odrpack – odrpack

Main driver routines for finding the weighted explicit or implicit orthogonal distance regression (ODR) or ordinary linear or nonlinear least squares (OLS) solution.

Uses

- odrpack_kinds
- iso_fortran_env
Help

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.

Used by

Help

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.

Subroutines

public impure subroutine odr(fcn, n, m, np, nq, beta, y, x, delta, we, wd, ifixb, ifixx, job, ndigit, taufac, sstol, partol, maxit, iprint, lunerr, lunrpt, stpb, stpd, sclb, scld, work, iwork, info, lower, upper)

Driver routine for finding the weighted explicit or implicit orthogonal distance regression (ODR) or ordinary linear or nonlinear least squares (OLS) solution.

Arguments

Type	Intent	Optional	Attributes		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)			::	nq	Number of responses per observation.
real(kind=wp),	intent(inout)			::	beta(:)	Function parameters. `Shape: (np)`.
real(kind=wp),	intent(in)			::	y(:,:)	Dependent variable. `Shape: (n, nq)`. Unused when the model is implicit.
real(kind=wp),	intent(in)			::	x(:,:)	Explanatory variable. `Shape: (n, m)`.
real(kind=wp),	intent(inout),	optional		::	delta(:,:)	Error in the `x` data. `Shape: (n, m)`. Initial guess on input and estimated value on output.
real(kind=wp),	intent(in),	optional		::	we(:,:,:)	`epsilon` weights. `Shape: (1<=ldwe<=n, 1<=ld2we<=nq, nq)`. See p. 25.
real(kind=wp),	intent(in),	optional		::	wd(:,:,:)	`delta` weights. `Shape: (1<=ldwd<=n, 1<=ld2wd<=m, m)`. See p. 26.
integer,	intent(in),	optional		::	ifixb(:)	Values designating whether the elements of `beta` are fixed at their input values or not. `Shape: (np)`.
integer,	intent(in),	optional		::	ifixx(:,:)	Values designating whether the elements of `x` are fixed at their input values or not. `Shape: (1<=ldifx<=n, m)`. See p. 27.
integer,	intent(in),	optional		::	job	Variable controlling problem initialization and computational method.
integer,	intent(in),	optional		::	ndigit	Number of accurate digits in the function results, as supplied by the user.
real(kind=wp),	intent(in),	optional		::	taufac	Factor used to compute the initial trust region diameter.
real(kind=wp),	intent(in),	optional		::	sstol	Sum-of-squares convergence stopping tolerance.
real(kind=wp),	intent(in),	optional		::	partol	Parameter convergence stopping tolerance.
integer,	intent(in),	optional		::	maxit	Maximum number of iterations allowed.
integer,	intent(in),	optional		::	iprint	Print control variable.
integer,	intent(in),	optional		::	lunerr	Logical unit number for error messages. Available options are: 0 => no output. 6 => output to standard error. other => output to logical unit number `lunerr`.
integer,	intent(in),	optional		::	lunrpt	Logical unit number for computation reports. Available options are: 0 => no output. 6 => output to standard error. other => output to logical unit number `lunrpt`.
real(kind=wp),	intent(in),	optional		::	stpb(:)	Relative step for computing finite difference derivatives with respect to `beta`. `Shape: (np)`.
real(kind=wp),	intent(in),	optional		::	stpd(:,:)	Relative step for computing finite difference derivatives with respect to `delta`. `Shape: (1<=ldstpd<=n, m)`. See p. 31.
real(kind=wp),	intent(in),	optional		::	sclb(:)	Scaling values for `beta`. `Shape: (np)`.
real(kind=wp),	intent(in),	optional		::	scld(:,:)	Scaling values for `delta`. `Shape: (1<=ldscld<=n, m)`. See p. 32.
real(kind=wp),	intent(inout),	optional,	target	::	work(:)	Real work space.
integer,	intent(inout),	optional,	target	::	iwork(:)	Integer work space.
integer,	intent(out),	optional		::	info	Variable designating why the computations were stopped.
real(kind=wp),	intent(in),	optional		::	lower(:)	Lower bound on `beta`. `Shape: (np)`.
real(kind=wp),	intent(in),	optional		::	upper(:)	Upper bound on `beta`. `Shape: (np)`.

public impure subroutine dodcnt(fcn, n, m, np, nq, beta, y, ldy, x, ldx, we, ldwe, ld2we, wd, ldwd, ld2wd, ifixb, ifixx, ldifx, job, ndigit, taufac, sstol, partol, maxit, iprint, lunerr, lunrpt, stpb, stpd, ldstpd, sclb, scld, ldscld, work, lwork, tempret, iwork, liwork, info, lower, upper)

Driver routine for finding the weighted explicit or implicit orthogonal distance regression (ODR) or ordinary linear or nonlinear least squares (OLS) solution.

Arguments

Type	Intent		Name
procedure(fcn_t)		::	fcn	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)	::	y(ldy,nq)	The dependent variable. Unused when the model is implicit.
integer,	intent(in)	::	ldy	The leading dimension of array `y`.
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(inout)	::	we(ldwe,ld2we,nq)	The `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 `delta` weights.
integer,	intent(in)	::	ldwd	The leading dimension of array `wd`.
integer,	intent(in)	::	ld2wd	The second dimension of array `wd`.
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(inout)	::	job	The variable controlling problem initialization and computational method.
integer,	intent(in)	::	ndigit	The number of accurate digits in the function results, as supplied by the user.
real(kind=wp),	intent(in)	::	taufac	The factor used to compute the initial trust region diameter.
real(kind=wp),	intent(in)	::	sstol	The sum-of-squares convergence stopping tolerance.
real(kind=wp),	intent(in)	::	partol	The user-supplied parameter convergence stopping tolerance.
integer,	intent(in)	::	maxit	The maximum number of iterations allowed.
integer,	intent(in)	::	iprint	The print control variables.
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)	::	stpb(np)	The relative step for computing finite difference derivatives with respect to `beta`.
real(kind=wp),	intent(in)	::	stpd(ldstpd,m)	The relative step for computing finite difference derivatives with respect to `delta`.
integer,	intent(in)	::	ldstpd	The leading dimension of array `stpd`.
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`.
integer,	intent(in)	::	ldscld	The leading dimension of array `scld`.
real(kind=wp),	intent(inout)	::	work(lwork)	The real work space.
integer,	intent(in)	::	lwork	The length of vector `work`.
real(kind=wp),	intent(inout)	::	tempret(:,:)	Temporary work array for holding return values before copying to a lower rank array.
integer,	intent(inout)	::	iwork(liwork)	The integer work space.
integer,	intent(in)	::	liwork	The length of vector `iwork`.
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 impure subroutine doddrv(head, fstitr, prtpen, fcn, n, m, np, nq, beta, y, ldy, x, ldx, we, ldwe, ld2we, wd, ldwd, ld2wd, ifixb, ifixx, ldifx, job, ndigit, taufac, sstol, partol, maxit, iprint, lunerr, lunrpt, stpb, stpd, ldstpd, sclb, scld, ldscld, work, lwork, tempret, iwork, liwork, maxit1, tstimp, info, lower, upper)

Perform error checking and initialization, and begin procedure for performing orthogonal distance regression (ODR) or ordinary linear or nonlinear least squares (OLS).

Arguments

Type	Intent		Name
logical,	intent(inout)	::	head	The variable designating whether the heading is to be printed (`head = .true.`) or not (`head = .false.`).
logical,	intent(inout)	::	fstitr	The variable designating whether this is the first iteration (`fstitr = .true.`) or not (`fstitr = .false.`).
logical,	intent(inout)	::	prtpen	The variable designating whether the penalty parameter is to be printed in the iteration report (`prtpen = .true.`) or not (`prtpen = .false.`).
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)	::	y(ldy,nq)	The dependent variable. Unused when the model is implicit.
integer,	intent(in)	::	ldy	The leading dimension of array `y`.
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(inout)	::	we(ldwe,ld2we,nq)	The `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 `delta` weights.
integer,	intent(in)	::	ldwd	The leading dimension of array `wd`.
integer,	intent(in)	::	ld2wd	The second dimension of array `wd`.
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(inout)	::	job	The variable controlling problem initialization and computational method.
integer,	intent(in)	::	ndigit	The number of accurate digits in the function results, as supplied by the user.
real(kind=wp),	intent(in)	::	taufac	The factor used to compute the initial trust region diameter.
real(kind=wp),	intent(in)	::	sstol	The sum-of-squares convergence stopping tolerance.
real(kind=wp),	intent(in)	::	partol	The parameter convergence stopping tolerance.
integer,	intent(in)	::	maxit	The maximum number of iterations allowed.
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)	::	stpb(np)	The step size for finite difference derivatives with respect to `beta`.
real(kind=wp),	intent(in)	::	stpd(ldstpd,m)	The step size for finite difference derivatives with respect to `delta`.
integer,	intent(in)	::	ldstpd	The leading dimension of array `stpd`.
real(kind=wp),	intent(in)	::	sclb(np)	The scaling values for `beta`.
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(inout)	::	work(lwork)	The real work space.
integer,	intent(in)	::	lwork	The length of vector `work`.
real(kind=wp),	intent(inout)	::	tempret(:,:)	Temporary work array for holding return values before copying to a lower rank array.
integer,	intent(inout)	::	iwork(liwork)	The integer work space.
integer,	intent(in)	::	liwork	The length of vector `iwork`.
integer,	intent(out)	::	maxit1	For implicit models, the iterations allowed for the next penalty parameter value.
real(kind=wp),	intent(out)	::	tstimp	The relative change in the parameters between the initial values and the solution.
integer,	intent(inout)	::	info	The variable designating why the computations were stopped.
real(kind=wp),	intent(in)	::	lower(np)	The lower bound for `beta`.
real(kind=wp),	intent(in)	::	upper(np)	The upper bound for `beta`.

public impure subroutine dodmn(head, fstitr, prtpen, fcn, n, m, np, nq, job, beta, y, ldy, x, ldx, we, we1, ldwe, ld2we, wd, ldwd, ld2wd, ifixb, ifixx, ldifx, betac, betan, betas, s, delta, deltan, deltas, lower, upper, t, f, fn, fs, fjacb, msgb, fjacd, msgd, ssf, ss, tt, ldtt, stpb, stpd, ldstpd, xplusd, wrk, lwrk, work, lwork, tempret, iwork, liwork, info, bound)

Iteratively compute least squares solution.

Arguments

Type	Intent		Name
logical,	intent(inout)	::	head	The variable designating whether the heading is to be printed (`head = .true.`) or not (`head = .false.`).
logical,	intent(inout)	::	fstitr	The variable designating whether this is the first iteration (`fstitr = .true.`) or not (`fstitr = .false.`).
logical,	intent(inout)	::	prtpen	The value designating whether the penalty parameter is to be printed in the iteration report (`prtpen = .true.`) or not (`prtpen = .false.`).
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.
integer,	intent(inout)	::	job	The variable controlling problem initialization and computational method.
real(kind=wp),	intent(inout)	::	beta(np)	The function parameters.
real(kind=wp),	intent(in)	::	y(ldy,nq)	The dependent variable. Unused when the model is implicit.
integer,	intent(in)	::	ldy	The leading dimension of array `y`.
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)	::	we(ldwe,ld2we,nq)	The `epsilon` weights.
real(kind=wp),	intent(in)	::	we1(ldwe,ld2we,nq)	The square root of the `epsilon` weights.
integer,	intent(in)	::	ldwe	The leading dimension of arrays `we` and `we1`.
integer,	intent(in)	::	ld2we	The second dimension of arrays `we` and `we1`.
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`.
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(inout)	::	betac(np)	The current estimated values of the unfixed `beta`s.
real(kind=wp),	intent(out)	::	betan(np)	The new estimated values of the unfixed `beta`s.
real(kind=wp),	intent(inout)	::	betas(np)	The saved estimated values of the unfixed `beta`s.
real(kind=wp),	intent(out)	::	s(np)	The step for `beta`.
real(kind=wp),	intent(inout)	::	delta(n,m)	The estimated errors in the explanatory variables.
real(kind=wp),	intent(out)	::	deltan(n,m)	The new estimated errors in the explanatory variables.
real(kind=wp),	intent(inout)	::	deltas(n,m)	The saved estimated errors in the explanatory variables.
real(kind=wp),	intent(in)	::	lower(np)	The lower bound for unfixed `beta`s.
real(kind=wp),	intent(in)	::	upper(np)	The upper bound for unfixed `beta`s.
real(kind=wp),	intent(out)	::	t(n,m)	The step for `delta`.
real(kind=wp),	intent(inout)	::	f(n,nq)	The (weighted) estimated values of `epsilon`.
real(kind=wp),	intent(out)	::	fn(n,nq)	The new predicted values from the function.
real(kind=wp),	intent(out)	::	fs(n,nq)	The saved predicted values from the function.
real(kind=wp),	intent(out)	::	fjacb(n,np,nq)	The Jacobian with respect to `beta`.
integer,	intent(in)	::	msgb(nq*np+1)	The error checking results for the Jacobian with respect to `beta`.
real(kind=wp),	intent(out)	::	fjacd(n,m,nq)	The Jacobian with respect to `delta`.
integer,	intent(in)	::	msgd(nq*m+1)	The error checking results for the Jacobian with respect to `delta`.
real(kind=wp),	intent(in)	::	ssf(np)	The scaling values used for `beta`.
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 scaling values used for `delta`.
integer,	intent(in)	::	ldtt	The leading dimension of array `tt`.
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 `delta`.
integer,	intent(in)	::	ldstpd	The leading dimension of array `stpd`.
real(kind=wp),	intent(out)	::	xplusd(n,m)	The values of `x + delta`.
real(kind=wp),	intent(inout)	::	wrk(lwrk)	A work array, equivalenced to `wrk1` and `wrk2`.
integer,	intent(in)	::	lwrk	The length of vector `wrk`.
real(kind=wp),	intent(inout)	::	work(lwork)	The real (wp) workspace.
integer,	intent(in)	::	lwork	The length of vector `work`.
real(kind=wp),	intent(inout)	::	tempret(:,:)	Temporary work array for holding return values before copying to a lower rank array.
integer,	intent(inout)	::	iwork(liwork)	The integer workspace.
integer,	intent(in)	::	liwork	The length of vector `iwork`.
integer,	intent(inout)	::	info	The variable designating why the computations were stopped.
integer,	intent(out)	::	bound(np)	The values of the bounds for `beta`.

public pure subroutine workspace_dimensions(n, m, np, nq, isodr, lwork, liwork)

Calculate the dimensions of the workspace arrays.

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.
logical,	intent(in)	::	isodr	The variable designating whether the solution is by ODR (`isodr = .true.`) or by OLS (`isodr = .false.`).
integer,	intent(out)	::	lwork	Length of `work` array.
integer,	intent(out)	::	liwork	Length of `iwork` array.

odrpack Module

Contents

Subroutines

Uses

Used by

Subroutines

public impure subroutine odr(fcn, n, m, np, nq, beta, y, x, delta, we, wd, ifixb, ifixx, job, ndigit, taufac, sstol, partol, maxit, iprint, lunerr, lunrpt, stpb, stpd, sclb, scld, work, iwork, info, lower, upper)

Arguments

public impure subroutine dodcnt(fcn, n, m, np, nq, beta, y, ldy, x, ldx, we, ldwe, ld2we, wd, ldwd, ld2wd, ifixb, ifixx, ldifx, job, ndigit, taufac, sstol, partol, maxit, iprint, lunerr, lunrpt, stpb, stpd, ldstpd, sclb, scld, ldscld, work, lwork, tempret, iwork, liwork, info, lower, upper)

Arguments

Arguments

Arguments

public pure subroutine workspace_dimensions(n, m, np, nq, isodr, lwork, liwork)

Arguments