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[Algorithm] hyplas DL : 11: ************************************************************************ * * * * * THIS IS THE H Y P L A S 2.0 README FILE * * ----------------- * * * * HYPLAS is a finite element program for implicit small and large * * strain analisys of hyperelastic and elasto-plastic two-dimensional * * and axisymmetric solids * * * * HYPLAS v2.0 is the companion software to the textbook: * * EA de Souza Neto, D Peric & DRJ Owen. Computational Methods for * * Plasticity: Theory and Applications. Wiley, Chichester, 2008. * * (www.wiley.com/go/desouzaneto) * * * * Copyright (c) 1998-2008 EA de Souza Neto, D Peric, D.R.J. Owen * *----------------------------------------------------------------------* * File last updated: 18 October 2008 * * * * This file belongs in the directory ../HYPLAS_v2.0 * ************************************************************************ * * * I M P O R T A N T * * * * READ SECTIONS 0 TO 3 OF THIS FILE CAREFULLY BEFORE ATTEMPTING * * TO COMPILE AND RUN THE PROGRAM HYPLAS ON YOUR COMPUTER !! * * * * THE AUTHORS DO NOT GUARANTEE THAT ANY SUGGESTIONS/INSTRUCTIONS * * GIVEN IN THIS README FILE WILL WORK ON ANY PARTICULAR OPERATING * * SYSTEM. IF YOU DECIDE TO FOLLOW ANY SUGGESTIONS/INSTRUCTIONS * * GIVEN HERE YOU MUST DO SO AT YOUR OWN RISK. * * * * * * BUG REPORTS: Please send bug reports to * * * * hyplas_v2.0@live.co.uk * * * * Messages sent to the authors' personal email addresses * * will NOT be answered. * ************************************************************************ This file contains the following sections: 0. Copyright statement and disclaimer 0.(a) Copyright statement 0.(b) Disclaimer 0.(c) Conditions of use 1. Introduction 1.(a) Note on portability 2. Compiling and running HYPLAS 2.(a) Memory requirements 2.(b) Testing a newly compiled executable 3. The HYPLAS directory tree 4. Cross-referencing between the source code and the textbook 5. HYPLAS error messaging 6. Further remarks on HYPLAS ************************************************************************ 0. COPYRIGHT STATEMENT AND DISCLAIMER ================================== 0.(a) Copyright statement ------------------- You may only use this program for your own private purposes. You are not allowed, in any circumstances, to distribute this program (including its source code, executable and any other files related to it, either in their original version or any modifications introduced by you, the authors or any other party) in whole or in part, either freely or otherwise, in any medium, without the prior written consent of the copyright holders. 0.(b) Disclaimer ---------- This program (including its source code, executable and any other files related to it) is provided "as is" without warranty of any kind, either expressed or implied, including, but not limited to, any implied warranties of fitness for purpose. In particular, THIS PROGRAM IS BY NO MEANS GUARANTEED TO BE FREE FROM ERRORS. This program (or any modification incorporated to it by you, the authors or any other party) will run entirely at your risk. The results produced by this program are in no way guaranteed to be fit for any purpose. Under no circumstances will the authors/copyright holders be liable to anyone for damages, including any general, special, incidental or consequential damages arising from the use or inability to use the program (including, but not limited to, loss or corruption of data, failure of the program to operate in any particular way as well as damages arising from the use of any results produced by the program for any purpose). 0.(c) Conditions of use ----------------- You may only use this program if you fully understand and agree with the terms of the above disclaimer. You must not use this program if you do not agree with or do not understand (fully or in part) these conditions of use. 1. INTRODUCTION ============ HYPLAS is a finite element code for small and large strain analysis of hyperelastic and elasto-plastic solids. Most procedures implemented in HYPLAS are described in detail in its companion textbook: EA de Souza Neto, D Peric & DRJ Owen. Computational Methods for Plasticity: Theory and Applications. Wiley, Chichester, 2008 (www.wiley.com/go/desouzaneto). 1.(a) Note on Portability ------------------- HYPLAS has been written in standard ANSI FORTRAN 77. Currently, the only known (and deliberate) exceptions to the FORTRAN 77 ANSI standard are the instructions: INCLUDE '' used in many routines to include the HYPLAS database files (common blocks and global variables), and; CALL GETENV('HYPLASHOME',HYPLASHOME) used in subroutine "ERRPRT" (file ../HYPLAS_v2.0/src/GENERAL/errprt.f). This instruction inquires the name of the system environment variable HYPLASHOME and writes it on the character string HYPLASHOME. This instruction is NOT part of the ANSI FORTRAN 77 standard, but seems to work in most currently available FORTRAN 77 compilers. 2. COMPILING AND RUNNING H Y P L A S ================================== The HYPLAS source code is stored in directory ../HYPLAS_v2.0/src/ (../HYPLAS_v2.0/ being the current directory) and all its subdirectories. To generate an executable file, you just need to compile the FORTRAN source files: ../HYPLAS_v2.0/src/hyplas.f and ../HYPLAS_v2.0/src/*/*.f together. We recommend that the executable HYPLAS be stored in the directory ../HYPLAS_v2.0/bin to which the environment variable HYPLASHOME should be set (see below how to set a system environmental variable). WINDOWS (R) systems ------------------- On Microsoft Windows(R) systems, HYPLAS has been successfully compiled using Intel Visual Fortran Compiler(R) integrated with Microsoft Visual Studio(R). Here you only need to create a project that contains all Fortran source files mentioned above as well as the include files ..\HYPLAS_v2.0\src\*.INC On a Windows XP system, the system environment variable HYPLASHOME can be set as follows: 1. Open a File Manager 2. Right-click on the "My Computer" icon 3. Select "Properties" on the drop-down menu 4. A new window named "System Properties" will pop-up. Here select the "Advanced" tab. 5. On the "Advanced" tab, click the "Environment Variables" button. 6. A new window titled "Environment Variables" will pop-up. Here click the button "New" in the "System Variables" section of the window. 7. A new window will pop-up titled "New System Variable". Here you should fill the fields "Variable name" and "Variable Value", respectively, with HYPLASHOME and the path name (in full) of the directory ..\HYPLAS_v2.0\bin. 8. Press "OK" on the relevant pop-up windows. 9. The next time the computer is REBOOTED, this variable will be set to the correct path and HYPLAS should be able to find the error messages file ERROR.RUN if required. UNIX/LINUX systems ------------------ In a UNIX/LINUX operating system using a C-shell, for instance, the HYPLASHOME environment variable should be set with the command: setenv HYPLASHOME where here denotes the full path to the directory ../HYPLAS_v2.0/bin. To compile HYPLAS (from directory ../HYPLAS_v2.0/src) with a FORTRAN 77 compiler such as g77, you can use the command: g77 -o ../bin/hyplas hyplas.f */*.f Note that the executable file "hyplas" will be stored in the directory ../HYPLAS_2.0/bin (i.e. the directory set in the HYPLASHOME environment variable). Alternatively, you may use the Makefile provided (with suitable modifications, if needed) to create the HYPLAS executable. IMPORTANT: Before generating a HYPLAS executable, read Sections 2.(a) and 2.(b) below. 2.(a) Memory Requirements ------------------- HYPLAS memory requirements depend on the array dimensioning parameters set in files: ../HYPLAS_v2.0/src/ ELEMENTS.INC GLBDBASE.INC MATERIAL.INC MAXDIM.INC Files ELEMENTS.INC, GLBDBASE.INC and MATERIAL.INC contain parameters which are associated with the currently implemented finite elements and materials. DO NOT MODIFY THEM ! unless you are absolutely sure of what you are doing (only developers coding new elements or new material models/analysis types may need to modify them by changing the existing dimensioning parameters and/or including new parameters). The ONLY dimensioning file that can be safely modified by the average user is the file MAXDIM.INC This file contains the array dimensioning parameters related to the maximum permissible dimension of problems to be analysed by HYPLAS. These parameters include the maximum number of nodes, elements, element groups, etc. If necessary, CHANGE THESE PARAMETERS TO SUIT YOUR PROBLEM SIZE/MEMORY REQUIREMENTS before compiling HYPLAS. 2.(b) Testing a newly compiled executable ----------------------------------- After you have successfully compiled the HYPLAS source code and created an executable file, the next step is to run some tests to verify that HYPLAS is working well. To do this, proceed as follows: The directory ../HYPLAS_v2.0/book_examples/data_files contains a series of data files named .dat of benchmarked examples described in the companion textbook. The corresponding (benchmarked) result files are in the directory ../HYPLAS_v2.0/book_examples/result_files This directory contains a series of result files named .res generated with the current version of HYPLAS on a tested platform. All these files have been named such that their names start with the textbook section number where the corresponding example is described. For instance, files 14_9_2_tresca.dat and 14_9_2_tresca.res refer to a problem described in section 14.9.2 of the textbook, and so on. To check that HYPLAS is working well on your platform, after compiling HYPLAS, run the program HYPLAS for the examples of files .dat and compare the newly generated results .res with their benchmarked counterparts (of the same filename) in the result_files directory. To run an example, execute HYPLAS and use the keyboard to enter the name of the corresponding data file in full (including the extension .dat). To compare the benchmarked .res files against their newly generated you may proceed as follows: 1. On MICROSOFT WINDOWS systems - Here we have successfully used the software "ExamDiff" (the task was made particularly easy by selecting "View" and then the "Show Differences Only" option - this refers to version 1.8 of this software). 2. On UNIX/LINUX systems - Here we use the "diff" command from a shell window (and set the option to ignore blank spaces). A shell script may be used to perform this task automatically (including running HYPLAS and checking for result file differences) for all benchmarked examples provided. IMPORTANT: THE ONLY ACCEPTABLE DIFFERENCES BETWEEN A THE NEWLY GENERATED RESULT FILES AND THEIR BENCHMARKED COUNTERPARTS ARE THE DIMENSIONING PARAMETERS (FROM FILE MAXDIM.INC) USED TO COMPILE THE NEW EXECUTABLE (THESE PARAMETERS ARE PRINTED RIGHT AT THE BEGINNING OF THE RESULT FILES) AND NUMERICAL DIFFERENCES IN RESULTS DUE TO NUMERICAL "ROUNDING-OFF" (THESE ARE VERY SMALL DIFFERENCES THAT DEPEND ON THE PRECISION OF ARITHMETIC OPERATIONS IN THE PLATFORM USED). ALSO NOTE THAT THE EXAMPLES OF THE COMPANION TEXTBOOK DO NOT COVER ALL FEATURES OF HYPLAS. HENCE THIS TEST DOES NOT GUARANTEE THAT EVERYTHING IS WORKING PROPERLY. 3. THE H Y P L A S DIRECTORY TREE ================================ 3.(a) Summary ------- ../ HYPLAS_v2.0/ bin/ book_examples/ data_files/ result_files/ man/ html/ src/ CRYSTAL/ DAMAGE/ DAMAGED_ELASTIC/ DRUCKER_PRAGER/ ELASTIC/ ELEMENTS/ GENERAL/ MATERIALS/ MATHS/ MOHR_COULOMB/ OGDEN/ TRESCA/ VON_MISES/ VON_MISES_MIXED/ 3.(b) Description ----------- The HYPLAS program directory tree is organised as follows: ../HYPLAS_v2.0/ (this directory) This is the HYPLAS root directory, where the HYPLAS directory tree starts. ../HYPLAS_v2.0/bin/ This directory contains the file ERROR.RUN where most HYPLAS error/warning messages are. IMPORTANT: the environment variable HYPLASHOME should be set to this directory. Otherwise, HYPLAS will not find its error/warning messages when required. We also recommend that the EXECUTABLE of HYPLAS be stored in this directory. ../HYPLAS_v2.0/book_examples/ This directory has the following subdirectories: ../HYPLAS_v2.0/book_examples/data_files ../HYPLAS_v2.0/book_examples/result_files Refer to Section 2.(b) above for further details. ../HYPLAS_v2.0/man/ This is the HYPLAS documentation/manuals directory. It contains the following files: input_man.txt - A concise input data manual for HYPLAS in ASCII format; hyplas_calltree.txt - Contains a flowgraph (shows the call tree) of HYPLAS in ASCII-format. Note: calls to function subprograms are not included in this flowgraph; and the subdirectory: ../HYPLAS_v2.0/man/html This directory contains the hypertext (HTML) format Fortran source code and of manual pages of the entire HYPLAS program. Manual pages with descriptions of each function/subprogram including their argument list are linked to their corresponding HTML-format source code. This allows the user the navigate through the HYPLAS source code using a web browser. To start at the main program, use your web browser to open the file hyplas.html. This facility should be helpful to those trying to understand the flow of program HYPLAS. ../HYPLAS_v2.0/src/ This directory (and its subdirectories) contains the Fortran source code of HYPLAS. The files containing the sources are named following the standard practice: .f where is the name of the FORTRAN procedure (subroutine, function subprogram, etc.) whose source code is in file .f. The source code of the HYPLAS main program is in file hyplas.f and the HYPLAS database (COMMON blocks, array dimensioning parameters and other global parameters) is coded in the "include files" ELEMENTS.INC GLDBASE.INC MATERIAL.INC MAXDIM.INC in this directory. In addition, this directory contains a file named "Makefile" (UNIX-LINUX Release only) which may be used for compiling and linking HYPLAS in UNIX/LINUX systems. The subdirectories of ../HYPLAS_v2.0/src are as follows: ../HYPLAS_v2.0/src/CRYSTAL Contains the source code of all procedures related to the finite strain single crystal plasticity model implemented in HYPLAS. ../HYPLAS_v2.0/src/DAMAGE Source files of the procedures related to the Lemaitre ductile damage model implementation. ../HYPLAS_v2.0/src/DAMAGED_ELASTIC Source files of the procedures related to the damaged elasticity model with crack closure effect. ../HYPLAS_v2.0/src/DRUCKER_PRAGER Source files of the procedures related to the implemented Drucker-Prager plasticity model. ../HYPLAS_v2.0/src/ELASTIC Source files of the procedures related to the linear elasticity model (Hencky model under large strains) implemented. ../HYPLAS_v2.0/src/ELEMENTS Source files of the element interfaces and element-related procedures. ../HYPLAS_v2.0/src/GENERAL Source files of general procedures. ../HYPLAS_v2.0/src/MATERIALS Source files of the material interfaces. ../HYPLAS_v2.0/src/MATHS Source files of the mathematical procedures. ../HYPLAS_v2.0/src/MOHR_COULOMB Source files of the procedures related to the implemented Mohr-Coulomb plasticity model. ../HYPLAS_v2.0/src/OGDEN Source files of the procedures related to the implemented Ogden hyperelasticity model. ../HYPLAS_v2.0/src/TRESCA Source files of the procedures related to the implemented Tresca plasticity model. ../HYPLAS_v2.0/src/VON_MISES Source files of the procedures related to the implemented von Mises plasticity model with isotropic hardening. ../HYPLAS_v2.0/src/VON_MISES_MIXED Source files of the procedures related to the implemented von Mises plasticity model with mixed isotropic/kinematic hardening. 4. CROSS-REFERENCING BETWEEN THE SOURCE CODE AND THE TEXTBOOK ========================================================== Many references are made in the textbook to various subprograms of HYPLAS. These are usually made when a particular procedure described in the text is implemented in the program. The reader should refer to the textbook index. Also, a substantial number of comment lines have been added to the source code of HYPLAS with reference to sections, figures, boxes, etc of the textbook related to the part of the code in question. Such references are usually displayed after the word "REFERENCE:" (in capitals) on commented lines. Searching for this word will take you to the line of code where the particular routine has a reference to the textbook. NOTE: Occasional references to other textbooks/journal papers are also made following the word "REFERENCE:" on commented lines. 5. HYPLAS ERROR MESSAGING ====================== Most error/warning messages issued by HYPLAS are in the ASCII-format file ERROR.RUN (kept in the HYPLASHOME directory - ../HYPLAS_v2.0/bin). All such error/warning messages have an identification code (e.g. ED0015) which is printed both to the standard output (this is usually the computer screen) and to the relevant results file. If you wish to find where in the source code a particular message is being issued, then perform a search for the corresponding message identification code in the entire source code of HYPLAS. 6. FURTHER REMARKS ON HYPLAS ========================= 6.(a) Program efficiency THIS SECTION IS OF INTEREST ONLY TO THOSE WANTING TO MAKE HYPLAS RUN FASTER. It is particularly stressed in the textbook that this program has not been designed having efficiency in mind (refer to Section 5.1.2 of the textbook). Its structure has been designed mainly to illustrate in a relatively clear manner the computer implementation of the techniques and algorithms described in the text, with a particular view to the implementation of solid constitutive models and finite elements. For those who are especially interested in the speed of the code, there are a few tips that could help in this direction. Unfortunately, these involve modifications to the source code which is probably most appropriate to readers with a good level of experience in finite element programming. To those with this particular interest, we can suggest the following: (i) The use of faster linear solvers This is probably the change that would result in a greater gain in efficiency. The Frontal Method adopted in subroutine FRONT (file ../HYPLAS_v2.0/src/GENERAL/front.f) has been designed originally to save memory (back in the days when computer memory was severely limited). There are currently a vast number of methodologies which focus on speeding up the linear solution, in addition to reducing memory storage requirements (which is a particularly important issue in the solution of large scale problems). Some of these are extensions/refinements of the original Frontal solver. We remark that a number of such procedures (with their respective source codes) are available (conditions may apply) from the LAPACK (Linear Algebra PACKage - http://www.netlib.org/lapack) repository or from the HSL Library (http://www.cse.cse.scitech.ac.uk/nag/hsl). For the reader interested in gaining speed, we would recommend the replacement of the existing solver of FRONT by a faster one. We remark though that this is a substantial programming task. Another aspect here is the fact that computing times in FRONT are directly linked to the frontwidth of the system which, in the present version of HYPLAS is fixed and depends, for a given mesh, on how the degrees of freedom are numbered (node numbering). The incorporation of a frontwidth optimiser (which re-numbers the degrees of freedom in order to minimise the frontwidth) in FRONT could produce some good savings in computing times. Such savings become particularly noticeable in larger problems where the original node numbering produces an excessively large frontwidth. (ii) Material-specific computations The issues pointed out here affect only the computing times for specific material models and are expected to have a much lower impact in overall speed than the linear solver issue discussed above. Some of the material model-specific computations carried out in HYPLAS could be made a bit faster. For example, for isotropic models whose stress update is carried out in the principal stress space (such as the Tresca and Mohr-Coulomb models - see routines SUTR and SUMC, files ../HYPLAS_v2.0/src/TRESCA/sutr.f and ../HYPLAS_v2.0/MOHR_COULOMB/sumc.f, respectively) the spectral decomposition of the stress in carried out in the state update update routine and then repeated in the corresponding routine for computation of the consistent tangent operator (refer to files ../HYPLAS_v2.0/src/TRESCA/cttr.f and ../HYPLAS_v2.0/src/MOHR_COULOMB/ctmc.f, respectively, for the Tresca and Mohr-Coulomb plasticity models). Some savings in computing time can be achieved here by storing the stress eigenprojection tensors (these can be stored as state variables) during the execution of the state updating and then retrieving them later for use in the computation of the consistent tangent operator. This change can be incorporated to the code relatively easily. The computation of the exponential map and is derivative for the single crystal plasticity model (routines EXPMAP, file ../HYPLAS_v2.0/src/CRYSTAL/expmap.f and DEXPMP, file ../HYPLAS_v2.0/src/CRYSTAL/dexpmp.f) is carried out in three dimensions (these routines have been adapted from an earlier three-dimensional code). To improve efficiency, these can be adapted to work only in two-dimensional problems by removing the unnecessary operations related to the third dimension. 6.(b) Output of nodal averaged values The reader should be aware that the way in which nodal averaged values of stresses and other variables are calculated in HYPLAS is very basic (and rudimentary). This feature of the program is made available only to help those interested in producing contour plots, etc from results presented in HYPLAS result files and should be useful in many circumstances of interest. This facility has in fact been used in producing many of the figures presented in the textbook. But note, for example, that the values of incremental plastic multipliers for plasticity models may take (inadmissible) negative values when extrapolated from Gauss-point to nodes and averaged. We remark that more sophisticated and refined techniques of transferring Gauss point values of variables to nodal points and obtaining the corresponding smoothed field are available in the current literature. These fall outside the scope of the companion textbook of HYPLAS.
Date : 2011-07-29 Size : 10.5mb User : gtcewli3
[Algorithm] polyn DL : 0: 多项式相加减求导-Polynomials modified derivative
Date : 2026-01-10 Size : 2kb User : 陈可
[Algorithm] mjyna DL : 3: Evaluate a sequence of Bessel functions of the first and second kinds and their derivatives with integer orders and real arguments-Evaluate a sequence of Bessel functions of the first and second kinds and their derivative s with integer orders and real arguments
Date : 2026-01-10 Size : 3kb User : zxh
[Algorithm] Devirate DL : 0: 利用样条插值求取一组数据点在各点的导数 (只提供函数)-using spline interpolation to strike a group of data points in the points in the derivative (only provide functions)
Date : 2026-01-10 Size : 1kb User :
[Algorithm] Eular_fixed_a_co2(xiu) DL : 0: Eular法解分数阶微分方程,分数阶导数定义系数通过fourier法计算-eular method of fractional differential equations, fractional derivative definition coefficient calculated by fourier
Date : 2026-01-10 Size : 1kb User : liangqin
[Algorithm] BDF_fixed_a_co2 DL : 1: BDF法解分数阶微分方程,分数阶导数定义系数通过fourier法计算-BDF method of fractional differential equations, fractional derivative definition coefficient calculated by fourier
Date : 2026-01-10 Size : 1kb User : liangqin
[Algorithm] legendrecof DL : 0: 勒让德多项式德生成，在matlab 中德勒让德多项式不能直接用于求导数等计算，故可以自己定义-Legendre polynomials Germany generation, Dragulescu in Matlab which allow polynomials not be directly used for such derivative, it can own definition
Date : 2026-01-10 Size : 1kb User : 刘宁
[Algorithm] duoyuanhanshuerjiedaoshu DL : 0: 用C++编的多元函数求二阶导数，能使用,我已经调试过了-C series of the multi-function for second derivative, in use, I have over the debugging
Date : 2026-01-10 Size : 237kb User : 王华
[Algorithm] powell1 DL : 0: powell优化算法的C语言原代码，该算法不需要求导数，应用场合较多-powell optimization algorithm in C language source code that the algorithm is not derivative, the more applications
Date : 2026-01-10 Size : 2kb User : shenjianguo
[Algorithm] HermiteThree DL : 0: 该程序是一个分段三次Hermite插值函数，给出自变量的值和相应的函数值及一阶导数值，可以用来另外已知自变量值的函数值-that the procedure was a Hermite cubic interpolation function, from the variable to the value and the corresponding function and a derivative values can be used to the other variables known to value the function
Date : 2026-01-10 Size : 1kb User : 陈林
[Algorithm] MAIRYA DL : 0: 本Fortran程序用来实现高等数学中的一类特殊函数-Airy函数及其导数.-The Fortran program used to achieve the higher mathematics of a class of special functions-Airy function and its derivative.
Date : 2026-01-10 Size : 2kb User : 王天华
[Algorithm] yangtiaochazhi DL : 0: 该程序能实现第一型三次样条插值，边界条件是端点的一阶导数。结果可以同时显示每段区间的插值多项式。-The program to achieve the first-type cubic spline interpolation, boundary conditions is the endpoint of the first order derivative. Results can be displayed at the same time each interval of the interpolation polynomial.
Date : 2026-01-10 Size : 1kb User : 潘晓惠
[Algorithm] newton DL : 0: 牛顿下山算法，给出了实例，求导数时自己把公式输入，希望有人能改变能自动求解导数，可以联系我。-Newton downhill algorithm, given examples, and derivatives of the formula when their own input, hope someone can change automatically solve the derivative, you can contact me.
Date : 2026-01-10 Size : 1kb User :
[Algorithm] dgwaveform DL : 0: 计算高斯各阶导函数的C程序 Computing Gaussian derivative waveforms of any order. Dgwaveform efficiently creates Gaussian derivative wavelets-Calculation of Gaussian derivative function of the C program Computing Gaussian derivative waveforms of any order.Dgwaveform efficiently creates Gaussian derivative wavelets
Date : 2026-01-10 Size : 8kb User : danielwood
[Algorithm] three_spline DL : 0: 对于给定（n+1)个节点上的函数值，采用三次样条的方法进行差值，这是一个高阶的插值方法，它既有良好的收敛性又比较光滑。它实际上是由分段三次曲线连接而成，在接点处有2阶连续导数。-For a given (n+ 1) nodes on the function value, using cubic spline approach the margin, this is a high-order interpolation methods, it has both a good convergence also relatively smooth. It is actually the third curve from the sub-linking in contact there is 2-order continuous derivative.
Date : 2026-01-10 Size : 3kb User : 白雪
[Algorithm] qiudao DL : 0: 求给定表达式的导数表达式环境vs2008-For a given expression expression environment Derivative vs2008
Date : 2026-01-10 Size : 45kb User : Wangyunhong
[Algorithm] multifunctionvariablemetricmethod DL : 0: 解具有导数的多元函数的无约束极小值点或具有导数的非线性方程组的近似解-Solution with multi-function derivative of the unconstrained point or derivative of the nonlinear equations of the approximate solution
Date : 2026-01-10 Size : 82kb User : 张趋
[Algorithm] scyt DL : 0: 三次样条插值函数，可以用于计算插值，一阶导数，二阶导数-Cubic spline interpolation function can be used to calculate the interpolation, first derivative, second derivative
Date : 2026-01-10 Size : 1kb User : 大龙
[Algorithm] Pochodna DL : 0: derivative of function i JAVA
Date : 2026-01-10 Size : 1kb User : marchew
[Algorithm] maspline DL : 0: 插值方法：三次样条插值源代码（一阶导数边界条件）-Interpolation Method: Cubic Spline Interpolation source code (a derivative boundary condition)
Date : 2026-01-10 Size : 1kb User : malanxiang

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