CMinpack使用介紹

時間 2020-04-18

標籤 cminpack 使用介紹简体版

原文原文鏈接

github： https://github.com/devernay/cminpack 主頁： http://devernay.github.io/cminpack/ 使用手冊： http://devernay.github.io/cminpack/man.htmlhtml

CMinpack配置

從github中clone下來源文件，進入目錄後新建build，使用cmake對上一層目錄內容進行編譯configure->generate。git

命令行不熟練可使用cmake-gui指令，須要選中examples選項纔會對樣例進行編譯。github

完成後進入build/examples目錄，執行make命令，能夠看到已經生成可執行文件，運行其中任意程序進行測試。算法

再進入到build/cmake目錄，執行make命令和make install命令，將cminpack.pc安裝到指定目錄（個人電腦上安裝到了/usr/local/lib64/pkgconfig），最後將這個目錄經過/etc/profile添加到pkg的路徑當中（別忘了source運行一下）。在命令行中輸入pkg-config opencv –libs –cflags ，若是可以顯示路徑則成功。 [NOTE] 我對pkg-config的使用並非很瞭解，是模仿着opencv進行配置的。數組

CMake相關詳解

[NOTE] 所以本身對CMake使用還很不熟練，所以找機會對CMakeList.txt進行學習。緩存

${CMINPACK_SOURCE_DIR}/CMakeList.txt

# 由於Markdown沒有支持CMakeList.txt的高亮，所以用Makefile的高亮將就一下。

# The name of our project is "CMINPACK". CMakeLists files in this project can
# refer to the root source directory of the project as ${CMINPACK_SOURCE_DIR} and
# to the root binary directory of the project as ${CMINPACK_BINARY_DIR}.
# CMINPACK_SOURCE_DIR: CMinpack源代碼的根目錄
# CMINPACK_BINARY_DIR: CMinpack二進制文件的根目錄

# 要求的最小CMake版本號
cmake_minimum_required (VERSION 2.6)

# 項目名稱：CMINPACK
project (CMINPACK)

# PROJECT_NAME: CMINPACK
# PROJECT_NAME_LOWER: cminpack
string(TOLOWER ${PROJECT_NAME} PROJECT_NAME_LOWER)

# include其餘CMake命令
# 在cminpack_utils.cmake這個文件中定義了GET_OS_INFO和DISSECT_VERSION兩個宏指令，後面進行詳細介紹。
include(${PROJECT_SOURCE_DIR}/cmake/cminpack_utils.cmake)
# Set version and OS-specific settings
# CACHE: 緩存到本地文件
set(CMINPACK_VERSION 1.3.6 CACHE STRING "CMinpack version")
set(CMINPACK_SOVERSION 1 CACHE STRING "CMinpack API version")
# 在cminpack_utils.cmake中定義的兩個宏
DISSECT_VERSION()
GET_OS_INFO()

# Add an "uninstall" target
# CONFIGURE_FILE: 讓普通文件也能使用CMake中的變量
# 輸入文件: uninstall_target.cmake.in
# 輸出文件: uninstall_target.cmake
# IMMEDIATE: 暫時沒找到意思
# @ONLY: 限制只替換被@VAR@引用的變量（${VAR}格式的變量不會被替換）
CONFIGURE_FILE ("${PROJECT_SOURCE_DIR}/cmake/uninstall_target.cmake.in" "${PROJECT_BINARY_DIR}/uninstall_target.cmake" IMMEDIATE @ONLY)

# ADD_CUSTOM_TARGET: 增長一個沒有輸出的目標，使得它老是被構建
# CMAKE_COMMAND: 指向CMake可執行文件的完整路徑
ADD_CUSTOM_TARGET (uninstall "${CMAKE_COMMAND}" -P "${PROJECT_BINARY_DIR}/uninstall_target.cmake")

# 須要注意，ctest指望在build目錄下找到測試文件。
enable_testing()

if (OS_LINUX OR ${CMAKE_SYSTEM_NAME} STREQUAL "FreeBSD")
  option (USE_FPIC "Use the -fPIC compiler flag." ON)
else (OS_LINUX)
  option (USE_FPIC "Use the -fPIC compiler flag." OFF)
endif (OS_LINUX)

# 生成SHARED庫的選項
option (BUILD_SHARED_LIBS "Build shared libraries instead of static." OFF)
if (BUILD_SHARED_LIBS)
  message (STATUS "Building shared libraries.")
else ()
  message (STATUS "Building static libraries.")
  set(CMAKE_RELEASE_POSTFIX _s)
  set(CMAKE_RELWITHDEBINFO_POSTFIX _s)
  set(CMAKE_DEBUG_POSTFIX _s)
  set(CMAKE_MINSIZEREL_POSTFIX _s)
  if(WIN32)
    add_definitions(-DCMINPACK_NO_DLL)
  endif(WIN32)
endif ()

option(USE_BLAS "Compile cminpack using a blas library if possible" ON)

#set(CMAKE_INSTALL_PREFIX ${PROJECT_SOURCE_DIR}/../build)

# 添加頭文件目錄
if(NOT "${CMAKE_PREFIX_PATH}" STREQUAL "")
  include_directories(${CMAKE_PREFIX_PATH}/include)
endif()

# cminpack_srcs: 源代碼文件
set (cminpack_srcs
  cminpack.h cminpackP.h
  chkder.c  enorm.c   hybrd1.c  hybrj.c   lmdif1.c  lmstr1.c  qrfac.c   r1updt.c
  dogleg.c  fdjac1.c  hybrd.c   lmder1.c  lmdif.c   lmstr.c   qrsolv.c  rwupdt.c
  dpmpar.c  fdjac2.c  hybrj1.c  lmder.c   lmpar.c   qform.c   r1mpyq.c  covar.c covar1.c
  minpack.h
  chkder_.c enorm_.c  hybrd1_.c hybrj_.c  lmdif1_.c lmstr1_.c qrfac_.c  r1updt_.c
  dogleg_.c fdjac1_.c hybrd_.c  lmder1_.c lmdif_.c  lmstr_.c  qrsolv_.c rwupdt_.c
  dpmpar_.c fdjac2_.c hybrj1_.c lmder_.c  lmpar_.c  qform_.c  r1mpyq_.c covar_.c
  )
# cminpack_hdrs: 頭文件
set (cminpack_hdrs
    cminpack.h minpack.h)

# 添加一個名爲cminpack的庫
add_library (cminpack ${cminpack_srcs})

if (${CMAKE_SYSTEM_NAME} STREQUAL "FreeBSD")
  TARGET_LINK_LIBRARIES(cminpack m)
endif()

# Link with a BLAS library if requested
if (USE_BLAS)
  if (NOT BUILD_SHARED_LIBS)
    set(BLA_STATIC True)
  endif()
  find_package(BLAS)
  if (BLAS_FOUND)
    target_link_libraries(cminpack PUBLIC ${BLAS_LIBRARIES})
    set_target_properties(cminpack PROPERTIES LINK_FLAGS "${BLAS_LINKER_FLAGS}")
    target_compile_definitions(cminpack PUBLIC -DUSE_CBLAS)
  endif()
endif()

# install: 爲工程生成安裝規則
# TARGETS版本的install命令
install (TARGETS cminpack
   # 模塊庫
   LIBRARY DESTINATION ${CMINPACK_LIB_INSTALL_DIR} COMPONENT library
   # 靜態連接的庫文件
   ARCHIVE DESTINATION ${CMINPACK_LIB_INSTALL_DIR} COMPONENT library
   # 動態庫
   RUNTIME DESTINATION bin COMPONENT library)
# FILES版本的install命令
# 以相對路徑方式給出的文件名是相對當前源代碼路徑而言的，默認具備OWNER_WRITE, OWNER_READ, GROUP_READ和WORLD_READ權限
install (FILES ${cminpack_hdrs} DESTINATION ${CMINPACK_INCLUDE_INSTALL_DIR}
    COMPONENT cminpack_hdrs)

if (USE_FPIC AND NOT BUILD_SHARED_LIBS)
  set_target_properties (cminpack PROPERTIES COMPILE_FLAGS -fPIC)
endif ()

set_target_properties(cminpack PROPERTIES VERSION ${CMINPACK_VERSION} SOVERSION ${CMINPACK_SOVERSION})

# add_subdirectory: 添加子項目
add_subdirectory (cmake)
add_subdirectory (examples)

${CMINPACK_SOURCE_DIR}/cmake/cminpack_utils.cmake

# 獲取系統信息，設置安裝位置
macro(GET_OS_INFO)
    # string(REGEX MATCH 正則表達 輸出變量 )
    string(REGEX MATCH "Linux" OS_LINUX ${CMAKE_SYSTEM_NAME})
    string(REGEX MATCH "BSD" OS_BSD ${CMAKE_SYSTEM_NAME})
    if(WIN32)
        set(OS_WIN TRUE)
    endif(WIN32)

    if(NOT DEFINED CMINPACK_LIB_INSTALL_DIR)
    set(CMINPACK_LIB_INSTALL_DIR "lib")
    if(OS_LINUX)
        if(${CMAKE_SYSTEM_PROCESSOR} STREQUAL "x86_64")
            set(CMINPACK_LIB_INSTALL_DIR "lib64")
        else(${CMAKE_SYSTEM_PROCESSOR} STREQUAL "x86_64")
            set(CMINPACK_LIB_INSTALL_DIR "lib")
        endif(${CMAKE_SYSTEM_PROCESSOR} STREQUAL "x86_64")
        message (STATUS "Operating system is Linux")
    elseif(OS_BSD)
        message (STATUS "Operating system is BSD")
    elseif(OS_WIN)
        message (STATUS "Operating system is Windows")
    else(OS_LINUX)
        message (STATUS "Operating system is generic Unix")
    endif(OS_LINUX)
    endif(NOT DEFINED CMINPACK_LIB_INSTALL_DIR)
    # 好比/usr/local/include/cminpack-1
    set(CMINPACK_INCLUDE_INSTALL_DIR "include/${PROJECT_NAME_LOWER}-${CMINPACK_MAJOR_VERSION}")
endmacro(GET_OS_INFO)

# 解剖CMinpack版本號
macro(DISSECT_VERSION)
    # Find version components
    string(REGEX REPLACE "^([0-9]+).*" "\\1"
        CMINPACK_MAJOR_VERSION "${CMINPACK_VERSION}")
    string(REGEX REPLACE "^[0-9]+\\.([0-9]+).*" "\\1"
        CMINPACK_MINOR_VERSION "${CMINPACK_VERSION}")
    string(REGEX REPLACE "^[0-9]+\\.[0-9]+\\.([0-9]+)" "\\1"
        CMINPACK_REVISION_VERSION ${CMINPACK_VERSION})
    string(REGEX REPLACE "^[0-9]+\\.[0-9]+\\.[0-9]+(.*)" "\\1"
        CMINPACK_CANDIDATE_VERSION ${CMINPACK_VERSION})
endmacro(DISSECT_VERSION)

${CMINPACK_SOURCE_DIR}/examples/CMakeLists.txt

# 可選項
# option (選項名 "選項註釋" 默認內容)
option (BUILD_EXAMPLES "Build the examples and tests." ON)
option (BUILD_EXAMPLES_FORTRAN "Build the FORTRAN examples and tests." OFF)

if (BUILD_EXAMPLES)
  # Make sure the compiler can find include files from our cminpack library.
  include_directories (${CMINPACK_SOURCE_DIR})

  # Make sure the linker can find the cminpack library once it is built.
  link_directories (${CMINPACK_BINARY_DIR})

  # 設置變量內容
  # set(變量 內容)
  set (FPGM tchkder thybrd thybrd1 thybrj thybrj1 tlmder tlmder1 tlmdif tlmdif1 tlmstr tlmstr1)
  set (CPGM ${FPGM} tfdjac2)

  # cmpfile: 用於一行行地比較兩個文件的異同
  # cmpfiles could be used by runtest.cmake... for now it's unused
  # add_executable(可執行文件名稱 源文件)
  add_executable (cmpfiles cmpfiles.c)

  # inspired by http://www.netlib.org/clapack/clapack-3.2.1-CMAKE/TESTING/CMakeLists.txt
  # except that here we have to compare the output to a reference
  # 測試部分跳過不看
  macro(add_minpack_test testname reference)
    set(TEST_OUTPUT "${CMINPACK_BINARY_DIR}/examples/${testname}.out")
    set(TEST_REFERENCE "${CMINPACK_SOURCE_DIR}/examples/ref/${reference}.ref")
    get_target_property(TEST_LOC ${testname} LOCATION)
    add_test(${testname} "${CMAKE_COMMAND}"
      -DTEST=${TEST_LOC}
      -DOUTPUT=${TEST_OUTPUT} 
      -DREFERENCE=${TEST_REFERENCE} 
      -DINTDIR=${CMAKE_CFG_INTDIR}
      -P "${CMINPACK_SOURCE_DIR}/examples/runtest.cmake")
  endmacro(add_minpack_test)

  # 遍歷處理每個目標文件
  foreach (source ${CPGM})
    add_executable (${source}_ ${source}_.c)
    target_link_libraries (${source}_ cminpack)
    if (OS_LINUX)
      target_link_libraries (${source}_ m)
    endif (OS_LINUX)
    add_minpack_test(${source}_ ${source}c)
    add_executable (${source}c ${source}c.c)
    target_link_libraries (${source}c cminpack)
    if (OS_LINUX)
      target_link_libraries (${source}c m)
    endif (OS_LINUX)
    add_minpack_test(${source}c ${source}c)
  endforeach(source)
endif (BUILD_EXAMPLES)

# FORTRAN部分跳過不看

第一個CMinpack程序

根據咱們閱讀給出的測試樣例的CMake相關文件，咱們能夠開始動手寫本身的第一個CMinpack程序。新建目錄，目錄下放着咱們要運行的使用了CMinpack的程序my-cminpack-demo.c。開始編寫CMakeLists.txt文件，首先提取出咱們須要的內容：app

project(my-cminpack-demo)
cmake_minimum_required (VERSION 2.6)

include_directories (${CMINPACK_SOURCE_DIR})
link_directories (${CMINPACK_BINARY_DIR})

add_executable (my-cminpack-demo my-cminpack-demo.c)
target_link_libraries (my-cminpack-demo cminpack)
if (OS_LINUX)
  target_link_libraries (my-cminpack-demo m)
endif (OS_LINUX)

而後新建build目錄，在build目錄下運行cmake .. 發現會跳出找不到sqrt函數的錯誤，這個咱們可以一會兒聯想到是Linux系統下沒有鏈接到m庫文件的緣由。雖然我不知道這個判斷爲何沒法執行，可是咱們已知在Linux環境下，把它去掉。獲得最終的CMakeLists.txt：less

project(my-cminpack-demo)
cmake_minimum_required (VERSION 2.6)

include_directories (${CMINPACK_SOURCE_DIR})
link_directories (${CMINPACK_BINARY_DIR})

add_executable (my-cminpack-demo my-cminpack-demo.c)
target_link_libraries (my-cminpack-demo cminpack)
target_link_libraries (my-cminpack-demo m)

雖然咱們make獲得可執行文件，運行後查看結果（圖中我使用了tlmdif_.c做爲測試） ide

LMDIF使用說明

官方英文介紹：http://devernay.github.io/cminpack/lmdif_.html函數

包括函數名

lmdif, lmdif1_ - 最小化非線性函數平方和

函數概要

include <minpack.h>
void lmdif1_(void (*fcn)(int *m, int *n, double *x, double *fvec, int *iflag),
    int *m, int *n, double *x, double *fvec,
    double *tol, int *info, int *iwa, double *wa, int *lwa);


void lmdif_(void (*fcn)(int *m, int *n, double *x,  double *fvec, int *iflag),
            int *m, int *n, double *x, double *fvec,
            double *ftol, double *xtol, double *gtol, int *maxfev, double *epsfcn, double *diag, 
            int *mode, double *factor, int *nprint, int *info, int *nfev, double *fjac,
            int *ldfjac, int *ipvt, double *qtf,
            double *wa1, double *wa2, double *wa3, double *wa4 );

詳細描述

lmdif_的目的是最小化m個n元非線性方程的平方和，使用的方法是LM算法的改進。用戶須要提供計算方程的子程序。Jacobian矩陣會經過一個前向差分（forward-difference）近似計算獲得。 lmdif1_是相同的目的，可是調用方法更簡單一些。

語言備註

這些函數是經過FORTRAN寫的，若是從C調用，須要記住如下幾點：

名稱重編：
- 2.95/3.0版本的g77下，全部函數如下劃線結尾，後續版本可能會更改；
使用g77編譯：
- 即便你的程序所有用C語言寫成，你也須要使用gcc進行連接，由於這樣它會自動導入FORTRAN庫。只使用g77進行編譯是最方便的（它處理C語言也是OK的）；
經過引用調用：
- 全部函數參數都是指針；
列優先數組：
- z( i , j ) = z[ ( i - 1 ) + ( j - 1 ) * n
- fcn是用戶提供用於計算函數的子程序。在C語言當中fcn須要以下定義：

void fcn(int m, int n, double *x, double *fvec, int *iflag) {
    /* 計算函數在x點的值，經過fvec返回。*/
}

iflag的值不能被fcn所修改，除非用戶想要終止lmdif/lmdif1_。在這個例子中iflag設置爲負整數。

lmdif_和lmdif1_的共同參數

m：函數個數； n：變量個數（n<=m） x：長度爲n的數組，設置爲初始的估計解向量。輸出的時候x內容爲最終估計的解向量。 fvec：輸出長度爲m的數組，內容爲最終輸出x計算獲得的函數解。

lmdif1_的參數

tol：做爲輸入，非負數。用於函數終止的條件判斷：

平方和小於tol；
x之間的相對偏差小於tol；

info：做爲輸出。若是用戶終止了函數的執行，info將被設置爲iflag的值（負數）（詳細見fcn的描述），不然，info的值以下幾種狀況：

0：輸入參數不合適；
1：平方和的相對偏差小於tol；
2：x之間的相對偏差小於tol；
3：1/2兩種狀況同時符合；
4： fvec is orthogonal to the columns of the Jacobian to machine precision（這個狀況是什麼暫時不是很清楚）
5：調用fcn的次數達到了200*(n+1)次；
6：tol設置太小，平方和沒法達到那麼小；
7：tol設置太小，x的近似解沒法優化到偏差達到那麼小。

iwa：長度n的工做數組； wa：長度lwa的工做數組； lwa：做爲輸入，整數，不能小於mn+5n+m； [NOTE] 這三個輸入我也不知道做用，從樣例來看不須要初始化。

lmdif_的參數

暫時不用這部分，跳過。

官方樣例解讀

源碼： https://github.com/devernay/cminpack/blob/d1f5f5a273862ca1bbcf58394e4ac060d9e22c76/examples/tlmdif1_.c

/*     lmdif1 例子. */
#include <stdio.h>
#include <math.h>
#include <assert.h>
#include <minpack.h>
#define real __minpack_real__

// 用戶自定義的函數f()
// real -> __cminpack_real__ -> 浮點數(double)
void fcn(const int *m, const int *n, const real *x, real *fvec, int *iflag);

int main()
{
  int j, m, n, info, lwa, iwa[3], one=1;
  real tol, fnorm, x[3], fvec[15], wa[75];

  // 函數個數15; 變量數3
  m = 15;
  n = 3;

  // 初始位置作粗略估計
  // 1.e0 = 1.0e0 = 1.0
  x[0] = 1.e0;
  x[1] = 1.e0;
  x[2] = 1.e0;

  // 爲何要設置75?
  lwa = 75;

  /* set tol to the square root of the machine precision.  unless high
     precision solutions are required, this is the recommended
     setting. */
  // (建議打印一下看值是多少)

  tol = sqrt(__minpack_func__(dpmpar)(&one));

  // 須要注意指針
  __minpack_func__(lmdif1)(&fcn, &m, &n, x, fvec, &tol, &info, iwa, wa, &lwa);

  // 最終的2範數(即平方和開根號)
  fnorm = __minpack_func__(enorm)(&m, fvec);
  printf("      final l2 norm of the residuals%15.7g\n\n", (double)fnorm);
  printf("      exit parameter                %10i\n\n", info);
  printf("      final approximate solution\n");
  for (j=1; j<=n; j++) {
    printf("%s%15.7g", j%3==1?"\n ":"", (double)x[j-1]);
  }
  printf("\n");
  return 0;
}

//        The problem is to determine the values of x(1), x(2), and x(3)
//        which provide the best fit (in the least squares sense) of
//              x(1) + u(i)/(v(i)*x(2) + w(i)*x(3)),  i = 1, 15
//        to the data
//              y = (0.14,0.18,0.22,0.25,0.29,0.32,0.35,0.39,
//                   0.37,0.58,0.73,0.96,1.34,2.10,4.39),
//        where u(i) = i, v(i) = 16 - i, and w(i) = min(u(i),v(i)).  The
//        i-th component of FVEC is thus defined by
//              y(i) - (x(1) + u(i)/(v(i)*x(2) + w(i)*x(3))).

void fcn(const int *m, const int *n, const real *x, real *fvec, int *iflag)
{
  /* function fcn for lmdif1 example */

  int i;
  real tmp1,tmp2,tmp3;

  // 實際的y值
  real y[15]={1.4e-1,1.8e-1,2.2e-1,2.5e-1,2.9e-1,3.2e-1,3.5e-1,3.9e-1,
              3.7e-1,5.8e-1,7.3e-1,9.6e-1,1.34e0,2.1e0,4.39e0};
  assert(*m == 15 && *n == 3);


  if (*iflag == 0) {
    /*      insert print statements here when nprint is positive. */
    /* if the nprint parameter to lmder is positive, the function is
       called every nprint iterations with iflag=0, so that the
       function may perform special operations, such as printing
       residuals. */
    // 這段沒有很看懂，在??狀況下打印信息
    return;
  }

  /* compute residuals */

  for (i=0; i<15; i++) {
    tmp1 = i+1;
    tmp2 = 15 - i;
    tmp3 = tmp1;
    if (i >= 8) {
      tmp3 = tmp2;
    }
    fvec[i] = y[i] - (x[0] + tmp1/(x[1]*tmp2 + x[2]*tmp3));
  }
}

[NOTE] 其餘內容有待更新

原文出處：https://www.cnblogs.com/bemfoo/p/11203993.html