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-rw-r--r--ast/cminpack/CopyrightMINPACK.txt52
-rw-r--r--ast/cminpack/README.md128
-rw-r--r--ast/cminpack/cminpack.h370
-rw-r--r--ast/cminpack/cminpackP.h62
-rw-r--r--ast/cminpack/dpmpar.c201
-rw-r--r--ast/cminpack/enorm.c157
-rw-r--r--ast/cminpack/lmder.c526
-rw-r--r--ast/cminpack/lmder1.c167
-rw-r--r--ast/cminpack/lmpar.c338
-rw-r--r--ast/cminpack/qrfac.c285
-rw-r--r--ast/cminpack/qrsolv.c218
11 files changed, 2504 insertions, 0 deletions
diff --git a/ast/cminpack/CopyrightMINPACK.txt b/ast/cminpack/CopyrightMINPACK.txt
new file mode 100644
index 0000000..ae7984d
--- /dev/null
+++ b/ast/cminpack/CopyrightMINPACK.txt
@@ -0,0 +1,52 @@
+Minpack Copyright Notice (1999) University of Chicago. All rights reserved
+
+Redistribution and use in source and binary forms, with or
+without modification, are permitted provided that the
+following conditions are met:
+
+1. Redistributions of source code must retain the above
+copyright notice, this list of conditions and the following
+disclaimer.
+
+2. Redistributions in binary form must reproduce the above
+copyright notice, this list of conditions and the following
+disclaimer in the documentation and/or other materials
+provided with the distribution.
+
+3. The end-user documentation included with the
+redistribution, if any, must include the following
+acknowledgment:
+
+ "This product includes software developed by the
+ University of Chicago, as Operator of Argonne National
+ Laboratory.
+
+Alternately, this acknowledgment may appear in the software
+itself, if and wherever such third-party acknowledgments
+normally appear.
+
+4. WARRANTY DISCLAIMER. THE SOFTWARE IS SUPPLIED "AS IS"
+WITHOUT WARRANTY OF ANY KIND. THE COPYRIGHT HOLDER, THE
+UNITED STATES, THE UNITED STATES DEPARTMENT OF ENERGY, AND
+THEIR EMPLOYEES: (1) DISCLAIM ANY WARRANTIES, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO ANY IMPLIED WARRANTIES
+OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE, TITLE
+OR NON-INFRINGEMENT, (2) DO NOT ASSUME ANY LEGAL LIABILITY
+OR RESPONSIBILITY FOR THE ACCURACY, COMPLETENESS, OR
+USEFULNESS OF THE SOFTWARE, (3) DO NOT REPRESENT THAT USE OF
+THE SOFTWARE WOULD NOT INFRINGE PRIVATELY OWNED RIGHTS, (4)
+DO NOT WARRANT THAT THE SOFTWARE WILL FUNCTION
+UNINTERRUPTED, THAT IT IS ERROR-FREE OR THAT ANY ERRORS WILL
+BE CORRECTED.
+
+5. LIMITATION OF LIABILITY. IN NO EVENT WILL THE COPYRIGHT
+HOLDER, THE UNITED STATES, THE UNITED STATES DEPARTMENT OF
+ENERGY, OR THEIR EMPLOYEES: BE LIABLE FOR ANY INDIRECT,
+INCIDENTAL, CONSEQUENTIAL, SPECIAL OR PUNITIVE DAMAGES OF
+ANY KIND OR NATURE, INCLUDING BUT NOT LIMITED TO LOSS OF
+PROFITS OR LOSS OF DATA, FOR ANY REASON WHATSOEVER, WHETHER
+SUCH LIABILITY IS ASSERTED ON THE BASIS OF CONTRACT, TORT
+(INCLUDING NEGLIGENCE OR STRICT LIABILITY), OR OTHERWISE,
+EVEN IF ANY OF SAID PARTIES HAS BEEN WARNED OF THE
+POSSIBILITY OF SUCH LOSS OR DAMAGES.
+
diff --git a/ast/cminpack/README.md b/ast/cminpack/README.md
new file mode 100644
index 0000000..66bbc6f
--- /dev/null
+++ b/ast/cminpack/README.md
@@ -0,0 +1,128 @@
+C/C++ Minpack [![Build Status](https://api.travis-ci.org/devernay/cminpack.png?branch=master)](https://travis-ci.org/devernay/cminpack)
+==========
+
+This is a C version of the minpack minimization package.
+It has been derived from the fortran code using f2c and
+some limited manual editing. Note that you need to link
+against libf2c to use this version of minpack. Extern "C"
+linkage permits the package routines to be called from C++.
+Check ftp://netlib.bell-labs.com/netlib/f2c for the latest
+f2c version. For general minpack info and test programs, see
+the accompanying readme.txt and http://www.netlib.org/minpack/.
+
+Type `make` to compile and `make install` to install in /usr/local
+or modify the makefile to suit your needs.
+
+This software has been tested on a RedHat 7.3 Linux machine -
+usual 'use at your own risk' warnings apply.
+
+Manolis Lourakis -- lourakis at ics forth gr, July 2002
+ Institute of Computer Science,
+ Foundation for Research and Technology - Hellas
+ Heraklion, Crete, Greece
+
+Repackaging by Frederic Devernay -- frederic dot devernay at m4x dot org
+
+The project home page is at http://devernay.free.fr/hacks/cminpack/
+
+History
+------
+
+* version 1.3.3 (04/02/2014)::
+ - Add documentation and examples abouts how to add box constraints to the variables.
+ - continuous integration https://travis-ci.org/devernay/cminpack
+
+* version 1.3.2 (27/10/2013):
+ - Minor change in the CMake build: also set SOVERSION.
+
+* version 1.3.1 (02/10/2013):
+ - Fix CUDA examples compilation, and remove non-free files.
+
+* version 1.3.0 (09/06/2012):
+ - Optionally use LAPACK and CBLAS in lmpar, qrfac, and qrsolv. Added
+ "make lapack" to build the LAPACK-based cminpack and "make
+ checklapack" to test it (results of the test may depend on the
+ underlying LAPACK and BLAS implementations).
+ On 64-bits architectures, the preprocessor symbol __LP64__ must be
+ defined (see cminpackP.h) if the LAPACK library uses the LP64
+ interface (i.e. 32-bits integer, vhereas the ILP interface uses 64
+ bits integers).
+
+* version 1.2.2 (16/05/2012):
+ - Update Makefiles and documentation (see "Using CMinpack" above) for
+ easier building and testing.
+
+* version 1.2.1 (15/05/2012):
+ - The library can now be built as double, float or half
+ versions. Standard tests in the "examples" directory can now be
+ lauched using "make check" (to run common tests, including against
+ the float version), "make checkhalf" (to test the half version) and
+ "make checkfail" (to run all the tests, even those that fail).
+
+* version 1.2.0 (14/05/2012):
+- Added original FORTRAN sources for better testing (type "make" in
+ directory fortran, then "make" in examples and follow the
+ instructions). Added driver tests lmsdrv, chkdrv, hyjdrv,
+ hybdrv. Typing "make alltest" in the examples directory will run all
+ possible test combinations (make sure you have gfortran installed).
+
+* version 1.1.5 (04/05/2012):
+ - cminpack now works in CUDA, thanks to Jordi Bataller Mascarell, type
+ "make" in the "cuda" subdir (be careful, though: this is a
+ straightforward port from C, and each problem is solved using a
+ single thread). cminpack can now also be compiled with
+ single-precision floating point computation (define
+ __cminpack_real__ to float when compiling and using the
+ library). Fix cmake support for CMINPACK_LIB_INSTALL_DIR. Update the
+ reference files for tests.
+
+* version 1.1.4 (30/10/2011):
+ - Translated all the Levenberg-Marquardt code (lmder, lmdif, lmstr,
+ lmder1, lmdif1, lmstr1, lmpar, qrfac, qrsolv, fdjac2, chkder) to use
+ C-style indices.
+
+* version 1.1.3 (16/03/2011):
+ - Minor fix: Change non-standard strnstr() to strstr() in
+ genf77tests.c.
+
+* version 1.1.2 (07/01/2011):
+ - Fix Windows DLL building (David Graeff) and document covar in
+ cminpack.h.
+
+* version 1.1.1 (04/12/2010):
+ - Complete rewrite of the C functions (without trailing underscore in
+ the function name). Using the original FORTRAN code, the original
+ algorithms structure was recovered, and many goto's were converted
+ to if...then...else. The code should now be both more readable and
+ easier to optimize, both for humans and for compilers. Added lmddrv
+ and lmfdrv test drivers, which test a lot of difficult functions
+ (these functions are explained in Testing Unconstrained Optimization
+ Software by Moré et al.). Also added the pkg-config files to the
+ cmake build, as well as an "uninstall" target, contributed by
+ Geoffrey Biggs.
+
+* version 1.0.4 (18/10/2010):
+ - Support for shared library building using CMake, thanks to Goeffrey
+ Biggs and Radu Bogdan Rusu from Willow Garage. Shared libraries can be
+ enabled using cmake options, as in;
+ cmake -DUSE_FPIC=ON -DSHARED_LIBS=ON -DBUILD_EXAMPLES=OFF path_to_sources
+
+* version 1.0.3 (18/03/2010):
+ - Added CMake support.
+ - XCode build is now Universal.
+ - Added tfdjac2_ and tfdjac2c examples, which test the accuracy of a
+ finite-differences approximation of the Jacobian.
+ - Bug fix in tlmstr1 (signaled by Thomas Capricelli).
+
+* version 1.0.2 (27/02/2009):
+ - Added Xcode and Visual Studio project files
+
+* version 1.0.1 (17/12/2007):
+ - bug fix in covar() and covar_(), the computation of tolr caused a
+ segfault (signaled by Timo Hartmann).
+
+* version 1.0.0 (24/04/2007):
+ - Added fortran and C examples
+ - Added documentation from Debian man pages
+ - Wrote pure C version
+ - Added covar() and covar_(), and use it in tlmdef/tlmdif
diff --git a/ast/cminpack/cminpack.h b/ast/cminpack/cminpack.h
new file mode 100644
index 0000000..6d3f757
--- /dev/null
+++ b/ast/cminpack/cminpack.h
@@ -0,0 +1,370 @@
+/* Header file for cminpack, by Frederic Devernay.
+ The documentation for all functions can be found in the file
+ minpack-documentation.txt from the distribution, or in the source
+ code of each function. */
+
+#ifndef __CMINPACK_H__
+#define __CMINPACK_H__
+
+/* The default floating-point type is "double" for C/C++ and "float" for CUDA,
+ but you can change this by defining one of the following symbols when
+ compiling the library, and before including cminpack.h when using it:
+ __cminpack_double__ for double
+ __cminpack_float__ for float
+ __cminpack_half__ for half from the OpenEXR library (in this case, you must
+ compile cminpack with a C++ compiler)
+*/
+#ifdef __cminpack_double__
+#define __cminpack_real__ double
+#endif
+
+#ifdef __cminpack_float__
+#define __cminpack_real__ float
+#endif
+
+#ifdef __cminpack_half__
+#include <OpenEXR/half.h>
+#define __cminpack_real__ half
+#endif
+
+#ifdef __cplusplus
+extern "C" {
+#endif /* __cplusplus */
+
+/* Cmake will define cminpack_EXPORTS on Windows when it
+configures to build a shared library. If you are going to use
+another build system on windows or create the visual studio
+projects by hand you need to define cminpack_EXPORTS when
+building a DLL on windows.
+*/
+#if defined (__GNUC__)
+#define CMINPACK_DECLSPEC_EXPORT __declspec(__dllexport__)
+#define CMINPACK_DECLSPEC_IMPORT __declspec(__dllimport__)
+#endif
+#if defined (_MSC_VER) || defined (__BORLANDC__)
+#define CMINPACK_DECLSPEC_EXPORT __declspec(dllexport)
+#define CMINPACK_DECLSPEC_IMPORT __declspec(dllimport)
+#endif
+#ifdef __WATCOMC__
+#define CMINPACK_DECLSPEC_EXPORT __export
+#define CMINPACK_DECLSPEC_IMPORT __import
+#endif
+#ifdef __IBMC__
+#define CMINPACK_DECLSPEC_EXPORT _Export
+#define CMINPACK_DECLSPEC_IMPORT _Import
+#endif
+
+#if !defined(CMINPACK_NO_DLL) && (defined(__WIN32__) || defined(WIN32) || defined (_WIN32))
+#if defined(cminpack_EXPORTS) || defined(CMINPACK_EXPORTS) || defined(CMINPACK_DLL_EXPORTS)
+ #define CMINPACK_EXPORT CMINPACK_DECLSPEC_EXPORT
+ #else
+ #define CMINPACK_EXPORT CMINPACK_DECLSPEC_IMPORT
+ #endif /* cminpack_EXPORTS */
+#else /* defined (_WIN32) */
+ #define CMINPACK_EXPORT
+#endif
+
+#if defined(__CUDA_ARCH__) || defined(__CUDACC__)
+#define __cminpack_attr__ __device__
+#ifndef __cminpack_real__
+#define __cminpack_float__
+#define __cminpack_real__ float
+#endif
+#define __cminpack_type_fcn_nn__ __cminpack_attr__ int fcn_nn
+#define __cminpack_type_fcnder_nn__ __cminpack_attr__ int fcnder_nn
+#define __cminpack_type_fcn_mn__ __cminpack_attr__ int fcn_mn
+#define __cminpack_type_fcnder_mn__ __cminpack_attr__ int fcnder_mn
+#define __cminpack_type_fcnderstr_mn__ __cminpack_attr__ int fcnderstr_mn
+#define __cminpack_decl_fcn_nn__
+#define __cminpack_decl_fcnder_nn__
+#define __cminpack_decl_fcn_mn__
+#define __cminpack_decl_fcnder_mn__
+#define __cminpack_decl_fcnderstr_mn__
+#define __cminpack_param_fcn_nn__
+#define __cminpack_param_fcnder_nn__
+#define __cminpack_param_fcn_mn__
+#define __cminpack_param_fcnder_mn__
+#define __cminpack_param_fcnderstr_mn__
+#else
+#define __cminpack_attr__
+#ifndef __cminpack_real__
+#define __cminpack_double__
+#define __cminpack_real__ double
+#endif
+#define __cminpack_type_fcn_nn__ typedef int (*cminpack_func_nn)
+#define __cminpack_type_fcnder_nn__ typedef int (*cminpack_funcder_nn)
+#define __cminpack_type_fcn_mn__ typedef int (*cminpack_func_mn)
+#define __cminpack_type_fcnder_mn__ typedef int (*cminpack_funcder_mn)
+#define __cminpack_type_fcnderstr_mn__ typedef int (*cminpack_funcderstr_mn)
+#define __cminpack_decl_fcn_nn__ cminpack_func_nn fcn_nn,
+#define __cminpack_decl_fcnder_nn__ cminpack_funcder_nn fcnder_nn,
+#define __cminpack_decl_fcn_mn__ cminpack_func_mn fcn_mn,
+#define __cminpack_decl_fcnder_mn__ cminpack_funcder_mn fcnder_mn,
+#define __cminpack_decl_fcnderstr_mn__ cminpack_funcderstr_mn fcnderstr_mn,
+#define __cminpack_param_fcn_nn__ fcn_nn,
+#define __cminpack_param_fcnder_nn__ fcnder_nn,
+#define __cminpack_param_fcn_mn__ fcn_mn,
+#define __cminpack_param_fcnder_mn__ fcnder_mn,
+#define __cminpack_param_fcnderstr_mn__ fcnderstr_mn,
+#endif
+
+#ifdef __cminpack_double__
+#define __cminpack_func__(func) func
+#endif
+
+#ifdef __cminpack_float__
+#define __cminpack_func__(func) s ## func
+#endif
+
+#ifdef __cminpack_half__
+#define __cminpack_func__(func) h ## func
+#endif
+
+/* Declarations for minpack */
+
+/* Function types: */
+/* The first argument can be used to store extra function parameters, thus */
+/* avoiding the use of global variables. */
+/* the iflag parameter is input-only (with respect to the FORTRAN */
+/* version), the output iflag value is the return value of the function. */
+/* If iflag=0, the function shoulkd just print the current values (see */
+/* the nprint parameters below). */
+
+/* for hybrd1 and hybrd: */
+/* calculate the functions at x and */
+/* return this vector in fvec. */
+/* return a negative value to terminate hybrd1/hybrd */
+__cminpack_type_fcn_nn__(void *p, int n, const __cminpack_real__ *x, __cminpack_real__ *fvec, int iflag );
+
+/* for hybrj1 and hybrj */
+/* if iflag = 1 calculate the functions at x and */
+/* return this vector in fvec. do not alter fjac. */
+/* if iflag = 2 calculate the jacobian at x and */
+/* return this matrix in fjac. do not alter fvec. */
+/* return a negative value to terminate hybrj1/hybrj */
+__cminpack_type_fcnder_nn__(void *p, int n, const __cminpack_real__ *x, __cminpack_real__ *fvec, __cminpack_real__ *fjac,
+ int ldfjac, int iflag );
+
+/* for lmdif1 and lmdif */
+/* calculate the functions at x and */
+/* return this vector in fvec. */
+/* if iflag = 1 the result is used to compute the residuals. */
+/* if iflag = 2 the result is used to compute the Jacobian by finite differences. */
+/* Jacobian computation requires exactly n function calls with iflag = 2. */
+/* return a negative value to terminate lmdif1/lmdif */
+__cminpack_type_fcn_mn__(void *p, int m, int n, const __cminpack_real__ *x, __cminpack_real__ *fvec,
+ int iflag );
+
+/* for lmder1 and lmder */
+/* if iflag = 1 calculate the functions at x and */
+/* return this vector in fvec. do not alter fjac. */
+/* if iflag = 2 calculate the jacobian at x and */
+/* return this matrix in fjac. do not alter fvec. */
+/* return a negative value to terminate lmder1/lmder */
+__cminpack_type_fcnder_mn__(void *p, int m, int n, const __cminpack_real__ *x, __cminpack_real__ *fvec,
+ __cminpack_real__ *fjac, int ldfjac, int iflag );
+
+/* for lmstr1 and lmstr */
+/* if iflag = 1 calculate the functions at x and */
+/* return this vector in fvec. */
+/* if iflag = i calculate the (i-1)-st row of the */
+/* jacobian at x and return this vector in fjrow. */
+/* return a negative value to terminate lmstr1/lmstr */
+__cminpack_type_fcnderstr_mn__(void *p, int m, int n, const __cminpack_real__ *x, __cminpack_real__ *fvec,
+ __cminpack_real__ *fjrow, int iflag );
+
+
+
+
+
+
+/* MINPACK functions: */
+/* the info parameter was removed from most functions: the return */
+/* value of the function is used instead. */
+/* The argument 'p' can be used to store extra function parameters, thus */
+/* avoiding the use of global variables. You can also think of it as a */
+/* 'this' pointer a la C++. */
+
+/* find a zero of a system of N nonlinear functions in N variables by
+ a modification of the Powell hybrid method (Jacobian calculated by
+ a forward-difference approximation) */
+__cminpack_attr__
+int CMINPACK_EXPORT __cminpack_func__(hybrd1)( __cminpack_decl_fcn_nn__
+ void *p, int n, __cminpack_real__ *x, __cminpack_real__ *fvec, __cminpack_real__ tol,
+ __cminpack_real__ *wa, int lwa );
+
+/* find a zero of a system of N nonlinear functions in N variables by
+ a modification of the Powell hybrid method (Jacobian calculated by
+ a forward-difference approximation, more general). */
+__cminpack_attr__
+int CMINPACK_EXPORT __cminpack_func__(hybrd)( __cminpack_decl_fcn_nn__
+ void *p, int n, __cminpack_real__ *x, __cminpack_real__ *fvec, __cminpack_real__ xtol, int maxfev,
+ int ml, int mu, __cminpack_real__ epsfcn, __cminpack_real__ *diag, int mode,
+ __cminpack_real__ factor, int nprint, int *nfev,
+ __cminpack_real__ *fjac, int ldfjac, __cminpack_real__ *r, int lr, __cminpack_real__ *qtf,
+ __cminpack_real__ *wa1, __cminpack_real__ *wa2, __cminpack_real__ *wa3, __cminpack_real__ *wa4);
+
+/* find a zero of a system of N nonlinear functions in N variables by
+ a modification of the Powell hybrid method (user-supplied Jacobian) */
+__cminpack_attr__
+int CMINPACK_EXPORT __cminpack_func__(hybrj1)( __cminpack_decl_fcnder_nn__ void *p, int n, __cminpack_real__ *x,
+ __cminpack_real__ *fvec, __cminpack_real__ *fjac, int ldfjac, __cminpack_real__ tol,
+ __cminpack_real__ *wa, int lwa );
+
+/* find a zero of a system of N nonlinear functions in N variables by
+ a modification of the Powell hybrid method (user-supplied Jacobian,
+ more general) */
+__cminpack_attr__
+int CMINPACK_EXPORT __cminpack_func__(hybrj)( __cminpack_decl_fcnder_nn__ void *p, int n, __cminpack_real__ *x,
+ __cminpack_real__ *fvec, __cminpack_real__ *fjac, int ldfjac, __cminpack_real__ xtol,
+ int maxfev, __cminpack_real__ *diag, int mode, __cminpack_real__ factor,
+ int nprint, int *nfev, int *njev, __cminpack_real__ *r,
+ int lr, __cminpack_real__ *qtf, __cminpack_real__ *wa1, __cminpack_real__ *wa2,
+ __cminpack_real__ *wa3, __cminpack_real__ *wa4 );
+
+/* minimize the sum of the squares of nonlinear functions in N
+ variables by a modification of the Levenberg-Marquardt algorithm
+ (Jacobian calculated by a forward-difference approximation) */
+__cminpack_attr__
+int CMINPACK_EXPORT __cminpack_func__(lmdif1)( __cminpack_decl_fcn_mn__
+ void *p, int m, int n, __cminpack_real__ *x, __cminpack_real__ *fvec, __cminpack_real__ tol,
+ int *iwa, __cminpack_real__ *wa, int lwa );
+
+/* minimize the sum of the squares of nonlinear functions in N
+ variables by a modification of the Levenberg-Marquardt algorithm
+ (Jacobian calculated by a forward-difference approximation, more
+ general) */
+__cminpack_attr__
+int CMINPACK_EXPORT __cminpack_func__(lmdif)( __cminpack_decl_fcn_mn__
+ void *p, int m, int n, __cminpack_real__ *x, __cminpack_real__ *fvec, __cminpack_real__ ftol,
+ __cminpack_real__ xtol, __cminpack_real__ gtol, int maxfev, __cminpack_real__ epsfcn,
+ __cminpack_real__ *diag, int mode, __cminpack_real__ factor, int nprint,
+ int *nfev, __cminpack_real__ *fjac, int ldfjac, int *ipvt,
+ __cminpack_real__ *qtf, __cminpack_real__ *wa1, __cminpack_real__ *wa2, __cminpack_real__ *wa3,
+ __cminpack_real__ *wa4 );
+
+/* minimize the sum of the squares of nonlinear functions in N
+ variables by a modification of the Levenberg-Marquardt algorithm
+ (user-supplied Jacobian) */
+__cminpack_attr__
+int CMINPACK_EXPORT __cminpack_func__(lmder1)( __cminpack_decl_fcnder_mn__
+ void *p, int m, int n, __cminpack_real__ *x, __cminpack_real__ *fvec, __cminpack_real__ *fjac,
+ int ldfjac, __cminpack_real__ tol, int *ipvt,
+ __cminpack_real__ *wa, int lwa );
+
+/* minimize the sum of the squares of nonlinear functions in N
+ variables by a modification of the Levenberg-Marquardt algorithm
+ (user-supplied Jacobian, more general) */
+__cminpack_attr__
+int CMINPACK_EXPORT __cminpack_func__(lmder)( __cminpack_decl_fcnder_mn__
+ void *p, int m, int n, __cminpack_real__ *x, __cminpack_real__ *fvec, __cminpack_real__ *fjac,
+ int ldfjac, __cminpack_real__ ftol, __cminpack_real__ xtol, __cminpack_real__ gtol,
+ int maxfev, __cminpack_real__ *diag, int mode, __cminpack_real__ factor,
+ int nprint, int *nfev, int *njev, int *ipvt,
+ __cminpack_real__ *qtf, __cminpack_real__ *wa1, __cminpack_real__ *wa2, __cminpack_real__ *wa3,
+ __cminpack_real__ *wa4 );
+
+/* minimize the sum of the squares of nonlinear functions in N
+ variables by a modification of the Levenberg-Marquardt algorithm
+ (user-supplied Jacobian, minimal storage) */
+__cminpack_attr__
+int CMINPACK_EXPORT __cminpack_func__(lmstr1)( __cminpack_decl_fcnderstr_mn__ void *p, int m, int n,
+ __cminpack_real__ *x, __cminpack_real__ *fvec, __cminpack_real__ *fjac, int ldfjac,
+ __cminpack_real__ tol, int *ipvt, __cminpack_real__ *wa, int lwa );
+
+/* minimize the sum of the squares of nonlinear functions in N
+ variables by a modification of the Levenberg-Marquardt algorithm
+ (user-supplied Jacobian, minimal storage, more general) */
+__cminpack_attr__
+int CMINPACK_EXPORT __cminpack_func__(lmstr)( __cminpack_decl_fcnderstr_mn__ void *p, int m,
+ int n, __cminpack_real__ *x, __cminpack_real__ *fvec, __cminpack_real__ *fjac,
+ int ldfjac, __cminpack_real__ ftol, __cminpack_real__ xtol, __cminpack_real__ gtol,
+ int maxfev, __cminpack_real__ *diag, int mode, __cminpack_real__ factor,
+ int nprint, int *nfev, int *njev, int *ipvt,
+ __cminpack_real__ *qtf, __cminpack_real__ *wa1, __cminpack_real__ *wa2, __cminpack_real__ *wa3,
+ __cminpack_real__ *wa4 );
+
+__cminpack_attr__
+void CMINPACK_EXPORT __cminpack_func__(chkder)( int m, int n, const __cminpack_real__ *x, __cminpack_real__ *fvec, __cminpack_real__ *fjac,
+ int ldfjac, __cminpack_real__ *xp, __cminpack_real__ *fvecp, int mode,
+ __cminpack_real__ *err );
+
+__cminpack_attr__
+__cminpack_real__ CMINPACK_EXPORT __cminpack_func__(dpmpar)( int i );
+
+__cminpack_attr__
+__cminpack_real__ CMINPACK_EXPORT __cminpack_func__(enorm)( int n, const __cminpack_real__ *x );
+
+/* compute a forward-difference approximation to the m by n jacobian
+ matrix associated with a specified problem of m functions in n
+ variables. */
+__cminpack_attr__
+int CMINPACK_EXPORT __cminpack_func__(fdjac2)(__cminpack_decl_fcn_mn__
+ void *p, int m, int n, __cminpack_real__ *x, const __cminpack_real__ *fvec, __cminpack_real__ *fjac,
+ int ldfjac, __cminpack_real__ epsfcn, __cminpack_real__ *wa);
+
+/* compute a forward-difference approximation to the n by n jacobian
+ matrix associated with a specified problem of n functions in n
+ variables. if the jacobian has a banded form, then function
+ evaluations are saved by only approximating the nonzero terms. */
+__cminpack_attr__
+int CMINPACK_EXPORT __cminpack_func__(fdjac1)(__cminpack_decl_fcn_nn__
+ void *p, int n, __cminpack_real__ *x, const __cminpack_real__ *fvec, __cminpack_real__ *fjac, int ldfjac,
+ int ml, int mu, __cminpack_real__ epsfcn, __cminpack_real__ *wa1,
+ __cminpack_real__ *wa2);
+
+/* compute inverse(JtJ) after a run of lmdif or lmder. The covariance matrix is obtained
+ by scaling the result by enorm(y)**2/(m-n). If JtJ is singular and k = rank(J), the
+ pseudo-inverse is computed, and the result has to be scaled by enorm(y)**2/(m-k). */
+__cminpack_attr__
+void CMINPACK_EXPORT __cminpack_func__(covar)(int n, __cminpack_real__ *r, int ldr,
+ const int *ipvt, __cminpack_real__ tol, __cminpack_real__ *wa);
+
+/* covar1 estimates the variance-covariance matrix:
+ C = sigma**2 (JtJ)**+
+ where (JtJ)**+ is the inverse of JtJ or the pseudo-inverse of JtJ (in case J does not have full rank),
+ and sigma**2 = fsumsq / (m - k)
+ where fsumsq is the residual sum of squares and k is the rank of J.
+ The function returns 0 if J has full rank, else the rank of J.
+*/
+__cminpack_attr__
+int CMINPACK_EXPORT __cminpack_func__(covar1)(int m, int n, __cminpack_real__ fsumsq, __cminpack_real__ *r, int ldr,
+ const int *ipvt, __cminpack_real__ tol, __cminpack_real__ *wa);
+
+/* internal MINPACK subroutines */
+__cminpack_attr__
+void __cminpack_func__(dogleg)(int n, const __cminpack_real__ *r, int lr,
+ const __cminpack_real__ *diag, const __cminpack_real__ *qtb, __cminpack_real__ delta, __cminpack_real__ *x,
+ __cminpack_real__ *wa1, __cminpack_real__ *wa2);
+__cminpack_attr__
+void __cminpack_func__(qrfac)(int m, int n, __cminpack_real__ *a, int
+ lda, int pivot, int *ipvt, int lipvt, __cminpack_real__ *rdiag,
+ __cminpack_real__ *acnorm, __cminpack_real__ *wa);
+__cminpack_attr__
+void __cminpack_func__(qrsolv)(int n, __cminpack_real__ *r, int ldr,
+ const int *ipvt, const __cminpack_real__ *diag, const __cminpack_real__ *qtb, __cminpack_real__ *x,
+ __cminpack_real__ *sdiag, __cminpack_real__ *wa);
+__cminpack_attr__
+void __cminpack_func__(qform)(int m, int n, __cminpack_real__ *q, int
+ ldq, __cminpack_real__ *wa);
+__cminpack_attr__
+void __cminpack_func__(r1updt)(int m, int n, __cminpack_real__ *s, int
+ ls, const __cminpack_real__ *u, __cminpack_real__ *v, __cminpack_real__ *w, int *sing);
+__cminpack_attr__
+void __cminpack_func__(r1mpyq)(int m, int n, __cminpack_real__ *a, int
+ lda, const __cminpack_real__ *v, const __cminpack_real__ *w);
+__cminpack_attr__
+void __cminpack_func__(lmpar)(int n, __cminpack_real__ *r, int ldr,
+ const int *ipvt, const __cminpack_real__ *diag, const __cminpack_real__ *qtb, __cminpack_real__ delta,
+ __cminpack_real__ *par, __cminpack_real__ *x, __cminpack_real__ *sdiag, __cminpack_real__ *wa1,
+ __cminpack_real__ *wa2);
+__cminpack_attr__
+void __cminpack_func__(rwupdt)(int n, __cminpack_real__ *r, int ldr,
+ const __cminpack_real__ *w, __cminpack_real__ *b, __cminpack_real__ *alpha, __cminpack_real__ *cos,
+ __cminpack_real__ *sin);
+#ifdef __cplusplus
+}
+#endif /* __cplusplus */
+
+
+#endif /* __CMINPACK_H__ */
diff --git a/ast/cminpack/cminpackP.h b/ast/cminpack/cminpackP.h
new file mode 100644
index 0000000..4e8ba7b
--- /dev/null
+++ b/ast/cminpack/cminpackP.h
@@ -0,0 +1,62 @@
+/* Internal header file for cminpack, by Frederic Devernay. */
+#ifndef __CMINPACKP_H__
+#define __CMINPACKP_H__
+
+#ifndef __CMINPACK_H__
+#error "cminpackP.h in an internal cminpack header, and must be included after all other headers (including cminpack.h)"
+#endif
+
+#if (defined (USE_CBLAS) || defined (USE_LAPACK)) && !defined (__cminpack_double__)
+#error "cminpack can use cblas and lapack only in double precision mode"
+#endif
+
+#ifdef USE_CBLAS
+#ifdef __APPLE__
+#include <Accelerate/Accelerate.h>
+#else
+#include <cblas.h>
+#endif
+#define __cminpack_enorm__(n,x) cblas_dnrm2(n,x,1)
+#else
+#define __cminpack_enorm__(n,x) __cminpack_func__(enorm)(n,x)
+#endif
+
+#ifdef USE_LAPACK
+#ifdef __APPLE__
+#include <Accelerate/Accelerate.h>
+#else
+#if defined(__LP64__) /* In LP64 match sizes with the 32 bit ABI */
+typedef int __CLPK_integer;
+typedef int __CLPK_logical;
+typedef float __CLPK_real;
+typedef double __CLPK_doublereal;
+typedef __CLPK_logical (*__CLPK_L_fp)();
+typedef int __CLPK_ftnlen;
+#else
+typedef long int __CLPK_integer;
+typedef long int __CLPK_logical;
+typedef float __CLPK_real;
+typedef double __CLPK_doublereal;
+typedef __CLPK_logical (*__CLPK_L_fp)();
+typedef long int __CLPK_ftnlen;
+#endif
+//extern void dlartg_(double *f, double *g, double *cs, double *sn, double *r__);
+int dlartg_(__CLPK_doublereal *f, __CLPK_doublereal *g, __CLPK_doublereal *cs,
+ __CLPK_doublereal *sn, __CLPK_doublereal *r__)
+//extern void dgeqp3_(int *m, int *n, double *a, int *lda, int *jpvt, double *tau, double *work, int *lwork, int *info);
+int dgeqp3_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_doublereal *a, __CLPK_integer *
+ lda, __CLPK_integer *jpvt, __CLPK_doublereal *tau, __CLPK_doublereal *work, __CLPK_integer *lwork,
+ __CLPK_integer *info)
+//extern void dgeqrf_(int *m, int *n, double *a, int *lda, double *tau, double *work, int *lwork, int *info);
+int dgeqrf_(__CLPK_integer *m, __CLPK_integer *n, __CLPK_doublereal *a, __CLPK_integer *
+ lda, __CLPK_doublereal *tau, __CLPK_doublereal *work, __CLPK_integer *lwork, __CLPK_integer *info)
+#endif
+#endif
+
+#define real __cminpack_real__
+#define min(a,b) ((a) <= (b) ? (a) : (b))
+#define max(a,b) ((a) >= (b) ? (a) : (b))
+#define TRUE_ (1)
+#define FALSE_ (0)
+
+#endif /* !__CMINPACKP_H__ */
diff --git a/ast/cminpack/dpmpar.c b/ast/cminpack/dpmpar.c
new file mode 100644
index 0000000..81c6fcd
--- /dev/null
+++ b/ast/cminpack/dpmpar.c
@@ -0,0 +1,201 @@
+#include "cminpack.h"
+#include <float.h>
+#include "cminpackP.h"
+
+#define double_EPSILON DBL_EPSILON
+#define double_MIN DBL_MIN
+#define double_MAX DBL_MAX
+#define float_EPSILON FLT_EPSILON
+#define float_MIN FLT_MIN
+#define float_MAX FLT_MAX
+#define half_EPSILON HALF_EPSILON
+#define half_MIN HALF_NRM_MIN
+#define half_MAX HALF_MAX
+
+#define DPMPAR(type,X) _DPMPAR(type,X)
+#define _DPMPAR(type,X) type ## _ ## X
+
+__cminpack_attr__
+real __cminpack_func__(dpmpar)(int i)
+{
+/* ********** */
+
+/* Function dpmpar */
+
+/* This function provides double precision machine parameters */
+/* when the appropriate set of data statements is activated (by */
+/* removing the c from column 1) and all other data statements are */
+/* rendered inactive. Most of the parameter values were obtained */
+/* from the corresponding Bell Laboratories Port Library function. */
+
+/* The function statement is */
+
+/* double precision function dpmpar(i) */
+
+/* where */
+
+/* i is an integer input variable set to 1, 2, or 3 which */
+/* selects the desired machine parameter. If the machine has */
+/* t base b digits and its smallest and largest exponents are */
+/* emin and emax, respectively, then these parameters are */
+
+/* dpmpar(1) = b**(1 - t), the machine precision, */
+
+/* dpmpar(2) = b**(emin - 1), the smallest magnitude, */
+
+/* dpmpar(3) = b**emax*(1 - b**(-t)), the largest magnitude. */
+
+/* Argonne National Laboratory. MINPACK Project. November 1996. */
+/* Burton S. Garbow, Kenneth E. Hillstrom, Jorge J. More' */
+
+/* ********** */
+
+/* Machine constants for the IBM 360/370 series, */
+/* the Amdahl 470/V6, the ICL 2900, the Itel AS/6, */
+/* the Xerox Sigma 5/7/9 and the Sel systems 85/86. */
+
+/* data mcheps(1),mcheps(2) / z34100000, z00000000 / */
+/* data minmag(1),minmag(2) / z00100000, z00000000 / */
+/* data maxmag(1),maxmag(2) / z7fffffff, zffffffff / */
+
+/* Machine constants for the Honeywell 600/6000 series. */
+
+/* data mcheps(1),mcheps(2) / o606400000000, o000000000000 / */
+/* data minmag(1),minmag(2) / o402400000000, o000000000000 / */
+/* data maxmag(1),maxmag(2) / o376777777777, o777777777777 / */
+
+/* Machine constants for the CDC 6000/7000 series. */
+
+/* data mcheps(1) / 15614000000000000000b / */
+/* data mcheps(2) / 15010000000000000000b / */
+
+/* data minmag(1) / 00604000000000000000b / */
+/* data minmag(2) / 00000000000000000000b / */
+
+/* data maxmag(1) / 37767777777777777777b / */
+/* data maxmag(2) / 37167777777777777777b / */
+
+/* Machine constants for the PDP-10 (KA processor). */
+
+/* data mcheps(1),mcheps(2) / "114400000000, "000000000000 / */
+/* data minmag(1),minmag(2) / "033400000000, "000000000000 / */
+/* data maxmag(1),maxmag(2) / "377777777777, "344777777777 / */
+
+/* Machine constants for the PDP-10 (KI processor). */
+
+/* data mcheps(1),mcheps(2) / "104400000000, "000000000000 / */
+/* data minmag(1),minmag(2) / "000400000000, "000000000000 / */
+/* data maxmag(1),maxmag(2) / "377777777777, "377777777777 / */
+
+/* Machine constants for the PDP-11. */
+
+/* data mcheps(1),mcheps(2) / 9472, 0 / */
+/* data mcheps(3),mcheps(4) / 0, 0 / */
+
+/* data minmag(1),minmag(2) / 128, 0 / */
+/* data minmag(3),minmag(4) / 0, 0 / */
+
+/* data maxmag(1),maxmag(2) / 32767, -1 / */
+/* data maxmag(3),maxmag(4) / -1, -1 / */
+
+/* Machine constants for the Burroughs 6700/7700 systems. */
+
+/* data mcheps(1) / o1451000000000000 / */
+/* data mcheps(2) / o0000000000000000 / */
+
+/* data minmag(1) / o1771000000000000 / */
+/* data minmag(2) / o7770000000000000 / */
+
+/* data maxmag(1) / o0777777777777777 / */
+/* data maxmag(2) / o7777777777777777 / */
+
+/* Machine constants for the Burroughs 5700 system. */
+
+/* data mcheps(1) / o1451000000000000 / */
+/* data mcheps(2) / o0000000000000000 / */
+
+/* data minmag(1) / o1771000000000000 / */
+/* data minmag(2) / o0000000000000000 / */
+
+/* data maxmag(1) / o0777777777777777 / */
+/* data maxmag(2) / o0007777777777777 / */
+
+/* Machine constants for the Burroughs 1700 system. */
+
+/* data mcheps(1) / zcc6800000 / */
+/* data mcheps(2) / z000000000 / */
+
+/* data minmag(1) / zc00800000 / */
+/* data minmag(2) / z000000000 / */
+
+/* data maxmag(1) / zdffffffff / */
+/* data maxmag(2) / zfffffffff / */
+
+/* Machine constants for the Univac 1100 series. */
+
+/* data mcheps(1),mcheps(2) / o170640000000, o000000000000 / */
+/* data minmag(1),minmag(2) / o000040000000, o000000000000 / */
+/* data maxmag(1),maxmag(2) / o377777777777, o777777777777 / */
+
+/* Machine constants for the Data General Eclipse S/200. */
+
+/* Note - it may be appropriate to include the following card - */
+/* static dmach(3) */
+
+/* data minmag/20k,3*0/,maxmag/77777k,3*177777k/ */
+/* data mcheps/32020k,3*0/ */
+
+/* Machine constants for the Harris 220. */
+
+/* data mcheps(1),mcheps(2) / '20000000, '00000334 / */
+/* data minmag(1),minmag(2) / '20000000, '00000201 / */
+/* data maxmag(1),maxmag(2) / '37777777, '37777577 / */
+
+/* Machine constants for the Cray-1. */
+
+/* data mcheps(1) / 0376424000000000000000b / */
+/* data mcheps(2) / 0000000000000000000000b / */
+
+/* data minmag(1) / 0200034000000000000000b / */
+/* data minmag(2) / 0000000000000000000000b / */
+
+/* data maxmag(1) / 0577777777777777777777b / */
+/* data maxmag(2) / 0000007777777777777776b / */
+
+/* Machine constants for the Prime 400. */
+
+/* data mcheps(1),mcheps(2) / :10000000000, :00000000123 / */
+/* data minmag(1),minmag(2) / :10000000000, :00000100000 / */
+/* data maxmag(1),maxmag(2) / :17777777777, :37777677776 / */
+
+/* Machine constants for the VAX-11. */
+
+/* data mcheps(1),mcheps(2) / 9472, 0 / */
+/* data minmag(1),minmag(2) / 128, 0 / */
+/* data maxmag(1),maxmag(2) / -32769, -1 / */
+
+/* Machine constants for IEEE machines. */
+
+/* data dmach(1) /2.22044604926d-16/ */
+/* data dmach(2) /2.22507385852d-308/ */
+/* data dmach(3) /1.79769313485d+308/ */
+
+ switch(i) {
+ case 1:
+ return DPMPAR(real,EPSILON); /* 2.2204460492503131e-16 | 1.19209290e-07F */
+ case 2:
+ return DPMPAR(real,MIN); /* 2.2250738585072014e-308 | 1.17549435e-38F */
+ default:
+ return DPMPAR(real,MAX); /* 1.7976931348623157e+308 | 3.40282347e+38F */
+ }
+
+/* Last card of function dpmpar. */
+
+} /* dpmpar_ */
+
+#undef mcheps
+#undef maxmag
+#undef minmag
+#undef dmach
+
+
diff --git a/ast/cminpack/enorm.c b/ast/cminpack/enorm.c
new file mode 100644
index 0000000..ad10824
--- /dev/null
+++ b/ast/cminpack/enorm.c
@@ -0,0 +1,157 @@
+#include "cminpack.h"
+#include <math.h>
+#include "cminpackP.h"
+
+/*
+ About the values for rdwarf and rgiant.
+
+ The original values, both in signe-precision FORTRAN source code and in double-precision code were:
+#define rdwarf 3.834e-20
+#define rgiant 1.304e19
+ See for example:
+ http://www.netlib.org/slatec/src/denorm.f
+ http://www.netlib.org/slatec/src/enorm.f
+ However, rdwarf is smaller than sqrt(FLT_MIN) = 1.0842021724855044e-19, so that rdwarf**2 will
+ underflow. This contradicts the constraints expressed in the comments below.
+
+ We changed these constants to be sqrt(dpmpar(2))*0.9 and sqrt(dpmpar(3))*0.9, as proposed by the
+ implementation found in MPFIT http://cow.physics.wisc.edu/~craigm/idl/fitting.html
+*/
+
+#define double_dwarf (1.4916681462400413e-154*0.9)
+#define double_giant (1.3407807929942596e+154*0.9)
+#define float_dwarf (1.0842021724855044e-19f*0.9f)
+#define float_giant (1.8446743523953730e+19f*0.9f)
+#define half_dwarf (2.4414062505039999e-4f*0.9f)
+#define half_giant (255.93749236874225497222f*0.9f)
+
+#define dwarf(type) _dwarf(type)
+#define _dwarf(type) type ## _dwarf
+#define giant(type) _giant(type)
+#define _giant(type) type ## _giant
+
+#define rdwarf dwarf(real)
+#define rgiant giant(real)
+
+__cminpack_attr__
+real __cminpack_func__(enorm)(int n, const real *x)
+{
+#ifdef USE_CBLAS
+ return cblas_dnrm2(n, x, 1);
+#else /* !USE_CBLAS */
+ /* System generated locals */
+ real ret_val, d1;
+
+ /* Local variables */
+ int i;
+ real s1, s2, s3, xabs, x1max, x3max, agiant, floatn;
+
+/* ********** */
+
+/* function enorm */
+
+/* given an n-vector x, this function calculates the */
+/* euclidean norm of x. */
+
+/* the euclidean norm is computed by accumulating the sum of */
+/* squares in three different sums. the sums of squares for the */
+/* small and large components are scaled so that no overflows */
+/* occur. non-destructive underflows are permitted. underflows */
+/* and overflows do not occur in the computation of the unscaled */
+/* sum of squares for the intermediate components. */
+/* the definitions of small, intermediate and large components */
+/* depend on two constants, rdwarf and rgiant. the main */
+/* restrictions on these constants are that rdwarf**2 not */
+/* underflow and rgiant**2 not overflow. the constants */
+/* given here are suitable for every known computer. */
+
+/* the function statement is */
+
+/* double precision function enorm(n,x) */
+
+/* where */
+
+/* n is a positive integer input variable. */
+
+/* x is an input array of length n. */
+
+/* subprograms called */
+
+/* fortran-supplied ... dabs,dsqrt */
+
+/* argonne national laboratory. minpack project. march 1980. */
+/* burton s. garbow, kenneth e. hillstrom, jorge j. more */
+
+/* ********** */
+
+ s1 = 0.;
+ s2 = 0.;
+ s3 = 0.;
+ x1max = 0.;
+ x3max = 0.;
+ floatn = (real) (n);
+ agiant = rgiant / floatn;
+ for (i = 0; i < n; ++i) {
+ xabs = fabs(x[i]);
+ if (xabs <= rdwarf || xabs >= agiant) {
+ if (xabs > rdwarf) {
+
+/* sum for large components. */
+
+ if (xabs > x1max) {
+ /* Computing 2nd power */
+ d1 = x1max / xabs;
+ s1 = 1. + s1 * (d1 * d1);
+ x1max = xabs;
+ } else {
+ /* Computing 2nd power */
+ d1 = xabs / x1max;
+ s1 += d1 * d1;
+ }
+ } else {
+
+/* sum for small components. */
+
+ if (xabs > x3max) {
+ /* Computing 2nd power */
+ d1 = x3max / xabs;
+ s3 = 1. + s3 * (d1 * d1);
+ x3max = xabs;
+ } else {
+ if (xabs != 0.) {
+ /* Computing 2nd power */
+ d1 = xabs / x3max;
+ s3 += d1 * d1;
+ }
+ }
+ }
+ } else {
+
+/* sum for intermediate components. */
+
+ /* Computing 2nd power */
+ s2 += xabs * xabs;
+ }
+ }
+
+/* calculation of norm. */
+
+ if (s1 != 0.) {
+ ret_val = x1max * sqrt(s1 + (s2 / x1max) / x1max);
+ } else {
+ if (s2 != 0.) {
+ if (s2 >= x3max) {
+ ret_val = sqrt(s2 * (1. + (x3max / s2) * (x3max * s3)));
+ } else {
+ ret_val = sqrt(x3max * ((s2 / x3max) + (x3max * s3)));
+ }
+ } else {
+ ret_val = x3max * sqrt(s3);
+ }
+ }
+ return ret_val;
+
+/* last card of function enorm. */
+#endif /* !USE_CBLAS */
+} /* enorm_ */
+
diff --git a/ast/cminpack/lmder.c b/ast/cminpack/lmder.c
new file mode 100644
index 0000000..7f57428
--- /dev/null
+++ b/ast/cminpack/lmder.c
@@ -0,0 +1,526 @@
+#include "cminpack.h"
+#include <math.h>
+#include "cminpackP.h"
+
+__cminpack_attr__
+int __cminpack_func__(lmder)(__cminpack_decl_fcnder_mn__ void *p, int m, int n, real *x,
+ real *fvec, real *fjac, int ldfjac, real ftol,
+ real xtol, real gtol, int maxfev, real *
+ diag, int mode, real factor, int nprint,
+ int *nfev, int *njev, int *ipvt, real *qtf,
+ real *wa1, real *wa2, real *wa3, real *wa4)
+{
+ /* Initialized data */
+
+#define p1 .1
+#define p5 .5
+#define p25 .25
+#define p75 .75
+#define p0001 1e-4
+
+ /* System generated locals */
+ real d1, d2;
+
+ /* Local variables */
+ int i, j, l;
+ real par, sum;
+ int iter;
+ real temp, temp1, temp2;
+ int iflag;
+ real delta = 0.;
+ real ratio;
+ real fnorm, gnorm, pnorm, xnorm = 0., fnorm1, actred, dirder,
+ epsmch, prered;
+ int info;
+
+/* ********** */
+
+/* subroutine lmder */
+
+/* the purpose of lmder is to minimize the sum of the squares of */
+/* m nonlinear functions in n variables by a modification of */
+/* the levenberg-marquardt algorithm. the user must provide a */
+/* subroutine which calculates the functions and the jacobian. */
+
+/* the subroutine statement is */
+
+/* subroutine lmder(fcn,m,n,x,fvec,fjac,ldfjac,ftol,xtol,gtol, */
+/* maxfev,diag,mode,factor,nprint,info,nfev, */
+/* njev,ipvt,qtf,wa1,wa2,wa3,wa4) */
+
+/* where */
+
+/* fcn is the name of the user-supplied subroutine which */
+/* calculates the functions and the jacobian. fcn must */
+/* be declared in an external statement in the user */
+/* calling program, and should be written as follows. */
+
+/* subroutine fcn(m,n,x,fvec,fjac,ldfjac,iflag) */
+/* integer m,n,ldfjac,iflag */
+/* double precision x(n),fvec(m),fjac(ldfjac,n) */
+/* ---------- */
+/* if iflag = 1 calculate the functions at x and */
+/* return this vector in fvec. do not alter fjac. */
+/* if iflag = 2 calculate the jacobian at x and */
+/* return this matrix in fjac. do not alter fvec. */
+/* ---------- */
+/* return */
+/* end */
+
+/* the value of iflag should not be changed by fcn unless */
+/* the user wants to terminate execution of lmder. */
+/* in this case set iflag to a negative integer. */
+
+/* m is a positive integer input variable set to the number */
+/* of functions. */
+
+/* n is a positive integer input variable set to the number */
+/* of variables. n must not exceed m. */
+
+/* x is an array of length n. on input x must contain */
+/* an initial estimate of the solution vector. on output x */
+/* contains the final estimate of the solution vector. */
+
+/* fvec is an output array of length m which contains */
+/* the functions evaluated at the output x. */
+
+/* fjac is an output m by n array. the upper n by n submatrix */
+/* of fjac contains an upper triangular matrix r with */
+/* diagonal elements of nonincreasing magnitude such that */
+
+/* t t t */
+/* p *(jac *jac)*p = r *r, */
+
+/* where p is a permutation matrix and jac is the final */
+/* calculated jacobian. column j of p is column ipvt(j) */
+/* (see below) of the identity matrix. the lower trapezoidal */
+/* part of fjac contains information generated during */
+/* the computation of r. */
+
+/* ldfjac is a positive integer input variable not less than m */
+/* which specifies the leading dimension of the array fjac. */
+
+/* ftol is a nonnegative input variable. termination */
+/* occurs when both the actual and predicted relative */
+/* reductions in the sum of squares are at most ftol. */
+/* therefore, ftol measures the relative error desired */
+/* in the sum of squares. */
+
+/* xtol is a nonnegative input variable. termination */
+/* occurs when the relative error between two consecutive */
+/* iterates is at most xtol. therefore, xtol measures the */
+/* relative error desired in the approximate solution. */
+
+/* gtol is a nonnegative input variable. termination */
+/* occurs when the cosine of the angle between fvec and */
+/* any column of the jacobian is at most gtol in absolute */
+/* value. therefore, gtol measures the orthogonality */
+/* desired between the function vector and the columns */
+/* of the jacobian. */
+
+/* maxfev is a positive integer input variable. termination */
+/* occurs when the number of calls to fcn with iflag = 1 */
+/* has reached maxfev. */
+
+/* diag is an array of length n. if mode = 1 (see */
+/* below), diag is internally set. if mode = 2, diag */
+/* must contain positive entries that serve as */
+/* multiplicative scale factors for the variables. */
+
+/* mode is an integer input variable. if mode = 1, the */
+/* variables will be scaled internally. if mode = 2, */
+/* the scaling is specified by the input diag. other */
+/* values of mode are equivalent to mode = 1. */
+
+/* factor is a positive input variable used in determining the */
+/* initial step bound. this bound is set to the product of */
+/* factor and the euclidean norm of diag*x if nonzero, or else */
+/* to factor itself. in most cases factor should lie in the */
+/* interval (.1,100.).100. is a generally recommended value. */
+
+/* nprint is an integer input variable that enables controlled */
+/* printing of iterates if it is positive. in this case, */
+/* fcn is called with iflag = 0 at the beginning of the first */
+/* iteration and every nprint iterations thereafter and */
+/* immediately prior to return, with x, fvec, and fjac */
+/* available for printing. fvec and fjac should not be */
+/* altered. if nprint is not positive, no special calls */
+/* of fcn with iflag = 0 are made. */
+
+/* info is an integer output variable. if the user has */
+/* terminated execution, info is set to the (negative) */
+/* value of iflag. see description of fcn. otherwise, */
+/* info is set as follows. */
+
+/* info = 0 improper input parameters. */
+
+/* info = 1 both actual and predicted relative reductions */
+/* in the sum of squares are at most ftol. */
+
+/* info = 2 relative error between two consecutive iterates */
+/* is at most xtol. */
+
+/* info = 3 conditions for info = 1 and info = 2 both hold. */
+
+/* info = 4 the cosine of the angle between fvec and any */
+/* column of the jacobian is at most gtol in */
+/* absolute value. */
+
+/* info = 5 number of calls to fcn with iflag = 1 has */
+/* reached maxfev. */
+
+/* info = 6 ftol is too small. no further reduction in */
+/* the sum of squares is possible. */
+
+/* info = 7 xtol is too small. no further improvement in */
+/* the approximate solution x is possible. */
+
+/* info = 8 gtol is too small. fvec is orthogonal to the */
+/* columns of the jacobian to machine precision. */
+
+/* nfev is an integer output variable set to the number of */
+/* calls to fcn with iflag = 1. */
+
+/* njev is an integer output variable set to the number of */
+/* calls to fcn with iflag = 2. */
+
+/* ipvt is an integer output array of length n. ipvt */
+/* defines a permutation matrix p such that jac*p = q*r, */
+/* where jac is the final calculated jacobian, q is */
+/* orthogonal (not stored), and r is upper triangular */
+/* with diagonal elements of nonincreasing magnitude. */
+/* column j of p is column ipvt(j) of the identity matrix. */
+
+/* qtf is an output array of length n which contains */
+/* the first n elements of the vector (q transpose)*fvec. */
+
+/* wa1, wa2, and wa3 are work arrays of length n. */
+
+/* wa4 is a work array of length m. */
+
+/* subprograms called */
+
+/* user-supplied ...... fcn */
+
+/* minpack-supplied ... dpmpar,enorm,lmpar,qrfac */
+
+/* fortran-supplied ... dabs,dmax1,dmin1,dsqrt,mod */
+
+/* argonne national laboratory. minpack project. march 1980. */
+/* burton s. garbow, kenneth e. hillstrom, jorge j. more */
+
+/* ********** */
+
+/* epsmch is the machine precision. */
+
+ epsmch = __cminpack_func__(dpmpar)(1);
+
+ info = 0;
+ iflag = 0;
+ *nfev = 0;
+ *njev = 0;
+
+/* check the input parameters for errors. */
+
+ if (n <= 0 || m < n || ldfjac < m || ftol < 0. || xtol < 0. ||
+ gtol < 0. || maxfev <= 0 || factor <= 0.) {
+ goto TERMINATE;
+ }
+ if (mode == 2) {
+ for (j = 0; j < n; ++j) {
+ if (diag[j] <= 0.) {
+ goto TERMINATE;
+ }
+ }
+ }
+
+/* evaluate the function at the starting point */
+/* and calculate its norm. */
+
+ iflag = fcnder_mn(p, m, n, x, fvec, fjac, ldfjac, 1);
+ *nfev = 1;
+ if (iflag < 0) {
+ goto TERMINATE;
+ }
+ fnorm = __cminpack_enorm__(m, fvec);
+
+/* initialize levenberg-marquardt parameter and iteration counter. */
+
+ par = 0.;
+ iter = 1;
+
+/* beginning of the outer loop. */
+
+ for (;;) {
+
+/* calculate the jacobian matrix. */
+
+ iflag = fcnder_mn(p, m, n, x, fvec, fjac, ldfjac, 2);
+ ++(*njev);
+ if (iflag < 0) {
+ goto TERMINATE;
+ }
+
+/* if requested, call fcn to enable printing of iterates. */
+
+ if (nprint > 0) {
+ iflag = 0;
+ if ((iter - 1) % nprint == 0) {
+ iflag = fcnder_mn(p, m, n, x, fvec, fjac, ldfjac, 0);
+ }
+ if (iflag < 0) {
+ goto TERMINATE;
+ }
+ }
+
+/* compute the qr factorization of the jacobian. */
+
+ __cminpack_func__(qrfac)(m, n, fjac, ldfjac, TRUE_, ipvt, n,
+ wa1, wa2, wa3);
+
+/* on the first iteration and if mode is 1, scale according */
+/* to the norms of the columns of the initial jacobian. */
+
+ if (iter == 1) {
+ if (mode != 2) {
+ for (j = 0; j < n; ++j) {
+ diag[j] = wa2[j];
+ if (wa2[j] == 0.) {
+ diag[j] = 1.;
+ }
+ }
+ }
+
+/* on the first iteration, calculate the norm of the scaled x */
+/* and initialize the step bound delta. */
+
+ for (j = 0; j < n; ++j) {
+ wa3[j] = diag[j] * x[j];
+ }
+ xnorm = __cminpack_enorm__(n, wa3);
+ delta = factor * xnorm;
+ if (delta == 0.) {
+ delta = factor;
+ }
+ }
+
+/* form (q transpose)*fvec and store the first n components in */
+/* qtf. */
+
+ for (i = 0; i < m; ++i) {
+ wa4[i] = fvec[i];
+ }
+ for (j = 0; j < n; ++j) {
+ if (fjac[j + j * ldfjac] != 0.) {
+ sum = 0.;
+ for (i = j; i < m; ++i) {
+ sum += fjac[i + j * ldfjac] * wa4[i];
+ }
+ temp = -sum / fjac[j + j * ldfjac];
+ for (i = j; i < m; ++i) {
+ wa4[i] += fjac[i + j * ldfjac] * temp;
+ }
+ }
+ fjac[j + j * ldfjac] = wa1[j];
+ qtf[j] = wa4[j];
+ }
+
+/* compute the norm of the scaled gradient. */
+
+ gnorm = 0.;
+ if (fnorm != 0.) {
+ for (j = 0; j < n; ++j) {
+ l = ipvt[j]-1;
+ if (wa2[l] != 0.) {
+ sum = 0.;
+ for (i = 0; i <= j; ++i) {
+ sum += fjac[i + j * ldfjac] * (qtf[i] / fnorm);
+ }
+ /* Computing MAX */
+ d1 = fabs(sum / wa2[l]);
+ gnorm = max(gnorm,d1);
+ }
+ }
+ }
+
+/* test for convergence of the gradient norm. */
+
+ if (gnorm <= gtol) {
+ info = 4;
+ }
+ if (info != 0) {
+ goto TERMINATE;
+ }
+
+/* rescale if necessary. */
+
+ if (mode != 2) {
+ for (j = 0; j < n; ++j) {
+ /* Computing MAX */
+ d1 = diag[j], d2 = wa2[j];
+ diag[j] = max(d1,d2);
+ }
+ }
+
+/* beginning of the inner loop. */
+
+ do {
+
+/* determine the levenberg-marquardt parameter. */
+
+ __cminpack_func__(lmpar)(n, fjac, ldfjac, ipvt, diag, qtf, delta,
+ &par, wa1, wa2, wa3, wa4);
+
+/* store the direction p and x + p. calculate the norm of p. */
+
+ for (j = 0; j < n; ++j) {
+ wa1[j] = -wa1[j];
+ wa2[j] = x[j] + wa1[j];
+ wa3[j] = diag[j] * wa1[j];
+ }
+ pnorm = __cminpack_enorm__(n, wa3);
+
+/* on the first iteration, adjust the initial step bound. */
+
+ if (iter == 1) {
+ delta = min(delta,pnorm);
+ }
+
+/* evaluate the function at x + p and calculate its norm. */
+
+ iflag = fcnder_mn(p, m, n, wa2, wa4, fjac, ldfjac, 1);
+ ++(*nfev);
+ if (iflag < 0) {
+ goto TERMINATE;
+ }
+ fnorm1 = __cminpack_enorm__(m, wa4);
+
+/* compute the scaled actual reduction. */
+
+ actred = -1.;
+ if (p1 * fnorm1 < fnorm) {
+ /* Computing 2nd power */
+ d1 = fnorm1 / fnorm;
+ actred = 1. - d1 * d1;
+ }
+
+/* compute the scaled predicted reduction and */
+/* the scaled directional derivative. */
+
+ for (j = 0; j < n; ++j) {
+ wa3[j] = 0.;
+ l = ipvt[j]-1;
+ temp = wa1[l];
+ for (i = 0; i <= j; ++i) {
+ wa3[i] += fjac[i + j * ldfjac] * temp;
+ }
+ }
+ temp1 = __cminpack_enorm__(n, wa3) / fnorm;
+ temp2 = (sqrt(par) * pnorm) / fnorm;
+ prered = temp1 * temp1 + temp2 * temp2 / p5;
+ dirder = -(temp1 * temp1 + temp2 * temp2);
+
+/* compute the ratio of the actual to the predicted */
+/* reduction. */
+
+ ratio = 0.;
+ if (prered != 0.) {
+ ratio = actred / prered;
+ }
+
+/* update the step bound. */
+
+ if (ratio <= p25) {
+ if (actred >= 0.) {
+ temp = p5;
+ } else {
+ temp = p5 * dirder / (dirder + p5 * actred);
+ }
+ if (p1 * fnorm1 >= fnorm || temp < p1) {
+ temp = p1;
+ }
+ /* Computing MIN */
+ d1 = pnorm / p1;
+ delta = temp * min(delta,d1);
+ par /= temp;
+ } else {
+ if (par == 0. || ratio >= p75) {
+ delta = pnorm / p5;
+ par = p5 * par;
+ }
+ }
+
+/* test for successful iteration. */
+
+ if (ratio >= p0001) {
+
+/* successful iteration. update x, fvec, and their norms. */
+
+ for (j = 0; j < n; ++j) {
+ x[j] = wa2[j];
+ wa2[j] = diag[j] * x[j];
+ }
+ for (i = 0; i < m; ++i) {
+ fvec[i] = wa4[i];
+ }
+ xnorm = __cminpack_enorm__(n, wa2);
+ fnorm = fnorm1;
+ ++iter;
+ }
+
+/* tests for convergence. */
+
+ if (fabs(actred) <= ftol && prered <= ftol && p5 * ratio <= 1.) {
+ info = 1;
+ }
+ if (delta <= xtol * xnorm) {
+ info = 2;
+ }
+ if (fabs(actred) <= ftol && prered <= ftol && p5 * ratio <= 1. && info == 2) {
+ info = 3;
+ }
+ if (info != 0) {
+ goto TERMINATE;
+ }
+
+/* tests for termination and stringent tolerances. */
+
+ if (*nfev >= maxfev) {
+ info = 5;
+ }
+ if (fabs(actred) <= epsmch && prered <= epsmch && p5 * ratio <= 1.) {
+ info = 6;
+ }
+ if (delta <= epsmch * xnorm) {
+ info = 7;
+ }
+ if (gnorm <= epsmch) {
+ info = 8;
+ }
+ if (info != 0) {
+ goto TERMINATE;
+ }
+
+/* end of the inner loop. repeat if iteration unsuccessful. */
+
+ } while (ratio < p0001);
+
+/* end of the outer loop. */
+
+ }
+TERMINATE:
+
+/* termination, either normal or user imposed. */
+
+ if (iflag < 0) {
+ info = iflag;
+ }
+ if (nprint > 0) {
+ fcnder_mn(p, m, n, x, fvec, fjac, ldfjac, 0);
+ }
+ return info;
+
+/* last card of subroutine lmder. */
+
+} /* lmder_ */
+
diff --git a/ast/cminpack/lmder1.c b/ast/cminpack/lmder1.c
new file mode 100644
index 0000000..581462e
--- /dev/null
+++ b/ast/cminpack/lmder1.c
@@ -0,0 +1,167 @@
+#include "cminpack.h"
+#include "cminpackP.h"
+
+__cminpack_attr__
+int __cminpack_func__(lmder1)(__cminpack_decl_fcnder_mn__ void *p, int m, int n, real *x,
+ real *fvec, real *fjac, int ldfjac, real tol,
+ int *ipvt, real *wa, int lwa)
+{
+ /* Initialized data */
+
+ const real factor = 100.;
+
+ /* Local variables */
+ int mode, nfev, njev;
+ real ftol, gtol, xtol;
+ int maxfev, nprint;
+ int info;
+
+/* ********** */
+
+/* subroutine lmder1 */
+
+/* the purpose of lmder1 is to minimize the sum of the squares of */
+/* m nonlinear functions in n variables by a modification of the */
+/* levenberg-marquardt algorithm. this is done by using the more */
+/* general least-squares solver lmder. the user must provide a */
+/* subroutine which calculates the functions and the jacobian. */
+
+/* the subroutine statement is */
+
+/* subroutine lmder1(fcn,m,n,x,fvec,fjac,ldfjac,tol,info, */
+/* ipvt,wa,lwa) */
+
+/* where */
+
+/* fcn is the name of the user-supplied subroutine which */
+/* calculates the functions and the jacobian. fcn must */
+/* be declared in an external statement in the user */
+/* calling program, and should be written as follows. */
+
+/* subroutine fcn(m,n,x,fvec,fjac,ldfjac,iflag) */
+/* integer m,n,ldfjac,iflag */
+/* double precision x(n),fvec(m),fjac(ldfjac,n) */
+/* ---------- */
+/* if iflag = 1 calculate the functions at x and */
+/* return this vector in fvec. do not alter fjac. */
+/* if iflag = 2 calculate the jacobian at x and */
+/* return this matrix in fjac. do not alter fvec. */
+/* ---------- */
+/* return */
+/* end */
+
+/* the value of iflag should not be changed by fcn unless */
+/* the user wants to terminate execution of lmder1. */
+/* in this case set iflag to a negative integer. */
+
+/* m is a positive integer input variable set to the number */
+/* of functions. */
+
+/* n is a positive integer input variable set to the number */
+/* of variables. n must not exceed m. */
+
+/* x is an array of length n. on input x must contain */
+/* an initial estimate of the solution vector. on output x */
+/* contains the final estimate of the solution vector. */
+
+/* fvec is an output array of length m which contains */
+/* the functions evaluated at the output x. */
+
+/* fjac is an output m by n array. the upper n by n submatrix */
+/* of fjac contains an upper triangular matrix r with */
+/* diagonal elements of nonincreasing magnitude such that */
+
+/* t t t */
+/* p *(jac *jac)*p = r *r, */
+
+/* where p is a permutation matrix and jac is the final */
+/* calculated jacobian. column j of p is column ipvt(j) */
+/* (see below) of the identity matrix. the lower trapezoidal */
+/* part of fjac contains information generated during */
+/* the computation of r. */
+
+/* ldfjac is a positive integer input variable not less than m */
+/* which specifies the leading dimension of the array fjac. */
+
+/* tol is a nonnegative input variable. termination occurs */
+/* when the algorithm estimates either that the relative */
+/* error in the sum of squares is at most tol or that */
+/* the relative error between x and the solution is at */
+/* most tol. */
+
+/* info is an integer output variable. if the user has */
+/* terminated execution, info is set to the (negative) */
+/* value of iflag. see description of fcn. otherwise, */
+/* info is set as follows. */
+
+/* info = 0 improper input parameters. */
+
+/* info = 1 algorithm estimates that the relative error */
+/* in the sum of squares is at most tol. */
+
+/* info = 2 algorithm estimates that the relative error */
+/* between x and the solution is at most tol. */
+
+/* info = 3 conditions for info = 1 and info = 2 both hold. */
+
+/* info = 4 fvec is orthogonal to the columns of the */
+/* jacobian to machine precision. */
+
+/* info = 5 number of calls to fcn with iflag = 1 has */
+/* reached 100*(n+1). */
+
+/* info = 6 tol is too small. no further reduction in */
+/* the sum of squares is possible. */
+
+/* info = 7 tol is too small. no further improvement in */
+/* the approximate solution x is possible. */
+
+/* ipvt is an integer output array of length n. ipvt */
+/* defines a permutation matrix p such that jac*p = q*r, */
+/* where jac is the final calculated jacobian, q is */
+/* orthogonal (not stored), and r is upper triangular */
+/* with diagonal elements of nonincreasing magnitude. */
+/* column j of p is column ipvt(j) of the identity matrix. */
+
+/* wa is a work array of length lwa. */
+
+/* lwa is a positive integer input variable not less than 5*n+m. */
+
+/* subprograms called */
+
+/* user-supplied ...... fcn */
+
+/* minpack-supplied ... lmder */
+
+/* argonne national laboratory. minpack project. march 1980. */
+/* burton s. garbow, kenneth e. hillstrom, jorge j. more */
+
+/* ********** */
+
+/* check the input parameters for errors. */
+
+ if (n <= 0 || m < n || ldfjac < m || tol < 0. || lwa < n * 5 + m) {
+ return 0;
+ }
+
+/* call lmder. */
+
+ maxfev = (n + 1) * 100;
+ ftol = tol;
+ xtol = tol;
+ gtol = 0.;
+ mode = 1;
+ nprint = 0;
+ info = __cminpack_func__(lmder)(__cminpack_param_fcnder_mn__ p, m, n, x, fvec, fjac, ldfjac,
+ ftol, xtol, gtol, maxfev, wa, mode, factor, nprint,
+ &nfev, &njev, ipvt, &wa[n], &wa[(n << 1)], &
+ wa[n * 3], &wa[(n << 2)], &wa[n * 5]);
+ if (info == 8) {
+ info = 4;
+ }
+ return info;
+
+/* last card of subroutine lmder1. */
+
+} /* lmder1_ */
+
diff --git a/ast/cminpack/lmpar.c b/ast/cminpack/lmpar.c
new file mode 100644
index 0000000..108e687
--- /dev/null
+++ b/ast/cminpack/lmpar.c
@@ -0,0 +1,338 @@
+/* lmpar.f -- translated by f2c (version 20020621).
+ You must link the resulting object file with the libraries:
+ -lf2c -lm (in that order)
+*/
+
+#include "cminpack.h"
+#include <math.h>
+#include "cminpackP.h"
+
+__cminpack_attr__
+void __cminpack_func__(lmpar)(int n, real *r, int ldr,
+ const int *ipvt, const real *diag, const real *qtb, real delta,
+ real *par, real *x, real *sdiag, real *wa1,
+ real *wa2)
+{
+ /* Initialized data */
+
+#define p1 .1
+#define p001 .001
+
+ /* System generated locals */
+ real d1, d2;
+
+ /* Local variables */
+ int j, l;
+ real fp;
+ real parc, parl;
+ int iter;
+ real temp, paru, dwarf;
+ int nsing;
+ real gnorm;
+ real dxnorm;
+
+/* ********** */
+
+/* subroutine lmpar */
+
+/* given an m by n matrix a, an n by n nonsingular diagonal */
+/* matrix d, an m-vector b, and a positive number delta, */
+/* the problem is to determine a value for the parameter */
+/* par such that if x solves the system */
+
+/* a*x = b , sqrt(par)*d*x = 0 , */
+
+/* in the least squares sense, and dxnorm is the euclidean */
+/* norm of d*x, then either par is zero and */
+
+/* (dxnorm-delta) .le. 0.1*delta , */
+
+/* or par is positive and */
+
+/* abs(dxnorm-delta) .le. 0.1*delta . */
+
+/* this subroutine completes the solution of the problem */
+/* if it is provided with the necessary information from the */
+/* qr factorization, with column pivoting, of a. that is, if */
+/* a*p = q*r, where p is a permutation matrix, q has orthogonal */
+/* columns, and r is an upper triangular matrix with diagonal */
+/* elements of nonincreasing magnitude, then lmpar expects */
+/* the full upper triangle of r, the permutation matrix p, */
+/* and the first n components of (q transpose)*b. on output */
+/* lmpar also provides an upper triangular matrix s such that */
+
+/* t t t */
+/* p *(a *a + par*d*d)*p = s *s . */
+
+/* s is employed within lmpar and may be of separate interest. */
+
+/* only a few iterations are generally needed for convergence */
+/* of the algorithm. if, however, the limit of 10 iterations */
+/* is reached, then the output par will contain the best */
+/* value obtained so far. */
+
+/* the subroutine statement is */
+
+/* subroutine lmpar(n,r,ldr,ipvt,diag,qtb,delta,par,x,sdiag, */
+/* wa1,wa2) */
+
+/* where */
+
+/* n is a positive integer input variable set to the order of r. */
+
+/* r is an n by n array. on input the full upper triangle */
+/* must contain the full upper triangle of the matrix r. */
+/* on output the full upper triangle is unaltered, and the */
+/* strict lower triangle contains the strict upper triangle */
+/* (transposed) of the upper triangular matrix s. */
+
+/* ldr is a positive integer input variable not less than n */
+/* which specifies the leading dimension of the array r. */
+
+/* ipvt is an integer input array of length n which defines the */
+/* permutation matrix p such that a*p = q*r. column j of p */
+/* is column ipvt(j) of the identity matrix. */
+
+/* diag is an input array of length n which must contain the */
+/* diagonal elements of the matrix d. */
+
+/* qtb is an input array of length n which must contain the first */
+/* n elements of the vector (q transpose)*b. */
+
+/* delta is a positive input variable which specifies an upper */
+/* bound on the euclidean norm of d*x. */
+
+/* par is a nonnegative variable. on input par contains an */
+/* initial estimate of the levenberg-marquardt parameter. */
+/* on output par contains the final estimate. */
+
+/* x is an output array of length n which contains the least */
+/* squares solution of the system a*x = b, sqrt(par)*d*x = 0, */
+/* for the output par. */
+
+/* sdiag is an output array of length n which contains the */
+/* diagonal elements of the upper triangular matrix s. */
+
+/* wa1 and wa2 are work arrays of length n. */
+
+/* subprograms called */
+
+/* minpack-supplied ... dpmpar,enorm,qrsolv */
+
+/* fortran-supplied ... dabs,dmax1,dmin1,dsqrt */
+
+/* argonne national laboratory. minpack project. march 1980. */
+/* burton s. garbow, kenneth e. hillstrom, jorge j. more */
+
+/* ********** */
+
+/* dwarf is the smallest positive magnitude. */
+
+ dwarf = __cminpack_func__(dpmpar)(2);
+
+/* compute and store in x the gauss-newton direction. if the */
+/* jacobian is rank-deficient, obtain a least squares solution. */
+
+ nsing = n;
+ for (j = 0; j < n; ++j) {
+ wa1[j] = qtb[j];
+ if (r[j + j * ldr] == 0. && nsing == n) {
+ nsing = j;
+ }
+ if (nsing < n) {
+ wa1[j] = 0.;
+ }
+ }
+# ifdef USE_CBLAS
+ cblas_dtrsv(CblasColMajor, CblasUpper, CblasNoTrans, CblasNonUnit, nsing, r, ldr, wa1, 1);
+# else
+ if (nsing >= 1) {
+ int k;
+ for (k = 1; k <= nsing; ++k) {
+ j = nsing - k;
+ wa1[j] /= r[j + j * ldr];
+ temp = wa1[j];
+ if (j >= 1) {
+ int i;
+ for (i = 0; i < j; ++i) {
+ wa1[i] -= r[i + j * ldr] * temp;
+ }
+ }
+ }
+ }
+# endif
+ for (j = 0; j < n; ++j) {
+ l = ipvt[j]-1;
+ x[l] = wa1[j];
+ }
+
+/* initialize the iteration counter. */
+/* evaluate the function at the origin, and test */
+/* for acceptance of the gauss-newton direction. */
+
+ iter = 0;
+ for (j = 0; j < n; ++j) {
+ wa2[j] = diag[j] * x[j];
+ }
+ dxnorm = __cminpack_enorm__(n, wa2);
+ fp = dxnorm - delta;
+ if (fp <= p1 * delta) {
+ goto TERMINATE;
+ }
+
+/* if the jacobian is not rank deficient, the newton */
+/* step provides a lower bound, parl, for the zero of */
+/* the function. otherwise set this bound to zero. */
+
+ parl = 0.;
+ if (nsing >= n) {
+ for (j = 0; j < n; ++j) {
+ l = ipvt[j]-1;
+ wa1[j] = diag[l] * (wa2[l] / dxnorm);
+ }
+# ifdef USE_CBLAS
+ cblas_dtrsv(CblasColMajor, CblasUpper, CblasTrans, CblasNonUnit, n, r, ldr, wa1, 1);
+# else
+ for (j = 0; j < n; ++j) {
+ real sum = 0.;
+ if (j >= 1) {
+ int i;
+ for (i = 0; i < j; ++i) {
+ sum += r[i + j * ldr] * wa1[i];
+ }
+ }
+ wa1[j] = (wa1[j] - sum) / r[j + j * ldr];
+ }
+# endif
+ temp = __cminpack_enorm__(n, wa1);
+ parl = fp / delta / temp / temp;
+ }
+
+/* calculate an upper bound, paru, for the zero of the function. */
+
+ for (j = 0; j < n; ++j) {
+ real sum;
+# ifdef USE_CBLAS
+ sum = cblas_ddot(j+1, &r[j*ldr], 1, qtb, 1);
+# else
+ int i;
+ sum = 0.;
+ for (i = 0; i <= j; ++i) {
+ sum += r[i + j * ldr] * qtb[i];
+ }
+# endif
+ l = ipvt[j]-1;
+ wa1[j] = sum / diag[l];
+ }
+ gnorm = __cminpack_enorm__(n, wa1);
+ paru = gnorm / delta;
+ if (paru == 0.) {
+ paru = dwarf / min(delta,(real)p1) /* / p001 ??? */;
+ }
+
+/* if the input par lies outside of the interval (parl,paru), */
+/* set par to the closer endpoint. */
+
+ *par = max(*par,parl);
+ *par = min(*par,paru);
+ if (*par == 0.) {
+ *par = gnorm / dxnorm;
+ }
+
+/* beginning of an iteration. */
+
+ for (;;) {
+ ++iter;
+
+/* evaluate the function at the current value of par. */
+
+ if (*par == 0.) {
+ /* Computing MAX */
+ d1 = dwarf, d2 = p001 * paru;
+ *par = max(d1,d2);
+ }
+ temp = sqrt(*par);
+ for (j = 0; j < n; ++j) {
+ wa1[j] = temp * diag[j];
+ }
+ __cminpack_func__(qrsolv)(n, r, ldr, ipvt, wa1, qtb, x, sdiag, wa2);
+ for (j = 0; j < n; ++j) {
+ wa2[j] = diag[j] * x[j];
+ }
+ dxnorm = __cminpack_enorm__(n, wa2);
+ temp = fp;
+ fp = dxnorm - delta;
+
+/* if the function is small enough, accept the current value */
+/* of par. also test for the exceptional cases where parl */
+/* is zero or the number of iterations has reached 10. */
+
+ if (fabs(fp) <= p1 * delta || (parl == 0. && fp <= temp && temp < 0.) || iter == 10) {
+ goto TERMINATE;
+ }
+
+/* compute the newton correction. */
+
+# ifdef USE_CBLAS
+ for (j = 0; j < nsing; ++j) {
+ l = ipvt[j]-1;
+ wa1[j] = diag[l] * (wa2[l] / dxnorm);
+ }
+ for (j = nsing; j < n; ++j) {
+ wa1[j] = 0.;
+ }
+ /* exchange the diagonal of r with sdiag */
+ cblas_dswap(n, r, ldr+1, sdiag, 1);
+ /* solve lower(r).x = wa1, result id put in wa1 */
+ cblas_dtrsv(CblasColMajor, CblasLower, CblasNoTrans, CblasNonUnit, nsing, r, ldr, wa1, 1);
+ /* exchange the diagonal of r with sdiag */
+ cblas_dswap( n, r, ldr+1, sdiag, 1);
+# else /* !USE_CBLAS */
+ for (j = 0; j < n; ++j) {
+ l = ipvt[j]-1;
+ wa1[j] = diag[l] * (wa2[l] / dxnorm);
+ }
+ for (j = 0; j < n; ++j) {
+ wa1[j] /= sdiag[j];
+ temp = wa1[j];
+ if (n > j+1) {
+ int i;
+ for (i = j+1; i < n; ++i) {
+ wa1[i] -= r[i + j * ldr] * temp;
+ }
+ }
+ }
+# endif /* !USE_CBLAS */
+ temp = __cminpack_enorm__(n, wa1);
+ parc = fp / delta / temp / temp;
+
+/* depending on the sign of the function, update parl or paru. */
+
+ if (fp > 0.) {
+ parl = max(parl,*par);
+ }
+ if (fp < 0.) {
+ paru = min(paru,*par);
+ }
+
+/* compute an improved estimate for par. */
+
+ /* Computing MAX */
+ d1 = parl, d2 = *par + parc;
+ *par = max(d1,d2);
+
+/* end of an iteration. */
+
+ }
+TERMINATE:
+
+/* termination. */
+
+ if (iter == 0) {
+ *par = 0.;
+ }
+
+/* last card of subroutine lmpar. */
+
+} /* lmpar_ */
+
diff --git a/ast/cminpack/qrfac.c b/ast/cminpack/qrfac.c
new file mode 100644
index 0000000..1573772
--- /dev/null
+++ b/ast/cminpack/qrfac.c
@@ -0,0 +1,285 @@
+#include "cminpack.h"
+#include <math.h>
+#ifdef USE_LAPACK
+#include <stdlib.h>
+#include <string.h>
+#include <assert.h>
+#endif
+#include "cminpackP.h"
+
+__cminpack_attr__
+void __cminpack_func__(qrfac)(int m, int n, real *a, int
+ lda, int pivot, int *ipvt, int lipvt, real *rdiag,
+ real *acnorm, real *wa)
+{
+#ifdef USE_LAPACK
+ __CLPK_integer m_ = m;
+ __CLPK_integer n_ = n;
+ __CLPK_integer lda_ = lda;
+ __CLPK_integer *jpvt;
+
+ int i, j, k;
+ double t;
+ double* tau = wa;
+ const __CLPK_integer ltau = m > n ? n : m;
+ __CLPK_integer lwork = -1;
+ __CLPK_integer info = 0;
+ double* work;
+
+ if (pivot) {
+ assert( lipvt >= n );
+ if (sizeof(__CLPK_integer) != sizeof(ipvt[0])) {
+ jpvt = malloc(n*sizeof(__CLPK_integer));
+ } else {
+ /* __CLPK_integer is actually an int, just do a cast */
+ jpvt = (__CLPK_integer *)ipvt;
+ }
+ /* set all columns free */
+ memset(jpvt, 0, sizeof(int)*n);
+ }
+
+ /* query optimal size of work */
+ lwork = -1;
+ if (pivot) {
+ dgeqp3_(&m_,&n_,a,&lda_,jpvt,tau,tau,&lwork,&info);
+ lwork = (int)tau[0];
+ assert( lwork >= 3*n+1 );
+ } else {
+ dgeqrf_(&m_,&n_,a,&lda_,tau,tau,&lwork,&info);
+ lwork = (int)tau[0];
+ assert( lwork >= 1 && lwork >= n );
+ }
+
+ assert( info == 0 );
+
+ /* alloc work area */
+ work = (double *)malloc(sizeof(double)*lwork);
+ assert(work != NULL);
+
+ /* set acnorm first (from the doc of qrfac, acnorm may point to the same area as rdiag) */
+ if (acnorm != rdiag) {
+ for (j = 0; j < n; ++j) {
+ acnorm[j] = __cminpack_enorm__(m, &a[j * lda]);
+ }
+ }
+
+ /* QR decomposition */
+ if (pivot) {
+ dgeqp3_(&m_,&n_,a,&lda_,jpvt,tau,work,&lwork,&info);
+ } else {
+ dgeqrf_(&m_,&n_,a,&lda_,tau,work,&lwork,&info);
+ }
+ assert(info == 0);
+
+ /* set rdiag, before the diagonal is replaced */
+ memset(rdiag, 0, sizeof(double)*n);
+ for(i=0 ; i<n ; ++i) {
+ rdiag[i] = a[i*lda+i];
+ }
+
+ /* modify lower trinagular part to look like qrfac's output */
+ for(i=0 ; i<ltau ; ++i) {
+ k = i*lda+i;
+ t = tau[i];
+ a[k] = t;
+ for(j=i+1 ; j<m ; j++) {
+ k++;
+ a[k] *= t;
+ }
+ }
+
+ free(work);
+ if (pivot) {
+ /* convert back jpvt to ipvt */
+ if (sizeof(__CLPK_integer) != sizeof(ipvt[0])) {
+ for(i=0; i<n; ++i) {
+ ipvt[i] = jpvt[i];
+ }
+ free(jpvt);
+ }
+ }
+#else /* !USE_LAPACK */
+ /* Initialized data */
+
+#define p05 .05
+
+ /* System generated locals */
+ real d1;
+
+ /* Local variables */
+ int i, j, k, jp1;
+ real sum;
+ real temp;
+ int minmn;
+ real epsmch;
+ real ajnorm;
+
+/* ********** */
+
+/* subroutine qrfac */
+
+/* this subroutine uses householder transformations with column */
+/* pivoting (optional) to compute a qr factorization of the */
+/* m by n matrix a. that is, qrfac determines an orthogonal */
+/* matrix q, a permutation matrix p, and an upper trapezoidal */
+/* matrix r with diagonal elements of nonincreasing magnitude, */
+/* such that a*p = q*r. the householder transformation for */
+/* column k, k = 1,2,...,min(m,n), is of the form */
+
+/* t */
+/* i - (1/u(k))*u*u */
+
+/* where u has zeros in the first k-1 positions. the form of */
+/* this transformation and the method of pivoting first */
+/* appeared in the corresponding linpack subroutine. */
+
+/* the subroutine statement is */
+
+/* subroutine qrfac(m,n,a,lda,pivot,ipvt,lipvt,rdiag,acnorm,wa) */
+
+/* where */
+
+/* m is a positive integer input variable set to the number */
+/* of rows of a. */
+
+/* n is a positive integer input variable set to the number */
+/* of columns of a. */
+
+/* a is an m by n array. on input a contains the matrix for */
+/* which the qr factorization is to be computed. on output */
+/* the strict upper trapezoidal part of a contains the strict */
+/* upper trapezoidal part of r, and the lower trapezoidal */
+/* part of a contains a factored form of q (the non-trivial */
+/* elements of the u vectors described above). */
+
+/* lda is a positive integer input variable not less than m */
+/* which specifies the leading dimension of the array a. */
+
+/* pivot is a logical input variable. if pivot is set true, */
+/* then column pivoting is enforced. if pivot is set false, */
+/* then no column pivoting is done. */
+
+/* ipvt is an integer output array of length lipvt. ipvt */
+/* defines the permutation matrix p such that a*p = q*r. */
+/* column j of p is column ipvt(j) of the identity matrix. */
+/* if pivot is false, ipvt is not referenced. */
+
+/* lipvt is a positive integer input variable. if pivot is false, */
+/* then lipvt may be as small as 1. if pivot is true, then */
+/* lipvt must be at least n. */
+
+/* rdiag is an output array of length n which contains the */
+/* diagonal elements of r. */
+
+/* acnorm is an output array of length n which contains the */
+/* norms of the corresponding columns of the input matrix a. */
+/* if this information is not needed, then acnorm can coincide */
+/* with rdiag. */
+
+/* wa is a work array of length n. if pivot is false, then wa */
+/* can coincide with rdiag. */
+
+/* subprograms called */
+
+/* minpack-supplied ... dpmpar,enorm */
+
+/* fortran-supplied ... dmax1,dsqrt,min0 */
+
+/* argonne national laboratory. minpack project. march 1980. */
+/* burton s. garbow, kenneth e. hillstrom, jorge j. more */
+
+/* ********** */
+ (void)lipvt;
+
+/* epsmch is the machine precision. */
+
+ epsmch = __cminpack_func__(dpmpar)(1);
+
+/* compute the initial column norms and initialize several arrays. */
+
+ for (j = 0; j < n; ++j) {
+ acnorm[j] = __cminpack_enorm__(m, &a[j * lda + 0]);
+ rdiag[j] = acnorm[j];
+ wa[j] = rdiag[j];
+ if (pivot) {
+ ipvt[j] = j+1;
+ }
+ }
+
+/* reduce a to r with householder transformations. */
+
+ minmn = min(m,n);
+ for (j = 0; j < minmn; ++j) {
+ if (pivot) {
+
+/* bring the column of largest norm into the pivot position. */
+
+ int kmax = j;
+ for (k = j; k < n; ++k) {
+ if (rdiag[k] > rdiag[kmax]) {
+ kmax = k;
+ }
+ }
+ if (kmax != j) {
+ for (i = 0; i < m; ++i) {
+ temp = a[i + j * lda];
+ a[i + j * lda] = a[i + kmax * lda];
+ a[i + kmax * lda] = temp;
+ }
+ rdiag[kmax] = rdiag[j];
+ wa[kmax] = wa[j];
+ k = ipvt[j];
+ ipvt[j] = ipvt[kmax];
+ ipvt[kmax] = k;
+ }
+ }
+
+/* compute the householder transformation to reduce the */
+/* j-th column of a to a multiple of the j-th unit vector. */
+
+ ajnorm = __cminpack_enorm__(m - (j+1) + 1, &a[j + j * lda]);
+ if (ajnorm != 0.) {
+ if (a[j + j * lda] < 0.) {
+ ajnorm = -ajnorm;
+ }
+ for (i = j; i < m; ++i) {
+ a[i + j * lda] /= ajnorm;
+ }
+ a[j + j * lda] += 1.;
+
+/* apply the transformation to the remaining columns */
+/* and update the norms. */
+
+ jp1 = j + 1;
+ if (n > jp1) {
+ for (k = jp1; k < n; ++k) {
+ sum = 0.;
+ for (i = j; i < m; ++i) {
+ sum += a[i + j * lda] * a[i + k * lda];
+ }
+ temp = sum / a[j + j * lda];
+ for (i = j; i < m; ++i) {
+ a[i + k * lda] -= temp * a[i + j * lda];
+ }
+ if (pivot && rdiag[k] != 0.) {
+ temp = a[j + k * lda] / rdiag[k];
+ /* Computing MAX */
+ d1 = 1. - temp * temp;
+ rdiag[k] *= sqrt((max((real)0.,d1)));
+ /* Computing 2nd power */
+ d1 = rdiag[k] / wa[k];
+ if (p05 * (d1 * d1) <= epsmch) {
+ rdiag[k] = __cminpack_enorm__(m - (j+1), &a[jp1 + k * lda]);
+ wa[k] = rdiag[k];
+ }
+ }
+ }
+ }
+ }
+ rdiag[j] = -ajnorm;
+ }
+
+/* last card of subroutine qrfac. */
+#endif /* !USE_LAPACK */
+} /* qrfac_ */
+
diff --git a/ast/cminpack/qrsolv.c b/ast/cminpack/qrsolv.c
new file mode 100644
index 0000000..6ab9e98
--- /dev/null
+++ b/ast/cminpack/qrsolv.c
@@ -0,0 +1,218 @@
+#include "cminpack.h"
+#include <math.h>
+#include "cminpackP.h"
+
+__cminpack_attr__
+void __cminpack_func__(qrsolv)(int n, real *r, int ldr,
+ const int *ipvt, const real *diag, const real *qtb, real *x,
+ real *sdiag, real *wa)
+{
+ /* Initialized data */
+
+#define p5 .5
+#define p25 .25
+
+ /* Local variables */
+ int i, j, k, l;
+ real cos, sin, sum, temp;
+ int nsing;
+ real qtbpj;
+
+/* ********** */
+
+/* subroutine qrsolv */
+
+/* given an m by n matrix a, an n by n diagonal matrix d, */
+/* and an m-vector b, the problem is to determine an x which */
+/* solves the system */
+
+/* a*x = b , d*x = 0 , */
+
+/* in the least squares sense. */
+
+/* this subroutine completes the solution of the problem */
+/* if it is provided with the necessary information from the */
+/* qr factorization, with column pivoting, of a. that is, if */
+/* a*p = q*r, where p is a permutation matrix, q has orthogonal */
+/* columns, and r is an upper triangular matrix with diagonal */
+/* elements of nonincreasing magnitude, then qrsolv expects */
+/* the full upper triangle of r, the permutation matrix p, */
+/* and the first n components of (q transpose)*b. the system */
+/* a*x = b, d*x = 0, is then equivalent to */
+
+/* t t */
+/* r*z = q *b , p *d*p*z = 0 , */
+
+/* where x = p*z. if this system does not have full rank, */
+/* then a least squares solution is obtained. on output qrsolv */
+/* also provides an upper triangular matrix s such that */
+
+/* t t t */
+/* p *(a *a + d*d)*p = s *s . */
+
+/* s is computed within qrsolv and may be of separate interest. */
+
+/* the subroutine statement is */
+
+/* subroutine qrsolv(n,r,ldr,ipvt,diag,qtb,x,sdiag,wa) */
+
+/* where */
+
+/* n is a positive integer input variable set to the order of r. */
+
+/* r is an n by n array. on input the full upper triangle */
+/* must contain the full upper triangle of the matrix r. */
+/* on output the full upper triangle is unaltered, and the */
+/* strict lower triangle contains the strict upper triangle */
+/* (transposed) of the upper triangular matrix s. */
+
+/* ldr is a positive integer input variable not less than n */
+/* which specifies the leading dimension of the array r. */
+
+/* ipvt is an integer input array of length n which defines the */
+/* permutation matrix p such that a*p = q*r. column j of p */
+/* is column ipvt(j) of the identity matrix. */
+
+/* diag is an input array of length n which must contain the */
+/* diagonal elements of the matrix d. */
+
+/* qtb is an input array of length n which must contain the first */
+/* n elements of the vector (q transpose)*b. */
+
+/* x is an output array of length n which contains the least */
+/* squares solution of the system a*x = b, d*x = 0. */
+
+/* sdiag is an output array of length n which contains the */
+/* diagonal elements of the upper triangular matrix s. */
+
+/* wa is a work array of length n. */
+
+/* subprograms called */
+
+/* fortran-supplied ... dabs,dsqrt */
+
+/* argonne national laboratory. minpack project. march 1980. */
+/* burton s. garbow, kenneth e. hillstrom, jorge j. more */
+
+/* ********** */
+
+/* copy r and (q transpose)*b to preserve input and initialize s. */
+/* in particular, save the diagonal elements of r in x. */
+
+ for (j = 0; j < n; ++j) {
+ for (i = j; i < n; ++i) {
+ r[i + j * ldr] = r[j + i * ldr];
+ }
+ x[j] = r[j + j * ldr];
+ wa[j] = qtb[j];
+ }
+
+/* eliminate the diagonal matrix d using a givens rotation. */
+
+ for (j = 0; j < n; ++j) {
+
+/* prepare the row of d to be eliminated, locating the */
+/* diagonal element using p from the qr factorization. */
+
+ l = ipvt[j]-1;
+ if (diag[l] != 0.) {
+ for (k = j; k < n; ++k) {
+ sdiag[k] = 0.;
+ }
+ sdiag[j] = diag[l];
+
+/* the transformations to eliminate the row of d */
+/* modify only a single element of (q transpose)*b */
+/* beyond the first n, which is initially zero. */
+
+ qtbpj = 0.;
+ for (k = j; k < n; ++k) {
+
+/* determine a givens rotation which eliminates the */
+/* appropriate element in the current row of d. */
+
+ if (sdiag[k] != 0.) {
+# ifdef USE_LAPACK
+ dlartg_( &r[k + k * ldr], &sdiag[k], &cos, &sin, &temp );
+# else /* !USE_LAPACK */
+ if (fabs(r[k + k * ldr]) < fabs(sdiag[k])) {
+ real cotan;
+ cotan = r[k + k * ldr] / sdiag[k];
+ sin = p5 / sqrt(p25 + p25 * (cotan * cotan));
+ cos = sin * cotan;
+ } else {
+ real tan;
+ tan = sdiag[k] / r[k + k * ldr];
+ cos = p5 / sqrt(p25 + p25 * (tan * tan));
+ sin = cos * tan;
+ }
+
+/* compute the modified diagonal element of r and */
+/* the modified element of ((q transpose)*b,0). */
+
+# endif /* !USE_LAPACK */
+ temp = cos * wa[k] + sin * qtbpj;
+ qtbpj = -sin * wa[k] + cos * qtbpj;
+ wa[k] = temp;
+
+/* accumulate the tranformation in the row of s. */
+# ifdef USE_CBLAS
+ cblas_drot( n-k, &r[k + k * ldr], 1, &sdiag[k], 1, cos, sin );
+# else /* !USE_CBLAS */
+ r[k + k * ldr] = cos * r[k + k * ldr] + sin * sdiag[k];
+ if (n > k+1) {
+ for (i = k+1; i < n; ++i) {
+ temp = cos * r[i + k * ldr] + sin * sdiag[i];
+ sdiag[i] = -sin * r[i + k * ldr] + cos * sdiag[i];
+ r[i + k * ldr] = temp;
+ }
+ }
+# endif /* !USE_CBLAS */
+ }
+ }
+ }
+
+/* store the diagonal element of s and restore */
+/* the corresponding diagonal element of r. */
+
+ sdiag[j] = r[j + j * ldr];
+ r[j + j * ldr] = x[j];
+ }
+
+/* solve the triangular system for z. if the system is */
+/* singular, then obtain a least squares solution. */
+
+ nsing = n;
+ for (j = 0; j < n; ++j) {
+ if (sdiag[j] == 0. && nsing == n) {
+ nsing = j;
+ }
+ if (nsing < n) {
+ wa[j] = 0.;
+ }
+ }
+ if (nsing >= 1) {
+ for (k = 1; k <= nsing; ++k) {
+ j = nsing - k;
+ sum = 0.;
+ if (nsing > j+1) {
+ for (i = j+1; i < nsing; ++i) {
+ sum += r[i + j * ldr] * wa[i];
+ }
+ }
+ wa[j] = (wa[j] - sum) / sdiag[j];
+ }
+ }
+
+/* permute the components of z back to components of x. */
+
+ for (j = 0; j < n; ++j) {
+ l = ipvt[j]-1;
+ x[l] = wa[j];
+ }
+ return;
+
+/* last card of subroutine qrsolv. */
+
+} /* qrsolv_ */
+
generated by cgit v0.12 at 2024-11-18 01:41:00 (GMT)