intent(in)	::	ldtt	Leading dimension of array `tt`.
integer,	intent(in)	::	neta	Number of accurate digits in the function results.
real(kind=wp),	intent(in)	::	fn(n,q)	Predicted values of the function at the current point.
real(kind=wp),	intent(out)	::	stp(n)	Step used for computing finite difference derivatives with respect to `delta`.
real(kind=wp),	intent(out)	::	wrk1(n,m,q)	Work array of `(n, m, q)` elements.
real(kind=wp),	intent(out)	::	wrk2(n,q)	Work array of `(n, q)` elements.
real(kind=wp),	intent(out)	::	wrk3(np)	Work array of `(np)` elements.
real(kind=wp),	intent(out)	::	wrk6(n,np,q)	Work array of `(n, np, q)` elements.
real(kind=wp),	intent(inout)	::	tempret(:,:)	Temporary work array for holding return values before copying to a lower rank array.
real(kind=wp),	intent(out)	::	fjacb(n,np,q)	Jacobian with respect to `beta`.
logical,	intent(in)	::	isodr	Variable designating whether the solution is by ODR (`.true.`) or by OLS (`.false.`).
real(kind=wp),	intent(out)	::	fjacd(n,m,q)	Jacobian with respect to `delta`.
real(kind=wp),	intent(in)	::	we1(ldwe,ld2we,q)	Square roots of the `epsilon` weights in array `we`.
integer,	intent(in)	::	ldwe	Leading dimension of arrays `we` and `we1`.
integer,	intent(in)	::	ld2we	Second dimension of arrays `we` and `we1`.
integer,	intent(inout)	::	njev	Number of Jacobian evaluations.
integer,	intent(inout)	::	nfev	Number of function evaluations.
integer,	intent(out)	::	istop	Variable designating that the user wishes the computations stopped.
integer,	intent(out)	::	info	Variable designating why the computations were stopped.
real(kind=wp),	intent(in)	::	lower(np)	Lower bound of `beta`.
real(kind=wp),	intent(in)	::	upper(np)	Upper bound of `beta`.

public pure subroutine fctr(oksemi, a, lda, n, info)

Factor the positive (semi)definite matrix a using a modified Cholesky factorization.

Arguments

Type	Intent		Name
logical,	intent(in)	::	oksemi	Flag indicating whether the factored array can be positive semidefinite (`.true.`) or whether it must be found to be positive definite (`.false.`).
real(kind=wp),	intent(inout)	::	a(lda,n)	Array to be factored. Upon return, `a` contains the upper triangular matrix `r` so that `a = trans(r)*r` where the strict lower triangle is set to zero. If `info /= 0`, the factorization is not complete.
integer,	intent(in)	::	lda	Leading dimension of array `a`.
integer,	intent(in)	::	n	Number of rows and columns of data in array `a`.
integer,	intent(out)	::	info	Output flag. `0`: Factorization was completed. `k`: Error condition. The leading minor of order `k` is not positive (semi)definite.

public pure subroutine fctrw(n, m, q, npp, isodr, we, ldwe, ld2we, wd, ldwd, ld2wd, wrk0, wrk4, we1, nnzw, info)

Check input parameters, indicating errors found using nonzero values of argument info as described in the ODRPACK95 reference guide.

Arguments

Type	Intent		Name
integer,	intent(in)	::	n	Number of observations.
integer,	intent(in)	::	m	Number of columns of data in the explanatory variable.
integer,	intent(in)	::	q	Number of responses per observation.
integer,	intent(in)	::	npp	Number of function parameters being estimated.
logical,	intent(in)	::	isodr	Variable designating whether the solution is by ODR (`.true`) or by OLS (`.false`).
real(kind=wp),	intent(in)	::	we(ldwe,ld2we,q)	Squared `epsilon` weights.
integer,	intent(in)	::	ldwe	Leading dimension of array `we`.
integer,	intent(in)	::	ld2we	Second dimension of array `we`.
real(kind=wp),	intent(in)	::	wd(ldwd,ld2wd,m)	Squared `delta` weights.
integer,	intent(in)	::	ldwd	Leading dimension of array `wd`.
integer,	intent(in)	::	ld2wd	Second dimension of array `wd`.
real(kind=wp),	intent(out)	::	wrk0(q,q)	Work array of `(q, q)` elements.
real(kind=wp),	intent(out)	::	wrk4(m,m)	Work array of `(m, m)` elements.
real(kind=wp),	intent(out)	::	we1(ldwe,ld2we,q)	Factored `epsilon` weights, such that `trans(we1)*we1 = we`.
integer,	intent(out)	::	nnzw	Number of nonzero weighted observations.
integer,	intent(out)	::	info	Variable designating why the computations were stopped.

public pure subroutine set_flags(job, restart, initd, dovcv, redoj, anajac, cdjac, chkjac, isodr, implicit)

Set flags indicating conditions specified by job.

Arguments

Type	Intent		Name
integer,	intent(in)	::	job	Variable controlling problem initialization and computational method.
logical,	intent(out)	::	restart	Variable designating whether the call is a restart (`.true.`) or not (`.false.`).
logical,	intent(out)	::	initd	Variable designating whether `delta` is to be initialized to zero (`.true.`) or to the first `n` by `m` elements of array `rwork` (`.false.`).
logical,	intent(out)	::	dovcv	Variable designating whether the covariance matrix is to be computed (`.true.`) or not (`.false.`).
logical,	intent(out)	::	redoj	Variable designating whether the Jacobian matrix is to be recomputed for the computation of the covariance matrix (`.true.`) or not (`.false.`).
logical,	intent(out)	::	anajac	Variable designating whether the Jacobians are computed by finite differences (`.false.`) or not (`.true.`).
logical,	intent(out)	::	cdjac	Variable designating whether the Jacobians are computed by central differences (`.true.`) or by forward differences (`.false.`).
logical,	intent(out)	::	chkjac	Variable designating whether the user-supplied Jacobians are to be checked (`.true.`) or not (`.false.`).
logical,	intent(out)	::	isodr	Variable designating whether the solution is by ODR (`.true.`) or by OLS (`.false.`).
logical,	intent(out)	::	implicit	Variable designating whether the solution is by implicit ODR (`.true.`) or explicit ODR (`.false.`).

public pure subroutine set_ifix(n, m, ifix, ldifix, t, ldt, tfix, ldtfix)

Set elements of t to zero according to ifix.

Arguments

Type	Intent		Name
integer,	intent(in)	::	n	Number of rows of data in the array.
integer,	intent(in)	::	m	Number of columns of data in the array.
integer,	intent(in)	::	ifix(ldifix,m)	Array designating whether an element of `t` is to be set to zero.
integer,	intent(in)	::	ldifix	Leading dimension of array `ifix`.
real(kind=wp),	intent(in)	::	t(ldt,m)	Array being set to zero according to the elements of `ifix`.
integer,	intent(in)	::	ldt	Leading dimension of array `t`.
real(kind=wp),	intent(out)	::	tfix(ldtfix,m)	Resulting array.
integer,	intent(in)	::	ldtfix	Leading dimension of array `tfix`.

public pure subroutine loc_iwork(m, q, np, msgbi, msgdi, ifix2i, istopi, nnzwi, nppi, idfi, jobi, iprinti, lunerri, lunrpti, nrowi, ntoli, netai, maxiti, niteri, nfevi, njevi, int2i, iranki, ldtti, boundi, liwkmin)

Get storage locations within integer work space.

Arguments

Type	Intent		Name
integer,	intent(in)	::	m	Number of columns of data in the independent variable.
integer,	intent(in)	::	q	Number of responses per observation.
integer,	intent(in)	::	np	Number of function parameters.
integer,	intent(out)	::	msgbi	Starting location in array `iwork` of array `msgb`.
integer,	intent(out)	::	msgdi	Starting location in array `iwork` of array `msgd`.
integer,	intent(out)	::	ifix2i	Starting location in array `iwork` of array `ifix2`.
integer,	intent(out)	::	istopi	Location in array `iwork` of variable `istop`.
integer,	intent(out)	::	nnzwi	Location in array `iwork` of variable `nnzw`.
integer,	intent(out)	::	nppi	Location in array `iwork` of variable `npp`.
integer,	intent(out)	::	idfi	Location in array `iwork` of variable `idf`.
integer,	intent(out)	::	jobi	Location in array `iwork` of variable `job`.
integer,	intent(out)	::	iprinti	Location in array `iwork` of variable `iprint`.
integer,	intent(out)	::	lunerri	Location in array `iwork` of variable `lunerr`.
integer,	intent(out)	::	lunrpti	Location in array `iwork` of variable `lunrpt`.
integer,	intent(out)	::	nrowi	Location in array `iwork` of variable `nrow`.
integer,	intent(out)	::	ntoli	Location in array `iwork` of variable `ntol`.
integer,	intent(out)	::	netai	Location in array `iwork` of variable `neta`.
integer,	intent(out)	::	maxiti	Location in array `iwork` of variable `maxit`.
integer,	intent(out)	::	niteri	Location in array `iwork` of variable `niter`.
integer,	intent(out)	::	nfevi	Location in array `iwork` of variable `nfev`.
integer,	intent(out)	::	njevi	Location in array `iwork` of variable `njev`.
integer,	intent(out)	::	int2i	Location in array `iwork` of variable `int2`.
integer,	intent(out)	::	iranki	Location in array `iwork` of variable `irank`.
integer,	intent(out)	::	ldtti	Location in array `iwork` of variable `ldtt`.
integer,	intent(out)	::	boundi	Location in array `iwork` of variable `bound`.
integer,	intent(out)	::	liwkmin	Minimum acceptable length of array `iwork`.

public pure subroutine loc_rwork(n, m, q, np, ldwe, ld2we, isodr, deltai, epsi, xplusdi, fni, sdi, vcvi, rvari, wssi, wssdeli, wssepsi, rcondi, etai, olmavgi, taui, alphai, actrsi, pnormi, rnormsi, prersi, partoli, sstoli, taufaci, epsmaci, beta0i, betaci, betasi, betani, si, ssi, ssfi, qrauxi, ui, fsi, fjacbi, we1i, diffi, deltasi, deltani, ti, tti, omegai, fjacdi, wrk1i, wrk2i, wrk3i, wrk4i, wrk5i, wrk6i, wrk7i, loweri, upperi, lrwkmin)

Get storage locations within real work space.

Arguments

Type	Intent		Name
integer,	intent(in)	::	n	Number of observations.
integer,	intent(in)	::	m	Number of columns of data in the explanatory variable.
integer,	intent(in)	::	q	Number of responses per observation.
integer,	intent(in)	::	np	Number of function parameters.
integer,	intent(in)	::	ldwe	Leading dimension of array `we`.
integer,	intent(in)	::	ld2we	Second dimension of array `we`.
logical,	intent(in)	::	isodr	Variable designating whether the solution is by ODR (`.true.`) or by OLS (`.false.`).
integer,	intent(out)	::	deltai	Starting location in array `rwork` of array `delta(n, m)`.
integer,	intent(out)	::	epsi	Starting location in array `rwork` of array `eps(n, q)`.
integer,	intent(out)	::	xplusdi	Starting location in array `rwork` of array `xplusd(n, m)`.
integer,	intent(out)	::	fni	Starting location in array `rwork` of array `fn(n, q)`.
integer,	intent(out)	::	sdi	Starting location in array `rwork` of array `sd(np)`.
integer,	intent(out)	::	vcvi	Starting location in array `rwork` of array `vcv(np**2)`.
integer,	intent(out)	::	rvari	Location in array `rwork` of variable `rvar`.
integer,	intent(out)	::	wssi	Location in array `rwork` of variable `wss`.
integer,	intent(out)	::	wssdeli	Location in array `rwork` of variable `wssdel`.
integer,	intent(out)	::	wssepsi	Location in array `rwork` of variable `wsseps`.
integer,	intent(out)	::	rcondi	Location in array `rwork` of variable `rcondi`.
integer,	intent(out)	::	etai	Location in array `rwork` of variable `eta`.
integer,	intent(out)	::	olmavgi	Location in array `rwork` of variable `olmavg`.
integer,	intent(out)	::	taui	Location in array `rwork` of variable `tau`.
integer,	intent(out)	::	alphai	Location in array `rwork` of variable `alpha`.
integer,	intent(out)	::	actrsi	Location in array `rwork` of variable `actrs`.
integer,	intent(out)	::	pnormi	Location in array `rwork` of variable `pnorm`.
integer,	intent(out)	::	rnormsi	Location in array `rwork` of variable `rnorms`.
integer,	intent(out)	::	prersi	Location in array `rwork` of variable `prers`.
integer,	intent(out)	::	partoli	Location in array `rwork` of variable `partol`.
integer,	intent(out)	::	sstoli	Location in array `rwork` of variable `sstol`.
integer,	intent(out)	::	taufaci	Location in array `rwork` of variable `taufac`.
integer,	intent(out)	::	epsmaci	Location in array `rwork` of variable `epsmac`.
integer,	intent(out)	::	beta0i	Starting location in array `rwork` of array `beta0(np)`.
integer,	intent(out)	::	betaci	Starting location in array `rwork` of array `betac(np)`.
integer,	intent(out)	::	betasi	Starting location in array `rwork` of array `betas(np)`.
integer,	intent(out)	::	betani	Starting location in array `rwork` of array `betan(np)`.
integer,	intent(out)	::	si	Starting location in array `rwork` of array `s(np)`.
integer,	intent(out)	::	ssi	Starting location in array `rwork` of array `ss(np)`.
integer,	intent(out)	::	ssfi	Starting location in array `rwork` of array `ssf(np)`.
integer,	intent(out)	::	qrauxi	Starting location in array `rwork` of array `qraux(np)`.
integer,	intent(out)	::	ui	Starting location in array `rwork` of array `u(np)`.
integer,	intent(out)	::	fsi	Starting location in array `rwork` of array `fs(n, q)`.
integer,	intent(out)	::	fjacbi	Starting location in array `rwork` of array `fjacb(n, np, q)`.
integer,	intent(out)	::	we1i	Starting location in array `rwork` of array `we1(ldwe, ldwe2, q)`.
integer,	intent(out)	::	diffi	Starting location in array `rwork` of array `diff(q*(np + m))`.
integer,	intent(out)	::	deltasi	Starting location in array `rwork` of array `deltas(n, m)`.
integer,	intent(out)	::	deltani	Starting location in array `rwork` of array `deltan(n, m)`.
integer,	intent(out)	::	ti	Starting location in array `rwork` of array `t(n, m)`.
integer,	intent(out)	::	tti	Starting location in array `rwork` of array `tt(n, m)`.
integer,	intent(out)	::	omegai	Starting location in array `rwork` of array `omega(q**2)`.
integer,	intent(out)	::	fjacdi	Starting location in array `rwork` of array `fjacd(n, m, q)`.
integer,	intent(out)	::	wrk1i	Starting location in array `rwork` of array `wrk1(n, m, q)`.
integer,	intent(out)	::	wrk2i	Starting location in array `rwork` of array `wrk2(n, q)`.
integer,	intent(out)	::	wrk3i	Starting location in array `rwork` of array `wrk3(np)`.
integer,	intent(out)	::	wrk4i	Starting location in array `rwork` of array `wrk4(m, m)`.
integer,	intent(out)	::	wrk5i	Starting location in array `rwork` of array `wrk5(m)`.
integer,	intent(out)	::	wrk6i	Starting location in array `rwork` of array `wrk6(n, np, q)`.
integer,	intent(out)	::	wrk7i	Starting location in array `rwork` of array `wrk7(5*q)`.
integer,	intent(out)	::	loweri	Starting location in array `rwork` of array `lower(np)`.
integer,	intent(out)	::	upperi	Starting location in array `rwork` of array `upper(np)`.
integer,	intent(out)	::	lrwkmin	Minimum acceptable length of vector `rwork`.

public pure subroutine init_work(n, m, np, rwork, lrwork, iwork, liwork, x, ifixx, ldifx, scld, ldscld, beta, sclb, sstol, partol, maxit, taufac, job, iprint, lunerr, lunrpt, lower, upper, epsmai, sstoli, partli, maxiti, taufci, jobi, iprini, luneri, lunrpi, ssfi, tti, ldtti, deltai, loweri, upperi, boundi)

Initialize work vectors as necessary.

Arguments

Type	Intent		Name
integer,	intent(in)	::	n	Number of observations.
integer,	intent(in)	::	m	Number of columns of data in the independent variable.
integer,	intent(in)	::	np	Number of function parameters.
real(kind=wp),	intent(out)	::	rwork(lrwork)	Real work space.
integer,	intent(in)	::	lrwork	Length of vector `rwork`.
integer,	intent(out)	::	iwork(liwork)	Integer work space.
integer,	intent(in)	::	liwork	Length of vector `iwork`.
real(kind=wp),	intent(in)	::	x(n,m)	Independent variable.
integer,	intent(in)	::	ifixx(ldifx,m)	Values designating whether the elements of `x` are fixed at their input values or not.
integer,	intent(in)	::	ldifx	Leading dimension of array `ifixx`.
real(kind=wp),	intent(in)	::	scld(ldscld,m)	Scaling values for `delta`.
integer,	intent(in)	::	ldscld	Leading dimension of array `scld`.
real(kind=wp),	intent(in)	::	beta(np)	Function parameters.
real(kind=wp),	intent(in)	::	sclb(np)	Scaling values for `beta`.
real(kind=wp),	intent(in)	::	sstol	Sum-of-squares convergence stopping criteria.
real(kind=wp),	intent(in)	::	partol	Parameter convergence stopping criteria.
integer,	intent(in)	::	maxit	Maximum number of iterations allowed.
real(kind=wp),	intent(in)	::	taufac	Factor used to compute the initial trust region diameter.
integer,	intent(in)	::	job	Variable controlling problem initialization and computational method.
integer,	intent(in)	::	iprint	Print control variable.
integer,	intent(in)	::	lunerr	Logical unit number used for error messages.
integer,	intent(in)	::	lunrpt	Logical unit number used for computation reports.
real(kind=wp),	intent(in)	::	lower(np)	Lower bounds for the function parameters.
real(kind=wp),	intent(in)	::	upper(np)	Upper bounds for the function parameters.
integer,	intent(in)	::	epsmai	Location in array `rwork` of variable `epsmac`.
integer,	intent(in)	::	sstoli	Location in array `rwork` of variable `sstol`.
integer,	intent(in)	::	partli	Location in array `rwork` of variable `partol`.
integer,	intent(in)	::	maxiti	Location in array `iwork` of variable `maxit`.
integer,	intent(in)	::	taufci	Location in array `rwork` of variable `taufac`.
integer,	intent(in)	::	jobi	Location in array `iwork` of variable `job`.
integer,	intent(in)	::	iprini	Location in array `iwork` of variable `iprint`.
integer,	intent(in)	::	luneri	Location in array `iwork` of variable `lunerr`.
integer,	intent(in)	::	lunrpi	Location in array `iwork` of variable `lunrpt`.
integer,	intent(in)	::	ssfi	Starting location in array `rwork` of array `ssf`.
integer,	intent(in)	::	tti	Starting location in array `rwork` of the array `tt`.
integer,	intent(in)	::	ldtti	Leading dimension of array `tt`.
integer,	intent(in)	::	deltai	Starting location in array `rwork` of array `delta`.
integer,	intent(in)	::	loweri	Starting location in array `iwork` of array `lower`.
integer,	intent(in)	::	upperi	Starting location in array `iwork` of array `upper`.
integer,	intent(in)	::	boundi	Location in array `iwork` of variable `bound`.

public subroutine jac_cdiff(fcn, n, m, np, q, beta, x, delta, xplusd, ifixb, ifixx, ldifx, stpb, stpd, ldstpd, ssf, tt, ldtt, neta, fn, stp, wrk1, wrk2, wrk3, wrk6, fjacb, isodr, fjacd, nfev, istop, info, lower, upper)

Compute central difference approximations to the Jacobian wrt the estimated betas and wrt the deltas.

Arguments

Type	Intent		Name
procedure(fcn_t)		::	fcn	User supplied subroutine for evaluating the model.
integer,	intent(in)	::	n	Number of observations.
integer,	intent(in)	::	m	Number of columns of data in the explanatory variable.
integer,	intent(in)	::	np	Number of function parameters.
integer,	intent(in)	::	q	Number of responses per observation.
real(kind=wp),	intent(inout)	::	beta(np)	Function parameters.
real(kind=wp),	intent(in)	::	x(n,m)	Explanatory variable.
real(kind=wp),	intent(in)	::	delta(n,m)	Estimated errors in the explanatory variables.
real(kind=wp),	intent(inout)	::	xplusd(n,m)	Values of `x + delta`.
integer,	intent(in)	::	ifixb(np)	Values designating whether the elements of `beta` are fixed at their input values or not.
integer,	intent(in)	::	ifixx(ldifx,m)	Values designating whether the elements of `x` are fixed at their input values or not.
integer,	intent(in)	::	ldifx	Leading dimension of array `ifixx`.
real(kind=wp),	intent(in)	::	stpb(np)	Relative step used for computing finite difference derivatives with respect to each `beta`.
real(kind=wp),	intent(in)	::	stpd(ldstpd,m)	Relative step used for computing finite difference derivatives with respect to each `delta`.
integer,	intent(in)	::	ldstpd	Leading dimension of array `stpd`.
real(kind=wp),	intent(in)	::	ssf(np)	Scaling values used for `beta`.
real(kind=wp),	intent(in)	::	tt(ldtt,m)	Scaling values used for `delta`.
integer,	intent(in)	::	ldtt	Leading dimension of array `tt`.
integer,	intent(in)	::	neta	Number of good digits in the function results.
real(kind=wp),	intent(in)	::	fn(n,q)	New predicted values from the function. Used when parameter is on a boundary.
real(kind=wp),	intent(out)	::	stp(n)	Step used for computing finite difference derivatives with respect to each `delta`.
real(kind=wp),	intent(out)	::	wrk1(n,m,q)	A work array of `(n, m, q)` elements.
real(kind=wp),	intent(out)	::	wrk2(n,q)	A work array of `(n, q)` elements.
real(kind=wp),	intent(out)	::	wrk3(np)	A work array of `(np)` elements.
real(kind=wp),	intent(out)	::	wrk6(n,np,q)	A work array of `(n, np, q)` elements.
real(kind=wp),	intent(out)	::	fjacb(n,np,q)	Jacobian with respect to `beta`.
logical,	intent(in)	::	isodr	Variable designating whether the solution is by ODR (`.true.`) or by OLS (`.false.`).
real(kind=wp),	intent(out)	::	fjacd(n,m,q)	Jacobian with respect to `delta`.
integer,	intent(inout)	::	nfev	Number of function evaluations.
integer,	intent(out)	::	istop	Variable designating whether there are problems computing the function at the current `beta` and `delta`.
integer,	intent(out)	::	info	Variable designating why the computations were stopped.
real(kind=wp),	intent(in)	::	lower(np)	Lower bound on `beta`.
real(kind=wp),	intent(in)	::	upper(np)	Upper bound on `beta`.

public subroutine jac_fwdiff(fcn, n, m, np, q, beta, x, delta, xplusd, ifixb, ifixx, ldifx, stpb, stpd, ldstpd, ssf, tt, ldtt, neta, fn, stp, wrk1, wrk2, wrk3, wrk6, fjacb, isodr, fjacd, nfev, istop, info, lower, upper)

Compute forward difference approximations to the Jacobian wrt the estimated betas and wrt the deltas.

Arguments

Type	Intent		Name
procedure(fcn_t)		::	fcn	User supplied subroutine for evaluating the model.
integer,	intent(in)	::	n	Number of observations.
integer,	intent(in)	::	m	Number of columns of data in the explanatory variable.
integer,	intent(in)	::	np	Number of function parameters.
integer,	intent(in)	::	q	Number of responses per observation.
real(kind=wp),	intent(inout)	::	beta(np)	Function parameters.
real(kind=wp),	intent(in)	::	x(n,m)	Explanatory variable.
real(kind=wp),	intent(in)	::	delta(n,m)	Estimated errors in the explanatory variables.
real(kind=wp),	intent(inout)	::	xplusd(n,m)	Values of `x + delta`.
integer,	intent(in)	::	ifixb(np)	Values designating whether the elements of `beta` are fixed at their input values or not.
integer,	intent(in)	::	ifixx(ldifx,m)	Values designating whether the elements of `x` are fixed at their input values or not.
integer,	intent(in)	::	ldifx	Leading dimension of array `ifixx`.
real(kind=wp),	intent(in)	::	stpb(np)	Relative step used for computing finite difference derivatives with respect to each `beta`.
real(kind=wp),	intent(in)	::	stpd(ldstpd,m)	Relative step used for computing finite difference derivatives with respect to each `delta`.
integer,	intent(in)	::	ldstpd	Leading dimension of array `stpd`.
real(kind=wp),	intent(in)	::	ssf(np)	Scaling values used for `beta`.
real(kind=wp),	intent(in)	::	tt(ldtt,m)	Scaling values used for `delta`.
integer,	intent(in)	::	ldtt	Leading dimension of array `tt`.
integer,	intent(in)	::	neta	Number of good digits in the function results.
real(kind=wp),	intent(in)	::	fn(n,q)	New predicted values from the function. Used when parameter is on a boundary.
real(kind=wp),	intent(out)	::	stp(n)	Step used for computing finite difference derivatives with respect to each `delta`.
real(kind=wp),	intent(out)	::	wrk1(n,m,q)	A work array of `(n, m, q)` elements.
real(kind=wp),	intent(out)	::	wrk2(n,q)	A work array of `(n, q)` elements.
real(kind=wp),	intent(out)	::	wrk3(np)	A work array of `(np)` elements.
real(kind=wp),	intent(out)	::	wrk6(n,np,q)	A work array of `(n, np, q)` elements.
real(kind=wp),	intent(out)	::	fjacb(n,np,q)	Jacobian with respect to `beta`.
logical,	intent(in)	::	isodr	Variable designating whether the solution is by ODR (`.true.`) or by OLS (`.false.`).
real(kind=wp),	intent(out)	::	fjacd(n,m,q)	Jacobian with respect to `delta`.
integer,	intent(inout)	::	nfev	Number of function evaluations.
integer,	intent(out)	::	istop	Variable designating whether there are problems computing the function at the current `beta` and `delta`.
integer,	intent(out)	::	info	Variable designating why the computations were stopped.
real(kind=wp),	intent(in)	::	lower(np)	Lower bound on `beta`.
real(kind=wp),	intent(in)	::	upper(np)	Upper bound on `beta`.

public subroutine check_jac(fcn, n, m, np, q, beta, betaj, xplusd, ifixb, ifixx, ldifx, stpb, stpd, ldstpd, ssf, tt, ldtt, eta, neta, ntol, nrow, isodr, epsmac, pv0i, fjacb, fjacd, msgb, msgd, diff, istop, nfev, njev, wrk1, wrk2, wrk6, interval)

Driver routine for the derivative checking process.

Arguments

Type	Intent		Name
procedure(fcn_t)		::	fcn	User supplied subroutine for evaluating the model.
integer,	intent(in)	::	n	Number of observations.
integer,	intent(in)	::	m	Number of columns of data in the explanatory variable.
integer,	intent(in)	::	np	Number of function parameters.
integer,	intent(in)	::	q	Number of responses per observation.
real(kind=wp),	intent(inout)	::	beta(np)	Function parameters.
real(kind=wp),	intent(inout)	::	betaj(np)	Function parameters offset such that steps don't cross bounds.
real(kind=wp),	intent(inout)	::	xplusd(n,m)	Values of `x + delta`.
integer,	intent(in)	::	ifixb(np)	Values designating whether the elements of `beta` are fixed at their input values or not.
integer,	intent(in)	::	ifixx(ldifx,m)	Values designating whether the elements of `x` are fixed at their input values or not.
integer,	intent(in)	::	ldifx	Leading dimension of array `ifixx`.
real(kind=wp),	intent(in)	::	stpb(np)	Step size for finite difference derivatives wrt `beta`.
real(kind=wp),	intent(in)	::	stpd(ldstpd,m)	Step size for finite difference derivatives wrt `delta`.
integer,	intent(in)	::	ldstpd	Leading dimension of array `stpd`.
real(kind=wp),	intent(in)	::	ssf(np)	Scaling values used for `beta`.
real(kind=wp),	intent(in)	::	tt(ldtt,m)	Scaling values used for `delta`.
integer,	intent(in)	::	ldtt	Leading dimension of array `tt`.
real(kind=wp),	intent(in)	::	eta	Relative noise in the function results.
integer,	intent(in)	::	neta	Number of reliable digits in the model results.
integer,	intent(out)	::	ntol	Number of digits of agreement required between the numerical derivatives and the user supplied derivatives.
integer,	intent(in)	::	nrow	Row number of the explanatory variable array at which the derivative is checked.
logical,	intent(in)	::	isodr	Variable designating whether the solution is by ODR (`.true.`) or by OLS (`.false.`).
real(kind=wp),	intent(in)	::	epsmac	Value of machine precision.
real(kind=wp),	intent(in)	::	pv0i(n,q)	Predicted values using the user supplied parameter estimates.
real(kind=wp),	intent(out)	::	fjacb(n,np,q)	Jacobian with respect to `beta`.
real(kind=wp),	intent(out)	::	fjacd(n,m,q)	Jacobian with respect to `delta`.
integer,	intent(out)	::	msgb(1+q*np)	Error checking results for the Jacobian wrt `beta`.
integer,	intent(out)	::	msgd(1+q*m)	Error checking results for the Jacobian wrt `delta`.
real(kind=wp),	intent(out)	::	diff(q,np+m)	Relative differences between the user supplied and finite difference derivatives for each derivative checked.
integer,	intent(out)	::	istop	Variable designating whether there are problems computing the function at the current `beta` and `delta`
integer,	intent(inout)	::	nfev	Number of function evaluations.
integer,	intent(inout)	::	njev	Number of Jacobian evaluations.
real(kind=wp),	intent(out)	::	wrk1(n,m,q)	A work array of `(n, m, q)` elements.
real(kind=wp),	intent(out)	::	wrk2(n,q)	A work array of `(n, q)` elements.
real(kind=wp),	intent(out)	::	wrk6(n,np,q)	A work array of `(n, np, q)` elements.
integer,	intent(in)	::	interval(np)	Specifies which checks can be performed when checking derivatives based on the interval of the bound constraints.

public subroutine check_jac_curv(fcn, n, m, np, q, beta, xplusd, ifixb, ifixx, ldifx, eta, tol, nrow, epsmac, j, lq, hc, iswrtb, fd, typj, pvpstp, stp0, pv, d, diffj, msg, istop, nfev, wrk1, wrk2, wrk6)

Check whether high curvature could be the cause of the disagreement between the numerical and analytic derviatives.

Arguments

Type	Intent		Name
procedure(fcn_t)		::	fcn	User supplied subroutine for evaluating the model.
integer,	intent(in)	::	n	Number of observations.
integer,	intent(in)	::	m	Number of columns of data in the explanatory variable.
integer,	intent(in)	::	np	Number of function parameters.
integer,	intent(in)	::	q	Number of responses per observation.
real(kind=wp),	intent(inout)	::	beta(np)	Function parameters.
real(kind=wp),	intent(inout)	::	xplusd(n,m)	Values of `x` + `delta`.
integer,	intent(in)	::	ifixb(np)	Values designating whether the elements of `beta` are fixed at their input values or not.
integer,	intent(in)	::	ifixx(ldifx,m)	Values designating whether the elements of `x` are fixed at their input values or not.
integer,	intent(in)	::	ldifx	Leading dimension of array `ifixx`.
real(kind=wp),	intent(in)	::	eta	Relative noise in the model.
real(kind=wp),	intent(in)	::	tol	Agreement tolerance.
integer,	intent(in)	::	nrow	Row number of the explanatory variable array at which the derivative is to be checked.
real(kind=wp),	intent(in)	::	epsmac	Value of machine precision.
integer,	intent(in)	::	j	Index of the partial derivative being examined.
integer,	intent(in)	::	lq	Response currently being examined.
real(kind=wp),	intent(in)	::	hc	Relative step size for central finite differences.
logical,	intent(in)	::	iswrtb	Variable designating whether the derivatives wrt `beta` (`iswrtb = .true.`) or `delta` (`iswrtb = .false.`) are being checked.
real(kind=wp),	intent(out)	::	fd	Forward difference derivative wrt the `j`-th parameter.
real(kind=wp),	intent(in)	::	typj	Typical size of the `j`-th unknown `beta` or `delta`.
real(kind=wp),	intent(out)	::	pvpstp	Predicted value for row `nrow` of the model based on the current parameter estimates for all but the `j`-th parameter value, which is `beta(j) + stp0`.
real(kind=wp),	intent(in)	::	stp0	Initial step size for the finite difference derivative.
real(kind=wp),	intent(in)	::	pv	Predicted value of the model for row `nrow`.
real(kind=wp),	intent(in)	::	d	Derivative with respect to the `j`-th unknown parameter.
real(kind=wp),	intent(out)	::	diffj	Relative differences between the user supplied and finite difference derivatives for the derivative being checked.
integer,	intent(out)	::	msg(q,j)	Error checking results.
integer,	intent(out)	::	istop	Variable designating whether there are problems computing the function at the current `beta` and `delta`.
integer,	intent(inout)	::	nfev	Number of function evaluations.
real(kind=wp),	intent(out)	::	wrk1(n,m,q)	A work array of `(n, m, q)` elements.
real(kind=wp),	intent(out)	::	wrk2(n,q)	A work array of `(n, q)` elements.
real(kind=wp),	intent(out)	::	wrk6(n,np,q)	A work array of `(n, np, q)` elements.

public subroutine check_jac_fp(fcn, n, m, np, q, beta, xplusd, ifixb, ifixx, ldifx, eta, tol, nrow, j, lq, iswrtb, fd, typj, pvpstp, stp0, curve, pv, d, diffj, msg, istop, nfev, wrk1, wrk2, wrk6)

Check whether finite precision arithmetic could be the cause of the disagreement between the derivatives.

Arguments

Type	Intent		Name
procedure(fcn_t)		::	fcn	User supplied subroutine for evaluating the model.
integer,	intent(in)	::	n	Number of observations.
integer,	intent(in)	::	m	Number of columns of data in the explanatory variable.
integer,	intent(in)	::	np	Number of function parameters.
integer,	intent(in)	::	q	Number of responses per observation.
real(kind=wp),	intent(inout)	::	beta(np)	Function parameters.
real(kind=wp),	intent(inout)	::	xplusd(n,m)	Values of `x + delta`.
integer,	intent(in)	::	ifixb(np)	Values designating whether the elements of `beta` are fixed at their input values or not.
integer,	intent(in)	::	ifixx(ldifx,m)	Values designating whether the elements of `x` are fixed at their input values or not.
integer,	intent(in)	::	ldifx	Leading dimension of array `ifixx`.
real(kind=wp),	intent(in)	::	eta	Relative noise in the model.
real(kind=wp),	intent(in)	::	tol	Agreement tolerance.
integer,	intent(in)	::	nrow	Row number of the explanatory variable array at which the derivative is to be checked.
integer,	intent(in)	::	j	Index of the partial derivative being examined.
integer,	intent(in)	::	lq	Response currently being examined.
logical,	intent(in)	::	iswrtb	Variable designating whether the derivatives wrt `beta` (`iswrtb = .true.`) or `delta` (`iswrtb = .false.`) are being checked.
real(kind=wp),	intent(out)	::	fd	Forward difference derivative wrt the `j`-th parameter.
real(kind=wp),	intent(in)	::	typj	Typical size of the `j`-th unknown `beta` or `delta`.
real(kind=wp),	intent(out)	::	pvpstp	Predicted value for row `nrow` of the model based on the current parameter estimates for all but the `j`-th parameter value, which is `beta(j) + stp0`.
real(kind=wp),	intent(in)	::	stp0	Step size for the finite difference derivative.
real(kind=wp),	intent(inout)	::	curve	A measure of the curvature in the model.
real(kind=wp),	intent(in)	::	pv	Predicted value for row `nrow`.
real(kind=wp),	intent(in)	::	d	Derivative with respect to the `j`-th unknown parameter.
real(kind=wp),	intent(out)	::	diffj	Relative differences between the user supplied and finite difference derivatives for the derivative being checked.
integer,	intent(out)	::	msg(q,j)	Error checking results.
integer,	intent(out)	::	istop	Variable designating whether there are problems computing the function at the current `beta` and `delta`.
integer,	intent(inout)	::	nfev	Number of function evaluations.
real(kind=wp),	intent(out)	::	wrk1(n,m,q)	A work array of `(n, m, q)` elements.
real(kind=wp),	intent(out)	::	wrk2(n,q)	A work array of `(n, q)` elements.
real(kind=wp),	intent(out)	::	wrk6(n,np,q)	A work array of `(n, np, q)` elements.

public subroutine check_jac_value(fcn, n, m, np, q, beta, xplusd, ifixb, ifixx, ldifx, eta, tol, nrow, epsmac, j, lq, typj, h0, hc0, iswrtb, pv, d, diffj, msg1, msg, istop, nfev, wrk1, wrk2, wrk6, interval)

Check user supplied analytic derivatives against numerical derivatives.

Arguments

Type	Intent		Name
procedure(fcn_t)		::	fcn	User supplied subroutine for evaluating the model.
integer,	intent(in)	::	n	Number of observations.
integer,	intent(in)	::	m	Number of columns of data in the explanatory variable.
integer,	intent(in)	::	np	Number of function parameters.
integer,	intent(in)	::	q	Number of responses per observation.
real(kind=wp),	intent(inout)	::	beta(np)	Function parameters.
real(kind=wp),	intent(inout)	::	xplusd(n,m)	Values of `x + delta`.
integer,	intent(in)	::	ifixb(np)	Values designating whether the elements of `beta` are fixed at their input values or not.
integer,	intent(in)	::	ifixx(ldifx,m)	Values designating whether the elements of `x` are fixed at their input values or not.
integer,	intent(in)	::	ldifx	Leading dimension of array `ifixx`.
real(kind=wp),	intent(in)	::	eta	Relative noise in the model.
real(kind=wp),	intent(in)	::	tol	Agreement tolerance.
integer,	intent(in)	::	nrow	Row number of the explanatory variable array at which the derivative is to be checked.
real(kind=wp),	intent(in)	::	epsmac	Value of machine precision.
integer,	intent(in)	::	j	Index of the partial derivative being examined.
integer,	intent(in)	::	lq	Response currently being examined.
real(kind=wp),	intent(in)	::	typj	Typical size of the `j`-th unknown `beta` or `delta`.
real(kind=wp),	intent(in)	::	h0	Initial step size for the finite difference derivative.
real(kind=wp),	intent(in)	::	hc0	Relative step size for central finite differences.
logical,	intent(in)	::	iswrtb	Variable designating whether the derivatives wrt `beta` (`iswrtb = .true.`) or `delta` (`iswrtb = .false.`) are being checked.
real(kind=wp),	intent(in)	::	pv	Predicted value for row `nrow`.
real(kind=wp),	intent(in)	::	d	Derivative with respect to the `j`-th unknown parameter.
real(kind=wp),	intent(out)	::	diffj	Relative differences between the user supplied and finite difference derivatives for the derivative being checked.
integer,	intent(out)	::	msg1	First set of error checking results.
integer,	intent(out)	::	msg(q,j)	Error checking results.
integer,	intent(out)	::	istop	Variable designating whether there are problems computing the function at the current `beta` and `delta`.
integer,	intent(inout)	::	nfev	Number of function evaluations.
real(kind=wp),	intent(out)	::	wrk1(n,m,q)	A work array of `(n, m, q)` elements.
real(kind=wp),	intent(out)	::	wrk2(n,q)	A work array of `(n, q)` elements.
real(kind=wp),	intent(out)	::	wrk6(n,np,q)	A work array of `(n, np, q)` elements.
integer,	intent(in)	::	interval(np)	Specifies which checks can be performed when checking derivatives based on the interval of the bound constraints.

public subroutine check_jac_zero(fcn, n, m, np, q, beta, xplusd, ifixb, ifixx, ldifx, nrow, epsmac, j, lq, iswrtb, tol, d, fd, typj, pvpstp, stp0, pv, diffj, msg, istop, nfev, wrk1, wrk2, wrk6)

Recheck the derivatives in the case where the finite difference derivative disagrees with the analytic derivative and the analytic derivative is zero.

Arguments

Type	Intent		Name
procedure(fcn_t)		::	fcn	User supplied subroutine for evaluating the model.
integer,	intent(in)	::	n	Number of observations.
integer,	intent(in)	::	m	Number of columns of data in the explanatory variable.
integer,	intent(in)	::	np	Number of function parameters.
integer,	intent(in)	::	q	Number of responses per observation.
real(kind=wp),	intent(inout)	::	beta(np)	Function parameters.
real(kind=wp),	intent(inout)	::	xplusd(n,m)	Values of `x + delta`.
integer,	intent(in)	::	ifixb(np)	Values designating whether the elements of `beta` are fixed at their input values or not.
integer,	intent(in)	::	ifixx(ldifx,m)	Values designating whether the elements of `x` are fixed at their input values or not.
integer,	intent(in)	::	ldifx	Leading dimension of array `ifixx`.
integer,	intent(in)	::	nrow	Row number of the explanatory variable array at which the derivative is to be checked.
real(kind=wp),	intent(in)	::	epsmac	Value of machine precision.
integer,	intent(in)	::	j	Index of the partial derivative being examined.
integer,	intent(in)	::	lq	Response currently being examined.
logical,	intent(in)	::	iswrtb	Variable designating whether the derivatives wrt `beta` (`iswrtb = .true.`) or `delta` (`iswrtb = .false.`) are being checked.
real(kind=wp),	intent(in)	::	tol	Agreement tolerance.
real(kind=wp),	intent(in)	::	d	Derivative with respect to the `j`-th unknown parameter.
real(kind=wp),	intent(in)	::	fd	Forward difference derivative wrt the `j`-th parameter.
real(kind=wp),	intent(in)	::	typj	Typical size of the `j`-th unknown `beta` or `delta`.
real(kind=wp),	intent(in)	::	pvpstp	Predicted value for row `nrow` of the model using the current parameter estimates for all but the `j`-th parameter value, which is `beta(j) + stp0`.
real(kind=wp),	intent(in)	::	stp0	Initial step size for the finite difference derivative.
real(kind=wp),	intent(in)	::	pv	Predicted value from the model for row `nrow`.
real(kind=wp),	intent(out)	::	diffj	Relative differences between the user supplied and finite difference derivatives for the derivative being checked.
integer,	intent(out)	::	msg(q,j)	Error checking results.
integer,	intent(out)	::	istop	Variable designating whether there are problems computing the function at the current `beta` and `delta`.
integer,	intent(inout)	::	nfev	Number of function evaluations.
real(kind=wp),	intent(out)	::	wrk1(n,m,q)	A work array of `(n, m, q)` elements.
real(kind=wp),	intent(out)	::	wrk2(n,q)	A work array of `(n, q)` elements.
real(kind=wp),	intent(out)	::	wrk6(n,np,q)	A work array of `(n, np, q)` elements.

public pure subroutine check_inputs(n, m, np, q, isodr, anajac, beta, ifixb, ldifx, ldscld, ldstpd, ldwe, ld2we, ldwd, ld2wd, lrwork, lrwkmin, liwork, liwkmin, sclb, scld, stpb, stpd, info, lower, upper)

Check input parameters, indicating errors found using nonzero values of argument info.

Arguments

Type	Intent		Name
integer,	intent(in)	::	n	Number of observations.
integer,	intent(in)	::	m	Number of columns of data in the explanatory variable.
integer,	intent(in)	::	np	Number of function parameters.
integer,	intent(in)	::	q	Number of responses per observation.
logical,	intent(in)	::	isodr	Variable designating whether the solution is by ODR (`.true.`) or by OLS (`.false.`).
logical,	intent(in)	::	anajac	Variable designating whether the Jacobians are computed by finite differences (`.false.`) or not (`.true.`).
real(kind=wp),	intent(in)	::	beta(np)	Function parameters.
integer,	intent(in)	::	ifixb(np)	Values designating whether the elements of `beta` are fixed at their input values or not.
integer,	intent(in)	::	ldifx	Leading dimension of array `ifixx`.
integer,	intent(in)	::	ldscld	Leading dimension of array `scld`.
integer,	intent(in)	::	ldstpd	Leading dimension of array `stpd`.
integer,	intent(in)	::	ldwe	Leading dimension of array `we`.
integer,	intent(in)	::	ld2we	Second dimension of array `we`.
integer,	intent(in)	::	ldwd	Leading dimension of array `wd`.
integer,	intent(in)	::	ld2wd	Second dimension of array `wd`.
integer,	intent(in)	::	lrwork	Length of vector `rwork`.
integer,	intent(in)	::	lrwkmin	Minimum acceptable length of array `rwork`.
integer,	intent(in)	::	liwork	Length of vector `iwork`.
integer,	intent(in)	::	liwkmin	Minimum acceptable length of array `iwork`.
real(kind=wp),	intent(in)	::	sclb(np)	Scaling values for `beta`.
real(kind=wp),	intent(in)	::	scld(ldscld,m)	Scaling value for `delta`.
real(kind=wp),	intent(in)	::	stpb(np)	Step for the finite difference derivative wrt `beta`.
real(kind=wp),	intent(in)	::	stpd(ldstpd,m)	Step for the finite difference derivative wrt `delta`.
integer,	intent(out)	::	info	Variable designating why the computations were stopped.
real(kind=wp),	intent(in)	::	lower(np)	Lower bound on `beta`.
real(kind=wp),	intent(in)	::	upper(np)	Upper bound on `beta`.

public subroutine lcstep(n, m, np, q, npp, f, fjacb, fjacd, wd, ldwd, ld2wd, ss, tt, ldtt, delta, alpha, epsfcn, isodr, tfjacb, omega, u, qraux, kpvt, s, t, phi, irank, rcond, forvcv, wrk1, wrk2, wrk3, wrk4, wrk5, wrk, lwrk, istopc)

Compute locally constrained steps s and t, and phi(alpha).

Arguments

Type	Intent		Name
integer,	intent(in)	::	n	Number of observations.
integer,	intent(in)	::	m	Number of columns of data in the explanatory variable.
integer,	intent(in)	::	np	Number of function parameters.
integer,	intent(in)	::	q	Number of responses per observation.
integer,	intent(in)	::	npp	Number of function parameters being estimated.
real(kind=wp),	intent(in)	::	f(n,q)	Weighted estimated values of `epsilon`.
real(kind=wp),	intent(in)	::	fjacb(n,np,q)	Jacobian with respect to `beta`.
real(kind=wp),	intent(in)	::	fjacd(n,m,q)	Jacobian with respect to `delta`.
real(kind=wp),	intent(in)	::	wd(ldwd,ld2wd,m)	Squared `delta` weights.
integer,	intent(in)	::	ldwd	Leading dimension of array `wd`.
integer,	intent(in)	::	ld2wd	Second dimension of array `wd`.
real(kind=wp),	intent(in)	::	ss(np)	Scaling values for the unfixed `beta`s.
real(kind=wp),	intent(in)	::	tt(ldtt,m)	Scaling values for `delta`.
integer,	intent(in)	::	ldtt	Leading dimension of array `tt`.
real(kind=wp),	intent(in)	::	delta(n,m)	Estimated errors in the explanatory variables.
real(kind=wp),	intent(in)	::	alpha	Levenberg-Marquardt parameter.
real(kind=wp),	intent(in)	::	epsfcn	Function's precision.
logical,	intent(in)	::	isodr	Variable designating whether the solution is by ODR (`.true.`) or by OLS (`.false.`).
real(kind=wp),	intent(out)	::	tfjacb(n,q,np)	Array `omega*fjacb`.
real(kind=wp),	intent(out)	::	omega(q,q)	Array defined such that: `omegatrans(omega) = inv(I + fjacdinv(e)trans(fjacd)) = (I - fjacdinv(p)trans(fjacd))` where `e = d2 + alphatt*2` and `p = trans(fjacd)fjacd + d*2 + alphatt**2`.
real(kind=wp),	intent(out)	::	u(np)	Approximate null vector for `tfjacb`.
real(kind=wp),	intent(out)	::	qraux(np)	Array required to recover the orthogonal part of the Q-R decomposition.
integer,	intent(out)	::	kpvt(np)	Pivot vector.
real(kind=wp),	intent(out)	::	s(np)	Step for `beta`.
real(kind=wp),	intent(out)	::	t(n,m)	Step for `delta`.
real(kind=wp),	intent(out)	::	phi	Difference between the norm of the scaled step and the trust region diameter.
integer,	intent(out)	::	irank	Rank deficiency of the Jacobian wrt `beta`.
real(kind=wp),	intent(out)	::	rcond	Approximate reciprocal condition number of `tfjacb`.
logical,	intent(in)	::	forvcv	Variable designating whether this subroutine was called to set up for the covariance matrix computations (`forvcv = .true.`) or not (`forvcv = .false.`).
real(kind=wp),	intent(out)	::	wrk1(n,q,m)	A work array of `(n, q, m)` elements.
real(kind=wp),	intent(out)	::	wrk2(n,q)	A work array of `(n, q)` elements.
real(kind=wp),	intent(out)	::	wrk3(np)	A work array of `(np)` elements.
real(kind=wp),	intent(out)	::	wrk4(m,m)	A work array of `(m, m)` elements.
real(kind=wp),	intent(out)	::	wrk5(m)	A work array of `(m)` elements.
real(kind=wp),	intent(out)	::	wrk(lwrk)	A work array of `(lwrk)` elements, equivalenced to `wrk1` and `wrk2`.
integer,	intent(in)	::	lwrk	Length of vector `wrk`.
integer,	intent(inout)	::	istopc	Variable designating whether the computations were stopped due to a numerical error within subroutine `dodstp`.

public subroutine vcv_beta(n, m, np, q, npp, f, fjacb, fjacd, wd, ldwd, ld2wd, ssf, ss, tt, ldtt, delta, epsfcn, isodr, vcv, sd, wrk6, omega, u, qraux, jpvt, s, t, irank, rcond, rss, idf, rvar, ifixb, wrk1, wrk2, wrk3, wrk4, wrk5, wrk, lwrk, istopc)

Compute covariance matrix of estimated parameters.

Arguments

Type	Intent		Name
integer,	intent(in)	::	n	Number of observations.
integer,	intent(in)	::	m	Number of columns of data in the explanatory variable.
integer,	intent(in)	::	np	Number of function parameters.
integer,	intent(in)	::	q	Number of responses per observation.
integer,	intent(in)	::	npp	Number of function parameters being estimated.
real(kind=wp),	intent(in)	::	f(n,q)	Weighted estimated values of `epsilon`.
real(kind=wp),	intent(in)	::	fjacb(n,np,q)	Jacobian with respect to `beta`.
real(kind=wp),	intent(in)	::	fjacd(n,m,q)	Jacobian with respect to `delta`.
real(kind=wp),	intent(in)	::	wd(ldwd,ld2wd,m)	`delta` weights.
integer,	intent(in)	::	ldwd	Leading dimension of array `wd`.
integer,	intent(in)	::	ld2wd	Second dimension of array `wd`.
real(kind=wp),	intent(in)	::	ssf(np)	Scaling values used for `beta`.
real(kind=wp),	intent(in)	::	ss(np)	Scaling values for the unfixed `beta`s.
real(kind=wp),	intent(in)	::	tt(ldtt,m)	Scaling values for `delta`.
integer,	intent(in)	::	ldtt	Leading dimension of array `tt`.
real(kind=wp),	intent(in)	::	delta(n,m)	Estimated errors in the explanatory variables.
real(kind=wp),	intent(in)	::	epsfcn	Function's precision.
logical,	intent(in)	::	isodr	Variable designating whether the solution is by ODR (`.true.`) or by OLS (`.false.`).
real(kind=wp),	intent(out)	::	vcv(np,np)	Covariance matrix of the estimated `beta`s.
real(kind=wp),	intent(out)	::	sd(np)	Standard deviations of the estimated `beta`s.
real(kind=wp),	intent(out)	::	wrk6(n*q,np)	A work array of `(n*q, np)` elements.
real(kind=wp),	intent(out)	::	omega(q,q)	Array defined such that `omegatrans(omega) = inv(I + fjacdinv(e)trans(fjacd)) = (I - fjacdinv(p)*trans(fjacd))`.
real(kind=wp),	intent(out)	::	u(np)	Approximate null vector for `fjacb`.
real(kind=wp),	intent(out)	::	qraux(np)	Array required to recover the orthogonal part of the Q-R decomposition.
integer,	intent(out)	::	jpvt(np)	Pivot vector.
real(kind=wp),	intent(out)	::	s(np)	Step for `beta`.
real(kind=wp),	intent(out)	::	t(n,m)	Step for `delta`.
integer,	intent(out)	::	irank	Rank deficiency of the Jacobian wrt `beta`.
real(kind=wp),	intent(out)	::	rcond	Approximate reciprocal condition of `fjacb`.
real(kind=wp),	intent(inout)	::	rss	Residual sum of squares.
integer,	intent(out)	::	idf	Degrees of freedom of the fit, equal to the number of observations with nonzero weighted derivatives minus the number of parameters being estimated.
real(kind=wp),	intent(out)	::	rvar	Residual variance.
integer,	intent(in)	::	ifixb(np)	Values designating whether the elements of `beta` are fixed at their input values or not.
real(kind=wp),	intent(out)	::	wrk1(n,q,m)	A work array of `(n, q, m)` elements.
real(kind=wp),	intent(out)	::	wrk2(n,q)	A work array of `(n, q)` elements.
real(kind=wp),	intent(out)	::	wrk3(np)	A work array of `(np)` elements.
real(kind=wp),	intent(out)	::	wrk4(m,m)	A work array of `(m, m)` elements.
real(kind=wp),	intent(out)	::	wrk5(m)	A work array of `(m)` elements.
real(kind=wp),	intent(out)	::	wrk(lwrk)	A work array of `(lwrk)` elements, equivalenced to `wrk1` and `wrk2`.
integer,	intent(in)	::	lwrk	Length of vector `lwrk`.
integer,	intent(out)	::	istopc	Variable designating whether the computations were stoped due to a numerical error within subroutine `dodstp`.

public pure subroutine pack_vec(n2, n1, v1, v2, ifix)

Select the unfixed elements of v2 and return them in v1.

Arguments

Type	Intent		Name
integer,	intent(in)	::	n2	Number of items in `v2`.
integer,	intent(out)	::	n1	Number of items in `v1`.
real(kind=wp),	intent(out)	::	v1(n2)	Vector of the unfixed items from `v2`.
real(kind=wp),	intent(in)	::	v2(n2)	Vector of the fixed and unfixed items from which the unfixed elements are to be extracted.
integer,	intent(in)	::	ifix(n2)	Values designating whether the elements of `v2` are fixed at their input values or not.

public pure subroutine unpack_vec(n2, v1, v2, ifix)

Copy the elements of v1 into the locations of v2 which are unfixed.

Arguments

Type	Intent		Name
integer,	intent(in)	::	n2	Number of items in `v2`.
real(kind=wp),	intent(in)	::	v1(n2)	Vector of the unfixed items.
real(kind=wp),	intent(out)	::	v2(n2)	Vector of the fixed and unfixed items into which the elements of `v1` are to be inserted.
integer,	intent(in)	::	ifix(n2)	Values designating whether the elements of `v2` are fixed at their input values or not.

public subroutine fpvb(fcn, n, m, np, q, beta, xplusd, ifixb, ifixx, ldifx, nrow, j, lq, stp, istop, nfev, pvb, fjacd, f, fjacb)

Compute the nrow-th function value using beta(j) + stp.

Arguments

Type	Intent		Name
procedure(fcn_t)		::	fcn	User-supplied subroutine for evaluating the model.
integer,	intent(in)	::	n	Number of observations.
integer,	intent(in)	::	m	Number of columns of data in the independent variable.
integer,	intent(in)	::	np	Number of function parameters.
integer,	intent(in)	::	q	Number of responses per observation.
real(kind=wp),	intent(inout)	::	beta(np)	Function parameters.
real(kind=wp),	intent(in)	::	xplusd(n,m)	Values of `x + delta`.
integer,	intent(in)	::	ifixb(np)	Values designating whether the elements of `beta` are fixed at their input values or not.
integer,	intent(in)	::	ifixx(ldifx,m)	Values designating whether the elements of `x` are fixed at their input values or not.
integer,	intent(in)	::	ldifx	Leading dimension of array `ifixx`.
integer,	intent(in)	::	nrow	Row number of the independent variable array at which the derivative is to be checked.
integer,	intent(in)	::	j	Index of the partial derivative being examined.
integer,	intent(in)	::	lq	Response currently being examined.
real(kind=wp),	intent(in)	::	stp	Step size for the finite difference derivative.
integer,	intent(out)	::	istop	Variable designating whether there are problems computing the function at the current `beta` and `delta`.
integer,	intent(inout)	::	nfev	Number of function evaluations.
real(kind=wp),	intent(out)	::	pvb	Function value for the selected observation & response.
real(kind=wp),	intent(out)	::	fjacd(n,m,q)	Jacobian wrt delta.
real(kind=wp),	intent(out)	::	f(n,q)	Predicted function values.
real(kind=wp),	intent(out)	::	fjacb(n,np,q)	Jocobian wrt beta.

public subroutine fpvd(fcn, n, m, np, q, beta, xplusd, ifixb, ifixx, ldifx, nrow, j, lq, stp, istop, nfev, pvd, fjacd, f, fjacb)

Compute nrow-th function value using x(nrow, j) + delta(nrow, j) + stp.

Arguments

Type	Intent		Name
procedure(fcn_t)		::	fcn	User-supplied subroutine for evaluating the model.
integer,	intent(in)	::	n	Number of observations.
integer,	intent(in)	::	m	Number of columns of data in the independent variable.
integer,	intent(in)	::	np	Number of function parameters.
integer,	intent(in)	::	q	Number of responses per observation.
real(kind=wp),	intent(in)	::	beta(np)	Function parameters.
real(kind=wp),	intent(inout)	::	xplusd(n,m)	Values of `x + delta`.
integer,	intent(in)	::	ifixb(np)	Values designating whether the elements of `beta` are fixed at their input values or not.
integer,	intent(in)	::	ifixx(ldifx,m)	Values designating whether the elements of `x` are fixed at their input values or not.
integer,	intent(in)	::	ldifx	Leading dimension of array `ifixx`.
integer,	intent(in)	::	nrow	Row number of the independent variable array at which the derivative is to be checked.
integer,	intent(in)	::	j	Index of the partial derivative being examined.
integer,	intent(in)	::	lq	Response currently being examined.
real(kind=wp),	intent(in)	::	stp	Step size for the finite difference derivative.
integer,	intent(out)	::	istop	Variable designating whether there are problems computing the function at the current `beta` and `delta`.
integer,	intent(inout)	::	nfev	Number of function evaluations.
real(kind=wp),	intent(out)	::	pvd	Function value for the selected observation & response.
real(kind=wp),	intent(out)	::	fjacd(n,m,q)	Jacobian wrt delta.
real(kind=wp),	intent(out)	::	f(n,q)	Predicted function values.
real(kind=wp),	intent(out)	::	fjacb(n,np,q)	Jocobian wrt beta.

public pure subroutine scale_vec(n, m, scl, ldscl, t, ldt, sclt, ldsclt)

Scale t by the inverse of scl, i.e., compute t/scl.

Arguments

Type	Intent		Name
integer,	intent(in)	::	n	Number of rows of data in `t`.
integer,	intent(in)	::	m	Number of columns of data in `t`.
real(kind=wp),	intent(in)	::	scl(ldscl,m)	Scale values.
integer,	intent(in)	::	ldscl	Leading dimension of array `scl`.
real(kind=wp),	intent(in)	::	t(ldt,m)	Array to be inversely scaled by `scl`.
integer,	intent(in)	::	ldt	Leading dimension of array `t`.
real(kind=wp),	intent(out)	::	sclt(ldsclt,m)	Inversely scaled matrix.
integer,	intent(in)	::	ldsclt	Leading dimension of array `sclt`.

public pure subroutine scale_beta(np, beta, ssf)

Select scaling values for beta according to the algorithm given in the ODRPACK95 reference guide.

Arguments

Type	Intent		Name
integer,	intent(in)	::	np	Number of function parameters.
real(kind=wp),	intent(in)	::	beta(np)	Function parameters.
real(kind=wp),	intent(out)	::	ssf(np)	Scaling values for `beta`.

public pure subroutine scale_delta(n, m, x, tt, ldtt)

Select scaling values for delta according to the algorithm given in the ODRPACK95 reference guide.

Arguments

Type	Intent		Name
integer,	intent(in)	::	n	Number of observations.
integer,	intent(in)	::	m	Number of columns of data in the independent variable.
real(kind=wp),	intent(in)	::	x(n,m)	Independent variable.
real(kind=wp),	intent(out)	::	tt(ldtt,m)	Scaling values for `delta`.
integer,	intent(in)	::	ldtt	Leading dimension of array `tt`.

public pure subroutine select_row(n, m, x, nrow)

Select the row at which the derivative will be checked.

Arguments

Type	Intent		Name
integer,	intent(in)	::	n	Number of observations.
integer,	intent(in)	::	m	Number of columns of data in the independent variable.
real(kind=wp),	intent(in)	::	x(n,m)	Independent variable.
integer,	intent(inout)	::	nrow	Selected row number of the independent variable.

public pure subroutine solve_trl(n, t, ldt, b, job)

Solve systems of the form:

Arguments

Type	Intent		Name
integer,	intent(in)	::	n	Number of rows and columns of data in array `t`.
real(kind=wp),	intent(in)	::	t(ldt,n)	Upper or lower tridiagonal system.
integer,	intent(in)	::	ldt	Leading dimension of array `t`.
real(kind=wp),	intent(inout)	::	b(:)	On input: the right hand side; On exit: the solution.
integer,	intent(in)	::	job	What kind of system is to be solved: 1: Solve `t * x = b`, where `t` is lower triangular, 2: Solve `t * x = b`, where `t` is upper triangular, 3: Solve `trans(t) * x = b`, where `t` is lower triangular, 4: Solve `trans(t) * x = b`, where `t` is upper triangular.

public pure subroutine vevtr(m, q, indx, v, ldv, ld2v, e, lde, ve, ldve, ld2ve, vev, ldvev, wrk5)

Compute v*e*trans(v) for the (indx)th m by q array in v.

Arguments

Type	Intent		Name
integer,	intent(in)	::	m	Number of columns of data in the independent variable.
integer,	intent(in)	::	q	Number of responses per observation.
integer,	intent(in)	::	indx	Row in `v` in which the `m` by `q` array is stored.
real(kind=wp),	intent(in)	::	v(ldv,ld2v,q)	An array of `q` by `m` matrices.
integer,	intent(in)	::	ldv	Leading dimension of array `v`.
integer,	intent(in)	::	ld2v	Second dimension of array `v`.
real(kind=wp),	intent(in)	::	e(lde,m)	Matrix of the factors, so `ete = (d*2 + alphat**2)`.
integer,	intent(in)	::	lde	Leading dimension of array `e`.
real(kind=wp),	intent(out)	::	ve(ldve,ld2ve,m)	Array `ve = v * inv(e)`.
integer,	intent(in)	::	ldve	Leading dimension of array `ve`.
integer,	intent(in)	::	ld2ve	Second dimension of array `ve`.
real(kind=wp),	intent(out)	::	vev(ldvev,q)	Array `vev = v * inv(ete) * trans(v)`.
integer,	intent(in)	::	ldvev	Leading dimension of array `vev`.
real(kind=wp),	intent(out)	::	wrk5(m)	Work vector.

public pure subroutine scale_mat(n, m, wt, ldwt, ld2wt, t, wtt)

Scale matrix t using wt, i.e., compute wtt = wt*t.

Arguments

Type	Intent	Attributes		Name
integer,	intent(in)		::	n	Number of rows of data in `t`.
integer,	intent(in)		::	m	Number of columns of data in `t`.
real(kind=wp),	intent(in),	target	::	wt(..)	Array of shape conformable to `(ldwt,ld2wt,m)` holding the weights.
integer,	intent(in)		::	ldwt	Leading dimension of array `wt`.
integer,	intent(in)		::	ld2wt	Second dimension of array `wt`.
real(kind=wp),	intent(in),	target	::	t(..)	Array of shape conformable to `(n,m)` being scaled by `wt`.
real(kind=wp),	intent(out),	target	::	wtt(..)	Array of shape conformable to `(n,m)` holding the result of weighting array `t` by array `wt`. Array `wtt` can be the same as `t` only if the arrays in `wt` are upper triangular with zeros below the diagonal.

public pure subroutine move_beta(np, beta, lower, upper, ssf, stpb, neta, eta, interval)

Ensure range of bounds is large enough for derivative checking. Move beta away from bounds so that derivatives can be calculated.

Arguments

Type	Intent		Name
integer,	intent(in)	::	np	Number of parameters `np`.
real(kind=wp),	intent(inout)	::	beta(np)	Function parameters.
real(kind=wp),	intent(in)	::	lower(np)	!! Lower bound on `beta`.
real(kind=wp),	intent(in)	::	upper(np)	Upper bound on `beta`.
real(kind=wp),	intent(in)	::	ssf(np)	Scale used for the `beta`s.
real(kind=wp),	intent(in)	::	stpb(np)	Relative step used for computing finite difference derivatives with respect to `beta`.
integer,	intent(in)	::	neta	Number of good digits in the function results.
real(kind=wp),	intent(in)	::	eta	Relative noise in the function results.
integer,	intent(out)	::	interval(np)	Specifies which difference methods and step sizes are supported by the current interval `upper-lower`.

odrpack_core Module

Contents

Abstract Interfaces

Functions

Subroutines

Uses

Used by

Abstract Interfaces

abstract interface

public subroutine fcn_t(beta, xplusd, ifixb, ifixx, ideval, f, fjacb, fjacd, istop)

Arguments

Functions

public pure function derstep(itype, k, betak, ssf, stpb, neta) result(res)

Arguments

Return Value real(kind=wp)

public pure function hstep(itype, neta, i, j, stp, ldstp) result(res)

Arguments

Return Value real(kind=wp)

public pure function ppf_normal(p) result(res)

Arguments

Return Value real(kind=wp)

public pure function ppf_tstudent(p, idf) result(res)

Arguments

Return Value real(kind=wp)

Subroutines

public subroutine trust_region(n, m, np, q, npp, f, fjacb, fjacd, wd, ldwd, ld2wd, ss, tt, ldtt, delta, alpha2, tau, epsfcn, isodr, tfjacb, omega, u, qraux, jpvt, s, t, nlms, rcond, irank, wrk1, wrk2, wrk3, wrk4, wrk5, wrk, lwrk, istopc)

Arguments

Arguments

public pure subroutine esubi(n, m, wd, ldwd, ld2wd, alpha, tt, ldtt, i, e)

Arguments

public subroutine eta_fcn(fcn, n, m, np, q, xplusd, beta, epsmac, nrow, partmp, pv0, ifixb, ifixx, ldifx, istop, nfev, eta, neta, fjacd, f, fjacb, wrk7, info, lower, upper)

Arguments

public subroutine eval_jac(fcn, anajac, cdjac, n, m, np, q, betac, beta, stpb, ifixb, ifixx, ldifx, x, delta, xplusd, stpd, ldstpd, ssf, tt, ldtt, neta, fn, stp, wrk1, wrk2, wrk3, wrk6, tempret, fjacb, isodr, fjacd, we1, ldwe, ld2we, njev, nfev, istop, info, lower, upper)

Arguments

public pure subroutine fctr(oksemi, a, lda, n, info)

Arguments

public pure subroutine fctrw(n, m, q, npp, isodr, we, ldwe, ld2we, wd, ldwd, ld2wd, wrk0, wrk4, we1, nnzw, info)

Arguments

public pure subroutine set_flags(job, restart, initd, dovcv, redoj, anajac, cdjac, chkjac, isodr, implicit)

Arguments

public pure subroutine set_ifix(n, m, ifix, ldifix, t, ldt, tfix, ldtfix)

Arguments

public pure subroutine loc_iwork(m, q, np, msgbi, msgdi, ifix2i, istopi, nnzwi, nppi, idfi, jobi, iprinti, lunerri, lunrpti, nrowi, ntoli, netai, maxiti, niteri, nfevi, njevi, int2i, iranki, ldtti, boundi, liwkmin)

Arguments

Arguments

Arguments

public subroutine jac_cdiff(fcn, n, m, np, q, beta, x, delta, xplusd, ifixb, ifixx, ldifx, stpb, stpd, ldstpd, ssf, tt, ldtt, neta, fn, stp, wrk1, wrk2, wrk3, wrk6, fjacb, isodr, fjacd, nfev, istop, info, lower, upper)

Arguments

public subroutine jac_fwdiff(fcn, n, m, np, q, beta, x, delta, xplusd, ifixb, ifixx, ldifx, stpb, stpd, ldstpd, ssf, tt, ldtt, neta, fn, stp, wrk1, wrk2, wrk3, wrk6, fjacb, isodr, fjacd, nfev, istop, info, lower, upper)

Arguments

public subroutine check_jac(fcn, n, m, np, q, beta, betaj, xplusd, ifixb, ifixx, ldifx, stpb, stpd, ldstpd, ssf, tt, ldtt, eta, neta, ntol, nrow, isodr, epsmac, pv0i, fjacb, fjacd, msgb, msgd, diff, istop, nfev, njev, wrk1, wrk2, wrk6, interval)

Arguments

public subroutine check_jac_curv(fcn, n, m, np, q, beta, xplusd, ifixb, ifixx, ldifx, eta, tol, nrow, epsmac, j, lq, hc, iswrtb, fd, typj, pvpstp, stp0, pv, d, diffj, msg, istop, nfev, wrk1, wrk2, wrk6)

Arguments

public subroutine check_jac_fp(fcn, n, m, np, q, beta, xplusd, ifixb, ifixx, ldifx, eta, tol, nrow, j, lq, iswrtb, fd, typj, pvpstp, stp0, curve, pv, d, diffj, msg, istop, nfev, wrk1, wrk2, wrk6)

Arguments

public subroutine check_jac_value(fcn, n, m, np, q, beta, xplusd, ifixb, ifixx, ldifx, eta, tol, nrow, epsmac, j, lq, typj, h0, hc0, iswrtb, pv, d, diffj, msg1, msg, istop, nfev, wrk1, wrk2, wrk6, interval)

Arguments

public subroutine check_jac_zero(fcn, n, m, np, q, beta, xplusd, ifixb, ifixx, ldifx, nrow, epsmac, j, lq, iswrtb, tol, d, fd, typj, pvpstp, stp0, pv, diffj, msg, istop, nfev, wrk1, wrk2, wrk6)

Arguments

public pure subroutine check_inputs(n, m, np, q, isodr, anajac, beta, ifixb, ldifx, ldscld, ldstpd, ldwe, ld2we, ldwd, ld2wd, lrwork, lrwkmin, liwork, liwkmin, sclb, scld, stpb, stpd, info, lower, upper)

Arguments

public subroutine lcstep(n, m, np, q, npp, f, fjacb, fjacd, wd, ldwd, ld2wd, ss, tt, ldtt, delta, alpha, epsfcn, isodr, tfjacb, omega, u, qraux, kpvt, s, t, phi, irank, rcond, forvcv, wrk1, wrk2, wrk3, wrk4, wrk5, wrk, lwrk, istopc)

Arguments

public subroutine vcv_beta(n, m, np, q, npp, f, fjacb, fjacd, wd, ldwd, ld2wd, ssf, ss, tt, ldtt, delta, epsfcn, isodr, vcv, sd, wrk6, omega, u, qraux, jpvt, s, t, irank, rcond, rss, idf, rvar, ifixb, wrk1, wrk2, wrk3, wrk4, wrk5, wrk, lwrk, istopc)

Arguments

public pure subroutine pack_vec(n2, n1, v1, v2, ifix)

Arguments

public pure subroutine unpack_vec(n2, v1, v2, ifix)

Arguments

public subroutine fpvb(fcn, n, m, np, q, beta, xplusd, ifixb, ifixx, ldifx, nrow, j, lq, stp, istop, nfev, pvb, fjacd, f, fjacb)

Arguments

public subroutine fpvd(fcn, n, m, np, q, beta, xplusd, ifixb, ifixx, ldifx, nrow, j, lq, stp, istop, nfev, pvd, fjacd, f, fjacb)

Arguments

public pure subroutine scale_vec(n, m, scl, ldscl, t, ldt, sclt, ldsclt)

Arguments

public pure subroutine scale_beta(np, beta, ssf)

Arguments

public pure subroutine scale_delta(n, m, x, tt, ldtt)

Arguments