initial upload

archive/sh2xyz/.gitignore

@@ -0,0 +1,36 @@
+# Prerequisites
+*.d
+
+# Compiled Object files
+*.slo
+*.lo
+*.o
+*.obj
+
+# Precompiled Headers
+*.gch
+*.pch
+
+# Compiled Dynamic libraries
+*.so
+*.dylib
+*.dll
+
+# Fortran module files
+*.mod
+*.smod
+
+# Compiled Static libraries
+*.lai
+*.la
+*.a
+*.lib
+
+# Executables
+*.exe
+*.out
+*.app
+*.ex
+
+# Pdf documents
+*.pdf

archive/sh2xyz/CMakeLists.txt

@@ -0,0 +1,21 @@
+#Uncomment the following two lines to compile the sources as an individual cmake porject. Change the <project_name> as you wanted.
+#cmake_minimum_required(VERSION 3.15.2)
+#project(<project_name>)
+
+#Set executable name here
+set(name sh2xyz)
+
+aux_source_directory(. "${name}_src")
+add_executable(${name} ${${name}_src})
+set_target_properties(${name} PROPERTIES CXX_STANDARD 11)
+set(EXECUTABLE_OUTPUT_PATH ${PROJECT_BINARY_DIR}/bin)
+install(TARGETS ${name} RUNTIME DESTINATION sbin)
+
+#Find and link openmp library
+find_package(OpenMP REQUIRED)
+if (OpenMP_CXX_FOUND)
+	set (CMAKE_CXX_FLAGS "${CMAKE_CXX_FLAGS} ${OpenMP_CXX_FLAGS}")
+	set (CMAKE_EXE_LINKER_FLAGS "${CMAKE_EXE_LINKER_FLAGS} ${OpenMP_EXE_LINKER_FLAGS}")
+endif()
+
+target_link_libraries(${name} PUBLIC OpenMP::OpenMP_CXX)

archive/sh2xyz/NALF-SFCM.h

@@ -0,0 +1,143 @@
+// Fully normalized associated Legendre functions calculated by standard forward column methods
+// Holmes, S. A., & Featherstone, W. E. (2002).
+// A unified approach to the Clenshaw summation and the recursive computation of very high degree and order normalised associated Legendre functions.
+// Journal of Geodesy, 76(5), 279–299. https://doi.org/10.1007/s00190-002-0216-2
+// Author: Yi Zhang (zhangyi.cugwuhan@gmail.com)
+#ifndef _NALF_SFCM_H
+#define _NALF_SFCM_H
+#include "sysDefine.h"
+//计算向前列推的系数 避免重复计算 这里不要使用vector at() 速度比较慢 直接使用[] 注意调用size()函数也会降低执行效率
+_2dArray get_a_nm_array(int MaxOrder)
+{
+	int i,j;
+	_2dArray cs;
+	cs.resize(MaxOrder);
+	for (i = 0; i < MaxOrder; i++)
+		cs[i].resize(i+1);
+	//向下列推计算
+#pragma omp parallel for private(i,j) schedule(guided)
+	for (j = 0; j < MaxOrder; j++)
+	{
+		cs[j][j] = 0; //对角线上的值直接给0 反正用不到
+		for (i = j+1; i < MaxOrder; i++)
+		{
+			cs[i][j] = sqrt(((2.0*i-1)*(2.0*i+1))/((i-j)*(i+j)));
+		}
+	}
+	return cs;
+}
+
+_2dArray get_b_nm_array(int MaxOrder)
+{
+	int i,j;
+	_2dArray cs;
+	cs.resize(MaxOrder);
+	for (i = 0; i < MaxOrder; i++)
+		cs[i].resize(i+1);
+	//向下列推计算
+#pragma omp parallel for private(i,j) schedule(guided)
+	for (j = 0; j < MaxOrder; j++)
+	{
+		cs[j][j] = 0; //对角线上的值直接给0 反正用不到
+		for (i = j+1; i < MaxOrder; i++)
+		{
+			cs[i][j] = sqrt(((2.0*i+1)*(i+j-1)*(i-j-1))/((i-j)*(i+j)*(2.0*i-3)));
+		}
+	}
+	return cs;
+}
+
+// 计算标准前向列推法计算规格化的勒让德多项式 输入参数为需要计算的最大阶次MaxOrder 余纬度theta(度) 返回一个下半三角二维数组
+// 最大维度为MaxOrder+1，二维数组中行数代表阶数列数为次数
+_2dArray NALF_SFCM(int MaxOrder,_2dArray a_nm,_2dArray b_nm,double theta)
+{
+	//声明数组 初始化一个下半三角二维数组
+	_2dArray nalf;
+	nalf.resize(MaxOrder);
+	for (int i = 0; i < MaxOrder; i++)
+		nalf.at(i).resize(i+1);
+
+	//赋初值给前两个对角线上的值
+	nalf.at(0).at(0) = 1.0;
+	nalf.at(1).at(1) = sqrt(3.0)*sin(theta*pi/180.0);
+	//计算对角线上的值 递归计算 不能并行
+	for (int i = 2; i < nalf.size(); i++)
+		nalf.at(i).at(i) = sin(theta*pi/180.0)*sqrt(0.5*(2.0*i+1)/i)*nalf.at(i-1).at(i-1);
+
+	//声明系数和迭代变量
+	int i,j;
+	double Pn_2m,Pn_1m; //Pn-1,m Pn-2,m
+	//这里可以使用并行加速计算外层循环 内层计算因为是递归计算因此不能并行
+#pragma omp parallel for private(i,j,Pn_2m,Pn_1m) schedule(guided)
+	for (j = 0; j < nalf.size()-1; j++)
+	{
+		Pn_2m = 0;
+		Pn_1m = nalf.at(j).at(j);
+		for (i = j+1; i < nalf.size(); i++)
+		{
+			nalf.at(i).at(j) = a_nm.at(i).at(j)*cos(theta*pi/180.0)*Pn_1m - b_nm.at(i).at(j)*Pn_2m;
+
+			Pn_2m = nalf.at(i-1).at(j);
+			Pn_1m = nalf.at(i).at(j);
+		}
+	}
+	return nalf;
+}
+
+// 计算标准前向列推法计算规格化的勒让德多项式 输入参数 一个下半三角二维矩阵 余纬度theta(度) 无返回值
+// 二维数组中行数代表阶数列数为次数
+void NALF_SFCM2(_2dArray& nalf,_2dArray a_nm,_2dArray b_nm,double theta)
+{
+	//赋初值给前两个对角线上的值
+	nalf.at(0).at(0) = 1.0;
+	nalf.at(1).at(1) = sqrt(3.0)*sin(theta*pi/180.0);
+	//计算对角线上的值 递归计算 不能并行
+	for (int i = 2; i < nalf.size(); i++)
+		nalf.at(i).at(i) = sin(theta*pi/180.0)*sqrt(0.5*(2.0*i+1)/i)*nalf.at(i-1).at(i-1);
+
+	//声明系数和迭代变量
+	int i,j;
+	double Pn_2m,Pn_1m; //Pn-1,m Pn-2,m
+	//这里可以使用并行加速计算外层循环 内层计算因为是递归计算因此不能并行
+#pragma omp parallel for private(i,j,Pn_2m,Pn_1m) schedule(guided)
+	for (j = 0; j < nalf.size()-1; j++)
+	{
+		Pn_2m = 0;
+		Pn_1m = nalf.at(j).at(j);
+		for (i = j+1; i < nalf.size(); i++)
+		{
+			nalf.at(i).at(j) = a_nm.at(i).at(j)*cos(theta*pi/180.0)*Pn_1m - b_nm.at(i).at(j)*Pn_2m;
+
+			Pn_2m = nalf.at(i-1).at(j);
+			Pn_1m = nalf.at(i).at(j);
+		}
+	}
+}
+
+void NALF_SFCM3(_2dArray& nalf,_2dArray a_nm,_2dArray b_nm,int maxOrder,double theta,double norSum)
+{
+	//赋初值给前两个对角线上的值
+	//norSum为1时第一个值为1/sqrt(4.0*pi),归一化值为1, norSum为4.0*pi时第一个值为4.0*pi/sqrt(4.0*pi)=1,归一化值为4.0*pi
+	nalf[0][0] = sqrt(norSum)/sqrt(4.0*pi);
+	nalf[1][1] = sqrt(3.0)*sin(theta*pi/180.0);
+	//计算对角线上的值 递归计算 不能并行
+	for (int i = 2; i < maxOrder; i++)
+		nalf[i][i] = sin(theta*pi/180.0)*sqrt(0.5*(2.0*i+1)/i)*nalf[i-1][i-1];
+
+	//计算次对角线(m+1,m)上的值 递归计算 不能并行
+	for (int i = 0; i < maxOrder-1; i++)
+		nalf[i+1][i] = cos(theta*pi/180.0)*sqrt(2.0*i+3)*nalf[i][i];
+
+	//声明系数和迭代变量
+	int i,j;
+	//这里可以使用并行加速计算外层循环 内层计算因为是递归计算因此不能并行
+#pragma omp parallel for private(i,j) schedule(guided)
+	for (j = 0; j < maxOrder-1; j++)
+	{
+		for (i = j+2; i < maxOrder; i++)
+		{
+			nalf[i][j] = a_nm[i][j]*cos(theta*pi/180.0)*nalf[i-1][j] - b_nm[i][j]*nalf[i-2][j];
+		}
+	}
+}
+#endif

archive/sh2xyz/README.md

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+## Forward calculation of topographic or gravitational data using spherical harmonic coefficients
+
+### Introduction
+
+### Files and folders
+
+1. **CMakeLists.txt** CMake project file;
+2. **\*.h and \*.cpp** Source files;
+3. **README.md** This file;
+4. **example** Example files.
+
+#### Source file lists
+
+```shell
+main.cpp
+NALF-SFCM.h
+progressBar_imp.h
+sh2xyz.h
+sysDefine.h
+```
+
+### Installation
+
+This program is a toolkit of a [software collection](https://gitee.com/yizhangss/toolkits) that is developed and maintained by Dr. Yi Zhang (zhangyiss@icloud.com) , which could be compiled and installed using the [CMake](https://cmake.org) software. Follow the three step instructions bellow, if you want to compile this program out of the collection.
+
+1. Uncomment the first two lines in the `CMakeLists.txt` file,
+
+```cmake
+cmake_minimum_required(VERSION 3.15.2)
+project(<project_name>)
+```
+
+1. Compile the program as
+
+```shell
+mkdir build && cd build && make
+```
+
+3. Move or symlink the executable file to any directory included in your $PATH, for instance, `/usr/local/bin`.
+
+### Usage
+
+```bash
+sph2xyz -t<table> -r<lonmin>/<lonmax>/<latmin>/<latmax>[/<altitude>] -i<dlon>/<dlat> -d<type> -f<ln>/<lm>/<hn>/<hm> [-p<loc-file>] [-s<refr>/<refR>] [-g<GM>/<R>] [-n<type>] [-c<col1>,<col2>,<col3>,<col4>] [-z<alti-file>[+d<col1>,<col2>,<col3>]] [-h] > out-file
+```
+
+#### Options
+
++ __-t__: Input filename of the coefficients.
++ __-r__: Initialize the range of observation points. Altitude of the points is optional (will be 0 if no set).
++ __-i__: Intervals of the observation points.
++ __-d__: Types of forward calculation.
++ __-f__: Starting and ending order/degree that will be used for calculation.
++ __-p__: Interpolate the forward calculated data to spherical locations read from the file.
++ __-s__: short and long semi-radius of the reference coordinate system.
++ __-g__: Model parameters of gravity models. This option must be set if we are calculating gravitational data.
++ __-n__: Normalization type of the Associated Legendre Function.
++ __-c__: Select input columns of the coefficients.
++ __-z__: Initialize the observation's altitudes from the a input file.   
++ __-h__: Show help information.
+
+### Examples
+
+To forward calculating an `example.SHcoeffs` which maximal degree/order are both 360.
+
+```bash
+sh2xyz -t example.SHcoeffs -r -180/180/-90/90/0 -i 0.5/0.5 -f 0/0/360/360 -s 10000/10000 > example.txt
+```
+
+The calculated data is shown as below:
+![sh2xyz example](example/example.png)

archive/sh2xyz/main.cpp

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+#include "sh2xyz.h"
+
+void disp_help()
+{
+	cout << "sh2xyz - v0.1 calculated spherical harmonic coefficients to table data" << endl
+		<< "Author: zhangyi.cugwuhan@gmail.com" << endl << endl
+		<< "usage: sh2xyz -t<table> -r<lonmin>/<lonmax>/<latmin>/<latmax>[/<altitude>] -i<dlon>/<dlat> -d<type> -f<ln>/<lm>/<hn>/<hm> [-p<loc-file>] [-s<refr>/<refR>] [-g<GM>/<R>] [-n<type>] [-c<col1>,<col2>,<col3>,<col4>] [-z<alti-file>[+d<col1>,<col2>,<col3>]] [-h] > out-file" << endl
+		<< "-t\tinput spherical harmonic coefficients, four columns are needed at least" << endl
+		<< "-r\tcalculation range" << endl
+		<< "-i\tcalculation intervals" << endl
+		<< "-d\tcalculation types, \n\tt for topography (default)\n\td for gravity disturbance\n\tg for gravity anomaly and\n\tp for geo-potential\n\tr for radial gravity gradient" << endl
+		<< "-s\treference system" << endl
+		<< "-p\tinterpolating locations indicated by a input file, every line of the file has a longitudinal and a latitudinal value" << endl
+		<< "-g\tGM and R parameters for gravitational data's calculation" << endl
+		<< "-n\tnormalized sum of associated Legendre functions\n\tm for mathematic normalization which equal 1\n\tg for geodetic normalization which equal 4*pi (default)" << endl
+		<< "-f\tstart and end orders and degrees used for calculation" << endl
+		<< "-c\tselect data columns of the input table data. the default is 0,1,2,3" << endl
+		<< "-z\tprovide a input file for observations' altitudes. use +d to select input data columns, the default is 0,1,2" << endl
+		<< "-h\tshow this info" << endl;
+}
+
+int main(int argc, char* argv[])
+{
+	char infilename[1024] = "NULL";
+	char interfilename[1024] = "NULL";
+	char range[1024] = "NULL";
+	char interval[1024] = "NULL";
+	char type[1024] = "t";
+	char referSystem[1024] = "NULL";
+	char coffPara[1024] = "NULL";
+	char columns[1024] = "0,1,2,3";
+	char gravPara[1024] = "NULL";
+	char norType[1024] = "g";
+	char altiFile[1024] = "NULL";
+
+	opterr = 0; //内置参数 若不为0则会在发生遭遇错误时输出一条信息到屏幕
+
+	int curr;
+	/*循环拾取参数 最后一个参数为-1 需要变量的参数后跟一个冒号 可有可无参数跟两个冒号*/
+	while((curr = getopt(argc,argv,"ht:r:i:s:f:c:d:g:n:p:z:")) != -1)
+	{
+		/*匹配命令*/
+		switch (curr)
+		{
+			case 'h': //显示帮助信息
+				disp_help();
+				break;
+			case 't':
+				if (1!=sscanf(optarg,"%s",infilename))
+				{
+					cout << "error ==> wrong format of " << optarg << endl;
+				}
+				break;
+			case 'r':
+				if (1!=sscanf(optarg,"%s",range))
+				{
+					cout << "error ==> wrong format of " << optarg << endl;
+				}
+				break;
+			case 'i':
+				if (1!=sscanf(optarg,"%s",interval))
+				{
+					cout << "error ==> wrong format of " << optarg << endl;
+				}
+				break;
+			case 'd':
+				if (1!=sscanf(optarg,"%s",type))
+				{
+					cout << "error ==> wrong format of " << optarg << endl;
+				}
+				break;
+			case 'p':
+				if (1!=sscanf(optarg,"%s",interfilename))
+				{
+					cout << "error ==> wrong format of " << optarg << endl;
+				}
+				break;
+			case 's':
+				if (1!=sscanf(optarg,"%s",referSystem))
+				{
+					cout << "error ==> wrong format of " << optarg << endl;
+				}
+				break;
+			case 'g':
+				if (1!=sscanf(optarg,"%s",gravPara))
+				{
+					cout << "error ==> wrong format of " << optarg << endl;
+				}
+				break;
+			case 'n':
+				if (1!=sscanf(optarg,"%s",norType))
+				{
+					cout << "error ==> wrong format of " << optarg << endl;
+				}
+				break;
+			case 'f':
+				if (1!=sscanf(optarg,"%s",coffPara))
+				{
+					cout << "error ==> wrong format of " << optarg << endl;
+				}
+				break;
+			case 'c':
+				if (1!=sscanf(optarg,"%s",columns))
+				{
+					cout << "error ==> wrong format of " << optarg << endl;
+				}
+				break;
+			case 'z':
+				if (1!=sscanf(optarg,"%s",altiFile))
+				{
+					cout << "error ==> wrong format of " << optarg << endl;
+				}
+				break;
+			case '?': //处理未定义或错误参数
+				if (optopt == 't' || optopt == 'r' || optopt == 'i' || optopt == 's' || optopt == 'f' || optopt == 'c' || optopt == 'p' || optopt == 'z')
+				{
+					fprintf (stderr, "Option -%c requires an argument.\n", optopt);
+					return -1;
+				}
+				else if (isprint(optopt))
+				{
+					fprintf (stderr, "Unknown option `-%c'.\n", optopt);
+					return -1;
+				}
+				else
+				{
+					fprintf (stderr,"Unknown option character `\\x%x'.\n",optopt);
+					return -1;
+				}
+				break;
+			default:
+				abort();
+		}
+	}
+
+	sh2xyz sx;
+	//读入球谐系数文件
+	if(sx.readSHC(infilename,coffPara,columns)) return 0;
+	//初始化观测点位置
+	if(sx.initObs(range,interval,referSystem)) return 0;
+	//重定位观测点高程
+	if(sx.relocateAltitude(altiFile)) return 0;
+	//初始化矩阵
+	sx.initMatrix(type,gravPara,norType,altiFile);
+	//计算
+	if (!strcmp(altiFile,"NULL"))
+	{
+		sx.calSolution();
+	}
+	else sx.calSolution2(type);
+	//输出
+	sx.outObs(interfilename);
+	return 0;
+}

archive/sh2xyz/makefile

@@ -0,0 +1,15 @@
+CC = g++-8
+PROM = /usr/local/sbin/sh2xyz
+CFLAGS = -I.
+DEPS = $(shell find . -name "*.h")
+SRC = $(shell find . -name "*.cpp")
+OBJ = $(SRC:%.cpp=%.o)
+
+$(PROM): $(OBJ)
+	$(CC) -o $(PROM) $(OBJ) $(CFLAGS) -fopenmp -O2
+
+%.o:%.cpp $(DEPS)
+	$(CC) -c $< -o $@ $(CFLAGS) -fopenmp -O2
+
+clean:
+	rm -rf $(OBJ)

archive/sh2xyz/progressBar_imp.h

@@ -0,0 +1,154 @@
+#ifndef _PROGRESS_BAR_
+#define _PROGRESS_BAR_
+
+//#ifdef _WINDOWS
+//#include <windows.h>
+//#else
+//#include <sys/ioctl.h>
+//#endif
+
+#include <sys/ioctl.h>
+#include <iostream>
+#include <iomanip>
+#include <cstring>
+#include <thread>
+#include <chrono>
+
+#define TOTAL_PERCENTAGE 100.0
+#define CHARACTER_WIDTH_PERCENTAGE 4
+
+class ProgressBar
+{
+public: 
+
+    ProgressBar();
+    ProgressBar(unsigned long n_, const char *description_="", std::ostream& out_=std::cerr);
+
+    void SetFrequencyUpdate(unsigned long frequency_update_);
+    void SetStyle(const char* unit_bar_, const char* unit_space_);		
+
+    void Progressed(unsigned long idx_);
+
+private:
+	
+    unsigned long n;
+    unsigned int desc_width;
+    unsigned long frequency_update;
+    std::ostream* out;
+		
+    const char *description;
+    const char *unit_bar;
+    const char *unit_space;
+		
+    void ClearBarField();
+    int GetConsoleWidth();
+    int GetBarLength();
+
+};
+
+ProgressBar::ProgressBar() {}
+
+ProgressBar::ProgressBar(unsigned long n_, const char* description_, std::ostream& out_){
+    
+    n = n_;
+    frequency_update = n_;
+    description = description_;
+    out = &out_;
+    
+    unit_bar = "\u2588";
+    unit_space = "-";
+    desc_width = std::strlen(description);  // character width of description field
+
+}
+
+void ProgressBar::SetFrequencyUpdate(unsigned long frequency_update_){
+    
+    if(frequency_update_ > n){
+        frequency_update = n;    // prevents crash if freq_updates_ > n_
+    }
+    else{
+        frequency_update = frequency_update_;
+    }
+}
+
+void ProgressBar::SetStyle(const char* unit_bar_, const char* unit_space_){
+    
+    unit_bar = unit_bar_;
+    unit_space = unit_space_;
+}
+
+int ProgressBar::GetConsoleWidth(){
+
+    int width;
+
+    #ifdef _WINDOWS
+        CONSOLE_SCREEN_BUFFER_INFO csbi;
+        GetConsoleScreenBufferInfo(GetStdHandle(STD_OUTPUT_HANDLE), &csbi);
+        width = csbi.srWindow.Right - csbi.srWindow.Left;
+    #else
+        struct winsize win;
+        ioctl(0, TIOCGWINSZ, &win);
+        width = win.ws_col;
+    #endif
+
+    return width;
+}
+
+int ProgressBar::GetBarLength(){
+
+    // get console width and according adjust the length of the progress bar
+
+    int bar_length = static_cast<int>((GetConsoleWidth() - desc_width - CHARACTER_WIDTH_PERCENTAGE) / 2.);
+
+    return bar_length;
+}
+
+void ProgressBar::ClearBarField(){
+
+    for(int i=0;i<GetConsoleWidth();++i){
+        *out << " ";
+    }
+    *out << "\r" << std::flush;
+}
+
+void ProgressBar::Progressed(unsigned long idx_)
+{
+    try{
+        if(idx_ > n) throw idx_;
+
+        // determines whether to update the progress bar from frequency_update
+        if ((idx_ != n-1) && ((idx_+1) % (n/frequency_update) != 0)) return;
+
+        // calculate the size of the progress bar
+        int bar_size = GetBarLength();
+    
+        // calculate percentage of progress
+        double progress_percent = idx_* TOTAL_PERCENTAGE/(n-1);
+
+        // calculate the percentage value of a unit bar 
+        double percent_per_unit_bar = TOTAL_PERCENTAGE/bar_size;
+
+        // display progress bar
+        *out << " " << description << " |";
+
+        for(int bar_length=0;bar_length<=bar_size-1;++bar_length){
+            if(bar_length*percent_per_unit_bar<progress_percent){
+                *out << unit_bar;
+            }
+            else{
+                *out << unit_space;
+            }
+        }
+
+        if(idx_ == n-1)
+            *out << "|" << std::setw(CHARACTER_WIDTH_PERCENTAGE + 1) << std::setprecision(1) << std::fixed << progress_percent << "%\r" << std::flush << std::endl;
+        else *out << "|" << std::setw(CHARACTER_WIDTH_PERCENTAGE + 1) << std::setprecision(1) << std::fixed << progress_percent << "%\r" << std::flush;
+    }
+    catch(unsigned long e){
+        ClearBarField();
+        std::cerr << "PROGRESS_BAR_EXCEPTION: _idx (" << e << ") went out of bounds, greater than n (" << n << ")." << std::endl << std::flush;
+    }
+
+}
+
+#endif

archive/sh2xyz/sh2xyz.h

@@ -0,0 +1,535 @@
+#ifndef _FUNC_H
+#define _FUNC_H
+#include "sysDefine.h"
+#include "NALF-SFCM.h"
+#include "progressBar_imp.h"
+// 命令规则 n为阶数 m为次数
+class sh2xyz
+{
+public:
+	sh2xyz(){}
+	~sh2xyz(){}
+	int readSHC(char*,char*,char*); //读入球谐系数
+	int initMatrix(char*,char*,char*,char*); //初始化相关的矩阵大小
+	int initObs(char*,char*,char*); //初始化观测点 如只有范围参数则只初始化经纬度位置
+	int relocateAltitude(char*); //根据输入文件重新确定计算高程
+	int outObs(char*); //输出计算结果 如果有文件指定的位置则插值
+	int calSolution(); //计算球谐结果 同一高程观测值
+	int calSolution2(char*); //计算不同高程的观测值
+private:
+	_2dArray Anm;
+	_2dArray Bnm;
+	_2dArray Pnm; //伴随勒让德函数系数 这个函数只和观测位置的纬度/余纬度相关 同一纬度只需要计算一次
+	_2dArray mCos; //不同次数cos函数值 这个值只和观测位置的经度相关 行数为不同经度位置 列数为不同次数 矩阵维度即为经度个数*阶次 一般估算在1000*1000级别
+	_2dArray mSin; //不同次数sin函数值 其他与上同
+	_2dArray coff_S; //球谐系数sin参数
+	_2dArray coff_C; //球谐系数cos参数
+	_2dArray multi_array; //乘子矩阵
+	sphArray obsPoint; //计算地形是的观测位置 即计算半径值
+	sphArray outPoint; //输出计算值
+
+	double norSum;
+	double GM,R; //球谐系数中重力常数与质量的乘积 单位为SI标准 g 与 m
+	double multi_factor; // 乘子系数
+	int NN_size; //系数矩阵大小
+	int lon_size,lat_size;
+	double refr,refR,altitude;
+	double lonmin,lonmax,dlon;
+	double latmin,latmax,dlat;
+};
+//读取球谐参数文件 文件名 起止阶次 列序列
+int sh2xyz::readSHC(char* filename,char* para,char* orders)
+{
+	ifstream infile;
+	if (open_infile(infile,filename)) return -1;
+
+	int n_start,m_start,n_end,m_end;
+	if (4 != sscanf(para,"%d/%d/%d/%d",&n_start,&m_start,&n_end,&m_end))
+	{
+		cerr << BOLDRED << "error ==> " << RESET << "wrong parameter: " << para << endl;
+		return -1;
+	}
+	//识别列次序
+	int order[4];
+	if (4 != sscanf(orders,"%d,%d,%d,%d",&order[0],&order[1],&order[2],&order[3]))
+	{
+		cerr << BOLDRED << "error ==> " << RESET << "wrong parameter: " << orders << endl;
+		return -1;
+	}
+
+	//按照最大阶数初始化下半三角矩阵
+	NN_size = n_end + 1;
+	//对于二维vector来说 对行初始化的时候需要使用resize 而对于列的初始化而言使用reserve效率更高
+	coff_C.resize(NN_size);
+	coff_S.resize(NN_size);
+	for (int i = 0; i < NN_size; i++)
+	{
+		coff_C[i].resize(i+1,0.0);
+		coff_S[i].resize(i+1,0.0);
+	}
+
+	int n,m; //行列号
+	double temp_d,temp_c,temp_s;
+	_1dArray temp_row; temp_row.reserve(100); //出现初始化100个double的空间 这样读文件更快
+	string temp_str;
+	stringstream temp_ss;
+	while (getline(infile,temp_str))
+	{
+		if (*(temp_str.begin()) == '#') continue;
+		if (!temp_row.empty()) temp_row.clear();
+		temp_ss.str("");
+		temp_ss.clear();
+		temp_ss << temp_str;
+		while (temp_ss >> temp_d)
+			temp_row.push_back(temp_d);
+
+		n = int(temp_row[order[0]]);
+		m = int(temp_row[order[1]]);
+		temp_c = temp_row[order[2]];
+		temp_s = temp_row[order[3]];
+
+		if (n >= n_start && n <= n_end && m >= m_start && m <= m_end)
+		{
+			coff_C[n][m] = temp_c;
+			coff_S[n][m] = temp_s;
+		}
+	}
+	infile.close();
+	return 0;
+}
+
+int sh2xyz::initObs(char* r_para,char* i_para,char* refsys)
+{
+	//解析参考球
+	if (!strcmp(refsys,"NULL"))
+	{
+		refr = refR = 0.0;
+	}
+	else if (!strcmp(refsys,"WGS84"))
+	{
+		refr = WGS84_PoleRadius;
+		refR = WGS84_EquatorRadius;
+	}
+	else if (!strcmp(refsys,"EarthRadius"))
+	{
+		refr = EarthRadius;
+		refR = EarthRadius;
+	}
+	else if (!strcmp(refsys,"MoonRadius"))
+	{
+		refr = MoonRadius;
+		refR = MoonRadius;
+	}
+	else if (2 != sscanf(refsys,"%lf/%lf",&refr,&refR))
+	{
+		cerr << BOLDRED << "error ==> " << RESET << "wrong parameter: " << refsys << endl;
+		return -1;
+	}
+
+	//解析经纬度范围 按规则网络初始化观测点位置
+	if (5 != sscanf(r_para,"%lf/%lf/%lf/%lf/%lf",&lonmin,&lonmax,&latmin,&latmax,&altitude))
+	{
+		if (4 != sscanf(r_para,"%lf/%lf/%lf/%lf",&lonmin,&lonmax,&latmin,&latmax))
+		{
+			cerr << BOLDRED << "error ==> " << RESET << "wrong parameter: " << r_para << endl;
+			return -1;
+		}
+		else altitude = 0.0;
+	}
+
+	//解析间隔
+	if (2 != sscanf(i_para,"%lf/%lf",&dlon,&dlat))
+	{
+		cerr << BOLDRED << "error ==> " << RESET << "wrong parameter: " << i_para << endl;
+		return -1;
+	}
+
+	spoint temp_spoint;
+	double lon,lat;
+	lon_size = floor((lonmax-lonmin)/dlon) + 1;
+	lat_size = floor((latmax-latmin)/dlat) + 1;
+	obsPoint.reserve(lon_size*lat_size);
+	for (int i = 0; i < lat_size; i++)
+	{
+		for (int j = 0; j < lon_size; j++)
+		{
+			lat = latmin + i*dlat; lon = lonmin + j*dlon;
+			temp_spoint.lon = lon; temp_spoint.lat = lat;
+			temp_spoint.ref = refRadius(temp_spoint.lat,refr,refR);
+			temp_spoint.alti = altitude;
+			temp_spoint.rad = temp_spoint.ref + temp_spoint.alti;
+			temp_spoint.val = 0.0;
+			obsPoint.push_back(temp_spoint);
+		}
+	}
+	return 0;
+}
+
+int sh2xyz::relocateAltitude(char* filepara)
+{
+	char filename[1024];
+	int orders[3] = {0,1,2}; //默认的读入的数据列为前三列
+
+	if(!strcmp(filepara,"NULL")) return 0;
+
+	//解析文件名中是否含有+d标示 如果有则将+d以前解释为filename 之后为需要读入的数据列 默认为逗号分隔
+	//否则将filepara赋值为filename
+	if (4 != sscanf(filepara,"%[^+]+d%d,%d,%d",filename,&orders[0],&orders[1],&orders[2]))
+		strcpy(filename,filepara);
+
+	ifstream infile;
+	if (open_infile(infile,filename)) return -1;
+
+	int numM,numN,tempM,tempN;
+	string temp_str;
+	stringstream temp_ss;
+	double temp_d,temp_lon,temp_lat,temp_alti;
+	_1dArray temp_row;
+
+	numM = floor((latmax-latmin)/dlat)+1;
+	numN = floor((lonmax-lonmin)/dlon)+1;
+	while(getline(infile,temp_str))
+	{
+		if (*(temp_str.begin()) == '#') continue;
+
+		temp_ss.str(""); temp_ss.clear(); temp_ss << temp_str;
+		if(!temp_row.empty()) temp_row.clear();
+		while(temp_ss >> temp_d)
+			temp_row.push_back(temp_d);
+
+		temp_lon = temp_row[orders[0]];
+		temp_lat = temp_row[orders[1]];
+		temp_alti = temp_row[orders[2]];
+
+		tempM = round((temp_lat-latmin)/dlat);
+		tempN = round((temp_lon-lonmin)/dlon);
+		obsPoint[tempM*numN+tempN].alti = temp_alti;
+		obsPoint[tempM*numN+tempN].rad = obsPoint[tempM*numN+tempN].ref + temp_alti;
+	}
+	infile.close();
+	return 0;
+}
+
+//初始化矩阵
+int sh2xyz::initMatrix(char* type,char* para,char* norType,char* zfile)
+{
+	//初始化GM与R
+	if (strcmp(para,"NULL")) //如果para不为NULL则识别参数 否则将GM与R初始化为MAX_BDL
+	{
+		if (2 != sscanf(para,"%lf/%lf",&GM,&R))
+		{
+			cerr << BOLDRED << "error ==> " << RESET << "wrong parameter: " << para << endl;
+			return -1;
+		}
+	}
+	else GM = R = MAX_BDL;
+	//初始化归一化类型
+	if (!strcmp(norType,"g")) norSum = 4.0*pi;
+	else if (!strcmp(norType,"m")) norSum = 1.0;
+	else
+	{
+		cerr << BOLDRED << "error ==> " << RESET << "wrong parameter: " << norType << endl;
+		return -1;
+	}
+	//初始化伴随勒让德函数矩阵
+	Pnm.resize(NN_size);
+	for (int i = 0; i < NN_size; i++)
+		Pnm.at(i).resize(i+1,0.0);
+	//初始化sin和cos矩阵
+	mCos.resize(lon_size);
+	mSin.resize(lon_size);
+	for (int i = 0; i < lon_size; i++)
+	{
+		mCos[i].reserve(NN_size);
+		mSin[i].reserve(NN_size);
+	}
+	//计算mCos和mSin的值
+	int i,j;
+	double lon;
+#pragma omp parallel for private(i,j,lon) schedule(guided)
+	for (i = 0; i < lon_size; i++)
+	{
+		lon = lonmin + i*dlon;
+		for (j = 0; j < NN_size; j++)
+		{
+			mCos[i].push_back(cos(j*lon*pi/180.0));
+			mSin[i].push_back(sin(j*lon*pi/180.0));
+		}
+	}
+	//计算勒让德函数系数
+	Anm = get_a_nm_array(NN_size);
+	Bnm = get_b_nm_array(NN_size);
+	//计算乘子参数
+	if(!strcmp(type,"t")) //topography
+		multi_factor = 1.0;
+	else if (!strcmp(type,"d") || !strcmp(type,"g")) //gravity disturbance
+		multi_factor = 1e+5*GM/(R*R);
+	else if (!strcmp(type,"r")) //gravity disturbance
+		multi_factor = 1e+9*GM/(R*R);
+	else if (!strcmp(type,"p"))
+		multi_factor = 1e+5*GM/R;
+	else
+	{
+		cerr << BOLDRED << "error ==> " << RESET << "unknown calculation type of " << type << endl;
+		return -1;
+	}
+	//初始化乘子矩阵
+	multi_array.resize(lat_size);
+	for (i = 0; i < lat_size; i++)
+	{
+		multi_array[i].resize(NN_size,1.0); //初始化乘子矩阵为1 适用于地形等直接计算的类型
+	}
+	//如果计算高程不在同一高程 则不能使用multi_array 同时应该使用calSolution2()函数
+	if (strcmp(zfile,"NULL"))
+		return 0;
+	//如果计算类型不是地形等直接计算类型则需要检验-g选项是否已经设置
+	if (strcmp(type,"t"))
+	{
+		if (GM == MAX_BDL || R == MAX_BDL)
+		{
+			cerr << BOLDRED << "error ==> " << RESET << "-g option must be set for gravitational calculation" << endl;
+			return -1;
+		}
+	}
+	//根据不同类型计算乘子参数和乘子矩阵
+	if (!strcmp(type,"d")) //gravity disturbance
+	{
+#pragma omp parallel for private(i,j) shared(R,lon_size) schedule(guided)
+		for (i = 0; i < lat_size; i++)
+		{
+			for (j = 0; j < NN_size; j++)
+			{
+				multi_array[i][j] = pow(R/obsPoint[i*lon_size].rad,j+2)*(j+1);
+			}
+		}
+	}
+	else if (!strcmp(type,"r")) //gravity gradient
+	{
+#pragma omp parallel for private(i,j) shared(R,lon_size) schedule(guided)
+		for (i = 0; i < lat_size; i++)
+		{
+			for (j = 0; j < NN_size; j++)
+			{
+				multi_array[i][j] = pow(R/obsPoint[i*lon_size].rad,j+2)*(j+1)*(j+2)/obsPoint[i*lon_size].rad;
+			}
+		}
+	}
+	else if (!strcmp(type,"g")) //gravity anomaly
+	{
+#pragma omp parallel for private(i,j) shared(R,lon_size) schedule(guided)
+		for (i = 0; i < lat_size; i++)
+		{
+			for (j = 0; j < NN_size; j++)
+			{
+				multi_array[i][j] = pow(R/obsPoint[i*lon_size].rad,j+2)*(j-1);
+			}
+		}
+	}
+	else if (!strcmp(type,"p")) //geo-potential
+	{
+#pragma omp parallel for private(i,j) shared(R,lon_size) schedule(guided)
+		for (i = 0; i < lat_size; i++)
+		{
+			for (j = 0; j < NN_size; j++)
+			{
+				multi_array[i][j] = pow(R/obsPoint[i*lon_size].rad,j+1);
+			}
+		}
+	}
+	return 0;
+}
+
+int sh2xyz::outObs(char* filename)
+{
+	if (!strcmp(filename,"NULL")) //没有输入文件 直接输出规则网计算结果
+	{
+		cout << "# NaN value = 1e+30" << endl;
+		cout << "# lon(deg) lat(deg) reference-radius(m) altitude(m) topography(m)|gravitational-field(mGal)" << endl;
+		for (int i = 0; i < obsPoint.size(); i++)
+		{
+			obsPoint[i].info();
+		}
+	}
+	else
+	{
+		ifstream infile;
+		if(open_infile(infile,filename)) return -1;
+
+		spoint temp_sp;
+		string temp_str;
+		stringstream temp_ss;
+		while (getline(infile,temp_str))
+		{
+			if(*(temp_str.begin()) == '#') continue;
+
+			temp_ss.str("");
+			temp_ss.clear();
+			temp_ss << temp_str;
+			temp_ss >> temp_sp.lon >> temp_sp.lat;
+			temp_sp.ref = refRadius(temp_sp.lat,refr,refR);
+			temp_sp.alti = altitude;
+			outPoint.push_back(temp_sp);
+		}
+		infile.close();
+
+		int numM,numN,tempM,tempN;
+		double lon1,lon2,lat1,lat2;
+
+		numM = floor((latmax-latmin)/dlat)+1;
+		numN = floor((lonmax-lonmin)/dlon)+1;
+		for (int i = 0; i < outPoint.size(); i++)
+		{
+			tempM = floor((outPoint[i].lat-latmin)/dlat);
+			tempN = floor((outPoint[i].lon-lonmin)/dlon);
+
+			if (tempM == (numM-1))
+				tempM -= 1;
+			if (tempN == (numN-1))
+				tempN -= 1;
+
+			if (tempM >= 0 && tempN >= 0 && tempM <= numM-2 && tempN <= numN-2)
+			{
+				lon1 = lonmin+tempN*dlon;
+				lon2 = lonmin+(tempN+1)*dlon;
+				lat1 = latmin+tempM*dlat;
+				lat2 = latmin+(tempM+1)*dlat;
+				outPoint[i].val = SphBiInterp_deg(lat1,lat2,lon1,lon2,
+											outPoint[i].lat,outPoint[i].lon,
+											obsPoint[tempM*numN+tempN].val,
+											obsPoint[tempM*numN+tempN+1].val,
+											obsPoint[(tempM+1)*numN+tempN].val,
+											obsPoint[(tempM+1)*numN+tempN+1].val);
+			}
+		}
+
+		cout << "# NaN value = 1e+30" << endl;
+		cout << "# lon(deg) lat(deg) reference-radius(m) altitude(m) topography(m)|gravitational-field(mGal)" << endl;
+		for (int i = 0; i < outPoint.size(); i++)
+		{
+			outPoint[i].info();
+		}
+	}
+	return 0;
+}
+
+int sh2xyz::calSolution()
+{
+	//计算
+	int i,j,n,m;
+	double temp_d,lat;
+
+	ProgressBar *bar = new ProgressBar(lat_size,"Process");
+	for (i = 0; i < lat_size; i++)
+	{
+		bar->Progressed(i);
+		lat = latmin + dlat*i;
+		//计算伴随勒让德函数 对于同一个纬度只需要计算一次
+		NALF_SFCM3(Pnm,Anm,Bnm,NN_size,90.0-lat,norSum);
+		//这里可以使用并行加速计算外层循环 内层计算因为是递归计算因此不能并行
+		//一种并行方案更快一些
+#pragma omp parallel for private(j,n,m,temp_d) shared(i,multi_factor) schedule(guided)
+		for (j = 0; j < lon_size; j++)
+		{
+			temp_d = 0;
+			for (n = 0; n < NN_size; n++)
+			{
+				for (m = 0; m < n+1; m++)
+				{
+					temp_d += multi_array[i][n]*Pnm[n][m]*(coff_C[n][m]*mCos[j][m]+coff_S[n][m]*mSin[j][m]);
+				}
+			}
+			obsPoint[i*lon_size+j].val = multi_factor*temp_d;
+		}
+	}
+	return 0;
+}
+
+int sh2xyz::calSolution2(char* type)
+{
+	//计算
+	int i,j,n,m;
+	double temp_d,lat;
+
+	ProgressBar *bar = new ProgressBar(lat_size,"Process");
+	if (!strcmp(type,"d"))
+	{
+		for (i = 0; i < lat_size; i++)
+		{
+			bar->Progressed(i);
+			lat = latmin + dlat*i;
+			//计算伴随勒让德函数 对于同一个纬度只需要计算一次
+			NALF_SFCM3(Pnm,Anm,Bnm,NN_size,90.0-lat,norSum);
+			//这里可以使用并行加速计算外层循环 内层计算因为是递归计算因此不能并行
+			//一种并行方案更快一些
+#pragma omp parallel for private(j,n,m,temp_d) shared(i,multi_factor,lon_size) schedule(guided)
+			for (j = 0; j < lon_size; j++)
+			{
+				temp_d = 0;
+				for (n = 0; n < NN_size; n++)
+				{
+					for (m = 0; m < n+1; m++)
+					{
+						//pow(R/obsPoint[i*lon_size+j].rad,n+2)*(n+1)
+						temp_d += pow(R/obsPoint[i*lon_size+j].rad,n+2)*(n+1)*Pnm[n][m]*(coff_C[n][m]*mCos[j][m]+coff_S[n][m]*mSin[j][m]);
+					}
+				}
+				obsPoint[i*lon_size+j].val = multi_factor*temp_d;
+			}
+		}
+	}
+	else if (!strcmp(type,"g"))
+	{
+		for (i = 0; i < lat_size; i++)
+		{
+			bar->Progressed(i);
+			lat = latmin + dlat*i;
+			//计算伴随勒让德函数 对于同一个纬度只需要计算一次
+			NALF_SFCM3(Pnm,Anm,Bnm,NN_size,90.0-lat,norSum);
+			//这里可以使用并行加速计算外层循环 内层计算因为是递归计算因此不能并行
+			//一种并行方案更快一些
+#pragma omp parallel for private(j,n,m,temp_d) shared(i,multi_factor,lon_size) schedule(guided)
+			for (j = 0; j < lon_size; j++)
+			{
+				temp_d = 0;
+				for (n = 0; n < NN_size; n++)
+				{
+					for (m = 0; m < n+1; m++)
+					{
+						//pow(R/obsPoint[i*lon_size+j].rad,n+2)*(n-1)
+						temp_d += pow(R/obsPoint[i*lon_size+j].rad,n+2)*(n-1)*Pnm[n][m]*(coff_C[n][m]*mCos[j][m]+coff_S[n][m]*mSin[j][m]);
+					}
+				}
+				obsPoint[i*lon_size+j].val = multi_factor*temp_d;
+			}
+		}
+	}
+	else if (!strcmp(type,"p"))
+	{
+		for (i = 0; i < lat_size; i++)
+		{
+			bar->Progressed(i);
+			lat = latmin + dlat*i;
+			//计算伴随勒让德函数 对于同一个纬度只需要计算一次
+			NALF_SFCM3(Pnm,Anm,Bnm,NN_size,90.0-lat,norSum);
+			//这里可以使用并行加速计算外层循环 内层计算因为是递归计算因此不能并行
+			//一种并行方案更快一些
+#pragma omp parallel for private(j,n,m,temp_d) shared(i,multi_factor,lon_size) schedule(guided)
+			for (j = 0; j < lon_size; j++)
+			{
+				temp_d = 0;
+				for (n = 0; n < NN_size; n++)
+				{
+					for (m = 0; m < n+1; m++)
+					{
+						//pow(R/obsPoint[i*lon_size+j].rad,n+1)
+						temp_d += pow(R/obsPoint[i*lon_size+j].rad,n+1)*Pnm[n][m]*(coff_C[n][m]*mCos[j][m]+coff_S[n][m]*mSin[j][m]);
+					}
+				}
+				obsPoint[i*lon_size+j].val = multi_factor*temp_d;
+			}
+		}
+	}
+	return 0;
+}
+
+#endif

archive/sh2xyz/sysDefine.h

@@ -0,0 +1,106 @@
+#ifndef _SYSDEFINE_H
+#define _SYSDEFINE_H
+#include "iostream"
+#include "fstream"
+#include "sstream"
+#include "iomanip"
+#include "stdio.h"
+#include "stdlib.h"
+#include "unistd.h"
+#include "string.h"
+#include "cmath"
+#include "vector"
+#include "omp.h"
+
+#define pi (4.0*atan(1.0))
+#define MAX_BDL 1e+30
+#define WGS84_PoleRadius 6356752.314//WGS84椭球极半径
+#define WGS84_EquatorRadius 6378137//WGS84椭球长半径
+#define EarthRadius 6371000
+#define MoonRadius 1738000
+
+#define BOLDRED "\033[1m\033[31m"
+#define BOLDGREEN "\033[1m\033[32m"
+#define BOLDBLUE "\033[1m\033[34m"
+#define UNDERLINE "\033[1m\033[4m"
+#define RESET "\033[0m"
+#define MOVEUP(x) printf("\033[%dA", (x))
+#define MOVEDOWN(x) printf("\033[%dB", (x))
+#define MOVELEFT(x) printf("\033[%dD", (x))
+#define MOVERIGHT(x) printf("\033[%dC", (x))
+#define MOVETO(y,x) printf("\033[%d;%dH", (y), (x))
+#define CLEARLINE "\033[K"
+#define CLEARALL "\033[2J"
+
+using namespace std;
+
+typedef vector<double> _1dArray;
+typedef vector<vector<double> > _2dArray;
+
+struct spoint
+{
+	double lon,lat,ref,alti,rad,val;
+	spoint()
+	{
+		lon = lat = ref = alti = rad = val = MAX_BDL;
+	}
+	void info()
+	{
+		cout << setprecision(16) << lon << " " << lat << " "  << ref << " " << alti << " " << val << endl;
+	}
+};
+typedef vector<spoint> sphArray;
+
+//计算一个参考椭球或者参考球在纬度位置的半径
+double refRadius(double lati,double refr,double refR)
+{
+	return refr*refR/sqrt(pow(refr,2)*pow(cos((double) lati*pi/180.0),2)+pow(refR,2)*pow(sin((double) lati*pi/180.0),2));
+}
+//测试打开输入文件 如果成功则返回0并输出信息 否则返回1
+int open_infile(ifstream &infile,char* filename)
+{
+	infile.open(filename);
+	if (!infile)
+	{
+		cout << BOLDRED << "error ==> " << RESET << "file not found: " << filename << endl;
+		return -1;
+	}
+	return 0;
+}
+//测试打开输出文件 如果成功则返回0并输出信息 否则返回1
+int open_outfile(ofstream &outfile,char* filename)
+{
+	outfile.open(filename);
+	if (!outfile)
+	{
+		cout << BOLDRED << "error ==> " << RESET << "fail to create the file: " << filename << endl;
+		return -1;
+	}
+	return 0;
+}
+
+double cosd(double deg)
+{
+	return (cos(deg*pi/180.0));
+}
+/*
+lat
+|
+|
+h21----h22
+|       |
+|       |
+h11----h12----> lon
+*/
+// 球面双线性插值函数 以度为单位的版本 注意纬度为余纬度
+double SphBiInterp_deg(double CoLat1,double CoLat2,double Lon1,double Lon2,double CoLat0,double Lon0,double h11,double h12,double h21,double h22)
+{
+	double Delta=(Lon2-Lon1)*(cosd(CoLat2)-cosd(CoLat1));
+	double A=(Lon1*(h12-h22)+Lon2*(h21-h11))/Delta;
+	double B=(cosd(CoLat1)*(h21-h22)+cosd(CoLat2)*(h12-h11))/Delta;
+	double C=(h11+h22-h21-h12)/Delta;
+	double D=(Lon2*cosd(CoLat2)*h11-Lon2*cosd(CoLat1)*h21+Lon1*cosd(CoLat1)*h22-Lon1*cosd(CoLat2)*h12)/Delta;
+	double h0=A*cosd(CoLat0)+B*Lon0+C*Lon0*cosd(CoLat0)+D;
+	return h0;
+}
+#endif