int LinearFitting::computeFitting(double *fitting, double *model, int nModel,
int index1, int index2, double &xAtMin)
//The model is represented by an array of real numbers that are the
//exponentials. For example, if model={0, 0.5, 1.0, 2.0}, then,
//nModel would be 4; and y=c_0*x^0 + c_1*x^0.5 + c_2*x + c_3*x^2.0 .
//index1 and index2 are the starting index and endind index of the
//fitting range.
{
if( index1>index2 || index1<0 || index2>(nDim-1) )
return 1;
int M=index2-index1+1;
int N=nModel;
int i, j;
double lastMin, xx, val;
double inc=1.0/(nDim-1);
double *a=(double *)malloc(N*M*sizeof(double));
double *aa=(double *)malloc(N*nDim*sizeof(double));
for( i=0; i<N; i++){
for(j=0; j<M; j++){
*(a+i*M+j)=pow( (index1+j)*inc, model[i] );
}
}
for( i=0; i<N; i++)
for(j=0; j<nDim; j++){
*(aa+i*nDim+j)=pow( j*inc, model[i] );
}
double *b=(double *)malloc(M*sizeof(double));
for(i=0;i<M;i++) {
b[i]=raw[i+index1];
}
for(i=0;i<nDim;i++)
fitting[i]=0.0;
int NRHS=1;
int LWORK=5*M*N;
double *work=(double*)malloc(LWORK*sizeof(double));
/* = 0: successful exit
* < 0: if INFO = -i, the i-th argument had an illegal value.
* > 0: the algorithm for computing the SVD failed to converge;
* if INFO = i, i off-diagonal elements of an intermediate
* bidiagonal form did not converge to zero.
*/
int INFO=1000;
double *sv=(double*)malloc(N*sizeof(double)); // store singular values
//negative: so machine precision is used as minimun singular value;
double RCOND=-5.0;
int RANK=-3;
//Solve the minimum norm problem || b- A^T * X ||,
//M is the number of rows of A^T, the solution is stored in b.
dgelss(&M, &N, &NRHS, a, &M, b, &M, sv, &RCOND, &RANK, work, &LWORK,
&INFO);
for(i=0;i<nDim;i++)
for(j=0;j<N;j++)
fitting[i]+=b[j]*(*(aa+j*nDim+i));
printf("Linear fitting parameters for range %d to %d are:\n", index1, index2);
for(i=0;i<N;i++)
printf("x[%d]=%f\t", i, b[i]);
printf("RANK=%d INFO=%d \n", RANK, INFO);
// Find the first minimum after the starting point
xAtMin = index1 * inc;
lastMin = fitting[index1];
for (i = 0; i < (index2 + 1 - index1) * 10000; i++) {
xx = (index1 + (i + 1) / 10000.) * inc;
val = 0.;
for(j=0;j<N;j++)
val += b[j] * pow(xx, model[j]);
if (val > lastMin)
break;
xAtMin = xx;
lastMin = val;
}
free(a);
free(aa);
free(b);
free(work);
free(sv);
return INFO;
}
END_TEST
START_TEST( using_MKL_SVD )
{
PetscErrorCode ierr;
int Np = 7;
int m = Np, n = 3;
int lda = m;
double *a;
PetscMalloc(m*n*sizeof(double), &a);
double aa[21] = {1., -2.50725, 6.28632, 1., -1.7072, 2.91453, 1., -0.726423, 0.527691, 1., \
0.452286, 0.204562, 1., 1.81034, 3.27735, 1., 2.53149, 6.40844, 1., 3.76245, \
14.1561};
double at[21] = {1, 1, 1, 1, 1, 1, 1, -2.50725, -1.7072, -0.726423, 0.452286, 1.81034, \
2.53149, 3.76245, 3.14316, 1.45727, 0.263846, 0.102281, 1.63868, 3.20422, \
7.07805};
double y[7]={1, 2, 5, 9, 7, 6, 5};
for( int i = 0; i < m*n; i++ )
a[i] = at[i];
int ldb = Np;
int nrhs = 1;
double *b;
PetscMalloc(Np*nrhs*sizeof(double), &b);
PetscMemzero(b,Np*nrhs*sizeof(double));
// double bb[9] = {one, zero, zero,
// zero, one, zero,
// zero, zero, one};
// for( int i = 0; i < nrhs*m; i++)
// b[i] = bb[i];
/* NEED B matrix to be Np identity!!! */
for( int i = 0; i < Np*nrhs; i++)
b[i] = y[i];
// b[i+i*Np] = one;
double rcond = -1;
int lwork = 1000;
double *work;
PetscMalloc(lwork*sizeof(double), &work);
// PetscMemzero(work, lwork*sizeof(double));
int rank;
double *s;
PetscMalloc( m*sizeof(double), &s);
int info;
dgelss(
&m /* num rows in A */, //3
&n /* num cols in A */, //7
&nrhs /* num cols in B */,//3
a /* matrix A for SVD */,
&lda /* first dim of A = max( 1, m )*/, //3
b /* matrix B of RHS (become solution matrix x) */,
&ldb /* first dim of B = max( 1, m, n ) */, //7
s /* matrix of s.v */,
&rcond /* relative condition s.v. treated as zero */, //-1
&rank /* */,
work /* */,
&lwork /* size of work */,
&info /* */
);
printf("rank: %d\n", rank);
printf("work[0]: %f\n", work[0] );
printf("info: %d\n", info);
for( int i = 0; i < n+0*Np*nrhs; i++)
printf("b %d: %f\n", i, b[i]);
printf("\n");
for( int i = 0; i < 3; i++)
printf("s %d: %f\n", i, s[i]);
printf("\n");
for( int i = 0; i < m*n; i++)
printf("a %d: %f\n", i, a[i]);
printf("\n");
}
