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(n, m, np, nq, ldn, ldm, ldnp, beta, xplusd, ifixb, ifixx, ldifx, ideval, f, fjacb, fjacd, istop)

User-supplied subroutine for evaluating the model.

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.
integer,	intent(in)	::	nq	Number of responses per observation.
integer,	intent(in)	::	ldn	Leading dimension declarator equal or exceeding `n`.
integer,	intent(in)	::	ldm	Leading dimension declarator equal or exceeding `m`.
integer,	intent(in)	::	ldnp	Leading dimension declarator equal or exceeding `np`.
real(kind=wp),	intent(in)	::	beta(np)	Current values of parameters.
real(kind=wp),	intent(in)	::	xplusd(ldn,m)	Current value of explanatory variable, i.e., `x + delta`.
integer,	intent(in)	::	ifixb(np)	Indicators for "fixing" parameters (`beta`).
integer,	intent(in)	::	ifixx(ldifx,m)	Indicators for "fixing" explanatory variable (`x`).
integer,	intent(in)	::	ldifx	Leading dimension of array `ifixx`.
integer,	intent(in)	::	ideval	Indicator for selecting computation to be performed.
real(kind=wp),	intent(out)	::	f(ldn,nq)	Predicted function values.
real(kind=wp),	intent(out)	::	fjacb(ldn,ldnp,nq)	Jacobian with respect to `beta`.
real(kind=wp),	intent(out)	::	fjacd(ldn,ldm,nq)	Jacobian with respect to errors `delta`.
integer,	intent(out)	::	istop	Stopping condition, with meaning as follows. 0 means current `beta` and `x+delta` were acceptable and values were computed successfully. 1 means current `beta` and `x+delta` are not acceptable; 'odrpack' should select values closer to most recently used values if possible. -1 means current `beta` and `x+delta` are not acceptable; 'odrpack' should stop.

Functions

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

Compute step size for center and forward difference calculations.

Arguments

Type	Intent		Name
integer,	intent(in)	::	itype	The finite difference method being used, where: `itype = 0` indicates forward finite differences, and `itype = 1` indicates central finite differences.
integer,	intent(in)	::	k	Index into `beta` where `betak` resides.
real(kind=wp),	intent(in)	::	betak	The `k`-th function parameter.
real(kind=wp),	intent(in)	::	ssf(k)	The scale used for the `beta`s.
real(kind=wp),	intent(in)	::	stpb(k)	The 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 dhstep(itype, neta, i, j, stp, ldstp) result(dhstepr)

Set relative step size for finite difference derivatives.

Arguments

Type	Intent		Name
integer,	intent(in)	::	itype	The finite difference method being used, where: `itype = 0` indicates forward finite differences, and `itype = 1` indicates central finite differences.
integer,	intent(in)	::	neta	The number of good digits in the function results.
integer,	intent(in)	::	i	An identifier for selecting user-supplied step sizes.
integer,	intent(in)	::	j	An identifier for selecting user-supplied step sizes.
real(kind=wp),	intent(in)	::	stp(ldstp,j)	The step size for the finite difference derivative.
integer,	intent(in)	::	ldstp	The leading dimension of array `stp`.

Return Value real(kind=wp)

public pure function dppnml(p) result(dppnmlr)

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	The probability at which the percent point is to be evaluated. `p` must lie between 0.0 and 1.0, exclusive.

Return Value real(kind=wp)

public pure function dppt(p, idf) result(dpptr)

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	The probability at which the percent point is to be evaluated. `p` must lie between 0.0 and 1.0, exclusive.
integer,	intent(in)			::	idf	The (positive integer) degrees of freedom.

Return Value real(kind=wp)

Subroutines

public subroutine dodlm(n, m, np, nq, 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, tempret, 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	The number of observations.
integer,	intent(in)	::	m	The number of columns of data in the explanatory variable.
integer,	intent(in)	::	np	The number of function parameters.
integer,	intent(in)	::	nq	The number of responses per observation.
integer,	intent(in)	::	npp	The number of function parameters being estimated.
real(kind=wp),	intent(in)	::	f(n,nq)	The (weighted) estimated values of `epsilon`.
real(kind=wp),	intent(in)	::	fjacb(n,np,nq)	The Jacobian with respect to `beta`.
real(kind=wp),	intent(in)	::	fjacd(n,m,nq)	The Jacobian with respect to `delta`.
real(kind=wp),	intent(in)	::	wd(ldwd,ld2wd,m)	The `delta` weights.
integer,	intent(in)	::	ldwd	The leading dimension of array `wd`.
integer,	intent(in)	::	ld2wd	The second dimension of array `wd`.
real(kind=wp),	intent(in)	::	ss(np)	The scaling values used for the unfixed `beta`s.
real(kind=wp),	intent(in)	::	tt(ldtt,m)	The scale used for the `delta`s.
integer,	intent(in)	::	ldtt	The leading dimension of array `tt`.
real(kind=wp),	intent(in)	::	delta(n,m)	The estimated errors in the explanatory variables.
real(kind=wp),	intent(inout)	::	alpha2	The current Levenberg-Marquardt parameter.
real(kind=wp),	intent(inout)	::	tau	The trust region diameter.
real(kind=wp),	intent(in)	::	epsfcn	The function's precision.
logical,	intent(in)	::	isodr	The variable designating whether the solution is by ODR (`isodr = .true.`) or by OLS (`isodr = .false.`).
real(kind=wp),	intent(out)	::	tfjacb(n,nq,np)	The array `omega*fjacb`.
real(kind=wp),	intent(out)	::	omega(nq,nq)	The array `(I-fjacdinv(p)trans(fjacd))**(-1/2)`.
real(kind=wp),	intent(out)	::	u(np)	The approximate null vector for tfjacb.
real(kind=wp),	intent(out)	::	qraux(np)	The array required to recover the orthogonal part of the Q-R decomposition.
integer,	intent(out)	::	jpvt(np)	The pivot vector.
real(kind=wp),	intent(out)	::	s(np)	The step for `beta`.
real(kind=wp),	intent(out)	::	t(n,m)	The step for `delta`.
integer,	intent(out)	::	nlms	The number of Levenberg-Marquardt steps taken.
real(kind=wp),	intent(out)	::	rcond	The approximate reciprocal condition of `tfjacb`.
integer,	intent(out)	::	irank	The rank deficiency of the Jacobian wrt `beta`.
real(kind=wp),	intent(out)	::	wrk1(n,nq,m)	A work array of `(n, nq, m)` elements.
real(kind=wp),	intent(out)	::	wrk2(n,nq)	A work array of `(n, nq)` 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	The length of vector `wrk`.
real(kind=wp),	intent(inout)	::	tempret(:,:)	Temporary work array for holding return values before copying to a lower rank array.
integer,	intent(out)	::	istopc	The variable designating whether the computations were stopped due to some other numerical error detected within subroutine `dodstp`.

public pure subroutine dacces(n, m, np, nq, ldwe, ld2we, work, lwork, 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	The number of observations.
integer,	intent(in)	::	m	The number of columns of data in the explanatory variable.
integer,	intent(in)	::	np	The number of function parameters.
integer,	intent(in)	::	nq	The number of responses per observation.
integer,	intent(in)	::	ldwe	The leading dimension of array `we`.
integer,	intent(in)	::	ld2we	The second dimension of array `we`.
real(kind=wp),	intent(inout)	::	work(lwork)	The real work space.
integer,	intent(in)	::	lwork	The length of vector `work`.
integer,	intent(inout)	::	iwork(liwork)	The integer work space.
integer,	intent(in)	::	liwork	The length of vector `iwork`.
logical,	intent(in)	::	access	The variable designating whether information is to be accessed from the work arrays (`access = .true.`) or stored in them (`access = .false.`).
logical,	intent(in)	::	isodr	The variable designating whether the solution is to be found by ODR (`isodr = .true.`) or by OLS (`isodr = .false.`).
integer,	intent(out)	::	jpvt	The pivot vector.
integer,	intent(out)	::	omega	The starting location in array `work` of array `omega`.
integer,	intent(out)	::	u	The starting location in array `work` of array `u`.
integer,	intent(out)	::	qraux	The starting location in array `work` of array `qraux`.
integer,	intent(out)	::	sd	The starting location in array `work` of array `sd`.
integer,	intent(out)	::	vcv	The starting location in array `work` of array `vcv`.
integer,	intent(out)	::	wrk1	The starting location in array `work` of array `wrk1`.
integer,	intent(out)	::	wrk2	The starting location in array `work` of array `wrk2`.
integer,	intent(out)	::	wrk3	The starting location in array `work` of array `wrk3`.
integer,	intent(out)	::	wrk4	The starting location in array `work` of array `wrk4`.
integer,	intent(out)	::	wrk5	The starting location in array `work` of array `wrk5`.
integer,	intent(out)	::	wrk6	The starting location in array `work` of array `wrk6`.
integer,	intent(out)	::	nnzw	The number of nonzero weighted observations.
integer,	intent(out)	::	npp	The number of function parameters actually estimated.
integer,	intent(out)	::	job	The variable controlling problem initialization and computational method.
real(kind=wp),	intent(inout)	::	partol	The parameter convergence stopping tolerance.
real(kind=wp),	intent(inout)	::	sstol	The sum-of-squares convergence stopping tolerance.
integer,	intent(out)	::	maxit	The maximum number of iterations allowed.
real(kind=wp),	intent(out)	::	taufac	The factor used to compute the initial trust region diameter.
real(kind=wp),	intent(out)	::	eta	The relative noise in the function results.
integer,	intent(out)	::	neta	The number of accurate digits in the function results.
integer,	intent(out)	::	lunrpt	The logical unit number used for computation reports.
integer,	intent(out)	::	ipr1	The value of the fourth digit (from the right) of `iprint`, which controls the initial summary report.
integer,	intent(out)	::	ipr2	The value of the third digit (from the right) of `iprint`, which controls the iteration reports.
integer,	intent(out)	::	ipr2f	The value of the second digit (from the right) of `iprint`, which controls the frequency of the iteration reports.
integer,	intent(out)	::	ipr3	The value of the first digit (from the right) of `iprint`, which controls the final summary report.
real(kind=wp),	intent(inout)	::	wss(3)	The 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	The residual variance, i.e. the standard deviation squared.
integer,	intent(inout)	::	idf	The 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	The trust region diameter.
real(kind=wp),	intent(inout)	::	alpha	The Levenberg-Marquardt parameter.
integer,	intent(inout)	::	niter	The number of iterations taken.
integer,	intent(inout)	::	nfev	The number of function evaluations.
integer,	intent(inout)	::	njev	The number of Jacobian evaluations.
integer,	intent(inout)	::	int2	The number of internal doubling steps.
real(kind=wp),	intent(inout)	::	olmavg	The average number of Levenberg-Marquardt steps per iteration.
real(kind=wp),	intent(inout)	::	rcond	The approximate reciprocal condition of `fjacb`.
integer,	intent(inout)	::	irank	The rank deficiency of the Jacobian wrt `beta`.
real(kind=wp),	intent(inout)	::	actrs	The saved actual relative reduction in the sum-of-squares.
real(kind=wp),	intent(inout)	::	pnorm	The norm of the scaled estimated parameters.
real(kind=wp),	intent(inout)	::	prers	The saved predicted relative reduction in the sum-of-squares.
real(kind=wp),	intent(inout)	::	rnorms	The norm of the saved weighted `epsilons` and `deltas`.
integer,	intent(inout)	::	istop	The variable designating whether there are problems computing the function at the current `beta` and `delta`.

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

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

Arguments

Type	Intent		Name
integer,	intent(in)	::	n	The number of observations.
integer,	intent(in)	::	m	The number of columns of data in the independent variable.
real(kind=wp),	intent(in)	::	wd(ldwd,ld2wd,m)	The squared `delta` weights.
integer,	intent(in)	::	ldwd	The leading dimension of array `wd`.
integer,	intent(in)	::	ld2wd	The second dimension of array `wd`.
real(kind=wp),	intent(in)	::	alpha	The Levenberg-Marquardt parameter.
real(kind=wp),	intent(in)	::	tt(ldtt,m)	The scaling values used for `delta`.
integer,	intent(in)	::	ldtt	The leading dimension of array `tt`.
integer,	intent(in)	::	i	An indexing variable.
real(kind=wp),	intent(out)	::	e(m,m)	The value of the array `e = wd + alphatt*2`.

public subroutine detaf(fcn, n, m, np, nq, xplusd, beta, epsmac, nrow, partmp, pv0, ifixb, ifixx, ldifx, istop, nfev, eta, neta, wrk1, wrk2, wrk6, wrk7, info, lower, upper)

Compute noise and number of good digits in function results.

Arguments

Type	Intent		Name
procedure(fcn_t)		::	fcn	The user-supplied subroutine for evaluating the model.
integer,	intent(in)	::	n	The number of observations.
integer,	intent(in)	::	m	The number of columns of data in the explanatory variable.
integer,	intent(in)	::	np	The number of function parameters.
integer,	intent(in)	::	nq	The number of responses per observation.
real(kind=wp),	intent(in)	::	xplusd(n,m)	The values of `x + delta`.
real(kind=wp),	intent(in)	::	beta(np)	The function parameters.
real(kind=wp),	intent(in)	::	epsmac	The value of machine precision.
integer,	intent(in)	::	nrow	The row number at which the derivative is to be checked.
real(kind=wp),	intent(out)	::	partmp(np)	The model parameters.
real(kind=wp),	intent(in)	::	pv0(n,nq)	The original predicted values.
integer,	intent(in)	::	ifixb(np)	The values designating whether the elements of `beta` are fixed at their input values or not.
integer,	intent(in)	::	ifixx(ldifx,m)	The values designating whether the elements of `x` are fixed at their input values or not.
integer,	intent(in)	::	ldifx	The leading dimension of array `ifixx`.
integer,	intent(out)	::	istop	The variable designating whether there are problems computing the function at the current `beta` and `delta`.
integer,	intent(inout)	::	nfev	The number of function evaluations.
real(kind=wp),	intent(out)	::	eta	The noise in the model results.
integer,	intent(out)	::	neta	The number of accurate digits in the model results.
real(kind=wp),	intent(out)	::	wrk1(n,m,nq)	A work array of `(n, m, nq)` elements.
real(kind=wp),	intent(out)	::	wrk2(n,nq)	A work array of `(n, nq)` elements.
real(kind=wp),	intent(out)	::	wrk6(n,np,nq)	A work array of `(n, np, nq)` elements.
real(kind=wp),	intent(out)	::	wrk7(-2:2,nq)	A work array of `(5, nq)` elements.
integer,	intent(out)	::	info	The variable indicating the status of the computation.
real(kind=wp),	intent(in)	::	lower(np)	The lower bound of `beta`.
real(kind=wp),	intent(in)	::	upper(np)	The upper bound of `beta`.

public subroutine devjac(fcn, anajac, cdjac, n, m, np, nq, betac, beta, stpb, ifixb, ifixx, ldifx, x, ldx, 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	The user-supplied subroutine for evaluating the model.
logical,	intent(in)	::	anajac	The variable designating whether the Jacobians are computed by finite differences (`anajac = .false.`) or not (`anajac = .true.`).
logical,	intent(in)	::	cdjac	The variable designating whether the Jacobians are computed by central differences (`cdjac = .true.`) or by forward differences (`cdjac = .false.`).
integer,	intent(in)	::	n	The number of observations.
integer,	intent(in)	::	m	The number of columns of data in the independent variable.
integer,	intent(in)	::	np	The number of function parameters.
integer,	intent(in)	::	nq	The number of responses per observation.
real(kind=wp),	intent(in)	::	betac(np)	The current estimated values of the unfixed `beta`s.
real(kind=wp),	intent(out)	::	beta(np)	The function parameters.
real(kind=wp),	intent(in)	::	stpb(np)	The relative step used for computing finite difference derivatives with respect to `beta`.
integer,	intent(in)	::	ifixb(np)	The values designating whether the elements of `beta` are fixed at their input values or not.
integer,	intent(in)	::	ifixx(ldifx,m)	The values designating whether the elements of `delta` are fixed at their input values or not.
integer,	intent(in)	::	ldifx	The leading dimension of array `ifixx`.
real(kind=wp),	intent(in)	::	x(ldx,m)	The independent variable.
integer,	intent(in)	::	ldx	The leading dimension of array `x`.
real(kind=wp),	intent(in)	::	delta(n,m)	The estimated values of `delta`.
real(kind=wp),	intent(out)	::	xplusd(n,m)	The values of `x + delta`.
real(kind=wp),	intent(in)	::	stpd(ldstpd,m)	The relative step used for computing finite difference derivatives with respect to `delta`.
integer,	intent(in)	::	ldstpd	The leading dimension of array `stpd`.
real(kind=wp),	intent(in)	::	ssf(np)	The scale used for the `beta`s.
real(kind=wp),	intent(in)	::	tt(ldtt,m)	The scaling values used for `delta`.
integer,	intent(in)	::	ldtt	The leading dimension of array `tt`.
integer,	intent(in)	::	neta	The number of accurate digits in the function results.
real(kind=wp),	intent(in)	::	fn(n,nq)	The predicted values of the function at the current point.
real(kind=wp),	intent(out)	::	stp(n)	The step used for computing finite difference derivatives with respect to `delta`.
real(kind=wp),	intent(out)	::	wrk1(n,m,nq)	A work array of `(n, m, nq)` elements.
real(kind=wp),	intent(out)	::	wrk2(n,nq)	A work array of `(n, nq)` elements.
real(kind=wp),	intent(out)	::	wrk3(np)	A work array of `(np)` elements.
real(kind=wp),	intent(out)	::	wrk6(n,np,nq)	A work array of `(n, np, nq)` 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,nq)	The Jacobian with respect to `beta`.
logical,	intent(in)	::	isodr	The variable designating whether the solution is by ODR (`isodr = .true.`) or by OLS (`isodr = .false.`).
real(kind=wp),	intent(out)	::	fjacd(n,m,nq)	The Jacobian with respect to `delta`.
real(kind=wp),	intent(in)	::	we1(ldwe,ld2we,nq)	The square roots of the `epsilon` weights in array `we`.
integer,	intent(in)	::	ldwe	The leading dimension of arrays `we` and `we1`.
integer,	intent(in)	::	ld2we	The second dimension of arrays `we` and `we1`.
integer,	intent(inout)	::	njev	The number of Jacobian evaluations.
integer,	intent(inout)	::	nfev	The number of function evaluations.
integer,	intent(out)	::	istop	The variable designating that the user wishes the computations stopped.
integer,	intent(out)	::	info	The variable designating why the computations were stopped.
real(kind=wp),	intent(in)	::	lower(np)	The lower bound of `beta`.
real(kind=wp),	intent(in)	::	upper(np)	The upper bound of `beta`.

public pure subroutine dfctr(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	The indicating whether the factored array can be positive semidefinite (`oksemi = .true.`) or whether it must be found to be positive definite (`oksemi = .false.`).
real(kind=wp),	intent(inout)	::	a(lda,n)	The 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	The leading dimension of array `a`.
integer,	intent(in)	::	n	The number of rows and columns of data in array `a`.
integer,	intent(out)	::	info	An indicator variable, where if: `info = 0` then factorization was completed. `info = k` signals an error condition. The leading minor of order `k` is not positive (semi)definite.

public pure subroutine dfctrw(n, m, nq, 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	The number of observations.
integer,	intent(in)	::	m	The number of columns of data in the explanatory variable.
integer,	intent(in)	::	nq	The number of responses per observation.
integer,	intent(in)	::	npp	The number of function parameters being estimated.
logical,	intent(in)	::	isodr	The variable designating whether the solution is by ODR (`isodr = .true`) or by OLS (`isodr = .false`).
real(kind=wp),	intent(in)	::	we(ldwe,ld2we,nq)	The (squared) `epsilon` weights.
integer,	intent(in)	::	ldwe	The leading dimension of array `we`.
integer,	intent(in)	::	ld2we	The second dimension of array `we`.
real(kind=wp),	intent(in)	::	wd(ldwd,ld2wd,m)	The (squared) `delta` weights.
integer,	intent(in)	::	ldwd
integer,	intent(in)	::	ld2wd	The second dimension of array `wd`.
real(kind=wp),	intent(out)	::	wrk0(nq,nq)	A work array of `(nq, nq)` elements.
real(kind=wp),	intent(out)	::	wrk4(m,m)	A work array of `(m, m)` elements.
real(kind=wp),	intent(out)	::	we1(ldwe,ld2we,nq)	The factored `epsilon` weights, such that `trans(we1)*we1 = we`.
integer,	intent(out)	::	nnzw	The number of nonzero weighted observations.
integer,	intent(out)	::	info	The variable designating why the computations were stopped.

public pure subroutine dflags(job, restrt, initd, dovcv, redoj, anajac, cdjac, chkjac, isodr, implct)

Set flags indicating conditions specified by job.

Arguments

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

public pure subroutine difix(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	The number of rows of data in the array.
integer,	intent(in)	::	m	The number of columns of data in the array.
integer,	intent(in)	::	ifix(ldifix,m)	The array designating whether an element of `t` is to be set to zero.
integer,	intent(in)	::	ldifix	The leading dimension of array `ifix`.
real(kind=wp),	intent(in)	::	t(ldt,m)	The array being set to zero according to the elements of `ifix`.
integer,	intent(in)	::	ldt	The leading dimension of array `t`.
real(kind=wp),	intent(out)	::	tfix(ldtfix,m)	The resulting array.
integer,	intent(in)	::	ldtfix	The leading dimension of array `tfix`.

public pure subroutine diwinf(m, np, nq, msgbi, msgdi, ifix2i, istopi, nnzwi, nppi, idfi, jobi, iprini, luneri, lunrpi, nrowi, ntoli, netai, maxiti, niteri, nfevi, njevi, int2i, iranki, ldtti, boundi, liwkmn)

Get storage locations within integer work space.

Arguments

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

public pure subroutine diniwk(n, m, np, work, lwork, iwork, liwork, x, ldx, 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	The number of observations.
integer,	intent(in)	::	m	The number of columns of data in the independent variable.
integer,	intent(in)	::	np	The number of function parameters.
real(kind=wp),	intent(out)	::	work(lwork)	The real work space.
integer,	intent(in)	::	lwork	The length of vector `work`.
integer,	intent(out)	::	iwork(liwork)	The integer work space.
integer,	intent(in)	::	liwork	The length of vector `iwork`.
real(kind=wp),	intent(in)	::	x(ldx,m)	The independent variable.
integer,	intent(in)	::	ldx	The leading dimension of array `x`.
integer,	intent(in)	::	ifixx(ldifx,m)	The values designating whether the elements of `x` are fixed at their input values or not.
integer,	intent(in)	::	ldifx	The leading dimension of array `ifixx`.
real(kind=wp),	intent(in)	::	scld(ldscld,m)	The scaling values for `delta`.
integer,	intent(in)	::	ldscld	The leading dimension of array `scld`.
real(kind=wp),	intent(in)	::	beta(np)	The function parameters.
real(kind=wp),	intent(in)	::	sclb(np)	The scaling values for `beta`.
real(kind=wp),	intent(in)	::	sstol	The sum-of-squares convergence stopping criteria.
real(kind=wp),	intent(in)	::	partol	The parameter convergence stopping criteria.
integer,	intent(in)	::	maxit	The maximum number of iterations allowed.
real(kind=wp),	intent(in)	::	taufac	The factor used to compute the initial trust region diameter.
integer,	intent(in)	::	job	The variable controlling problem initialization and computational method.
integer,	intent(in)	::	iprint	The print control variable.
integer,	intent(in)	::	lunerr	The logical unit number used for error messages.
integer,	intent(in)	::	lunrpt	The logical unit number used for computation reports.
real(kind=wp),	intent(in)	::	lower(np)	The lower bounds for the function parameters.
real(kind=wp),	intent(in)	::	upper(np)	The upper bounds for the function parameters.
integer,	intent(in)	::	epsmai	The location in array `work` of variable `epsmac`.
integer,	intent(in)	::	sstoli	The location in array `work` of variable `sstol`.
integer,	intent(in)	::	partli	The location in array `work` of variable `partol`.
integer,	intent(in)	::	maxiti	The location in array `iwork` of variable `maxit`.
integer,	intent(in)	::	taufci	The location in array `work` of variable `taufac`.
integer,	intent(in)	::	jobi	The location in array `iwork` of variable `job`.
integer,	intent(in)	::	iprini	The location in array `iwork` of variable `iprint`.
integer,	intent(in)	::	luneri	The location in array `iwork` of variable `lunerr`.
integer,	intent(in)	::	lunrpi	The location in array `iwork` of variable `lunrpt`.
integer,	intent(in)	::	ssfi	The starting location in array `work` of array `ssf`.
integer,	intent(in)	::	tti	The starting location in array `work` of the array `tt`.
integer,	intent(in)	::	ldtti	The leading dimension of array `tt`.
integer,	intent(in)	::	deltai	The starting location in array `work` of array `delta`.
integer,	intent(in)	::	loweri	The starting location in array `iwork` of array `lower`.
integer,	intent(in)	::	upperi	The starting location in array `iwork` of array `upper`.
integer,	intent(in)	::	boundi	The location in array `iwork` of variable `bound`.

public subroutine djaccd(fcn, n, m, np, nq, beta, x, ldx, 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	The user supplied subroutine for evaluating the model.
integer,	intent(in)	::	n	The number of observations.
integer,	intent(in)	::	m	The number of columns of data in the explanatory variable.
integer,	intent(in)	::	np	The number of function parameters.
integer,	intent(in)	::	nq	The number of responses per observation.
real(kind=wp),	intent(inout)	::	beta(np)	The function parameters.
real(kind=wp),	intent(in)	::	x(ldx,m)	The explanatory variable.
integer,	intent(in)	::	ldx	The leading dimension of array `x`.
real(kind=wp),	intent(in)	::	delta(n,m)	The estimated errors in the explanatory variables.
real(kind=wp),	intent(inout)	::	xplusd(n,m)	The values of `x + delta`.
integer,	intent(in)	::	ifixb(np)	The values designating whether the elements of `beta` are fixed at their input values or not.
integer,	intent(in)	::	ifixx(ldifx,m)	The values designating whether the elements of `x` are fixed at their input values or not.
integer,	intent(in)	::	ldifx	The leading dimension of array `ifixx`.
real(kind=wp),	intent(in)	::	stpb(np)	The relative step used for computing finite difference derivatives with respect to each `beta`.
real(kind=wp),	intent(in)	::	stpd(ldstpd,m)	The relative step used for computing finite difference derivatives with respect to each `delta`.
integer,	intent(in)	::	ldstpd	The leading dimension of array `stpd`.
real(kind=wp),	intent(in)	::	ssf(np)	The scaling values used for `beta`.
real(kind=wp),	intent(in)	::	tt(ldtt,m)	The scaling values used for `delta`.
integer,	intent(in)	::	ldtt	The leading dimension of array `tt`.
integer,	intent(in)	::	neta	The number of good digits in the function results.
real(kind=wp),	intent(in)	::	fn(n,nq)	The new predicted values from the function. Used when parameter is on a boundary.
real(kind=wp),	intent(out)	::	stp(n)	The step used for computing finite difference derivatives with respect to each `delta`.
real(kind=wp),	intent(out)	::	wrk1(n,m,nq)	A work array of `(n, m, nq)` elements.
real(kind=wp),	intent(out)	::	wrk2(n,nq)	A work array of `(n, nq)` elements.
real(kind=wp),	intent(out)	::	wrk3(np)	A work array of `(np)` elements.
real(kind=wp),	intent(out)	::	wrk6(n,np,nq)	A work array of `(n, np, nq)` elements.
real(kind=wp),	intent(out)	::	fjacb(n,np,nq)	The Jacobian with respect to `beta`.
logical,	intent(in)	::	isodr	The variable designating whether the solution is by ODR (`isodr = .true.`) or by OLS (`isodr = .false.`).
real(kind=wp),	intent(out)	::	fjacd(n,m,nq)	The Jacobian with respect to `delta`.
integer,	intent(inout)	::	nfev	The number of function evaluations.
integer,	intent(out)	::	istop	The variable designating whether there are problems computing the function at the current `beta` and `delta`.
integer,	intent(out)	::	info	The variable designating why the computations were stopped.
real(kind=wp),	intent(in)	::	lower(np)	The lower bound on `beta`.
real(kind=wp),	intent(in)	::	upper(np)	The upper bound on `beta`.

public subroutine djacfd(fcn, n, m, np, nq, beta, x, ldx, 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	The user supplied subroutine for evaluating the model.
integer,	intent(in)	::	n	The number of observations.
integer,	intent(in)	::	m	The number of columns of data in the explanatory variable.
integer,	intent(in)	::	np	The number of function parameters.
integer,	intent(in)	::	nq	The number of responses per observation.
real(kind=wp),	intent(inout)	::	beta(np)	The function parameters.
real(kind=wp),	intent(in)	::	x(ldx,m)	The explanatory variable.
integer,	intent(in)	::	ldx	The leading dimension of array `x`.
real(kind=wp),	intent(in)	::	delta(n,m)	The estimated errors in the explanatory variables.
real(kind=wp),	intent(inout)	::	xplusd(n,m)	The values of `x + delta`.
integer,	intent(in)	::	ifixb(np)	The values designating whether the elements of `beta` are fixed at their input values or not.
integer,	intent(in)	::	ifixx(ldifx,m)	The values designating whether the elements of `x` are fixed at their input values or not.
integer,	intent(in)	::	ldifx	The leading dimension of array `ifixx`.
real(kind=wp),	intent(in)	::	stpb(np)	The relative step used for computing finite difference derivatives with respect to each `beta`.
real(kind=wp),	intent(in)	::	stpd(ldstpd,m)	The relative step used for computing finite difference derivatives with respect to each `delta`.
integer,	intent(in)	::	ldstpd	The leading dimension of array `stpd`.
real(kind=wp),	intent(in)	::	ssf(np)	The scaling values used for `beta`.
real(kind=wp),	intent(in)	::	tt(ldtt,m)	The scaling values used for `delta`.
integer,	intent(in)	::	ldtt	The leading dimension of array `tt`.
integer,	intent(in)	::	neta	The number of good digits in the function results.
real(kind=wp),	intent(in)	::	fn(n,nq)	The new predicted values from the function. Used when parameter is on a boundary.
real(kind=wp),	intent(out)	::	stp(n)	The step used for computing finite difference derivatives with respect to each `delta`.
real(kind=wp),	intent(out)	::	wrk1(n,m,nq)	A work array of `(n, m, nq)` elements.
real(kind=wp),	intent(out)	::	wrk2(n,nq)	A work array of `(n, nq)` elements.
real(kind=wp),	intent(out)	::	wrk3(np)	A work array of `(np)` elements.
real(kind=wp),	intent(out)	::	wrk6(n,np,nq)	A work array of `(n, np, nq)` elements.
real(kind=wp),	intent(out)	::	fjacb(n,np,nq)	The Jacobian with respect to `beta`.
logical,	intent(in)	::	isodr	The variable designating whether the solution is by ODR (`isodr = .true.`) or by OLS (`isodr = .false.`).
real(kind=wp),	intent(out)	::	fjacd(n,m,nq)	The Jacobian with respect to `delta`.
integer,	intent(inout)	::	nfev	The number of function evaluations.
integer,	intent(out)	::	istop	The variable designating whether there are problems computing the function at the current `beta` and `delta`.
integer,	intent(out)	::	info	The variable designating why the computations were stopped.
real(kind=wp),	intent(in)	::	lower(np)	The lower bound on `beta`.
real(kind=wp),	intent(in)	::	upper(np)	The upper bound on `beta`.

public subroutine djck(fcn, n, m, np, nq, 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	The user supplied subroutine for evaluating the model.
integer,	intent(in)	::	n	The number of observations.
integer,	intent(in)	::	m	The number of columns of data in the explanatory variable.
integer,	intent(in)	::	np	The number of function parameters.
integer,	intent(in)	::	nq	The number of responses per observation.
real(kind=wp),	intent(inout)	::	beta(np)	The function parameters.
real(kind=wp),	intent(inout)	::	betaj(np)	The function parameters offset such that steps don't cross bounds.
real(kind=wp),	intent(inout)	::	xplusd(n,m)	The values of `x + delta`.
integer,	intent(in)	::	ifixb(np)	The values designating whether the elements of `beta` are fixed at their input values or not.
integer,	intent(in)	::	ifixx(ldifx,m)	The values designating whether the elements of `x` are fixed at their input values or not.
integer,	intent(in)	::	ldifx	The leading dimension of array `ifixx`.
real(kind=wp),	intent(in)	::	stpb(np)	The step size for finite difference derivatives wrt `beta`.
real(kind=wp),	intent(in)	::	stpd(ldstpd,m)	The step size for finite difference derivatives wrt `delta`.
integer,	intent(in)	::	ldstpd	The leading dimension of array `stpd`.
real(kind=wp),	intent(in)	::	ssf(np)	The scaling values used for `beta`.
real(kind=wp),	intent(in)	::	tt(ldtt,m)	The scaling values used for `delta`.
integer,	intent(in)	::	ldtt	The leading dimension of array `tt`.
real(kind=wp),	intent(in)	::	eta	The relative noise in the function results.
integer,	intent(in)	::	neta	The number of reliable digits in the model results.
integer,	intent(out)	::	ntol	The number of digits of agreement required between the numerical derivatives and the user supplied derivatives.
integer,	intent(in)	::	nrow	The row number of the explanatory variable array at which the derivative is checked.
logical,	intent(in)	::	isodr	The variable designating whether the solution is by ODR (`isodr = .true.`) or by OLS (`isodr = .false.`).
real(kind=wp),	intent(in)	::	epsmac	The value of machine precision.
real(kind=wp),	intent(in)	::	pv0i(n,nq)	The predicted values using the user supplied parameter estimates.
real(kind=wp),	intent(out)	::	fjacb(n,np,nq)	The Jacobian with respect to `beta`.
real(kind=wp),	intent(out)	::	fjacd(n,m,nq)	The Jacobian with respect to `delta`.
integer,	intent(out)	::	msgb(1+nq*np)	The error checking results for the Jacobian wrt `beta`.
integer,	intent(out)	::	msgd(1+nq*m)	The error checking results for the Jacobian wrt `delta`.
real(kind=wp),	intent(out)	::	diff(nq,np+m)	The relative differences between the user supplied and finite difference derivatives for each derivative checked.
integer,	intent(out)	::	istop	The variable designating whether there are problems computing the function at the current `beta` and `delta`
integer,	intent(inout)	::	nfev	The number of function evaluations.
integer,	intent(inout)	::	njev	The number of Jacobian evaluations.
real(kind=wp),	intent(out)	::	wrk1(n,m,nq)	A work array of `(n, m, nq)` elements.
real(kind=wp),	intent(out)	::	wrk2(n,nq)	A work array of `(n, nq)` elements.
real(kind=wp),	intent(out)	::	wrk6(n,np,nq)	A work array of `(n, np, nq)` 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 djckc(fcn, n, m, np, nq, 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	The user supplied subroutine for evaluating the model.
integer,	intent(in)	::	n	The number of observations.
integer,	intent(in)	::	m	The number of columns of data in the explanatory variable.
integer,	intent(in)	::	np	The number of function parameters.
integer,	intent(in)	::	nq	The number of responses per observation.
real(kind=wp),	intent(inout)	::	beta(np)	The function parameters.
real(kind=wp),	intent(inout)	::	xplusd(n,m)	The values of `x` + `delta`.
integer,	intent(in)	::	ifixb(np)	The values designating whether the elements of `beta` are fixed at their input values or not.
integer,	intent(in)	::	ifixx(ldifx,m)	The values designating whether the elements of `x` are fixed at their input values or not.
integer,	intent(in)	::	ldifx	The leading dimension of array `ifixx`.
real(kind=wp),	intent(in)	::	eta	The relative noise in the model.
real(kind=wp),	intent(in)	::	tol	The agreement tolerance.
integer,	intent(in)	::	nrow	The row number of the explanatory variable array at which the derivative is to be checked.
real(kind=wp),	intent(in)	::	epsmac	The value of machine precision.
integer,	intent(in)	::	j	The index of the partial derivative being examined.
integer,	intent(in)	::	lq	The response currently being examined.
real(kind=wp),	intent(in)	::	hc	The relative step size for central finite differences.
logical,	intent(in)	::	iswrtb	The variable designating whether the derivatives wrt `beta` (`iswrtb = .true.`) or `delta` (`iswrtb = .false.`) are being checked.
real(kind=wp),	intent(out)	::	fd	The forward difference derivative wrt the `j`-th parameter.
real(kind=wp),	intent(in)	::	typj	The typical size of the `j`-th unknown `beta` or `delta`.
real(kind=wp),	intent(out)	::	pvpstp	The 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	The initial step size for the finite difference derivative.
real(kind=wp),	intent(in)	::	pv	The predicted value of the model for row `nrow`.
real(kind=wp),	intent(in)	::	d	The derivative with respect to the `j`-th unknown parameter.
real(kind=wp),	intent(out)	::	diffj	The relative differences between the user supplied and finite difference derivatives for the derivative being checked.
integer,	intent(out)	::	msg(nq,j)	The error checking results.
integer,	intent(out)	::	istop	The variable designating whether there are problems computing the function at the current `beta` and `delta`.
integer,	intent(inout)	::	nfev	The number of function evaluations.
real(kind=wp),	intent(out)	::	wrk1(n,m,nq)	A work array of `(n, m, nq)` elements.
real(kind=wp),	intent(out)	::	wrk2(n,nq)	A work array of `(n, nq)` elements.
real(kind=wp),	intent(out)	::	wrk6(n,np,nq)	A work array of `(n, np, nq)` elements.

public subroutine djckf(fcn, n, m, np, nq, 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	The user supplied subroutine for evaluating the model.
integer,	intent(in)	::	n	The number of observations.
integer,	intent(in)	::	m	The number of columns of data in the explanatory variable.
integer,	intent(in)	::	np	The number of function parameters.
integer,	intent(in)	::	nq	The number of responses per observation.
real(kind=wp),	intent(inout)	::	beta(np)	The function parameters.
real(kind=wp),	intent(inout)	::	xplusd(n,m)	The values of `x + delta`.
integer,	intent(in)	::	ifixb(np)	The values designating whether the elements of `beta` are fixed at their input values or not.
integer,	intent(in)	::	ifixx(ldifx,m)	The values designating whether the elements of `x` are fixed at their input values or not.
integer,	intent(in)	::	ldifx	The leading dimension of array `ifixx`.
real(kind=wp),	intent(in)	::	eta	The relative noise in the model.
real(kind=wp),	intent(in)	::	tol	The agreement tolerance.
integer,	intent(in)	::	nrow	The row number of the explanatory variable array at which the derivative is to be checked.
integer,	intent(in)	::	j	The index of the partial derivative being examined.
integer,	intent(in)	::	lq	The response currently being examined.
logical,	intent(in)	::	iswrtb	The variable designating whether the derivatives wrt `beta` (`iswrtb = .true.`) or `delta` (`iswrtb = .false.`) are being checked.
real(kind=wp),	intent(out)	::	fd	The forward difference derivative wrt the `j`-th parameter.
real(kind=wp),	intent(in)	::	typj	The typical size of the `j`-th unknown `beta` or `delta`.
real(kind=wp),	intent(out)	::	pvpstp	The 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	The 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	The predicted value for row `nrow`.
real(kind=wp),	intent(in)	::	d	The derivative with respect to the `j`-th unknown parameter.
real(kind=wp),	intent(out)	::	diffj	The relative differences between the user supplied and finite difference derivatives for the derivative being checked.
integer,	intent(out)	::	msg(nq,j)	The error checking results.
integer,	intent(out)	::	istop	The variable designating whether there are problems computing the function at the current `beta` and `delta`.
integer,	intent(inout)	::	nfev	The number of function evaluations.
real(kind=wp),	intent(out)	::	wrk1(n,m,nq)	A work array of `(n, m, nq)` elements.
real(kind=wp),	intent(out)	::	wrk2(n,nq)	A work array of `(n, nq)` elements.
real(kind=wp),	intent(out)	::	wrk6(n,np,nq)	A work array of `(n, np, nq)` elements.

public subroutine djckm(fcn, n, m, np, nq, 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	The user supplied subroutine for evaluating the model.
integer,	intent(in)	::	n	The number of observations.
integer,	intent(in)	::	m	The number of columns of data in the explanatory variable.
integer,	intent(in)	::	np	The number of function parameters.
integer,	intent(in)	::	nq	The number of responses per observation.
real(kind=wp),	intent(inout)	::	beta(np)	The function parameters.
real(kind=wp),	intent(inout)	::	xplusd(n,m)	The values of `x + delta`.
integer,	intent(in)	::	ifixb(np)	The values designating whether the elements of `beta` are fixed at their input values or not.
integer,	intent(in)	::	ifixx(ldifx,m)	The values designating whether the elements of `x` are fixed at their input values or not.
integer,	intent(in)	::	ldifx	The leading dimension of array `ifixx`.
real(kind=wp),	intent(in)	::	eta	The relative noise in the model.
real(kind=wp),	intent(in)	::	tol	The agreement tolerance.
integer,	intent(in)	::	nrow	The row number of the explanatory variable array at which the derivative is to be checked.
real(kind=wp),	intent(in)	::	epsmac	The value of machine precision.
integer,	intent(in)	::	j	The index of the partial derivative being examined.
integer,	intent(in)	::	lq	The response currently being examined.
real(kind=wp),	intent(in)	::	typj	The typical size of the `j`-th unknown `beta` or `delta`.
real(kind=wp),	intent(in)	::	h0	The initial step size for the finite difference derivative.
real(kind=wp),	intent(in)	::	hc0	The relative step size for central finite differences.
logical,	intent(in)	::	iswrtb	The variable designating whether the derivatives wrt `beta` (`iswrtb = .true.`) or `delta` (`iswrtb = .false.`) are being checked.
real(kind=wp),	intent(in)	::	pv	The predicted value for row `nrow`.
real(kind=wp),	intent(in)	::	d	The derivative with respect to the `j`-th unknown parameter.
real(kind=wp),	intent(out)	::	diffj	The relative differences between the user supplied and finite difference derivatives for the derivative being checked.
integer,	intent(out)	::	msg1	The first set of error checking results.
integer,	intent(out)	::	msg(nq,j)	The error checking results.
integer,	intent(out)	::	istop	The variable designating whether there are problems computing the function at the current `beta` and `delta`.
integer,	intent(inout)	::	nfev	The number of function evaluations.
real(kind=wp),	intent(out)	::	wrk1(n,m,nq)	A work array of `(n, m, nq)` elements.
real(kind=wp),	intent(out)	::	wrk2(n,nq)	A work array of `(n, nq)` elements.
real(kind=wp),	intent(out)	::	wrk6(n,np,nq)	A work array of `(n, np, nq)` 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 djckz(fcn, n, m, np, nq, 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	The user supplied subroutine for evaluating the model.
integer,	intent(in)	::	n	The number of observations.
integer,	intent(in)	::	m	The number of columns of data in the explanatory variable.
integer,	intent(in)	::	np	The number of function parameters.
integer,	intent(in)	::	nq	The number of responses per observation.
real(kind=wp),	intent(inout)	::	beta(np)	The function parameters.
real(kind=wp),	intent(inout)	::	xplusd(n,m)	The values of `x + delta`.
integer,	intent(in)	::	ifixb(np)	The values designating whether the elements of `beta` are fixed at their input values or not.
integer,	intent(in)	::	ifixx(ldifx,m)	The values designating whether the elements of `x` are fixed at their input values or not.
integer,	intent(in)	::	ldifx	The leading dimension of array `ifixx`.
integer,	intent(in)	::	nrow	The row number of the explanatory variable array at which the derivative is to be checked.
real(kind=wp),	intent(in)	::	epsmac	The value of machine precision.
integer,	intent(in)	::	j	The index of the partial derivative being examined.
integer,	intent(in)	::	lq	The response currently being examined.
logical,	intent(in)	::	iswrtb	The variable designating whether the derivatives wrt `beta` (`iswrtb = .true.`) or `delta` (`iswrtb = .false.`) are being checked.
real(kind=wp),	intent(in)	::	tol	The agreement tolerance.
real(kind=wp),	intent(in)	::	d	The derivative with respect to the `j`-th unknown parameter.
real(kind=wp),	intent(in)	::	fd	The forward difference derivative wrt the `j`-th parameter.
real(kind=wp),	intent(in)	::	typj	The typical size of the `j`-th unknown `beta` or `delta`.
real(kind=wp),	intent(in)	::	pvpstp	The 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	The initial step size for the finite difference derivative.
real(kind=wp),	intent(in)	::	pv	The predicted value from the model for row `nrow`.
real(kind=wp),	intent(out)	::	diffj	The relative differences between the user supplied and finite difference derivatives for the derivative being checked.
integer,	intent(out)	::	msg(nq,j)	The error checking results.
integer,	intent(out)	::	istop	The variable designating whether there are problems computing the function at the current `beta` and `delta`.
integer,	intent(inout)	::	nfev	The number of function evaluations.
real(kind=wp),	intent(out)	::	wrk1(n,m,nq)	A work array of `(n, m, nq)` elements.
real(kind=wp),	intent(out)	::	wrk2(n,nq)	A work array of `(n, nq)` elements.
real(kind=wp),	intent(out)	::	wrk6(n,np,nq)	A work array of `(n, np, nq)` elements.

public pure subroutine dodchk(n, m, np, nq, isodr, anajac, implct, beta, ifixb, ldx, ldifx, ldscld, ldstpd, ldwe, ld2we, ldwd, ld2wd, ldy, lwork, lwkmn, liwork, liwkmn, 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	The number of observations.
integer,	intent(in)	::	m	The number of columns of data in the explanatory variable.
integer,	intent(in)	::	np	The number of function parameters.
integer,	intent(in)	::	nq	The number of responses per observation.
logical,	intent(in)	::	isodr	The variable designating whether the solution is by ODR (`isodr = .true.`) or by OLS (`isodr = .false.`).
logical,	intent(in)	::	anajac	The variable designating whether the Jacobians are computed by finite differences (`anajac = .false.`) or not (`anajac = .true.`).
logical,	intent(in)	::	implct	The variable designating whether the solution is by implicit ODR (`implct = .true.`) or explicit ODR (`implct = .false.`).
real(kind=wp),	intent(in)	::	beta(np)	The function parameters.
integer,	intent(in)	::	ifixb(np)	The values designating whether the elements of `beta` are fixed at their input values or not.
integer,	intent(in)	::	ldx	The leading dimension of array `x`.
integer,	intent(in)	::	ldifx	The leading dimension of array `ifixx`.
integer,	intent(in)	::	ldscld	The leading dimension of array `scld`.
integer,	intent(in)	::	ldstpd	The leading dimension of array `stpd`.
integer,	intent(in)	::	ldwe	The leading dimension of array `we`.
integer,	intent(in)	::	ld2we	The second dimension of array `we`.
integer,	intent(in)	::	ldwd	The leading dimension of array `wd`.
integer,	intent(in)	::	ld2wd	The second dimension of array `wd`.
integer,	intent(in)	::	ldy	The leading dimension of array `y`.
integer,	intent(in)	::	lwork	The length of vector `work`.
integer,	intent(in)	::	lwkmn	The minimum acceptable length of array `work`.
integer,	intent(in)	::	liwork	The length of vector `iwork`.
integer,	intent(in)	::	liwkmn	The minimum acceptable length of array `iwork`.
real(kind=wp),	intent(in)	::	sclb(np)	The scaling values for `beta`.
real(kind=wp),	intent(in)	::	scld(ldscld,m)	The scaling value for `delta`.
real(kind=wp),	intent(in)	::	stpb(np)	The step for the finite difference derivative wrt `beta`.
real(kind=wp),	intent(in)	::	stpd(ldstpd,m)	The step for the finite difference derivative wrt `delta`.
integer,	intent(out)	::	info	The variable designating why the computations were stopped.
real(kind=wp),	intent(in)	::	lower(np)	The lower bound on `beta`.
real(kind=wp),	intent(in)	::	upper(np)	The upper bound on `beta`.

public subroutine dodstp(n, m, np, nq, 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, tempret, istopc)

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

Arguments

Type	Intent		Name
integer,	intent(in)	::	n	The number of observations.
integer,	intent(in)	::	m	The number of columns of data in the explanatory variable.
integer,	intent(in)	::	np	The number of function parameters.
integer,	intent(in)	::	nq	The number of responses per observation.
integer,	intent(in)	::	npp	The number of function parameters being estimated.
real(kind=wp),	intent(in)	::	f(n,nq)	The (weighted) estimated values of `epsilon`.
real(kind=wp),	intent(in)	::	fjacb(n,np,nq)	The Jacobian with respect to `beta`.
real(kind=wp),	intent(in)	::	fjacd(n,m,nq)	The Jacobian with respect to `delta`.
real(kind=wp),	intent(in)	::	wd(ldwd,ld2wd,m)	The (squared) `delta` weights.
integer,	intent(in)	::	ldwd	The leading dimension of array `wd`.
integer,	intent(in)	::	ld2wd	The second dimension of array `wd`.
real(kind=wp),	intent(in)	::	ss(np)	The scaling values for the unfixed `beta`s.
real(kind=wp),	intent(in)	::	tt(ldtt,m)	The scaling values for `delta`.
integer,	intent(in)	::	ldtt	The leading dimension of array `tt`.
real(kind=wp),	intent(in)	::	delta(n,m)	The estimated errors in the explanatory variables.
real(kind=wp),	intent(in)	::	alpha	The Levenberg-Marquardt parameter.
real(kind=wp),	intent(in)	::	epsfcn	The function's precision.
logical,	intent(in)	::	isodr	The variable designating whether the solution is by ODR (`isodr = .true.`) or by OLS (`isodr = .false.`).
real(kind=wp),	intent(out)	::	tfjacb(n,nq,np)	The array `omega*fjacb`.
real(kind=wp),	intent(out)	::	omega(nq,nq)	The 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)	The approximate null vector for `tfjacb`.
real(kind=wp),	intent(out)	::	qraux(np)	The array required to recover the orthogonal part of the Q-R decomposition.
integer,	intent(out)	::	kpvt(np)	The pivot vector.
real(kind=wp),	intent(out)	::	s(np)	The step for `beta`.
real(kind=wp),	intent(out)	::	t(n,m)	The step for `delta`.
real(kind=wp),	intent(out)	::	phi	The difference between the norm of the scaled step and the trust region diameter.
integer,	intent(out)	::	irank	The rank deficiency of the Jacobian wrt `beta`.
real(kind=wp),	intent(out)	::	rcond	The approximate reciprocal condition number of `tfjacb`.
logical,	intent(in)	::	forvcv	The 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,nq,m)	A work array of `(n, nq, m)` elements.
real(kind=wp),	intent(out)	::	wrk2(n,nq)	A work array of `(n, nq)` 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	The length of vector `wrk`.
real(kind=wp),	intent(inout)	::	tempret(:,:)	Temporary work array for holding return values before copying to a lower rank array.
integer,	intent(inout)	::	istopc	The variable designating whether the computations were stopped due to a numerical error within subroutine `dodstp`.

public subroutine dodvcv(n, m, np, nq, 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, tempret, istopc)

Compute covariance matrix of estimated parameters.

Arguments

Type	Intent		Name
integer,	intent(in)	::	n	The number of observations.
integer,	intent(in)	::	m	The number of columns of data in the explanatory variable.
integer,	intent(in)	::	np	The number of function parameters.
integer,	intent(in)	::	nq	The number of responses per observation.
integer,	intent(in)	::	npp	The number of function parameters being estimated.
real(kind=wp),	intent(in)	::	f(n,nq)	The (weighted) estimated values of `epsilon`.
real(kind=wp),	intent(in)	::	fjacb(n,np,nq)	The Jacobian with respect to `beta`.
real(kind=wp),	intent(in)	::	fjacd(n,m,nq)	The Jacobian with respect to `delta`.
real(kind=wp),	intent(in)	::	wd(ldwd,ld2wd,m)	The `delta` weights.
integer,	intent(in)	::	ldwd	The leading dimension of array `wd`.
integer,	intent(in)	::	ld2wd	The second dimension of array `wd`.
real(kind=wp),	intent(in)	::	ssf(np)	The scaling values used for `beta`.
real(kind=wp),	intent(in)	::	ss(np)	The scaling values for the unfixed `beta`s.
real(kind=wp),	intent(in)	::	tt(ldtt,m)	The scaling values for `delta`.
integer,	intent(in)	::	ldtt	The leading dimension of array `tt`.
real(kind=wp),	intent(in)	::	delta(n,m)	The estimated errors in the explanatory variables.
real(kind=wp),	intent(in)	::	epsfcn	The function's precision.
logical,	intent(in)	::	isodr	The variable designating whether the solution is by ODR (`isodr = .true.`) or by OLS (`isodr = .false.`).
real(kind=wp),	intent(out)	::	vcv(np,np)	The covariance matrix of the estimated `beta`s.
real(kind=wp),	intent(out)	::	sd(np)	The standard deviations of the estimated `beta`s.
real(kind=wp),	intent(out)	::	wrk6(n*nq,np)	A work array of `(n*nq, np)` elements.
real(kind=wp),	intent(out)	::	omega(nq,nq)	The array defined such that `omegatrans(omega) = inv(I + fjacdinv(e)trans(fjacd)) = (I - fjacdinv(p)*trans(fjacd))`.
real(kind=wp),	intent(out)	::	u(np)	The approximate null vector for `fjacb`.
real(kind=wp),	intent(out)	::	qraux(np)	The array required to recover the orthogonal part of the Q-R decomposition.
integer,	intent(out)	::	jpvt(np)	The pivot vector.
real(kind=wp),	intent(out)	::	s(np)	The step for `beta`.
real(kind=wp),	intent(out)	::	t(n,m)	The step for `delta`.
integer,	intent(out)	::	irank	The rank deficiency of the Jacobian wrt `beta`.
real(kind=wp),	intent(out)	::	rcond	The approximate reciprocal condition of `fjacb`.
real(kind=wp),	intent(inout)	::	rss	The residual sum of squares.
integer,	intent(out)	::	idf	The 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	The residual variance.
integer,	intent(in)	::	ifixb(np)	The values designating whether the elements of `beta` are fixed at their input values or not.
real(kind=wp),	intent(out)	::	wrk1(n,nq,m)	A work array of `(n, nq, m)` elements.
real(kind=wp),	intent(out)	::	wrk2(n,nq)	A work array of `(n, nq)` 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	The length of vector `lwrk`.
real(kind=wp),	intent(inout)	::	tempret(:,:)	Temporary work array for holding return values before copying to a lower rank array.
integer,	intent(out)	::	istopc	The variable designating whether the computations were stoped due to a numerical error within subroutine `dodstp`.

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

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

Arguments

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

public subroutine dpvb(fcn, n, m, np, nq, beta, xplusd, ifixb, ifixx, ldifx, nrow, j, lq, stp, istop, nfev, pvb, wrk1, wrk2, wrk6)

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

Arguments

Type	Intent		Name
procedure(fcn_t)		::	fcn	The user-supplied subroutine for evaluating the model.
integer,	intent(in)	::	n	The number of observations.
integer,	intent(in)	::	m	The number of columns of data in the independent variable.
integer,	intent(in)	::	np	The number of function parameters.
integer,	intent(in)	::	nq	The number of responses per observation.
real(kind=wp),	intent(inout)	::	beta(np)	The function parameters.
real(kind=wp),	intent(in)	::	xplusd(n,m)	The values of `x + delta`.
integer,	intent(in)	::	ifixb(np)	The values designating whether the elements of `beta` are fixed at their input values or not.
integer,	intent(in)	::	ifixx(ldifx,m)	The values designating whether the elements of `x` are fixed at their input values or not.
integer,	intent(in)	::	ldifx	The leading dimension of array `ifixx`.
integer,	intent(in)	::	nrow	The row number of the independent variable array at which the derivative is to be checked.
integer,	intent(in)	::	j	The index of the partial derivative being examined.
integer,	intent(in)	::	lq	The response currently being examined.
real(kind=wp),	intent(in)	::	stp	The step size for the finite difference derivative.
integer,	intent(out)	::	istop	The variable designating whether there are problems computing the function at the current `beta` and `delta`.
integer,	intent(inout)	::	nfev	The number of function evaluations.
real(kind=wp),	intent(out)	::	pvb	The function value for the selected observation & response.
real(kind=wp),	intent(out)	::	wrk1(n,m,nq)	Work array.
real(kind=wp),	intent(out)	::	wrk2(n,nq)	Work array.
real(kind=wp),	intent(out)	::	wrk6(n,np,nq)	Work array.

public subroutine dpvd(fcn, n, m, np, nq, beta, xplusd, ifixb, ifixx, ldifx, nrow, j, lq, stp, istop, nfev, pvd, wrk1, wrk2, wrk6)

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

Arguments

Type	Intent		Name
procedure(fcn_t)		::	fcn	The user-supplied subroutine for evaluating the model.
integer,	intent(in)	::	n	The number of observations.
integer,	intent(in)	::	m	The number of columns of data in the independent variable.
integer,	intent(in)	::	np	The number of function parameters.
integer,	intent(in)	::	nq	The number of responses per observation.
real(kind=wp),	intent(in)	::	beta(np)	The function parameters.
real(kind=wp),	intent(inout)	::	xplusd(n,m)	The values of `x + delta`.
integer,	intent(in)	::	ifixb(np)	The values designating whether the elements of `beta` are fixed at their input values or not.
integer,	intent(in)	::	ifixx(ldifx,m)	The values designating whether the elements of `x` are fixed at their input values or not.
integer,	intent(in)	::	ldifx	The leading dimension of array `ifixx`.
integer,	intent(in)	::	nrow	The row number of the independent variable array at which the derivative is to be checked.
integer,	intent(in)	::	j	The index of the partial derivative being examined.
integer,	intent(in)	::	lq	The response currently being examined.
real(kind=wp),	intent(in)	::	stp	The step size for the finite difference derivative.
integer,	intent(out)	::	istop	The variable designating whether there are problems computing the function at the current `beta` and `delta`.
integer,	intent(inout)	::	nfev	The number of function evaluations.
real(kind=wp),	intent(out)	::	pvd	The function value for the selected observation & response.
real(kind=wp),	intent(out)	::	wrk1(n,m,nq)	Work array.
real(kind=wp),	intent(out)	::	wrk2(n,nq)	Work array.
real(kind=wp),	intent(out)	::	wrk6(n,np,nq)	Work array.

public pure subroutine dscale(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	The number of rows of data in `t`.
integer,	intent(in)	::	m	The number of columns of data in `t`.
real(kind=wp),	intent(in)	::	scl(ldscl,m)	The scale values.
integer,	intent(in)	::	ldscl	The leading dimension of array `scl`.
real(kind=wp),	intent(in)	::	t(ldt,m)	The array to be inversely scaled by `scl`.
integer,	intent(in)	::	ldt	The leading dimension of array `t`.
real(kind=wp),	intent(out)	::	sclt(ldsclt,m)	The inversely scaled matrix.
integer,	intent(in)	::	ldsclt	The leading dimension of array `sclt`.

public pure subroutine dsclb(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	The number of function parameters.
real(kind=wp),	intent(in)	::	beta(np)	The function parameters.
real(kind=wp),	intent(out)	::	ssf(np)	The scaling values for `beta`.

public pure subroutine dscld(n, m, x, ldx, 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	The number of observations.
integer,	intent(in)	::	m	The number of columns of data in the independent variable.
real(kind=wp),	intent(in)	::	x(ldx,m)	The independent variable.
integer,	intent(in)	::	ldx	The leading dimension of array `x`.
real(kind=wp),	intent(out)	::	tt(ldtt,m)	The scaling values for `delta`.
integer,	intent(in)	::	ldtt	The leading dimension of array `tt`.

public pure subroutine dsetn(n, m, x, ldx, nrow)

Select the row at which the derivative will be checked.

Arguments

Type	Intent		Name
integer,	intent(in)	::	n	The number of observations.
integer,	intent(in)	::	m	The number of columns of data in the independent variable.
real(kind=wp),	intent(in)	::	x(ldx,m)	The independent variable.
integer,	intent(in)	::	ldx	The leading dimension of array `x`.
integer,	intent(inout)	::	nrow	The selected row number of the independent variable.

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

Solve systems of the form:

Arguments

Type	Intent		Name
integer,	intent(in)	::	n	The number of rows and columns of data in array `t`.
real(kind=wp),	intent(in)	::	t(ldt,n)	The upper or lower tridiagonal system.
integer,	intent(in)	::	ldt	The leading dimension of array `t`.
real(kind=wp),	intent(inout)	::	b(n)	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 dunpac(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	The number of items in `v2`.
real(kind=wp),	intent(in)	::	v1(n2)	The vector of the unfixed items.
real(kind=wp),	intent(out)	::	v2(n2)	The vector of the fixed and unfixed items into which the elements of `v1` are to be inserted.
integer,	intent(in)	::	ifix(n2)	The values designating whether the elements of `v2` are fixed at their input values or not.

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

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

Arguments

Type	Intent		Name
integer,	intent(in)	::	m	The number of columns of data in the independent variable.
integer,	intent(in)	::	nq	The number of responses per observation.
integer,	intent(in)	::	indx	The row in `v` in which the `m` by `nq` array is stored.
real(kind=wp),	intent(in)	::	v(ldv,ld2v,nq)	An array of `nq` by `m` matrices.
integer,	intent(in)	::	ldv	The leading dimension of array `v`.
integer,	intent(in)	::	ld2v	The second dimension of array `v`.
real(kind=wp),	intent(in)	::	e(lde,m)	The `m` by `m` matrix of the factors, so `ete = (d*2 + alphat**2)`.
integer,	intent(in)	::	lde	The leading dimension of array `e`.
real(kind=wp),	intent(out)	::	ve(ldve,ld2ve,m)	The `nq` by `m` array `ve = v * inv(e)`.
integer,	intent(in)	::	ldve	The leading dimension of array `ve`.
integer,	intent(in)	::	ld2ve	The second dimension of array `ve`.
real(kind=wp),	intent(out)	::	vev(ldvev,nq)	The `nq` by `nq` array `vev = v * inv(ete) * trans(v)`.
integer,	intent(in)	::	ldvev	The leading dimension of array `vev`.
real(kind=wp),	intent(out)	::	wrk5(m)	An `m` work vector.

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

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

Arguments

Type	Intent		Name
integer,	intent(in)	::	n	The number of rows of data in `t`.
integer,	intent(in)	::	m	The number of columns of data in `t`.
real(kind=wp),	intent(in)	::	wt(:,:,:)	The weights.
integer,	intent(in)	::	ldwt	The leading dimension of array `wt`.
integer,	intent(in)	::	ld2wt	The second dimension of array `wt`.
real(kind=wp),	intent(in)	::	t(:,:)	The array being scaled by `wt`.
real(kind=wp),	intent(out)	::	wtt(:,:)	The results of weighting array `t` by `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 dwinf(n, m, np, nq, ldwe, ld2we, isodr, deltai, epsi, xplusi, fni, sdi, vcvi, rvari, wssi, wssdei, wssepi, rcondi, etai, olmavi, taui, alphai, actrsi, pnormi, rnorsi, prersi, partli, sstoli, taufci, epsmai, beta0i, betaci, betasi, betani, si, ssi, ssfi, qrauxi, ui, fsi, fjacbi, we1i, diffi, deltsi, deltni, ti, tti, omegai, fjacdi, wrk1i, wrk2i, wrk3i, wrk4i, wrk5i, wrk6i, wrk7i, loweri, upperi, lwkmn)

Get storage locations within REAL (wp) work space.

Arguments

Type	Intent		Name
integer,	intent(in)	::	n	The number of observations.
integer,	intent(in)	::	m	The number of columns of data in the explanatory variable.
integer,	intent(in)	::	np	The number of function parameters.
integer,	intent(in)	::	nq	The number of responses per observation.
integer,	intent(in)	::	ldwe	The leading dimension of array `we`.
integer,	intent(in)	::	ld2we	The second dimension of array `we`.
logical,	intent(in)	::	isodr	The variable designating whether the solution is by ODR (`isodr`=.true.) or by OLS (`isodr`=.false.).
integer,	intent(out)	::	deltai	The starting location in array `work` of array `delta`.
integer,	intent(out)	::	epsi	The starting location in array `work` of array `eps`.
integer,	intent(out)	::	xplusi	The starting location in array `work` of array `xplusd`.
integer,	intent(out)	::	fni	The starting location in array `work` of array `fn`.
integer,	intent(out)	::	sdi	The starting location in array `work` of array `sd`.
integer,	intent(out)	::	vcvi	The starting location in array `work` of array `vcv`.
integer,	intent(out)	::	rvari	The location in array `work` of variable `rvar`.
integer,	intent(out)	::	wssi	The location in array `work` of variable `wss`.
integer,	intent(out)	::	wssdei	The location in array `work` of variable `wssdel`.
integer,	intent(out)	::	wssepi	The location in array `work` of variable `wsseps`.
integer,	intent(out)	::	rcondi	The location in array `work` of variable `rcondi`.
integer,	intent(out)	::	etai	The location in array `work` of variable `eta`.
integer,	intent(out)	::	olmavi	The location in array `work` of variable `olmavg`.
integer,	intent(out)	::	taui	The location in array `work` of variable `tau`.
integer,	intent(out)	::	alphai	The location in array `work` of variable `alpha`.
integer,	intent(out)	::	actrsi	The location in array `work` of variable `actrs`.
integer,	intent(out)	::	pnormi	The location in array `work` of variable `pnorm`.
integer,	intent(out)	::	rnorsi	The location in array `work` of variable `rnorms`.
integer,	intent(out)	::	prersi	The location in array `work` of variable `prers`.
integer,	intent(out)	::	partli	The location in array `work` of variable `partol`.
integer,	intent(out)	::	sstoli	The location in array `work` of variable `sstol`.
integer,	intent(out)	::	taufci	The location in array `work` of variable `taufac`.
integer,	intent(out)	::	epsmai	The location in array `work` of variable `epsmac`.
integer,	intent(out)	::	beta0i	The starting location in array `work` of array `beta0`.
integer,	intent(out)	::	betaci	The starting location in array `work` of array `betac`.
integer,	intent(out)	::	betasi	The starting location in array `work` of array `betas`.
integer,	intent(out)	::	betani	The starting location in array `work` of array `betan`.
integer,	intent(out)	::	si	The starting location in array `work` of array `s`.
integer,	intent(out)	::	ssi	The starting location in array `work` of array `ss`.
integer,	intent(out)	::	ssfi	The starting location in array `work` of array `ssf`.
integer,	intent(out)	::	qrauxi	The starting location in array `work` of array `qraux`.
integer,	intent(out)	::	ui	The starting location in array `work` of array `u`.
integer,	intent(out)	::	fsi	The starting location in array `work` of array `fs`.
integer,	intent(out)	::	fjacbi	The starting location in array `work` of array `fjacb`.
integer,	intent(out)	::	we1i	The starting location in array `work` of array `we1`.
integer,	intent(out)	::	diffi	The starting location in array `work` of array `diff`.
integer,	intent(out)	::	deltsi	The starting location in array `work` of array `deltas`.
integer,	intent(out)	::	deltni	The starting location in array `work` of array `deltan`.
integer,	intent(out)	::	ti	The starting location in array `work` of array `t`.
integer,	intent(out)	::	tti	The starting location in array `work` of array `tt`.
integer,	intent(out)	::	omegai	The starting location in array `work` of array `omega`.
integer,	intent(out)	::	fjacdi	The starting location in array `work` of array `fjacd`.
integer,	intent(out)	::	wrk1i	The starting location in array `work` of array `wrk1`.
integer,	intent(out)	::	wrk2i	The starting location in array `work` of array `wrk2`.
integer,	intent(out)	::	wrk3i	The starting location in array `work` of array `wrk3`.
integer,	intent(out)	::	wrk4i	The starting location in array `work` of array `wrk4`.
integer,	intent(out)	::	wrk5i	The starting location in array `work` of array `wrk5`.
integer,	intent(out)	::	wrk6i	The starting location in array `work` of array `wrk6`.
integer,	intent(out)	::	wrk7i	The starting location in array `work` of array `wrk7`.
integer,	intent(out)	::	loweri	The starting location in array `work` of array `lower`.
integer,	intent(out)	::	upperi	The starting location in array `work` of array `upper`.
integer,	intent(out)	::	lwkmn	The minimum acceptable length of vector `work`.

public pure subroutine mbfb(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	The 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)	The scale used for the `beta`s.
real(kind=wp),	intent(in)	::	stpb(np)	The 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	The 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(n, m, np, nq, ldn, ldm, ldnp, beta, xplusd, ifixb, ifixx, ldifx, ideval, f, fjacb, fjacd, istop)

Arguments

Functions

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

Arguments

Return Value real(kind=wp)

public pure function dhstep(itype, neta, i, j, stp, ldstp) result(dhstepr)

Arguments

Return Value real(kind=wp)

public pure function dppnml(p) result(dppnmlr)

Arguments

Return Value real(kind=wp)

public pure function dppt(p, idf) result(dpptr)

Arguments

Return Value real(kind=wp)

Subroutines

public subroutine dodlm(n, m, np, nq, 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, tempret, istopc)

Arguments

Arguments

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

Arguments

public subroutine detaf(fcn, n, m, np, nq, xplusd, beta, epsmac, nrow, partmp, pv0, ifixb, ifixx, ldifx, istop, nfev, eta, neta, wrk1, wrk2, wrk6, wrk7, info, lower, upper)

Arguments

public subroutine devjac(fcn, anajac, cdjac, n, m, np, nq, betac, beta, stpb, ifixb, ifixx, ldifx, x, ldx, 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 dfctr(oksemi, a, lda, n, info)

Arguments

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

Arguments

public pure subroutine dflags(job, restrt, initd, dovcv, redoj, anajac, cdjac, chkjac, isodr, implct)

Arguments

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

Arguments

public pure subroutine diwinf(m, np, nq, msgbi, msgdi, ifix2i, istopi, nnzwi, nppi, idfi, jobi, iprini, luneri, lunrpi, nrowi, ntoli, netai, maxiti, niteri, nfevi, njevi, int2i, iranki, ldtti, boundi, liwkmn)

Arguments

Arguments

public subroutine djaccd(fcn, n, m, np, nq, beta, x, ldx, 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 djacfd(fcn, n, m, np, nq, beta, x, ldx, 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 djck(fcn, n, m, np, nq, 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 djckc(fcn, n, m, np, nq, 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 djckf(fcn, n, m, np, nq, 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 djckm(fcn, n, m, np, nq, 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 djckz(fcn, n, m, np, nq, 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 dodchk(n, m, np, nq, isodr, anajac, implct, beta, ifixb, ldx, ldifx, ldscld, ldstpd, ldwe, ld2we, ldwd, ld2wd, ldy, lwork, lwkmn, liwork, liwkmn, sclb, scld, stpb, stpd, info, lower, upper)

Arguments

public subroutine dodstp(n, m, np, nq, 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, tempret, istopc)

Arguments

public subroutine dodvcv(n, m, np, nq, 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, tempret, istopc)

Arguments

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

Arguments

public subroutine dpvb(fcn, n, m, np, nq, beta, xplusd, ifixb, ifixx, ldifx, nrow, j, lq, stp, istop, nfev, pvb, wrk1, wrk2, wrk6)

Arguments

public subroutine dpvd(fcn, n, m, np, nq, beta, xplusd, ifixb, ifixx, ldifx, nrow, j, lq, stp, istop, nfev, pvd, wrk1, wrk2, wrk6)

Arguments

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

Arguments

public pure subroutine dsclb(np, beta, ssf)

Arguments

public pure subroutine dscld(n, m, x, ldx, tt, ldtt)

Arguments

public pure subroutine dsetn(n, m, x, ldx, nrow)

Arguments

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