釋出者：
釋出日期：2009年9月17日（最後更新：2009年9月21日）

C++ LAPACK

評分：4.1/5 (18 票)
*****
以下是一個使用 LAPACK 與 C++ 的框架。

有關更多資訊，請檢視 LAPACK 論壇
http://icl.cs.utk.edu/lapack-forum/
以及 netlib 儲存庫
http://www.netlib.org/clapack/
在上述網站上有 CLAPACK 和 BLAS 的編譯/安裝詳細資訊。

測試程式（可執行檔案 'fmat'）的編譯命令
1
2
3
4
 
CLAPACKPATH = path to clapack
g++  Fmatrix_test.cpp -I$(CLAPACKPATH)/SRC -I$(CLAPACKPATH) -c
g++  Fmatrix_test.o -o fmat $(CLAPACKPATH)/lapack_LINUX.a $(CLAPACKPATH)/blas_LINUX.a $(CLAPACKPATH)/F2CLIBS/libf2c.a -lm

Matrix 類：這只是一個容器 - 全部是 C++
我們使用模板來儲存 LAPACK 允許的不同資料型別。

矩陣“資料”（mat 成員）是一個一維陣列，必須這樣，以便 FORTRAN 可以使用它。
這意味著我們必須跟蹤矩陣中的位置。 A<i>[j] 由 A[ j*m+i ] 給出，其中 m 是行數。

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
 
#ifndef _FMATRIX_H
#define _FMATRIX_H

#include<iostream>

template <class T>
class Fmatrix
{
public:
    //default
    Fmatrix(): m(0), n(0), flag(0), mat(new T[0]){ this->settype(); }
    //blank
    Fmatrix(size_t _m): m(_m), n(1), flag(0), mat(new T[_m]){ this->settype(); }
    Fmatrix(size_t _m, size_t _n): m(_m), n(_n), flag(0), mat(new T[_m*_n])
    { this->settype(); }
    //copy
    Fmatrix(const Fmatrix<T>& B) :
    m(B.numrows()), n(B.numcols()), mat(new T[B.numelms()])
    {
        for(size_t i=0; i<B.numelms(); i++){ this->mat<i> = B<i>; }
        this->type=B.gettype();
    }

    ~Fmatrix(){ if(mat) delete[] mat; }

    inline T& operator() (size_t i, size_t j)
    { return this->mat[j*(this->m)+i]; }
    inline T  operator() (size_t i, size_t j) const
    { return this->mat[j*(this->m)+i]; }

    inline T& operator[] (size_t i)       { return mat<i>; }
    inline T  operator[] (size_t i) const { return mat<i>; }

    Fmatrix operator = (const Fmatrix<T>& B)
    {
        if(&B!=this){
            delete[] mat;
            this->m=B.numrows();
            this->n=B.numcols();
            this->flag=B.error();
            mat=new T[(this->m)*(this->n)];
            for(size_t i=0; i<B.numelms(); i++){ this->mat<i> = B<i>;}
        }
        return *this;
    }
    //these (+-*/) won't work for complex
    Fmatrix operator += (const Fmatrix<T>& B)
    {  for(size_t i=0; i< this->numelms(); i++){ this->mat<i>+=B<i>; }  }
    Fmatrix operator -= (const Fmatrix<T>& B)
    {  for(size_t i=0; i< this->numelms(); i++){ this->mat<i>-=B<i>; }  }
    Fmatrix operator *= (const T alpha)
    {  for(size_t i=0; i< this->numelms(); i++){ this->mat<i>*=alpha; }  }
    Fmatrix operator /= (const T beta)
    {  for(size_t i=0; i< this->numelms(); i++){ this->mat<i>/=beta; }  }

    inline T* begin(){ return mat; }

    inline const size_t numrows() const { return this->m; }
    inline const size_t numcols() const { return this->n; }
    inline const size_t numelms() const { return (this->m)*(this->n); }
    inline const bool   error()   const { return this->flag; }
    inline const char   gettype() const { return this->type; }
    
    void print(std::ostream &os=std::cout, char delim='\t')
    {
        for(size_t i=0;i<this->m;i++){for(size_t j=0;j<this->n;j++){
            os << (*this)(i,j) << delim;
        } os << std::endl; } os << std::endl;
    }
    
    void read(std::istream &is=std::cin)
    {
        for(size_t i=0;i<this->m;i++){for(size_t j=0;j<this->n;j++){
            is >> (*this)(i,j);
        } }
    }

private:
    size_t m,n;
    T *mat;
    char type;
    bool flag;

    inline const char settype()
    {
        char tstr[20], otyp[]="czu";
        strcpy(tstr,typeid(T).name());
        if(tstr[0]=='f'||tstr[0]=='d'||tstr[0]=='e') type=tstr[0];
        else if( strcmp(tstr,"7complex")==0 )        type=otyp[0];
        else if( strcmp(tstr,"13doublecomplex")==0 ) type=otyp[1];
        else                                         type=otyp[2];
    }
};

#endif /* _FMATRIX_H */


線性代數模組：這與 CLAPACK 掛鉤
注意包含項的 extern，它們是用 C 編寫的。
這裡的大多數函式都呼叫 LAPACK 函式，我會根據需要新增功能（LAPACK 非常龐大）。
要向 LAPACK 新增新的函式呼叫，您需要在 netlib 或其他地方查詢該函式，以確定需要傳遞的內容。
要傳遞矩陣資料，請使用 myMatrix.begin()
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
 
#ifndef _LINALG_H
#define _LINALG_H

#include <cstdlib>
#include <cstdio>
#include <cmath>
#include <iostream>
#include <fstream>

extern "C" {
    #include "f2c.h"
    #include "blaswrap.h"
    #include "clapack.h"
}

#include "Fmatrix.h"

//these scalar ops (+-*/) won't work for complex
template <class T>
const Fmatrix<T> operator + (const Fmatrix<T>& A, const Fmatrix<T>& B)
{  return Fmatrix<T>(A)+=B;  }
template <class T>
const Fmatrix<T> operator - (const Fmatrix<T>& A, const Fmatrix<T>& B)
{  return Fmatrix<T>(A)+=B;  }
template <class T>
const Fmatrix<T> operator * (const T alpha, const Fmatrix<T>& A)
{  return Fmatrix<T>(A)*=alpha;  }
template <class T>
const Fmatrix<T> operator / (const Fmatrix<T>& A, const T beta)
{  return Fmatrix<T>(A)/=beta;  }
template <class T>
const Fvector<T> operator * ( Fmatrix<T>& A, Fvector<T>& x)
{
    Fvector<T> y(A.numrows());
    gmv(A,x,y);
    return y;
}
template <class T>
const Fmatrix<T> operator * ( Fmatrix<T>& A, Fmatrix<T>& B)
{
    Fmatrix<T> C(A.numrows(),B.numcols());
    gmm(A,B,C);
    return C;
}

template <class T>
int gmv(Fmatrix<T>& A, Fvector<T>& x, Fvector<T>& y, char TRANSA='N',
            T alpha=1, T beta=0, integer INCX=1, integer INCY=1)
{
    integer M, N, LDA;

    M=(TRANSA=='N') ? A.numrows():A.numcols();
    N=(TRANSA=='N') ? A.numcols():A.numrows();
    LDA=M;

    //this still needs a switch on data type
    dgemv_(&TRANSA, &M, &N,
                        (doublereal*)&alpha,
                        (doublereal*)A.begin(), &LDA,
                        (doublereal*)x.begin(), &INCX,
                        (doublereal*)&beta,
                        (doublereal*)y.begin(), &INCY);


}


template <class T>
int gmm(Fmatrix<T>& A, Fmatrix<T>& B, Fmatrix<T>& C,
            char TRANSA='N', char TRANSB='N', T alpha=1, T beta=0)
{
    integer M, N, K, LDA, LDB, LDC;

    M=(TRANSA=='N') ? A.numrows():A.numcols();
    N=(TRANSB=='N') ? B.numcols():B.numrows();
    K=(TRANSA=='N') ? A.numcols():A.numrows();
    LDA=(TRANSA=='N') ? M:K;
    LDB=(TRANSB=='N') ? K:N;
    LDC=C.numrows();

    switch(A.gettype()){//cast explicitly otherwise compiler is cranky
        case 'f':
            sgemm_(&TRANSA, &TRANSB, &M, &N, &K,
                        (real*)&alpha,
                        (real*)A.begin(), &LDA,
                        (real*)B.begin(), &LDB,
                        (real*)&beta,
                        (real*)C.begin(), &LDC);
        break;
        case 'd':
            dgemm_(&TRANSA, &TRANSB, &M, &N, &K,
                        (doublereal*)&alpha,
                        (doublereal*)A.begin(), &LDA,
                        (doublereal*)B.begin(), &LDB,
                        (doublereal*)&beta,
                        (doublereal*)C.begin(), &LDC);
        break;
        case 'c':
            cgemm_(&TRANSA, &TRANSB, &M, &N, &K,
                        (complex*)&alpha,
                        (complex*)A.begin(), &LDA,
                        (complex*)B.begin(), &LDB,
                        (complex*)&beta,
                        (complex*)C.begin(), &LDC);
        break;
        case 'z':
            zgemm_(&TRANSA, &TRANSB, &M, &N, &K,
                        (doublecomplex*)&alpha,
                        (doublecomplex*)A.begin(), &LDA,
                        (doublecomplex*)B.begin(), &LDB,
                        (doublecomplex*)&beta,
                        (doublecomplex*)C.begin(), &LDC);
        break;
        default:
            std::cout << "\nERROR: Something wrong in GMM switch.\n\n";
    }
    return 0;
}

template <class T>
int pca(Fmatrix<T>& A, Fmatrix<T>& U, Fmatrix<T>& S, Fmatrix<T>& PC)
{
   std::ofstream PCoutx("pcx"), PCouty("pcy"), PCoutz("pcz"), PCoutw("pcw");
        PCoutx.precision(16); PCouty.precision(16);
        PCoutz.precision(16); PCoutw.precision(16);
        Fmatrix<T> Y(A.numcols(),A.numrows());
        T s,*mean;

        mean = new T[A.numrows()];
        for(int i=0; i<A.numrows(); i++) mean<i>=0;

        //find means
        for(int i=0; i<A.numrows(); i++){ for(int j=0; j<A.numcols(); j++){
            mean<i>+=A(i,j);
        } }
        for(int i=0; i<A.numrows(); i++) mean<i>/=A.numcols();

        //subtract means from data
        for(int i=0; i<A.numrows(); i++){ for(int j=0; j<A.numcols(); j++){
            A(i,j)-=mean<i>;
        } }

        //form matrix for SVD
        s=sqrt(A.numcols()-1);
        for(int i=0; i<A.numrows(); i++){ for(int j=0; j<A.numcols(); j++){
            Y(j,i)=A(i,j)/s;
        } }

        return svd(Y,U,S,PC);
}

template <class T>
int svd(Fmatrix<T>& A, Fmatrix<T>& U, Fmatrix<T>& S, Fmatrix<T>& V,
            char JOBU='A', char JOBVT='A')
{
    float  *wkf,*rwkc;
    double *wkd,*rwkz;
    complex *wkc;
    doublecomplex *wkz;
    integer M, N, mn, MN, LDA, LDU, LDVT, LWORK, INFO;

    M=A.numrows(); N=A.numcols(); LDA=M; LDU=M; LDVT=N;
    mn=min(M,N);
    MN=max(M,N);
    LWORK=2*max(3*mn+MN,5*mn);

    switch(A.gettype()){//cast explicitly otherwise compiler is cranky
        case 'f':
            wkf = new real[LWORK];
            sgesvd_(&JOBU, &JOBVT, &M, &N,
                        (real*)A.begin(), &LDA,
                        (real*)S.begin(),
                        (real*)U.begin(), &LDU,
                        (real*)V.begin(), &LDVT,
                        wkf, &LWORK, &INFO);
            delete[] wkf;
        break;
        case 'd':
            wkd = new doublereal[LWORK];
            dgesvd_(&JOBU, &JOBVT, &M, &N,
                        (doublereal*)A.begin(), &LDA,
                        (doublereal*)S.begin(),
                        (doublereal*)U.begin(), &LDU,
                        (doublereal*)V.begin(), &LDVT,
                        wkd, &LWORK, &INFO);
            delete[] wkd;
        break;
        case 'c':
            wkc = new complex[LWORK];
            rwkc = new real[5*mn];
            cgesvd_(&JOBU, &JOBVT, &M, &N,
                        (complex*)A.begin(), &LDA,
                        (real*)S.begin(),
                        (complex*)U.begin(), &LDU,
                        (complex*)V.begin(), &LDVT,
                        wkc, &LWORK, rwkc, &INFO);
            delete[] wkc; delete[] rwkc;
        break;
        case 'z':
            wkz = new doublecomplex[LWORK];
            rwkz = new doublereal[5*mn];
            zgesvd_(&JOBU, &JOBVT, &M, &N,
                        (doublecomplex*)A.begin(), &LDA,
                        (doublereal*)S.begin(),
                        (doublecomplex*)U.begin(), &LDU,
                        (doublecomplex*)V.begin(), &LDVT,
                        wkz, &LWORK, rwkz, &INFO);
            delete[] wkz; delete[] rwkz;
        break;
        default:
            std::cout << "\nERROR: Something wrong in SVD switch.\n\n";
    }

    return INFO;
}

#endif /* _LINALG_H */

Fmatrix_test.cpp：顯示一些功能

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
 
#include <cstdlib>
#include <cstdio>
#include <cmath>
#include <iostream>

#include "Flinalg.h"

using namespace std;

int main(int argc, char** argv)
{
    cout.precision(2);
    size_t M,N;

    cout << "input numrows: ";
    cin >> M;
    cout << "input numcols: ";
    cin >> N;
    Fmatrix<double> A(M,N); //instantiate MxN matrix
    Fmatrix<double> v(N),u(M); //instantiate Mx1 matrix i.e. vector
    cout << "A is " <<  A.numrows() << 'x' << A.numcols() << ", numelms: " << A.numelms() << endl;
    cout << "v is " <<  v.numrows() << 'x' << v.numcols() << ", numelms: " << v.numelms() << endl;
    cout << "u is " <<  u.numrows() << 'x' << u.numcols() << ", numelms: " << u.numelms() << endl << endl;

    cout << "Input data for matrix A by rows (" << A.numelms() << " numbers):" << endl;
    A.read();
    cout << endl << "A =" << endl;
    A.print();
    
    //Matrix-vector multiply by operator overload
    cout << endl << "Setting v to ones vector..." << endl;
    for(int i=0;i<v.numelms();i++)
        v<i>=1;
    cout << "A*v =" << endl;
    u=A*v;
    u.print();
    
    //generic matrix-matrix multiply
    Fmatrix<double> C(A.numrows(),A.numrows());
    gmm(A,A,C,'N','T');
    cout << "A*A' =" << endl; 
    C.print();
    
    cout << "computing svd..." << endl;
    Fmatrix<double> U(M,M),S(min(M,N)),V(N,N); //min is defined in clapack.h
    cout << "INFO: " << svd(A,U,S,V) << endl; //do svd, output error code
    cout << "singular values:" << endl;
    for (size_t i=0; i < min(M,N); i++)
    { cout << "S[ " << i+1 << " ]\t= " << S<i> << endl; } cout << endl;
    cout << "singular vectors:" << endl;     //rows of V so print transpose
    for(int i=0; i<V.numrows(); i++){ cout << "v" << i+1 <<'\t'; } cout << endl;
    for(int i=0; i<V.numrows(); i++){ for(size_t j=0;j<V.numcols();j++){
        cout << V(j,i) << '\t';
    } cout << endl; }

    return 0;
}


示例執行（輸入為粗體）

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
 
input numrows: <b>6</b>
input numcols: <b>5</b>
A is 6x5, numelms: 30
v is 5x1, numelms: 5
u is 6x1, numelms: 6

Input data for matrix A by rows (30 numbers):
<b>2 5 2 6 4
3 3.4 2 6 7
2 2 2 2 0
0 0 0 1.234 0
3 23 46 93 .001
1 2 3 4 5</b>

A =
2       5       2       6       4
3       3.4     2       6       7
2       2       2       2       0
0       0       0       1.2     0
3       23      46      93      0.001
1       2       3       4       5


Setting v to ones vector...
A*v =
19
21
8
1.2
1.7e+02
15



A*A' =
85      91      30      7.4     7.7e+02 62
91      1.1e+02 29      7.4     7.4e+02 75
30      29      16      2.5     3.3e+02 20
7.4     7.4     2.5     1.5     1.1e+02 4.9
7.7e+02 7.4e+02 3.3e+02 1.1e+02 1.1e+04 5.6e+02
62      75      20      4.9     5.6e+02 55

computing svd...
INFO: 0
singular values:
S[ 1 ]  = 1.1e+02
S[ 2 ]  = 11
S[ 3 ]  = 2.9
S[ 4 ]  = 1.9
S[ 5 ]  = 1.2

singular vectors:
v1      v2      v3      v4      v5
-0.032  -0.33   0.48    -0.35   -0.74
-0.22   -0.34   0.72    0.16    0.54
-0.43   0.088   -0.12   -0.84   0.29
-0.87   0.062   -0.13   0.39    -0.26
-0.0092 -0.88   -0.47   0.0089  0.079

它將求解方程組。是的，但是設定單變數單方程系統所需的工作量等同於求解它。

例如
要讓它解決
4x+2=54-7x+3
您需要告訴它 11x=55

這簡直是浪費時間（為 lapack 制定輸入）。

但是像這樣
1
2
3
 
12x +14y - 8z = 2
14x - 5y +  z = 4
  x +  y +  z = 4

才值得。
您還可以（某種程度上）求解欠定系統（變數多於方程的系統）。

你需要一個計算機代數系統 (CAS)。 Maple 在符號操作方面非常好（但價格昂貴）。 Octave/Matlab 也可以做到。 Octave 和 Matlab 實際上都使用 LAPACK