MathJaxとSyntax Highlighterのテスト

T.Kouya

10年前

　とりあえず，MathJaxのテスト。デフォルトをDisplay modeにして
\[ y(s) = f(s) + \int^b_a g(s, t) y(t) dt \]
数式が出るかしら？　ついでにインライン表示も・・・まぁこんなもんか。

　で，コード例も一つ。$n$次正方行列と次元ベクトルから作られる連立一次方程式
\[ A\mathbf{x} = \mathbf{b} \]
を未知ベクトルについて解くLAPACKプログラム。DGESVを使う最も簡単なもの。解の表示をコメントにしてあるのはでかい次元数のベンチマーク用に使ったからです。適宜はずしてお使い下さいませ。

/*************************************************/
/* LAPACK Tutorial                               */
/* Sample Program of DGESV                       */
/*                        with Intel Math Kernel */
/* Last Update: 2013-01-21 (Mon) T.Kouya         */
// icc -I/opt/intel/include -I/opt/intel/mkl/include -L/opt/intel/mkl/lib/intel64 -L/opt/intel/lib/intel64 blas1_mkl.c -Wl,--start-group /opt/intel/mkl/lib/intel64/libmkl_intel_lp64.a /opt/intel/mkl/lib/intel64/libmkl_sequential.a /opt/intel/mkl/lib/intel64/libmkl_core.a -Wl,--end-group -lpthread
/*************************************************/
#include <stdio.h>
#include <stdlib.h>
#include "mkl.h" // for Intel Math Kernel Library
#include "mkl_cblas.h"
#include "mkl_lapacke.h"

#define min(i, j) (((i) < (j)) ? (i) : (j))
#define max(i, j) (((i) > (j)) ? (i) : (j))

int main()
{
	MKL_INT i, j, dim; // dimension of vectors
	MKL_INT *pivot, info;
	double *ma, *vx, *vb;
	double alpha, beta;
	char str_mkl_version[1024];
	double running_time;

	// print MKL version
	MKL_Get_Version_String(str_mkl_version, 1024);
	printf("%s\n", str_mkl_version);

	// input dimension
	printf("Dim = "); scanf("%d", &dim);

	if(dim <= 0)
	{
		printf("Illigal dimension! (dim = %d)\n", dim);
		return EXIT_FAILURE;
	}

	// Initialize
	pivot = (MKL_INT *)calloc(sizeof(MKL_INT), dim);
	ma = (double *)calloc(sizeof(double), dim * dim);
	vx = (double *)calloc(sizeof(double), dim);
	vb = (double *)calloc(sizeof(double), dim);

	// input va and vb
	for(i = 0; i < dim; i++)
	{
		for(j = 0; j < dim; j++)
		{
			// A = hirbert matrix
			//*(ma + i * dim + j) = 1.0 / (double)(i + j + 1);
			// A = frank matrix
			*(ma + i * dim + j) = (double)(dim - max(i, j));
		}
		// x  = answer
		*(vx + i) = (double) (i + 1);
	}

	// b := A * x
	alpha = 1.0;
	beta = 0.0;
	cblas_dgemv(CblasRowMajor, CblasNoTrans, dim, dim, alpha, ma, dim, vx, 1, beta, vb, 1);

	// print
/*	printf("A = \n");
	for(i = 0; i < dim; i++)
	{
		printf("%3d: ", i);
		for(j = 0; j < dim; j++)
			printf("%10f ", *(ma + i * dim + j));
		printf("\n");

	}

	// print
	printf("x = \n");
	for(i = 0; i < dim; i++)
	{
		printf("%3d: ", i);
		printf("%10f ", *(vx + i));
		printf("\n");

	}

	// print
	printf("b = \n");
	for(i = 0; i < dim; i++)
	{
		printf("%3d: ", i);
		printf("%10f ", *(vb + i));
		printf("\n");
	}
*/

	// solve A * X = C -> C := X
	running_time = dsecnd(); // start 
	info = LAPACKE_dgesv(LAPACK_ROW_MAJOR, dim, 1, ma, dim, pivot, vb, 1);
	running_time = dsecnd() - running_time; // end

	// error occurs if info > 0
	if(info > 0)
	{
		printf("pivot ma[%d][%d] is zero!\n", info, info);
		return EXIT_FAILURE;
	}

	printf("Dimension: %d, Running Time(s): %g\n", dim, running_time);

	// print
/*	printf("calculated x = \n");
	for(i = 0; i < dim; i++)
	{
		printf("%3d: ", i);
		printf("%10f ", *(vb + i));
		printf("\n");

	}

	// diff
	printf("x - calculated x = \n");
	for(i = 0; i < dim; i++)
	{
		printf("%3d: ", i);
		printf("%10f ", fabs(*(vx + i) - *(vb + i)));
		printf("\n");
	}
*/

	// free
	free(pivot);
	free(ma);
	free(vb);
	free(vx);

	return EXIT_SUCCESS;
}

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/*************************************************/

/* LAPACK Tutorial */

/* Sample Program of DGESV */

/* with Intel Math Kernel */

/* Last Update: 2013-01-21 (Mon) T.Kouya */

// icc -I/opt/intel/include -I/opt/intel/mkl/include -L/opt/intel/mkl/lib/intel64 -L/opt/intel/lib/intel64 blas1_mkl.c -Wl,--start-group /opt/intel/mkl/lib/intel64/libmkl_intel_lp64.a /opt/intel/mkl/lib/intel64/libmkl_sequential.a /opt/intel/mkl/lib/intel64/libmkl_core.a -Wl,--end-group -lpthread

/*************************************************/

#include <stdio.h>

#include <stdlib.h>

#include "mkl.h" // for Intel Math Kernel Library

#include "mkl_cblas.h"

#include "mkl_lapacke.h"

#define min(i, j) (((i) < (j)) ? (i) : (j))

#define max(i, j) (((i) > (j)) ? (i) : (j))

int main()

{

MKL_INT i, j, dim; // dimension of vectors

MKL_INT *pivot, info;

double *ma, *vx, *vb;

double alpha, beta;

char str_mkl_version[1024];

double running_time;

// print MKL version

MKL_Get_Version_String(str_mkl_version, 1024);

printf("%s\n", str_mkl_version);

// input dimension

printf("Dim = "); scanf("%d", &dim);

if(dim <= 0)

{

printf("Illigal dimension! (dim = %d)\n", dim);

return EXIT_FAILURE;

}

// Initialize

pivot = (MKL_INT *)calloc(sizeof(MKL_INT), dim);

ma = (double *)calloc(sizeof(double), dim * dim);

vx = (double *)calloc(sizeof(double), dim);

vb = (double *)calloc(sizeof(double), dim);

// input va and vb

for(i = 0; i < dim; i++)

{

for(j = 0; j < dim; j++)

{

// A = hirbert matrix

//*(ma + i * dim + j) = 1.0 / (double)(i + j + 1);

// A = frank matrix

*(ma + i * dim + j) = (double)(dim - max(i, j));

}

// x = answer

*(vx + i) = (double) (i + 1);

}

// b := A * x

alpha = 1.0;

beta = 0.0;

cblas_dgemv(CblasRowMajor, CblasNoTrans, dim, dim, alpha, ma, dim, vx, 1, beta, vb, 1);

// print

/* printf("A = \n");

for(i = 0; i < dim; i++)

{

printf("%3d: ", i);

for(j = 0; j < dim; j++)

printf("%10f ", *(ma + i * dim + j));

printf("\n");

}

// print

printf("x = \n");

for(i = 0; i < dim; i++)

{

printf("%3d: ", i);

printf("%10f ", *(vx + i));

printf("\n");

}

// print

printf("b = \n");

for(i = 0; i < dim; i++)

{

printf("%3d: ", i);

printf("%10f ", *(vb + i));

printf("\n");

}

// solve A * X = C -> C := X

running_time = dsecnd(); // start

info = LAPACKE_dgesv(LAPACK_ROW_MAJOR, dim, 1, ma, dim, pivot, vb, 1);

running_time = dsecnd() - running_time; // end

// error occurs if info > 0

if(info > 0)

{

printf("pivot ma[%d][%d] is zero!\n", info, info);

return EXIT_FAILURE;

}

printf("Dimension: %d, Running Time(s): %g\n", dim, running_time);

// print

/* printf("calculated x = \n");

for(i = 0; i < dim; i++)

{

printf("%3d: ", i);

printf("%10f ", *(vb + i));

printf("\n");

}

// diff

printf("x - calculated x = \n");

for(i = 0; i < dim; i++)

{

printf("%3d: ", i);

printf("%10f ", fabs(*(vx + i) - *(vb + i)));

printf("\n");

}

// free

free(pivot);

free(ma);

free(vb);

free(vx);

return EXIT_SUCCESS;

}

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