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POLogic error for Gauss elimination
 

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  1. POLogic error for Gauss elimination
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    <p>Logic error problem with the Gaussian Elimination code...This code was from my Numerical Methods text in 1990's. The code is typed in from the book- not producing correct output...</p> <p>Sample Run: </p> <pre><code> SOLUTION OF SIMULTANEOUS LINEAR EQUATIONS USING GAUSSIAN ELIMINATION This program uses Gaussian Elimination to solve the system Ax = B, where A is the matrix of known coefficients, B is the vector of known constants and x is the column matrix of the unknowns. Number of equations: 3 Enter elements of matrix [A] A(1,1) = 0 A(1,2) = -6 A(1,3) = 9 A(2,1) = 7 A(2,2) = 0 A(2,3) = -5 A(3,1) = 5 A(3,2) = -8 A(3,3) = 6 Enter elements of [b] vector B(1) = -3 B(2) = 3 B(3) = -4 SOLUTION OF SIMULTANEOUS LINEAR EQUATIONS The solution is x(1) = 0.000000 x(2) = -1.#IND00 x(3) = -1.#IND00 Determinant = -1.#IND00 Press any key to continue . . . </code></pre> <p>The code as copied from the text...</p> <pre><code>//Modified Code from C Numerical Methods Text- June 2009 #include &lt;stdio.h&gt; #include &lt;math.h&gt; #define MAXSIZE 20 //function prototype int gauss (double a[][MAXSIZE], double b[], int n, double *det); int main(void) { double a[MAXSIZE][MAXSIZE], b[MAXSIZE], det; int i, j, n, retval; printf("\n \t SOLUTION OF SIMULTANEOUS LINEAR EQUATIONS"); printf("\n \t USING GAUSSIAN ELIMINATION \n"); printf("\n This program uses Gaussian Elimination to solve the"); printf("\n system Ax = B, where A is the matrix of known"); printf("\n coefficients, B is the vector of known constants"); printf("\n and x is the column matrix of the unknowns."); //get number of equations n = 0; while(n &lt;= 0 || n &gt; MAXSIZE) { printf("\n Number of equations: "); scanf ("%d", &amp;n); } //read matrix A printf("\n Enter elements of matrix [A]\n"); for (i = 0; i &lt; n; i++) for (j = 0; j &lt; n; j++) { printf(" A(%d,%d) = ", i + 1, j + 1); scanf("%lf", &amp;a[i][j]); } //read {B} vector printf("\n Enter elements of [b] vector\n"); for (i = 0; i &lt; n; i++) { printf(" B(%d) = ", i + 1); scanf("%lf", &amp;b[i]); } //call Gauss elimination function retval = gauss(a, b, n, &amp;det); //print results if (retval == 0) { printf("\n\t SOLUTION OF SIMULTANEOUS LINEAR EQUATIONS\n"); printf("\n\t The solution is"); for (i = 0; i &lt; n; i++) printf("\n \t x(%d) = %lf", i + 1, b[i]); printf("\n \t Determinant = %lf \n", det); } else printf("\n \t SINGULAR MATRIX \n"); return 0; } /* Solves the system of equations [A]{x} = {B} using */ /* the Gaussian elimination method with partial pivoting. */ /* Parameters: */ /* n - number of equations */ /* a[n][n] - coefficient matrix */ /* b[n] - right-hand side vector */ /* *det - determinant of [A] */ int gauss (double a[][MAXSIZE], double b[], int n, double *det) { double tol, temp, mult; int npivot, i, j, l, k, flag; //initialization *det = 1.0; tol = 1e-30; //initial tolerance value npivot = 0; //mult = 0; //forward elimination for (k = 0; k &lt; n; k++) { //search for max coefficient in pivot row- a[k][k] pivot element for (i = k + 1; i &lt; n; i++) { if (fabs(a[i][k]) &gt; fabs(a[k][k])) { //interchange row with maxium element with pivot row npivot++; for (l = 0; l &lt; n; l++) { temp = a[i][l]; a[i][l] = a[k][l]; a[k][l] = temp; } temp = b[i]; b[i] = b[k]; b[k] = temp; } } //test for singularity if (fabs(a[k][k]) &lt; tol) { //matrix is singular- terminate flag = 1; return flag; } //compute determinant- the product of the pivot elements *det = *det * a[k][k]; //eliminate the coefficients of X(I) for (i = k; i &lt; n; i++) { mult = a[i][k] / a[k][k]; b[i] = b[i] - b[k] * mult; //compute constants for (j = k; j &lt; n; j++) //compute coefficients a[i][j] = a[i][j] - a[k][j] * mult; } } //adjust the sign of the determinant if(npivot % 2 == 1) *det = *det * (-1.0); //backsubstitution b[n] = b[n] / a[n][n]; for(i = n - 1; i &gt; 1; i--) { for(j = n; j &gt; i + 1; j--) b[i] = b[i] - a[i][j] * b[j]; b[i] = b[i] / a[i - 1][i]; } flag = 0; return flag; } </code></pre> <p>The solution should be: 1.058824, 1.823529, 0.882353 with det as -102.000000</p> <p>Any insight is appreciated...</p>
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    1. USStefan Mai
    1. USiwanttoprogram
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    1. This table or related slice is empty.
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      1. POLogic error for Gauss elimination
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      1. VTUpMod
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      1. VTFavorite
    1. COWhat book are you using? Did you check for errata?
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      1. USBill the Lizard
    2. COI think you got the code wrong some where. Did you check them against other input? But again, the code looks right to me.
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      1. USGuru
    3. COas Bill said, check for errata
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      1. POLogic error for Gauss elimination
      1. USMitch Wheat
 

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