SP++3.0 User Guide
张明
2011-02
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目录
0 SP++导引.......................................................................................................................1
0.1 SP++概述 .......................................................................................................1
0.2 SP++安装 (Code
Blocks)...............................................................................1
0.3 SP++安装 (V
S2010) .....................................................................................4
0.4 SP++与Matl
ab混合编程................................................................................8
1 向量类模板..................................................................................................................11
1.1 基本向量类..................................................................................................11
1.2 常用数学函数的向量版本 ..........................................................................21
1.3 常用的辅助函数 ..........................................................................................26
1.4 简单计时器..................................................................................................36
2 矩阵类模板..................................................................................................................39
2.1 基本矩阵类..................................................................................................39
2.2 常用数学函数的矩阵版本 ..........................................................................51
2.3 实矩阵与复矩阵的Choles
ky分解 ...............................................................55
2.4 实矩阵与复矩阵的LU分解.........................................................................62
2.5 实矩阵与复矩阵的QR分解.........................................................................66
2.6 实矩阵与复矩阵的SVD分解 ......................................................................72
2.7 实矩阵与复矩阵的EVD分解......................................................................78
2.8 矩阵的逆与广义逆 ......................................................................................83
3 线性方程组..................................................................................................................91
3.1 常规线性方程组 ..........................................................................................91
3.2 超定与欠定线性方程组 ..............................................................................98
3.3 病态线性方程组 ........................................................................................104
4 非线性方程与方程组................................................................................................109
4.1 非线性方程求根 ........................................................................................109
4.2 非线性方程组求根 ....................................................................................110
4.3 Romberg数值积分 .....................................................................................112
5 插值与拟合................................................................................................................115
5.1 Newton插值 ...............................................................................................115
5.2 三次样条插值 ............................................................................................117
5.3 最小二乘拟合 ............................................................................................119
6 优化算法....................................................................................................................123
6.1 一维线搜索................................................................................................123
6.2 最速下降法................................................................................................123
6.3 共轭梯度法................................................................................................125
6.4 拟Newto
n法 ...............................................................................................128
7 Fourier分析 ................................................................................................................131
7.1 2 的整次幂FFT算法 ..................................................................................131
7.2 任意长度FFT算法 .....................................................................................135
7.3 普通信号FFT使用方法 .............................................................................142
