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authorWilliam Joye <wjoye@cfa.harvard.edu>2017-12-08 19:30:07 (GMT)
committerWilliam Joye <wjoye@cfa.harvard.edu>2017-12-08 19:30:07 (GMT)
commit9c81a48e2a38ab4487b8849d2b2db6ebbaeca9a7 (patch)
tree3de4f1c5f35381ecc749da5e05bfc3837d7cedaf /ast/cminpack
parent4432c8d7e1ccb371db03e13cdb5378fceaa5ad04 (diff)
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-rw-r--r--ast/cminpack/.deps/libast_la-dpmpar.Plo1
-rw-r--r--ast/cminpack/.deps/libast_la-enorm.Plo1
-rw-r--r--ast/cminpack/.deps/libast_la-lmder.Plo1
-rw-r--r--ast/cminpack/.deps/libast_la-lmder1.Plo1
-rw-r--r--ast/cminpack/.deps/libast_la-lmpar.Plo1
-rw-r--r--ast/cminpack/.deps/libast_la-qrfac.Plo1
-rw-r--r--ast/cminpack/.deps/libast_la-qrsolv.Plo1
-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
18 files changed, 0 insertions, 2511 deletions
diff --git a/ast/cminpack/.deps/libast_la-dpmpar.Plo b/ast/cminpack/.deps/libast_la-dpmpar.Plo
deleted file mode 100644
index 9ce06a8..0000000
--- a/ast/cminpack/.deps/libast_la-dpmpar.Plo
+++ /dev/null
@@ -1 +0,0 @@
-# dummy
diff --git a/ast/cminpack/.deps/libast_la-enorm.Plo b/ast/cminpack/.deps/libast_la-enorm.Plo
deleted file mode 100644
index 9ce06a8..0000000
--- a/ast/cminpack/.deps/libast_la-enorm.Plo
+++ /dev/null
@@ -1 +0,0 @@
-# dummy
diff --git a/ast/cminpack/.deps/libast_la-lmder.Plo b/ast/cminpack/.deps/libast_la-lmder.Plo
deleted file mode 100644
index 9ce06a8..0000000
--- a/ast/cminpack/.deps/libast_la-lmder.Plo
+++ /dev/null
@@ -1 +0,0 @@
-# dummy
diff --git a/ast/cminpack/.deps/libast_la-lmder1.Plo b/ast/cminpack/.deps/libast_la-lmder1.Plo
deleted file mode 100644
index 9ce06a8..0000000
--- a/ast/cminpack/.deps/libast_la-lmder1.Plo
+++ /dev/null
@@ -1 +0,0 @@
-# dummy
diff --git a/ast/cminpack/.deps/libast_la-lmpar.Plo b/ast/cminpack/.deps/libast_la-lmpar.Plo
deleted file mode 100644
index 9ce06a8..0000000
--- a/ast/cminpack/.deps/libast_la-lmpar.Plo
+++ /dev/null
@@ -1 +0,0 @@
-# dummy
diff --git a/ast/cminpack/.deps/libast_la-qrfac.Plo b/ast/cminpack/.deps/libast_la-qrfac.Plo
deleted file mode 100644
index 9ce06a8..0000000
--- a/ast/cminpack/.deps/libast_la-qrfac.Plo
+++ /dev/null
@@ -1 +0,0 @@
-# dummy
diff --git a/ast/cminpack/.deps/libast_la-qrsolv.Plo b/ast/cminpack/.deps/libast_la-qrsolv.Plo
deleted file mode 100644
index 9ce06a8..0000000
--- a/ast/cminpack/.deps/libast_la-qrsolv.Plo
+++ /dev/null
@@ -1 +0,0 @@
-# dummy
diff --git a/ast/cminpack/CopyrightMINPACK.txt b/ast/cminpack/CopyrightMINPACK.txt
deleted file mode 100644
index ae7984d..0000000
--- a/ast/cminpack/CopyrightMINPACK.txt
+++ /dev/null
@@ -1,52 +0,0 @@
-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
deleted file mode 100644
index 66bbc6f..0000000
--- a/ast/cminpack/README.md
+++ /dev/null
@@ -1,128 +0,0 @@
-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
deleted file mode 100644
index 6d3f757..0000000
--- a/ast/cminpack/cminpack.h
+++ /dev/null
@@ -1,370 +0,0 @@
-/* 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
deleted file mode 100644
index 4e8ba7b..0000000
--- a/ast/cminpack/cminpackP.h
+++ /dev/null
@@ -1,62 +0,0 @@
-/* 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
deleted file mode 100644
index 81c6fcd..0000000
--- a/ast/cminpack/dpmpar.c
+++ /dev/null
@@ -1,201 +0,0 @@
-#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
deleted file mode 100644
index ad10824..0000000
--- a/ast/cminpack/enorm.c
+++ /dev/null
@@ -1,157 +0,0 @@
-#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
deleted file mode 100644
index 7f57428..0000000
--- a/ast/cminpack/lmder.c
+++ /dev/null
@@ -1,526 +0,0 @@
-#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
deleted file mode 100644
index 581462e..0000000
--- a/ast/cminpack/lmder1.c
+++ /dev/null
@@ -1,167 +0,0 @@
-#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
deleted file mode 100644
index 108e687..0000000
--- a/ast/cminpack/lmpar.c
+++ /dev/null
@@ -1,338 +0,0 @@
-/* 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
deleted file mode 100644
index 1573772..0000000
--- a/ast/cminpack/qrfac.c
+++ /dev/null
@@ -1,285 +0,0 @@
-#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
deleted file mode 100644
index 6ab9e98..0000000
--- a/ast/cminpack/qrsolv.c
+++ /dev/null
@@ -1,218 +0,0 @@
-#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 2025-04-03 22:25:43 (GMT)