I have a Lagrange interpolation algorithm that begins to diverge after many time steps and I can't seem to figure out why. As a quick review, if I had two arrays
int x[11] = {0, 10, 20, 30, 40, 50, 60, 70, 80, 90, 100}
int y[11] = {0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20}
and I input an x-value of 15 into the algorithm, the output (i.e. interpolated y-value) should be 3. The following algorithm gets the interpolated value correct, but as I cycle through incremented inputs eventually the outputs begin to diverge. I am not sure what is causing the divergence. The code creates two arrays of integers going from -100 to +100 and interpolates the values based on an incremented x-input. The values begin matching as they should, but around 55 or so the interpolated y-value begins to diverge. The code is below. Any insight would be greatly appreciated.
#include <stdio.h>
#define SIZE 201
int main()
{
double x[SIZE], y[SIZE], value, sum, factor[SIZE];
for (int i = 0; i < SIZE; i++)
{
x[i] = -100 + i;
}
for (int i = 0; i < SIZE; i++)
{
y[i] = -100 + i;
}
value = 0.0;
while (1)
{
sum = 0.0;
printf("Input is: %lf\n", value);
for(int i = 0; i < SIZE; i++)
{
factor[i] = 1.0;
for(int j = 0; j < SIZE; j++)
{
if(i != j)
{
factor[i] = factor[i] * (value - x[j])/(x[i] - x[j]);
}
}
sum = sum + factor[i] * y[i];
}
printf("Output is: %lf\n", sum);
// if ((value - sum) > 0.01) break;
if (value < 100) value += 0.001;
else break;
}
return 0;
}
Given N samples, the Lagrange polynomial is of the degree of N, in your case, 200. It is a pretty large degree, and for a value large enough the intermediate results (i.e. factor) starts behaving quite erratically. I printed factor after each iteration of the outer loop, and this is what I have on my machine (where the code diverges at value 62.1):
Input is: 62.100000
0.000000
-0.000000
0.000000
-0.000000
0.000000
-0.000000
0.000000
-0.000000
0.000000
-0.000000
0.000000
-0.000000
0.000000
-0.000000
0.000000
-0.000000
0.000000
-0.000000
0.000000
-0.000000
0.000000
-0.000000
0.000000
-0.000000
0.000000
-0.000000
0.000000
-0.000000
0.000000
-0.000000
0.000000
-0.000000
0.000000
-0.000000
0.000002
-0.000010
0.000047
-0.000212
0.000916
-0.003834
0.015558
-0.061214
0.233667
-0.865800
3.115490
-10.892598
37.019453
-122.351630
393.413839
-1231.176112
3751.320027
-11132.603776
32188.920849
-90709.929863
249216.884601
-667734.556134
1745251.075381
-4451006.398268
11079451.201015
-26924437.939740
63892139.532124
-148088119.614110
335320733.480250
-741923910.135582
1604370277.576735
-3391407192.476863
7009154161.161494
-14165714298.372702
28000907070.092331
-54142322716.578796
102423636122.796417
-189594810732.400879
343460854643.929565
-608991796878.604858
1057024952593.679688
-1796190002106.606201
2988571833231.810547
-4869319260810.958008
7769844431032.450195
-12143392562153.164062
18590594785582.515625
-27881222667878.292969
40966915113033.500000
-58978430272092.585938
83200365623915.609375
-115016713573880.578125
155822462931701.031250
-206899948714767.906250
269263745978734.968750
-343484172924072.000000
429506076055356.812500
-526485323131795.875000
632668952077638.500000
-745344926690223.250000
860883054405210.375000
-974879663742953.625000
1082405867199472.750000
-1178344322529343.250000
1257784740974879.500000
-1316436663535827.500000
1351011674779421.000000
-1359527880018181.000000
1341497535715305.750000
-1297973187760748.750000
1231446261994579.000000
-1145611653890577.250000
1045029162299372.250000
-934724762872858.125000
819779917571950.250000
-704954924193421.250000
594383648437451.875000
-491363855983359.125000
398252366806871.062500
-316460003024013.937500
246529925760965.156250
-188275766805651.375000
140953330916004.437500
-103441104978326.546875
74409294797142.390625
-52463275136077.218750
36253867741005.359375
-24552698830046.890625
16295359517452.095703
-10597930155882.712891
6753701701870.307617
-4216931244837.877441
2579609371842.192871
-1545902253614.920410
907502140862.699341
-521815325006.697205
293869684950.453308
-162078786010.080200
87537719445.039368
-46294138480.248749
23970808358.990040
-12151499571.568396
6030219319.167710
-2929269302.567177
1392763710.430415
-648125926.103312
295175902.544337
-131559694.388017
57381635.324659
-24492187.039684
10230449.673919
-4182126.956840
1673313.368037
-655394.261464
251347.530884
-94414.677824
34753.964878
-12544.686326
4444.407825
-1547.546444
530.612164
-179.651152
60.317931
-20.218974
6.844738
-2.391284
0.904560
-0.429040
1.136162
0.029430
-0.003145
0.000450
-0.000070
0.000011
-0.000002
0.000000
-0.000000
0.000000
-0.000000
0.000000
-0.000000
0.000000
-0.000000
0.000000
-0.000000
0.000000
-0.000000
0.000000
-0.000000
0.000000
-0.000000
0.000000
-0.000000
0.000000
-0.000000
0.000000
-0.000000
0.000000
-0.000000
0.000000
-0.000000
0.000000
-0.000000
0.000000
-0.000000
0.000000
-0.000000
Output is: 67.164298
Sorry for the volume of paste.
You can see that the code operates with very large factors (e.g. 155822462931701.031250) while sum stays around 1. This leads to loss of precision due to normalization. And the loss of precision amplifies as value grows.
Bottom line is, the naive Lagrange interpolation is numerically unstable. Check out Notes.
Related
Same matrix should be printed but here outside the function its not printing any value of the matrix. What is the issue here?(I dont want the argument name in function and name of variable passed to be same.)
0.000000 0.000000 0.000000 0.000000 0.000000
1.000000 1.000000 1.000000 1.000000 1.000000
2.000000 2.000000 2.000000 2.000000 2.000000
3.000000 3.000000 3.000000 3.000000 3.000000
0.000000 0.000000 0.000000 0.000000 0.000000
0.000000 0.000000 0.000000 0.000000 0.000000
0.000000 0.000000 0.000000 0.000000 0.000000
0.000000 0.000000 0.000000 0.000000 0.000000
#include<stdio.h>
#include<stdlib.h>
void tryn(double *a)
{
int i,j;
a=(double *)calloc(20,sizeof(double));
for(i=0;i<4;i++)
{
for(j=0;j<5;j++)
{
*(a+i*5+j)=i;
}
}
for(i=0;i<4;i++)
{
for(j=0;j<5;j++)
{
printf("%lf ",*(a+i*5+j));
}
printf("\n");
}
}
int main()
{
int i,j;
double *arr;
tryn(arr);
for(i=0;i<4;i++)
{
for(j=0;j<5;j++)
{
printf("%lf ",(arr+i*5+j));
}
printf("\n");
}
free(arr);
}
the output its giving
Parameters to functions in C are pass by value. That means that changes to a in tryn are not reflected in the calling function, so arr in main remains uninitialized.
You need to pass the address of arr to your function:
tryn(&arr);
And change the parameter type in the function accordingly:
void tryn(double **arr)
{
double *a=calloc(20,sizeof(double));
...
*arr = a;
}
It seems simple enough, query 15 records and put them in an array.
The code compiles and runs, but the array looses the values entered into it.
I print the values as they are entered into the array, and it appears correct. Though in a for loop, the first row is correct but incorrect after that.
The code:
printf("SQL returned %d rows\n", mysql_num_rows(res)) ;
i = 0 ;
while ((row = mysql_fetch_row(res)) != NULL)
{
sscanf(row[0], "%lf", &data[i][0]) ;
sscanf(row[1], "%lf", &data[i][1]) ; // bid will always be below ask
sscanf(row[2], "%lf", &data[i][2]) ; // offer = ask in this DB
sscanf(row[3], "%lf", &data[i][3]) ; // mid = average of all bid/ask for each minute
data[i][4] = 0 ; // MA5
data[i][5] = 0 ; // MA15
printf("%.0lf %lf %lf %lf %lf %lf\n", data[i][0], data[i][1], data[i][2], data[i][3], data[i][4], data[i][5]) ;
i++ ;
}
printf("\n") ;
for (j=0; j<15; j++)
printf("%.0lf %lf %lf %lf %lf %lf\n", data[j][0], data[j][1], data[j][2], data[j][3], data[j][4], data[j][5]) ;
The first 15 rows match what is in the database, but only the first row of the for loop is printing correct values.
SQL returned 15 rows
1506594851 150.912000 150.932000 150.909265 0.000000 0.000000
1506594792 150.921000 150.941000 150.925761 0.000000 0.000000
1506594731 150.940000 150.963000 150.959714 0.000000 0.000000
1506594674 150.949000 150.971000 150.969609 0.000000 0.000000
1506594611 150.954000 150.976000 150.957382 0.000000 0.000000
1506594551 150.940000 150.964000 150.935012 0.000000 0.000000
1506594492 150.906000 150.927000 150.910357 0.000000 0.000000
1506594431 150.881000 150.906000 150.865748 0.000000 0.000000
1506594371 150.822000 150.846000 150.821062 0.000000 0.000000
1506594851 150.912000 150.932000 150.909265 0.000000 0.000000
1506594251 150.768000 150.794000 150.751332 0.000000 0.000000
1506594194 150.701000 150.724000 150.715379 0.000000 0.000000
1506594134 150.740000 150.757000 150.754935 0.000000 0.000000
1506594076 150.749000 150.772000 150.758302 0.000000 0.000000
1506594011 150.755000 150.774000 150.753550 0.000000 0.000000
1506594851 150.912000 150.932000 150.909265 0.000000 0.000000
1506594251 150.768000 150.794000 150.751332 0.000000 0.000000
1506594194 150.701000 150.724000 150.715379 0.000000 0.000000
1506594134 150.740000 150.757000 150.754935 0.000000 0.000000
1506594076 150.749000 150.772000 150.758302 0.000000 0.000000
1506594011 150.755000 150.774000 150.753550 0.000000 0.000000
1506594492 150.906000 150.927000 150.910357 0.000000 0.000000
1506594431 150.881000 150.906000 150.865748 0.000000 0.000000
1506594371 150.822000 150.846000 150.821062 0.000000 0.000000
1506594312 150.798000 150.824000 150.798255 0.000000 0.000000
0 0.000000 97795656476117789550858635641226156856160388037177544822378925818587375507523129063032745851654482135492440234643161088.000000 270721760232452916408621777331997134952922302290494666767651053623661202019325513025428600003963936853860599692342289934319616.000000 0.000000 0.000000
0 0.000000 0.000000 0.000000 0.000000 0.000000
0 0.000000 0.000000 0.000000 0.000000 0.000000
0 0.000000 0.000000 0.000000 0.000000 0.000000
0 0.000000 0.000000 0.000000 0.000000 0.000000
I am unable to figure out why the array is changing, though the print statements are identical, only one in a while and the other in a for loop.
Thanks in advance
#include <stdio.h>
#include <stdlib.h>
#include "/usr/include/mysql/mysql.h"
#include <string.h> // strncpy
int main(void)
{
int i = 0 ;
int j = 0 ;
int n = 0 ;
int position = 0 ;
double pairsid = 8 ;
char sql[300] ;
double tmpdbl = 0 ;
double data[6][15] ; // Stamp, bid, ask, mid, SMA5, SMA15
char *server = "localhost" ;
char *user = "x" ;
char *password = "x" ; // set me first
char *database = "x";
MYSQL *con1 ;
MYSQL_RES *res ;
MYSQL_ROW row ;
con1 = mysql_init(NULL) ;
// Connect to database
if (!mysql_real_connect(con1, server, user, password, database, 0, NULL, 0))
{
fprintf(stderr, "DB Connect Error %s\n", mysql_error(con1)) ;
exit(1);
}
sprintf(sql, "(SELECT stamp, bid, ask, mid FROM oanda WHERE pairsid = %.0lf ORDER BY stamp LIMIT %d) ORDER BY stamp DESC", pairsid, 15) ;
printf("%s\n", sql) ;
if (mysql_query(con1, sql))
{
fprintf(stderr, "Error running query %s\n", mysql_error(con1)) ;
exit(1) ;
}
res = mysql_store_result(con1) ;
printf("SQL returned %d rows\n", mysql_num_rows(res)) ;
i = 0 ;
while ((row = mysql_fetch_row(res)) != NULL)
{
sscanf(row[0], "%lf", &data[i][0]) ;
sscanf(row[1], "%lf", &data[i][1]) ; // bid will always be below ask
sscanf(row[2], "%lf", &data[i][2]) ; // offer = ask in this DB
sscanf(row[3], "%lf", &data[i][3]) ; // mid = average of all bid/ask for each minute
data[i][4] = 0 ; // MA5
data[i][5] = 0 ; // MA15
printf("%.0lf %lf %lf %lf %lf %lf\n", data[i][0], data[i][1], data[i][2], data[i][3], data[i][4], data[i][5]) ;
i++ ;
}
printf("\n") ;
for (j=0; j<15; j++)
printf("%.0lf %lf %lf %lf %lf %lf\n", data[j][0], data[j][1], data[j][2], data[j][3], data[j][4], data[j][5]) ;
printf("\n") ;
mysql_free_result(res) ;
mysql_close(con1) ;
}
OK, got it working now. Thanks all
while ((row = mysql_fetch_row(res)) != NULL)
{
sscanf(row[0], "%lf", &data[0][i]) ;
sscanf(row[1], "%lf", &data[1][i]) ; // bid will always be below ask
sscanf(row[2], "%lf", &data[2][i]) ; // offer = ask in this DB
sscanf(row[3], "%lf", &data[3][i]) ; // mid = average of all bid/ask for each minute
data[4][i] = 0 ; // MA5
data[5][i] = 0 ; // MA15
printf("Row %d %.0lf %lf %lf %lf %lf %lf\n", i, data[0][i], data[1][i], data[2][i], data[3][i], data[4][i], data[5][i]) ;
i++ ;
}
printf("\n") ;
for (j=0; j<15; j++)
printf("%.0lf %lf %lf %lf %lf %lf\n", data[0][j], data[1][j], data[2][j], data[3][j], data[4][j], data[5][j]) ;
gives me
SQL returned 15 rows
Row 0 1506594851 150.912000 150.932000 150.909265 0.000000 0.000000
Row 1 1506594792 150.921000 150.941000 150.925761 0.000000 0.000000
Row 2 1506594731 150.940000 150.963000 150.959714 0.000000 0.000000
Row 3 1506594674 150.949000 150.971000 150.969609 0.000000 0.000000
Row 4 1506594611 150.954000 150.976000 150.957382 0.000000 0.000000
Row 5 1506594551 150.940000 150.964000 150.935012 0.000000 0.000000
Row 6 1506594492 150.906000 150.927000 150.910357 0.000000 0.000000
Row 7 1506594431 150.881000 150.906000 150.865748 0.000000 0.000000
Row 8 1506594371 150.822000 150.846000 150.821062 0.000000 0.000000
Row 9 1506594312 150.798000 150.824000 150.798255 0.000000 0.000000
Row 10 1506594251 150.768000 150.794000 150.751332 0.000000 0.000000
Row 11 1506594194 150.701000 150.724000 150.715379 0.000000 0.000000
Row 12 1506594134 150.740000 150.757000 150.754935 0.000000 0.000000
Row 13 1506594076 150.749000 150.772000 150.758302 0.000000 0.000000
Row 14 1506594011 150.755000 150.774000 150.753550 0.000000 0.000000
1506594851 150.912000 150.932000 150.909265 0.000000 0.000000
1506594792 150.921000 150.941000 150.925761 0.000000 0.000000
1506594731 150.940000 150.963000 150.959714 0.000000 0.000000
1506594674 150.949000 150.971000 150.969609 0.000000 0.000000
1506594611 150.954000 150.976000 150.957382 0.000000 0.000000
1506594551 150.940000 150.964000 150.935012 0.000000 0.000000
1506594492 150.906000 150.927000 150.910357 0.000000 0.000000
1506594431 150.881000 150.906000 150.865748 0.000000 0.000000
1506594371 150.822000 150.846000 150.821062 0.000000 0.000000
1506594312 150.798000 150.824000 150.798255 0.000000 0.000000
1506594251 150.768000 150.794000 150.751332 0.000000 0.000000
1506594194 150.701000 150.724000 150.715379 0.000000 0.000000
1506594134 150.740000 150.757000 150.754935 0.000000 0.000000
1506594076 150.749000 150.772000 150.758302 0.000000 0.000000
1506594011 150.755000 150.774000 150.753550 0.000000 0.000000
I am beginner using SSE instructions, and I try to implement MMM. So, I implemented MMM using matriz 2by2, now I want to implement MMM using matrix NXN
#include <emmintrin.h>
#include <stdio.h>
#include <stdlib.h>
void simd_2x2(int lda, double *A, double *B, double *C)
{
__m128d a, b1, c1;
for (int k = 0; k < lda; k++) {
//printf("%f\n",C[k * lda]);
c1 = _mm_loadu_pd(C + k * lda); //load unaligned block in C
//c2 = _mm_loadu_pd(C + 1 * lda);
for (int i = 0; i < lda; ++i) {
a = _mm_load_pd(A + i * lda);//load aligned i-th column of A
b1 = _mm_load1_pd(B + i + k * lda); //load i-th row of B
//b2 = _mm_load1_pd(B + i + 1 * lda);
c1 = _mm_add_pd(c1, _mm_mul_pd(a, b1)); //rank-1 update
//c2 = _mm_add_pd(c2, _mm_mul_pd(a, b2));
}
_mm_storeu_pd(C + k * lda, c1); //store unaligned block in C
//_mm_storeu_pd(C + 1 * lda, c2);
}
}
int main() {
int n = 2;
double *buf = NULL;
buf = (double *)malloc(3 * n * n * sizeof(double));
double *A = buf + 0;
double *B = A + n * n;
double *C = B + n * n;
simd_2x2(n, A, B, C);
return 0;
}
When n=2 everything work fine:
A = 4.000000 3.000000
2.000000 4.000000
B = 1.000000 3.000000
2.000000 4.000000
C = 0.000000 0.000000
0.000000 0.000000
C = C + A * B = 10.000000 24.000000
10.000000 22.000000
but if n=4 I get the next:
A = 4.000000 0.000000 1.000000 4.000000
2.000000 1.000000 4.000000 0.000000
3.000000 1.000000 2.000000 1.000000
4.000000 1.000000 3.000000 1.000000
B = 1.000000 5.000000 9.000000 13.000000
2.000000 6.000000 10.000000 14.000000
3.000000 7.000000 11.000000 15.000000
4.000000 8.000000 12.000000 16.000000
C = 0.000000 0.000000 0.000000 0.000000
0.000000 0.000000 0.000000 0.000000
0.000000 0.000000 0.000000 0.000000
0.000000 0.000000 0.000000 0.000000
C = C + A * B = 23.000000 59.000000 95.000000 131.000000
16.000000 44.000000 72.000000 100.000000
0.000000 0.000000 0.000000 0.000000
0.000000 0.000000 0.000000 0.000000
The last two rows are not calculated, why is this? Can someone help me?
I have almost 5 days reading about SSE but I can not fully understand and neither solve this problem.
I am trying to initialize two copies of the same two-dimensional arrays in C. However, only one stores the correct data:
//convert 1D array to 2D array
double** myA = malloc(n*sizeof(double*));
for (j=0;j<n;j++)
myA[j]=&a[j*n];
double** myS = (double **) malloc(n*sizeof(double*));
for (i=0; i<n; i++)
for (j=0; j<n; j++){
myS[i] = (double *) malloc(n*sizeof(double));
myS[i][j] = myA[i][j];
}
printf("A:\n");
print_matrix(myA,n);
printf("S:\n");
print_matrix(myS,n);
I want to initialize two copies of A. One as myA and the other as myS. However, here is my output:
A:
0.000000 1.000000 2.000000 3.000000 4.000000
1.000000 1.414214 2.236068 3.162278 4.123106
2.000000 2.236068 2.828427 3.605551 4.472136
3.000000 3.162278 3.605551 4.242641 5.000000
4.000000 4.123106 4.472136 5.000000 5.656854
S:
-0.000000 -0.000000 -0.000000 -0.000000 4.000000
-0.000000 -0.000000 -0.000000 -0.000000 4.123106
-0.000000 -0.000000 -0.000000 -0.000000 4.472136
-0.000000 -0.000000 -0.000000 -0.000000 5.000000
-0.000000 -0.000000 -0.000000 -0.000000 5.656854
Why are all the columns but the last -0.000000?
You're overwriting each row buffer N-1 times (and leaking memory like a sieve leaks water in the process).
Change this:
for (i=0; i<n; i++)
for (j=0; j<n; j++){
myS[i] = (double *) malloc(n*sizeof(double));
myS[i][j] = myA[i][j];
}
To this:
for (i=0; i<n; i++)
{
myS[i] = malloc(n*sizeof(double));
for (j=0; j<n; j++)
myS[i][j] = a[i*n+j];
}
Note two things in the above code:
Don't cast malloc.
The myA temp array is not needed. You can do the math with the index yourself. Throw that entire thing out.
I am trying to solve a simple linear equations system using LAPACK. I use dbsvg method which is optimised for banded matrices. I've obsereved a realy strange behaviour. When I fill the AT matrix this way:
for(i=0; i<DIM;i++) AB[0][i] = -1;
for(i=0; i<DIM;i++) AB[1][i] = 2;
for(i=0; i<DIM;i++) AB[2][i] = -1;
for(i=0; i<3; i++)
for(j=0;j<DIM;j++) {
AT[i*DIM+j]=AB[i][j];
}
And call:
dgbsv_(&N, &KL, &KU, &NRHS, AT, &LDAB, myIpiv, x, &LDB, &INFO);
It works perfectly. However, when I do it this way:
for(i=0; i<DIM;i++) AT[i] = -1;
for(i=0; i<DIM;i++) AT[DIM+i] = 2;
for(i=0; i<DIM;i++) AT[2*DIM+i] = -1;
It results with a vector filled with NaN. Here are the declarations:
double AB[3][DIM], AT[3*DIM];
double x[DIM];
int myIpiv[DIM];
int N=DIM, KL=1, KU=1, NRHS=1, LDAB=DIM, LDB=DIM, INFO;
Any ideas?
You're not laying out the entries in the band storage properly; it was working before by a happy accident. The LAPACK docs say:
On entry, the matrix A in band storage, in rows KL+1 to
2*KL+KU+1; rows 1 to KL of the array need not be set.
The j-th column of A is stored in the j-th column of the
array AB as follows:
AB(KL+KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+KL)
On exit, details of the factorization: U is stored as an
upper triangular band matrix with KL+KU superdiagonals in
rows 1 to KL+KU+1, and the multipliers used during the
factorization are stored in rows KL+KU+2 to 2*KL+KU+1.
See below for further details.
So if you want a tridiagonal matrix with 2 on the diagonal and -1 above and below, the layout should be:
* * * * * * * ... * * * *
* -1 -1 -1 -1 -1 -1 ... -1 -1 -1 -1
2 2 2 2 2 2 2 ... 2 2 2 2
-1 -1 -1 -1 -1 -1 -1 ... -1 -1 -1 *
LDAB should be 4 in this case. Bear in mind that LAPACK uses a column-major layout, so the actual array should be look like this in memory:
{ *, *, 2.0, -1.0, *, -1.0, 2.0, -1.0, *, -1.0, 2.0, -1.0, ... }
dgbsv was giving different results for the two identical arrays because it was reading off the ends of the arrays that you had laid out.
Is this the exact code you used or just an example? I ran this code here (just cut and pasted from your posts, with a change of AT to AT2 in the second loop:
const int DIM=10;
double AB[DIM][DIM], AT[3*DIM], AT2[3*DIM];
int i,j;
for(i=0; i<DIM;i++) AB[0][i] = -1;
for(i=0; i<DIM;i++) AB[1][i] = 2;
for(i=0; i<DIM;i++) AB[2][i] = -1;
for(i=0; i<3; i++)
for(j=0;j<DIM;j++) {
AT[i*DIM+j]=AB[i][j];
}
printf("AT:");
for (i=0;i<3*DIM;++i) printf("%lf ",AT[i]);
printf("\n\n");
for(i=0; i<DIM;i++) AT2[i] = -1;
for(i=0; i<DIM;i++) AT2[DIM+i] = 2;
for(i=0; i<DIM;i++) AT2[2*DIM+i] = -1;
printf("AT2:");
for (i=0;i<3*DIM;++i) printf("%lf ",AT2[i]);
printf("\n\n");
printf("Diff:");
for (i=0;i<3*DIM;++i) printf("%lf ",AT[i]-AT2[i]);
printf("\n\n");
and got this output
AT:-1.000000 -1.000000 -1.000000 -1.000000 -1.000000 -1.000000 -1.000000 -1.0000
00 -1.000000 -1.000000 2.000000 2.000000 2.000000 2.000000 2.000000 2.000000 2.0
00000 2.000000 2.000000 2.000000 -1.000000 -1.000000 -1.000000 -1.000000 -1.0000
00 -1.000000 -1.000000 -1.000000 -1.000000 -1.000000
AT2:-1.000000 -1.000000 -1.000000 -1.000000 -1.000000 -1.000000 -1.000000 -1.000
000 -1.000000 -1.000000 2.000000 2.000000 2.000000 2.000000 2.000000 2.000000 2.
000000 2.000000 2.000000 2.000000 -1.000000 -1.000000 -1.000000 -1.000000 -1.000
000 -1.000000 -1.000000 -1.000000 -1.000000 -1.000000
Diff:0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.0
00000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.
000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0
.000000 0.000000 0.000000 0.000000
Apparently AT and AT2 are the same. Which I would expect.