C++ 积分（使用exp（A/2^n）^（2^n）=exp（A），求n，使A/2^n的范数很小，泰勒展开exp（A/2^n）=B。现在用n次乘法计算B^（2^n） gsl_blas_zgemm (CblasNoTrans, CblasNoTrans, GSL_CO

积分（使用exp（A/2^n）^（2^n）=exp（A），求n，使A/2^n的范数很小，泰勒展开exp（A/2^n）=B。现在用n次乘法计算B^（2^n）

gsl_blas_zgemm (CblasNoTrans, CblasNoTrans, GSL_COMPLEX_ONE, matA, matB, GSL_COMPLEX_ZERO, matC);

gsl_linalg_exponential_ss(&m.matrix, &em.matrix, .01);

#include <stdio.h>
#include <gsl/gsl_matrix.h>
#include <gsl/gsl_linalg.h>
#include <gsl/gsl_complex.h>
#include <gsl/gsl_complex_math.h>
void my_gsl_complex_matrix_exponential(gsl_matrix_complex *eA, gsl_matrix_complex *A, int dimx)
{
    int j,k=0;
    gsl_complex temp;
    gsl_matrix *matreal =gsl_matrix_alloc(2*dimx,2*dimx);
    gsl_matrix *expmatreal =gsl_matrix_alloc(2*dimx,2*dimx);
    //Converting the complex matrix into real one using A=[Areal, Aimag;-Aimag,Areal]
    for (j = 0; j < dimx;j++)
        for (k = 0; k < dimx;k++)
        {
            temp=gsl_matrix_complex_get(A,j,k);
            gsl_matrix_set(matreal,j,k,GSL_REAL(temp));
            gsl_matrix_set(matreal,dimx+j,dimx+k,GSL_REAL(temp));
            gsl_matrix_set(matreal,j,dimx+k,GSL_IMAG(temp));
            gsl_matrix_set(matreal,dimx+j,k,-GSL_IMAG(temp));
        }

    gsl_linalg_exponential_ss(matreal,expmatreal,.01);

    double realp;
    double imagp;
    for (j = 0; j < dimx;j++)
        for (k = 0; k < dimx;k++)
        {
            realp=gsl_matrix_get(expmatreal,j,k);
            imagp=gsl_matrix_get(expmatreal,j,dimx+k);
            gsl_matrix_complex_set(eA,j,k,gsl_complex_rect(realp,imagp));
        }
    gsl_matrix_free(matreal);
    gsl_matrix_free(expmatreal);
}

int main()
{
    int dimx=4;
    int i, j ;
    gsl_matrix_complex *A = gsl_matrix_complex_alloc (dimx, dimx);
    gsl_matrix_complex *eA = gsl_matrix_complex_alloc (dimx, dimx);

    for (i = 0; i < dimx;i++)
    {
        for (j = 0; j < dimx;j++)
        {
            gsl_matrix_complex_set(A,i,j,gsl_complex_rect(i+j,i-j));
            if ((i-j)>=0)
            printf("%d+%di ",i+j,i-j);
            else
            printf("%d%di  ",i+j,i-j);

        }
        printf(";\n");
    }
    my_gsl_complex_matrix_exponential(eA,A,dimx);
    printf("\n Printing the complex matrix exponential\n");
    gsl_complex compnum;
    for (i = 0; i < dimx;i++)
    {
        for (j = 0; j < dimx;j++)
        {
            compnum=gsl_matrix_complex_get(eA,i,j);
            if (GSL_IMAG(compnum)>=0)
                printf("%f+%fi\t ",GSL_REAL(compnum),GSL_IMAG(compnum));
            else
                printf("%f%fi\t ",GSL_REAL(compnum),GSL_IMAG(compnum));
        }
        printf("\n");
    }
    return(0);
}