/*
?*?INFO
?*?File:?cholesky.c
?*?Date:?2015-10-21
?*?Author:?Team?of?Zhangguoqing
?*
?*?EXEC:
?*?Build:?mpicc?-o?cholesky?-lm?cholesky.c?
?*?Run:?mpiexec?-np?numprocess?./cholesky?matrix-order
?*?Note:?matrix-order?=?m?*?numprocess
?*?Verify:?http://www.yunsuanzi.com/matrixcomputations/solvecholeskyfactorization.html
?*
?*?*/

#include?
#include?
#include?
#include?
#include?“mpi.h“


//Macro?Definition
#define?RANDMAX?10


void?initMatrix（double?*matrix?int?row?int?col）
{
	int?i?j;
????for（i=0;?i		for（j=0;?j????????	matrix[i*col+j]=0;
????	}
	}
}


void?printMatrix（double?*matrix?int?row?int?col）
{
	int?i?j;
????for（i=0;?i		for（j=0;?j????????	printf（“%10.4f“?matrix[i*col+j]）;
????	}
????????printf（“\n“）;
	}
}


void?printTriangleMatrix（double?*matrix?int?order）
{
	int?i?j;
????for（i=0;?i		for（j=0;?j<=i;?j++）{
????????	printf（“%10.4f“?matrix[i*order+j]）;
????	}
????????printf（“\n“）;
????}
}


/*
?*?Function?Purpose:
?*?Generate?a?positive?random?（semi-）definite?matrices
?*?
?*?Method:
?*?Given?an?arbitrary?matrix?A?compute?M?=?AT?*?A
?*?AT?means?A‘s?transposition?（constructing?a?Cholesky?decomposition）
?*
?*?Reference:
?*?http://stackoverflow.com/questions/619335/a-simple-algorithm-for-generating-positive-semidefinite-matrices
?*
?*?*/
void?generate（double?*matrix?int?order）
{
	int?i?j?k;
????double?*ori_matrix?=?（double*）malloc（sizeof（double）*order*order）;
????double?*tra_matrix?=?（double*）malloc（sizeof（double）*order*order）;

????//Generate?origin?matrix
????printf（“#####?Generate?%d*%d?semi-definite?matrix?#####\n“?order?order）;
????srand（time（0））;
????for（i=0;?i		for（j=0;?j????????????ori_matrix[i*order+j]=（double）（rand（）%RANDMAX）?+?1;
		}
	}
????printf（“\nRand?Arbitrary?Matrix:\n“）;
????printMatrix（ori_matrix?order?order）;

????//Transpose?ori_matrix?tra_matrix
????for（i=0;?i		for（j=0;?j????????????tra_matrix[j*order+i]?=?ori_matrix[i*order+j];
		}
	}
????printf（“\nTranspose?matrix:\n“）;
????printMatrix（tra_matrix?orderorder）;

????//matrix?=?ori_matrix?*?tra_matrix
????for（i=0;?i		for（j=0;?j		????for（k=0;?k????????????????matrix[i*order+j]?=?matrix[i*order+j]?+?tra_matrix[i*order+k]?*?ori_matrix[k*order+j];
????????????}
		}
	}
????printf（“\nSemi-definite?Matrix?one-dimension:\n“）;
????printMatrix（matrix?orderorder）;

????free（ori_matrix）;
????free（tra_matrix）;
}


void?serial_cholesky（double?*A_matrix?int?order）
{
????int?i?j?k;
????double?sum;
????double?*matrix?=?（double*）malloc（sizeof（double）*order*order）;
????for（i=0;i????????for（j=0;j????????????matrix[i*order+j]?=?A_matrix[i*order+j];
????????}
????}

	for（j=0;?j		sum?=?0.0;
		for（k=0;?k			sum?+=?matrix[j*order+k]?*?matrix[j*order+k];
		}
		matrix[j*order+j]?=?matrix[j*order+j]?-?sum;
		matrix[j*order+j]?=?sqrt（matrix[

?屬性????????????大小?????日期????時間???名稱
-----------?---------??----------?-----??----
?????目錄???????????0??2015-11-10?14:32??Cholesky?MPI并行C語言實現\
?????文件????????7936??2015-11-10?14:20??Cholesky?MPI并行C語言實現\cholesky.c
?????文件?????1854464??2015-11-10?14:28??Cholesky?MPI并行C語言實現\Cholesky并行分解-實驗報告.doc