PPOTRI
计算经过Cholesky分解后的矩阵的逆矩阵。
接口定义
C Interface：
void pspotri_(const char *uplo, const int *n, float *a, const int *ia, const int *ja, const int *desca, int *info)
void pdpotri_(const char *uplo, const int *n, double *a, const int *ia, const int *ja, const int *desca, int *info)
void pcpotri_(const char *uplo, const int *n, float _Complex *a, const int *ia, const int *ja, const int *desca, int *info)
void pzpotri_(const char *uplo, const int *n, double _Complex *a, const int *ia, const int *ja, const int *desca, int *info)
Fortran Interface：
PSPOTRI(uplo, n, a, ia, ja, desca, info)
PDPOTRI(uplo, n, a, ia, ja, desca, info)
PCPOTRI(uplo, n, a, ia, ja, desca, info)
PZPOTRI(uplo, n, a, ia, ja, desca, info)
参数
参数 |
类型 |
范围 |
说明 |
输入/输出 |
|---|---|---|---|---|
uplo |
字符 |
全局 |
U为上三角矩阵，L为下三角矩阵。 |
输入 |
n |
整型 |
全局 |
要操作的列数，比如子矩阵的列数。 |
输入 |
a |
|
本地 |
是全局实对称或Hermitiand的本地部分，在该接口中，为进行Cholesky分解后的矩阵。
|
输入，输出 |
ia |
整型 |
全局 |
子矩阵在全局矩阵中的行索引。 |
输入 |
ja |
整型 |
全局 |
子矩阵在全局矩阵中的列索引。 |
输入 |
desca |
整型数组 |
本地，全局 |
分布式矩阵A的矩阵描述符。 |
输入 |
info |
整型 |
全局 |
执行结果：
|
输出 |
依赖
#include <kscalapack.h>
示例
int izero=0;
int ione=1;
int myid, nprocs_mpi;
MPI_Init( &argc, &argv);
MPI_Comm_rank(MPI_COMM_WORLD, &myid);
MPI_Comm_size(MPI_COMM_WORLD, &nprocs_mpi);
int n = 8; // (Global) Matrix size
int nprow = 2; // Number of row procs
int npcol = 2; // Number of column procs
int nb = 4; // (Global) Block size
char uplo='L'; // Matrix is lower triangular
char layout='R'; // Block cyclic, Row major processor mapping
printf("Usage: ./test matrix_size block_size nprocs_row nprocs_col\n");
if(argc > 1) {
n = atoi(argv[1]);
}
if(argc > 2) {
nb = atoi(argv[2]);
}
if(argc > 3) {
nprow = atoi(argv[3]);
}
if(argc > 4) {
npcol = atoi(argv[4]);
}
assert(nprow * npcol == nprocs_mpi);
// Initialize BLACS
int iam, nprocs;
int zero = 0;
int ictxt, myrow, mycol;
blacs_pinfo_(&iam, &nprocs) ; // BLACS rank and world size
blacs_get_(&zero, &zero, &ictxt ); // -> Create context
blacs_gridinit_(&ictxt, &layout, &nprow, &npcol ); // Context -> Initialize the grid
blacs_gridinfo_(&ictxt, &nprow, &npcol, &myrow, &mycol ); // Context -> Context grid info (# procs row/col, current procs row/col)
ofstream f1;
string filename;
// Compute the size of the local matrices
int mpA = numroc_( &n, &nb, &myrow, &izero, &nprow ); // My proc -> row of local A
int nqA = numroc_( &n, &nb, &mycol, &izero, &npcol ); // My proc -> col of local A
//allocate and fill the matrices A and B
double *A;
A = (double *)calloc(mpA*nqA,sizeof(double)) ;
if (A==NULL){ printf("Error of memory allocation A on proc %dx%d\n",myrow,mycol); exit(0); }
int k = 0;
for (int j = 0; j < nqA; j++) { // local col
int l_j = j / nb; // which block
int x_j = j % nb; // where within that block
int J = (l_j * npcol + mycol) * nb + x_j; // global col
for (int i = 0; i < mpA; i++) { // local row
int l_i = i / nb; // which block
int x_i = i % nb; // where within that block
int I = (l_i * nprow + myrow) * nb + x_i; // global row
assert(I < n);
assert(J < n);
if(I == J) {
A[k] = nb * nb;
} else {
A[k] = I + J;
}
//printf("%d %d -> %d %d -> %f\n", i, j, I, J, A[k]);
k++;
}
}
//creat descriptor
int descA[9];
int info=0;
int lddA = mpA > 1 ? mpA : 1;
descinit_( descA, &n, &n, &nb, &nb, &izero, &izero, &ictxt, &lddA, &info);
if(info != 0) {
printf("Error in descinit, info = %d\n", info);
}
pdpotrf_(&uplo, &n, A, &ione, &ione, descA, &info);
filename = to_string(myid)+"begin.dat";
f1.open(filename);
k = 0;
for (int j = 0; j < nqA; j++) { // local col
int l_j = j / nb; // which block
int x_j = j % nb; // where within that block
int J = (l_j * npcol + mycol) * nb + x_j; // global col
for (int i = 0; i < mpA; i++) { // local row
int l_i = i / nb; // which block
int x_i = i % nb; // where within that block
int I = (l_i * nprow + myrow) * nb + x_i; // global row
assert(I < n);
assert(J < n);
f1 <<I << " "<<J << " " << A[k]<<endl;
k++;
}
}
f1.close();
//run pdpotri_ and time
double MPIt1 = MPI_Wtime();
printf("[%dx%d] Starting \n", myrow, mycol);
pdpotri_(&uplo, &n, A, &ione, &ione, descA, &info);
if (info != 0) {
printf("Error in caculate, info = %d\n", info);
}
double MPIt2 = MPI_Wtime();
printf("[%dx%d] Finishing \n", myrow, mycol);
filename = to_string(myid)+"end.dat";
f1.open(filename);
k = 0;
for (int j = 0; j < nqA; j++) { // local col
int l_j = j / nb; // which block
int x_j = j % nb; // where within that block
int J = (l_j * npcol + mycol) * nb + x_j; // global col
for (int i = 0; i < mpA; i++) { // local row
int l_i = i / nb; // which block
int x_i = i % nb; // where within that block
int I = (l_i * nprow + myrow) * nb + x_i; // global row
assert(I < n);
assert(J < n);
f1 <<I << " "<<J << " " << A[k]<<endl;
k++;
}
}
f1.close();
free(A);
//exit and finanlize
blacs_gridexit_(&ictxt);
MPI_Finalize();
return 0;
/*
输入矩阵A
[[ 4.000000 1.000000 2.000000 3.000000 4.000000 5.000000 6.000000 7.000000]
[ 0.250000 3.992180 3.000000 4.000000 5.000000 6.000000 7.000000 8.000000]
[ 0.500000 0.720158 3.902740 5.000000 6.000000 7.000000 8.000000 9.000000]
[ 0.750000 0.954992 1.008840 3.675290 7.000000 8.000000 9.000000 10.000000]
[ 1.000000 1.189830 1.189710 1.064810 3.321910 9.000000 10.000000 11.000000]
[ 1.250000 1.424660 1.370580 1.175220 0.955149 2.869830 11.000000 12.000000]
[ 1.500000 1.659490 1.551450 1.285620 0.996646 0.756689 2.317410 13.000000]
[ 1.750000 1.894330 1.732320 1.396030 1.038140 0.734271 0.500013 1.591320]]
输出矩阵A
[[ 8.797610e-02 1.000000e+00 2.000000e+00 3.000000e+00 4.000000e+00 5.000000e+00 6.000000e+00 7.000000e+00]
[ 2.352190e-02 9.302160e-02 3.000000e+00 4.000000e+00 5.000000e+00 6.000000e+00 7.000000e+00 8.000000e+00]
[ 2.091620e-02 1.902120e-02 9.982790e-02 5.000000e+00 6.000000e+00 7.000000e+00 8.000000e+00 9.000000e+00]
[ 1.726830e-02 1.542070e-02 1.295720e-02 1.095080e-01 7.000000e+00 8.000000e+00 9.000000e+00 1.000000e+01]
[ 1.179650e-02 1.001990e-02 7.651130e-03 4.334850e-03 1.243600e-01 9.000000e+00 1.000000e+01 1.100000e+01]
[ 2.676710e-03 1.018570e-03 -1.192280e-03 -4.287470e-03 -8.930260e-03 1.499980e-01 1.100000e+01 1.200000e+01]
[-1.556280e-02 -1.698410e-02 -1.887910e-02 -2.153210e-02 -2.551170e-02 -3.214420e-02 2.045910e-01 1.300000e+01]
[-7.028140e-02 -7.099200e-02 -7.193950e-02 -7.326610e-02 -7.525580e-02 -7.857210e-02 -8.520470e-02 3.948980e-01]]
*/
父主题： 矩阵求逆函数
