$Id: whats_new_05.omh 3686 2015-05-11 16:14:25Z bradbell $ /* -------------------------------------------------------------------------- CppAD: C++ Algorithmic Differentiation: Copyright (C) 2003-15 Bradley M. Bell CppAD is distributed under multiple licenses. This distribution is under the terms of the Eclipse Public License Version 1.0. A copy of this license is included in the COPYING file of this distribution. Please visit http://www.coin-or.org/CppAD/ for information on other licenses. -------------------------------------------------------------------------- */ $begin whats_new_05$$ $spell html Dir cppad.hpp acos asin autoconf ptr Erf CppADlib logdet valarray Jacobian bool yy mm dd pkzip gz Neg maxabs Romberg cos Le Lt Eq Ge Gt op gcc Cygwin std Lu CppADvector Jon Pearce namespace dsw dsp sln vcproj CondExp Microsoft inline scur Vec Rosen Runge-Kutta Linux typedef Cpp atan $$ $section Changes and Additions to CppAD During 2005$$ $head 12-24$$ Fix a memory leak that could occur during the $cref ForSparseJac$$ calculations. $head 12-23$$ The buffers that are used to do $cref RevSparseJac$$ and $cref RevSparseHes$$ calculations are now freed directly after use. $pre $$ The $cref TrackNewDel.cpp$$ example was missing from the Windows install examples and testing project file. This has been fixed. $head 12-22$$ The buffer that is are used to do $cref Reverse$$ mode calculations is now freed directly after use. This reduces the memory requirements attached to an $cref ADFun$$ object. $head 12-20$$ Buffers that are used to store the tape information corresponding to the $codei%AD<%Base%>%$$ type are now freed when the corresponding $cref ADFun$$ object is constructed. This reduces memory requirements and actually had better results with the $cref speed_cppad$$ tests. $pre $$ The $cref speed_cppad$$ test program now outputs the version of CppAD at the top (to help when comparing output between different versions). $head 12-19$$ The $cref TrackNewDel$$ routines were added for track memory allocation and deletion with $code new[]$$ and $code delete[]$$. This is in preparation for making CppAD more efficient in it's use of memory. The bug mentioned on $cref/12-01/whats_new_05/12-01/$$ resurfaced and the corresponding routine was changed as follows: $codep static ADTape *Tape(void) { // If we return &tape, instead of creating and returning ptr, // there seems to be a bug in g++ with -O2 option. static ADTape tape; static ADTape *ptr = &tape; return ptr; } $$ $head 12-16$$ The $cref NearEqual$$ function documentation for the relative error case was changed to $codei% | %x% - %y% | <= %r% * ( |%x%| + |%y%| ) %$$ so that there is no problem with division by zero when $icode x$$ and $icode y$$ are zero (the code was changed to that form also). The $code std::abs$$ function replaced the direct computation of the complex norms (for the complex case in $code NearEqual$$). In addition, more extensive testing was done in $cref near_equal.cpp$$. $head 12-15$$ Extend $cref NearEqual$$ and $cref NearEqualExt$$ to cover more cases while converting them from, a library function in $code lib/CppADlib.a$$ and an utility in $code example/NearEqualExt.h$$, to a template functions in $code cppad/near_equal.hpp$$ and $code cppad/local/NearEqualExt.h$$. This is another step along the way of removing the entire $code CppADlib.a$$ library. $pre $$ The change on $cref/12-14/whats_new_05/12-14/$$ broke the Microsoft project files $code example/Example.sln$$ and $code TestMore/TestMore.sln$$ used during CppAD installation on Windows. This has been fixed. $pre $$ Move $code lib/SpeedTest.cpp$$ to $code cppad/speed_test.hpp$$. This was the last change necessary in order to remove the CppAD library, so remove all commands related to building and linking $code CppADlib.a$$. The corresponding entry has been removed from the $cref WishList$$. $pre $$ One of the entries in the $cref WishList$$ corresponded to the $cref Integer$$ function. It has also been removed (because it is already implemented). $head 12-14$$ Extend $cref erf$$ to cover more cases while converting it from a function in $code lib/CppADlib.a$$ to a template function in $code cppad/local/Erf.h$$. This is one step along the way of removing the entire $code CppADlib.a$$ library. $head 12-11$$ Group routines that extend the domain for which an $cref ADFun$$ object is useful into the ExtendDomain section. $pre $$ Add an example of a C callable routine that computes derivatives using CppAD (see $cref interface2c.cpp$$). $head 12-08$$ Split out $cref LuFactor$$ with the $icode ratio$$ argument to a separate function called $cref LuRatio$$. This needed to be done because $cref LuRatio$$ is more restrictive and should not be part of the general template $cref library$$. $head 12-07$$ Improve $cref CheckSimpleVector$$ so that it tests element assignment. Change $cref check_simple_vector.cpp$$ so that it provides and example and test of a case where a simple vector returns a type different from the element type and the element assignment returns $code void$$. $head 12-06$$ The specifications for a $cref SimpleVector$$ template class were extended so that the return type of an element access is not necessarily the same as the type of the elements. This enables us to include $code std::vector$$ which packs multiple elements into a single storage location and returns a special type on element access (not the same as $code bool$$). To be more specific, if $icode x$$ is a $code std::vector$$ object and $icode i$$ has type $code size_t$$, $icode%x%[%i%]%$$ does not have type $code bool$$. $pre $$ Add a Home icon, that links to the $href% http://www.coin-or.org/CppAD/% CppAD home page %$$, to the top left of the navigation frame (left frame) for each documentation section. $head 12-05$$ The $cref RevSparseHes$$ reverse mode Hessian sparsity calculation has been added. $pre $$ The definition of a $cref/sparsity pattern/glossary/Sparsity Pattern/$$ has been corrected to properly correspond to the more efficient form mentioned under $cref/whats_new_05/whats_new_05/11-20/$$ below. $pre $$ The dates in this file used to correspond to local time for when the change was checked into the $href% http://projects.coin-or.org/CppAD/browser% subversion repository %$$. From now on the dates in this file will correspond to the first version of CppAD where the change appears; i.e., the date in the unix and windows download file names $codei%CppAD-%yy%-%mm%-%dd%$$. $head 12-03$$ There was a bug in the $cref RevSparseJac$$ reverse mode sparsity patterns when used with $cref VecAD$$ calculations. This bug was fixed and the calculations were made more efficient (fewer true entries). $head 12-02$$ There was a bug in the $cref ForSparseJac$$ forward mode sparsity patterns when used with $cref VecAD$$ calculations. This bug was fixed and the calculations were made more efficient (fewer true entries). $head 12-01$$ The speed test of $cref lu_vec_ad.cpp$$ has been reinstated. It appears that there is some sort of bug in the gcc compiler with the -O2 option whereby the following member function $codep static ADTape *Tape(void) { static ADTape tape; return &tape; } $$ (in $code cppad/local/AD.h$$) would sometimes return a null value (during $cref VecAD$$ operations). A speed improvement in $code cppad/local/ExtendBuffer.h$$ seems to prevent this problem. This fix is not well understood; i.e., we should watch to see if this problem reoccurs. $pre $$ The source code for $cref lu_vec_ad_ok.cpp$$ was mistakenly used for $code speed_cppad/LuSolveSpeed.cpp$$. This has been fixed. $head 11-23$$ The speed test of $cref lu_vec_ad.cpp$$ has been commented out because it sometimes generates a segmentation fault. Here is an explanation: $pre $$ If $icode X$$ is a $codei%AD<%Base%>%$$ object, $icode y$$ is a $icode Base$$ object, $icode%X%[%y%]%$$ uses pointer from the element back to the original vector. Optimizing compilers might reorder operations so that the vector is destroyed before the object is used. This can be avoided by changing the syntax for $cref VecAD$$ objects to use $code set$$ and $code get$$ member functions. $head 11-22$$ A much better $cref/example/vec_ad.cpp/$$ for using $cref VecAD$$ vectors has been provided. In addition, a bug in the computation of derivatives using $code VecAD$$ vectors has been fixed. $pre $$ CppAD now checks that the domain dimension during $cref Independent$$ and the range dimension during $cref ADFun$$ (provided that $code -DNDEBUG$$ is not defined). If either of these is zero, the $code CppADUsageError$$ macro is invoked. $head 11-20$$ The sparsity pattern routines $cref ForSparseJac$$ and $cref RevSparseJac$$ have been modified so that they are relative to the Jacobian at a single argument value. This enables us to return more efficient $cref/sparsity patterns/glossary/Sparsity Pattern/$$. $pre $$ An extra $cref/exception/VecAD/VecAD::reference/Exceptions/$$ has been added to the use of $cref VecAD$$ elements. This makes $code VecAD$$ some what more efficient. $head 11-19$$ Improve the output messages generated during execution of the $cref/configure/auto_tools/Configure/$$ command. $pre $$ Put a try and catch block around all of the uses of $code new$$ so that if a memory allocation error occurs, it will generate a $code CppADUsageError/$$ message. $pre $$ The $cref get_started.cpp$$ example has been simplified so that it is easier to understand. $head 11-15$$ Fix a memory leak in both the $cref ForSparseJac$$ and $cref RevSparseJac$$ calculations. $head 11-12$$ Add reverse mode $cref/Jacobian sparsity/RevSparseJac/$$ calculation. $head 11-09$$ Add prototype documentation for $cref/logdet/LuSolve/logdet/$$ in the $cref LuSolve$$ function. $pre $$ Add the optional $icode ratio$$ argument to the $cref LuFactor$$ routine. (This has since been moved to a separate routine called $cref LuRatio$$.) $head 11-07$$ Remove some blank lines from the example files listed directly below (under 11-06). Comments for computing the entire Jacobian $cref/entire sparsity pattern/ForSparseJac/Entire Sparsity Pattern/$$ was added. $head 11-06$$ The cases of $code std::vector$$, $code std::valarray$$, and $code CppAD::vector$$ were folded into the standard example and tests format for the following cases: $cref rev_two.cpp$$, $cref rev_one.cpp$$, $code Reverse.cpp$$, $cref hessian.cpp$$, $cref jacobian.cpp$$, $cref forward.cpp$$, $cref for_two.cpp$$, $cref for_one.cpp$$, $code Fun.cpp$$ ($code Fun.cpp$$ has since been replaced by $cref independent.cpp$$, $code Reverse.cpp$$ has since been replaced by $cref reverse_one.cpp$$ and $code reverse_any.cpp$$). $head 11-01$$ Add forward mode $cref/Jacobian sparsity/ForSparseJac/$$ calculation. $head 10-20$$ Add $cref/sparsity patterns/glossary/Sparsity Pattern/$$ to the whish list. $head 10-18$$ The Unix install $cref/configure/auto_tools/Configure/$$ command was missing the $code --$$ before of the $code prefix$$ command line argument. $head 10-14$$ The template class $cref CppAD_vector$$ uses a try/catch block during the allocation of memory (for error reporting). This may be slow down memory allocation and hence it is now replaced by simple memory allocation when the preprocessor variable $code NDEBUG$$ is defined. $pre $$ The specialization of $code CppAD::vector$$ was moved to $cref/vectorBool/CppAD_vector/vectorBool/$$ so that $code CppAD::vector$$ does not pack one bit per value (which can be slow to access). $head 10-12$$ Change the $cref/configure/auto_tools/Configure/$$ script so that compilation of the $cref get_started.cpp$$ and $cref print_for_cout.cpp$$ examples are optional. $pre $$ One of the dates in the Unix installation extraction discussion was out of date. This has been fixed. $head 10-06$$ Change the Unix install $code configure$$ script so that is reports information using the same order and notation as its $cref/documentation/auto_tools/Configure/$$. $pre $$ Some compiler errors in the $cref ode_gear_control.cpp$$ and $cref ode_stiff.cpp$$ examples were fixed. $head 09-29$$ Add a specialization to $cref CppAD_vector$$ for the $code CppAD::vector$$ case. A test for the $code push_back$$ member function as well as a $cref CheckSimpleVector$$ test has been added to $cref cppad_vector.cpp$$. The source code for this template vector class, $code cppad/vector.hpp$$, has been removed from the documentation. $head 09-27$$ Add the $cref/prefix_dir/auto_tools/prefix_dir/$$ and $icode postfix_dir$$ ($icode postfix_dir$$ has since been removed) options to the $code configure$$ command line. This gives the user more control over the location where CppAD is installed. $head 09-24$$ The stiff Ode routines, $cref OdeGear$$ and $cref OdeGearControl$$, were added to the $cref library$$. A comparison various Ode solvers on a stiff problem $cref ode_stiff.cpp$$ was added. In addition, $code OdeGear$$ and $code OdeGearControl$$ were added to the $cref library$$ and the library was reorganized. $head 09-20$$ The Microsoft compiler project files $code example/Example.vcproj$$ and $code TestMore/TestMore.vcproj$$ were not up to date. This has been fixed. In addition, the example $cref numeric_type.cpp$$ has been added. $pre $$ Make the building of the $code Example$$, $code TestMore$$, and $code Speed$$, directories optional during the $cref/configure/auto_tools/Configure/$$ command. The $cref/Unix installation instructions/auto_tools/$$ were overhauled to make the larger set of options easy to understand. $head 09-14$$ Added the $cref NumericType$$ concept and made the following library routines require this concept for their floating point template parameter type: $cref LuSolve$$, $cref LuFactor$$, $cref RombergOne$$, $cref RombergMul$$, $cref Runge45$$, $cref Rosen34$$, and $cref OdeErrControl$$. This is more restrictive than the previous requirements for these routines but it enables future changes to the implementation of these routines (for optimization purposes) with out affecting their specifications. $head 09-09$$ Add the $cref UnaryPlus$$ operator and move the $code Neg$$ examples and tests to $cref UnaryMinus$$. $head 09-07$$ Change name of distribution files from $code CppAD.unix.tar.gz$$ and $code CppAD.dos.tar.gz$$ to $codei%CppAD-%yy%-%mm%-%dd%.tar.gz%$$ and $codei%CppAD-%yy%-%mm%-%dd%.zip%$$ (the $icode%*%.zip%$$ file uses pkzip compression). $head 08-30$$ The $icode maxabs$$ argument has been added to the $cref OdeErrControl$$ function so that it can be used with relative errors where components of the ODE solution may be zero (some of the time). In addition, some of the rest of the OdeErrControl documentation has been improved. $pre $$ The documentation for replacing defaults in CppAD error macros has been improved. $head 08-24$$ Changed $code Romberg$$ to $cref RombergOne$$ and added $cref RombergMul$$. In addition, added missing entries to $cref ListAllExamples$$ and reorganized $cref library$$. $head 08-20$$ Backed out addition of $code Romberg$$ integration routine (at this point uncertain of the interface that is most useful in the context of AD.) $head 08-19$$ Added a $code Romberg$$ integration routine for where the argument types are template parameters (for use with AD types). $head 08-15$$ The Microsoft project files $code example/Example.vcproj$$ and $code TestMore/TestMore.vcproj$$ were missing some necessary routines. In addition, $code Speed/Speed.vcproj$$ was generating a warning. This has been fixed. $head 08-14$$ An $cref Integer$$ conversion function as been added. $pre $$ The $cref value.cpp$$ example has been improved and the old example has been moved into the $code TestMore$$ directory. $head 08-13$$ The $cref unary_standard_math$$ functions $code sinh$$, and $code cosh$$ have been added. In addition, more correctness testing has been added for the $code sin$$ and $code cos$$ functions. $pre $$ The $cref OdeErrControl$$ routine could lock in an infinite loop. This has been fixed and a test case has been added to check for this problem. $head 08-07$$ The $cref/conditional expression/CondExp/$$ function has been changed from just $code CondExp$$ to $code CondExpLt$$, $code CondExpLe$$, $code CondExpEq$$, $code CondExpGe$$, $code CondExpGt$$. This should make code with conditional expressions easier to understand. In addition, it should reduce the number of tape operations because one need not create as many temporaries to do comparisons with. The old $code CondExp$$ function has been deprecated. $head 07-21$$ Remove unnecessary no-op that was left in tape for the $cref unary_standard_math$$ functions $code acos$$, $code asin$$, $code atan$$, $code cos$$. $pre $$ Improve the index entries in the documentation that corresponds to the $code cppad/local$$ directory source code. $head 07-19$$ The $cref WishList$$ and $code Bugs$$ information were moved out of this section and into their own separate sections (the Bugs section has been removed; see the $code bug$$ subdirectory instead). $pre $$ A discussion of $cref/VecAD speed and memory/VecAD/Speed and Memory/$$ was added as well as an entry in the $cref WishList$$ to make it more efficient. $head 07-15$$ The $code BOOST_DIR$$ and $code CPP_ERROR_WARN$$ $cref/configure/auto_tools/Configure/$$ options were not properly implemented for compiling the $code lib$$ sub-directory. This has been fixed. $pre $$ Some compiler warnings in the file $code lib/ErrFun.cpp$$, which computes the $cref erf$$ function, have been fixed. $head 07-11$$ The $cref/push_back/CppAD_vector/push_back/$$ function has been added to the $code CppAD::vector$$ template class. $pre $$ It appears that the $code TestMore/Runge45.cpp$$ file was missing an include of $code example/NearEqualExt.h$$. This has been fixed. $head 07-08$$ The documentation for $cref Forward$$ and $cref Reverse$$ has been improved. $head 07-05$$ The $cref rosen_34.cpp$$ example mixed the $cref/CppAD::vector/CppAD_vector/$$ and $code CppADvector$$ vector types. This caused the compilation of the examples to fail when $code CppADvector$$ was defined as something other than $code CppAD::vector$$ (found by Jon Pearce). This has been fixed. $pre $$ The $cref CheckSimpleVector$$ run time code has been improved so that it is only run once per case that is being checked. $pre $$ Simple Vector concept checking ($cref CheckSimpleVector$$) was added to the routines: $cref ForOne$$, $cref ForTwo$$, $cref Forward$$, $cref ADFun$$, $cref Hessian$$, $cref Independent$$, $cref Jacobian$$, $cref RevOne$$, $cref RevTwo$$, and $cref Reverse$$. $head 07-04$$ Simple Vector concept checking ($cref CheckSimpleVector$$) was added to the routines: $cref LuFactor$$, $cref LuSolve$$, $cref LuInvert$$, $cref OdeErrControl$$, $cref Runge45$$, and $cref Rosen34$$. $pre $$ The previous version of the routine $cref OdeErrControl$$ was mistakenly in the global namespace. It has been moved to the $code CppAD$$ namespace (where all the other $cref library$$ routines are). $pre $$ The previous distribution (version 05-07-02) was missing the file $code cppad/local/Default.h$$. This has been fixed. $head 07-03$$ Added $cref CheckSimpleVector$$, a C++ concept checking utility that checks if a vector type has all the necessary conditions to be a $cref SimpleVector$$ class with a specific element type. $head 07-02$$ Version 7 of Microsoft's C++ compiler supports the standard declaration for a friend template function. Version 6 did not and CppAD used macros to substitute the empty string for $code $$, $code < AD >$$, and $code < VecAD >$$ in these declarations. These macro substitutions have been removed because Version 6 of Microsoft's C++ compiler is no longer supported by CppAD. $pre $$ The copy base section was split into the default constructor and the construction for the base type. The construction from base type has been extended to include any type that is convertible to the base type. As a special case, this provides the previous wish list item of a constructor from an arbitrary $icode Base$$ to a $codei%AD< AD<%Base%> >%$$, $codei%AD< AD< AD<%Base%> > >%$$ etc. $head 07-01$$ The permissions were set as executable for many of the no-executable files in the distribution; for example, the $code README$$, file. This has been fixed. $head 06-25$$ Some improvements were made to the README, AUTHORS, COPYING, and INSTALL files. In addition, the file $code UWCopy040507.html$$ which contains the University of Washington's copyright policy (see Section 2) was added to the distribution. $head 06-24$$ The $code List2Vector$$ $cref/example utility/ExampleUtility/$$ is no longer used and has been removed. $head 06-18$$ CppAD is now supported by Microsoft Visual C++ version 7 or higher. The version 6 project files $icode%*%.dsw%$$ and $icode%*%.dsp%$$ have been replaced by the version 7 project files $icode%*%.sln%$$ and $icode%*%.vcproj%$$. $head 06-14$$ A new $cref/CondExp example/cond_exp.cpp/$$ has been added and the old $cref CondExp$$ example has been moved to the $code TestMore$$ directory (it is now only a test). $head 06-13$$ The changes made on 06-06 do not run under Microsoft Visual C++ version 6.0 (even though they are within the C++ standard). Preliminary testing under version 7 indicates that Microsoft has fixed this problem in later versions of their C++ compiler. $head 06-06$$ Converted the routines $cref Forward$$ and $cref Reverse$$ to allow for any $cref SimpleVector$$ instead of just $code CppADvector$$. In addition, separated the syntax of the function call from the prototype for each of the arguments. This was also done for all the easy to use $cref Drivers$$ as well as the $cref Independent$$ function and the $cref ADFun$$ constructor. $pre $$ Add a section containing a list of $cref/all the examples/ListAllExamples/$$. $head 05-19$$ A significant improvement in speed was obtained by moving the buffer extension to a separate function and then inline the rest of putting operators in the tape. For example, here is part of the speed test output before this change: $codep Tape of Expansion by Minors Determinant: Length = 350, Memory = 6792 size = 5 rate = 230 size = 4 rate = 1,055 size = 3 rate = 3,408 size = 2 rate = 7,571 size = 1 rate = 13,642 $$ and here is the same output after this change: $codep Tape of Expansion by Minors Determinant: Length = 350, Memory = 6792 size = 5 rate = 448 size = 4 rate = 2,004 size = 3 rate = 5,761 size = 2 rate = 10,221 size = 1 rate = 14,734 $$ Note that your results will vary depending on operating system and machine. $head 05-18$$ Change name of $code OdeControl$$ to $cref OdeErrControl$$ and improve its documentation. $pre $$ Correct the syntax for the $cref/Parameter and Variable/ParVar/$$ functions. $head 05-16$$ Change $cref OdeErrControl$$ to have method return its order instead of having a separate argument to $code OdeErrControl$$. $pre $$ Add the argument $icode scur$$ to $code OdeErrControl$$, improve $code OdeErrControl$$ choice of step size and documentation. $head 05-12$$ Using profiling, the $cref/multiplication operator/ad_binary/$$ was show to take a significant amount of time. It was reorganized in order to make it faster. The profiling indicated an improvement so that same change was made to the $cref ad_binary$$ and $cref compute_assign$$ operators. $head 05-06$$ The documentation for $cref SimpleVector$$ and $cref NearEqual$$ were changed to use more syntax (what the user enters) and simpler prototypes (the compiler oriented description of the arguments). In addition, exercises were added at the end of the $cref SimpleVector$$, $cref CppAD_vector$$, and $cref NearEqual$$ documentation. $pre $$ There was a undesired divide by zero case in the file $code TestMore/VecUnary.cpp$$ that just happened to work in corresponding $cref NearEqual$$ check. The $code NearEqual$$ routine has been changed to return false if either of the values being compared is infinite or not a number. In addition, the divide by zero has been removed from the $code TestMore/VecUnary.cpp$$ test. $head 05-01$$ The doubly linked list was also removed from the $cref VecAD$$ internal data structure because this method of coding is simpler and it makes it more like the rest of CppAD. $head 04-21$$ The profiling indicated that the destructor for an AD object was using a significant amount of time. The internal data structure of an AD object had a doubly linked list that pointed to the current variables and this was modified when an AD object was destroyed. In order to speed AD operations in general, the internal data structure of an AD object has been changed so that this list is no longer necessary (a tape id number is used in its place) $pre $$ During the process above, the function $cref/Variable/ParVar/$$ was added. $head 04-20$$ Add $cref/profiling/auto_tools/Profiling CppAD/$$ to the speed tests. $head 04-19$$ Remove an extra (not necessary) semi-colon from the file $code cppad/local/Operator.h$$. $head 03-26$$ The new routine $cref OdeErrControl$$ does automatic step size control for the ODE solvers. $head 03-23$$ The routine $cref Rosen34$$ is an improved stiff integration method that has an optional error estimate in the calling sequence. You must change all your calls to $code OdeImplicit$$ to use $code Rosen34$$ (but do not need to change other arguments because error estimate is optional). $head 03-22$$ The routine $cref Runge45$$ is an improved Runge-Kutta method that has an optional error estimate in the calling sequence. You must change all your calls to $code OdeRunge$$ to use $code Runge45$$ (but do not need to change other arguments because error estimate is optional). $head 03-09$$ Some extra semi-colons (empty statements) were generating warnings on some compilers. The ones that occurred after the macros $code CppADStandardMathBinaryFun$$, $code CppADCompareMember$$, $code CppADBinaryMember$$, and $code CppADFoldBinaryOperator$$ have been removed. $head 03-04$$ An new multiple level of AD example $cref mul_level$$ was added. $head 03-01$$ An option that specifies error and warning $cref/flags/auto_tools/cxx_flags/$$ for all the C++ compile commands, was added to the $cref/Unix installation instructions/auto_tools/$$. $head 02-24$$ The routine $cref LuSolve$$ was split into $cref LuFactor$$ and $cref LuInvert$$. This enables one to efficiently solve equations where the matrix does not change and the right hand side for one equation depends on the left hand side for a previous equation. $pre $$ An extra requirement was added to the $cref SimpleVector$$ template class. There must be a typedef for $code value_type$$ which is the type of elements in the vector $pre $$ Under Mandrake Linux 10.1, some template friend declarations were failing because the corresponding operations were not declared before being indicated as friends (found by $href%mailto:Jean-Pierre.Dussault@Usherbrooke.ca%Jean-Pierre Dussault%$$). This has been fixed. $head 01-08$$ The $cref erf$$ function was added. The implementation of this function used conditional expressions ($cref CondExp$$) and some times the expression that was not valid in a region caused division by zero. For this reason, the check and abort on division by zero has been removed. $end