Convert symmetric matrix between packed and full storage?

Question

I\'m new to numerical linear algebra, and I have just started using LAPACK and BLAS.

Is there a routine that can copy/convert a symmetric matrix between packed and f

Answer 1

The obvious solution is to symmetrize the matrix by a "home-made/diy" code, the risk being to re-invent the wheel. It is pretty easy to write the for loops needed to symmetrize the matrix after dtpttr.

for(i=0;i<n;i++){
  for(j=i+1;j<n;j++){
    a[i*n+j]=a[j*n+i];
  }
}

Is it efficient enough for your application ? On a 10000x10000 matrix, these for loops last 0.88s on my PC, while dtpttr lasts 0.24s.

Here is the test code. Compile it with gcc main.c -o main -llapack -lblas -lm :

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <time.h>

void dtrttp_(char* UPLO,int* N,double* A,int* LDA,double* AP,int* INFO);
void dtpttr_(char* UPLO,int* N,double* AP,double* A,int* LDA,int* INFO);
void daxpy_(int* N,double* DA,double* DX,int* INCX,double* DY,int* INCY);

void dtpttf_(char* TRANSR,char* UPLO,int* N,double* AP,double* ARF,int* INFO);

int main(int argc, char **argv)
{

    int n=10;
    int info;

    double *a=malloc(n*n*sizeof(double));
    double *packed=malloc((n*(n+1))/2*sizeof(double));

    int i,j;
    for(i=0;i<n;i++){
        for(j=0;j<n;j++){
            a[i*n+j]=i+j;
        }
    }

    printf("matrix before pack\n");
    for(i=0;i<n;i++){
        for(j=0;j<n;j++){
            printf("%g ",a[i*n+j]);
        }
        printf("\n");
    }

    printf("\n");
    //pack
    dtrttp_("U",&n,a,&n,packed,&info);

    //unpack
    memset(a,0,n*n*sizeof(double));
    dtpttr_("U",&n,packed,a,&n,&info);

    for(i=0;i<n;i++){
        for(j=i+1;j<n;j++){
            a[i*n+j]=a[j*n+i];
        }
    }

    printf("matrix after unpack\n");
    for(i=0;i<n;i++){
        for(j=0;j<n;j++){
            printf("%g ",a[i*n+j]);
        }
        printf("\n");
    }

    free(a);
    free(packed);

    printf("timing...\n");

    n=10000;

    a=malloc(n*n*sizeof(double));
    packed=malloc((n*(n+1))/2*sizeof(double));

    for(i=0;i<n;i++){
        for(j=0;j<n;j++){
            a[i*n+j]=i+j;
        }
    }

    //pack
    dtrttp_("U",&n,a,&n,packed,&info);

    //unpack
    memset(a,0,n*n*sizeof(double));
    clock_t t;
    t = clock();
    dtpttr_("U",&n,packed,a,&n,&info);
    t = clock() - t;
    printf ("dtpttr took %f seconds.\n",((double)t)/CLOCKS_PER_SEC);
    t = clock();
    for(i=0;i<n;i++){
        for(j=i+1;j<n;j++){
            a[i*n+j]=a[j*n+i];
        }
    }
    t = clock() - t;
    printf ("symmetrize took %f seconds.\n",((double)t)/CLOCKS_PER_SEC);
    free(a);
    free(packed);

    return 0;
}