function solaxbr(dataForm){
// Main program for solving the system Ax = b.
// Assumes all entries are real numbers.
// Gets input from a textarea box via sub-routine tinabr.
var MAXDIM = 12; // Maximum size, N, of system accepted by this script.
var dataFormElements = dataForm.elements; // Reference to the form elements array.
var textareaIndex = 0; // The form array index for the textarea element
var textareaString = "";
var MATRIXDIM = 0; // The dimension, N, of the system to be entered.
var inverseAFlag = 0; // Assume determinant AND inverse will be computed
var dummy; // Float variable
var A = new Array(MAXDIM);
var PMatrix = new Array(MAXDIM); // Permutation Matrix
var LowerMatrix = new Array(MAXDIM); // Lower Matrix
var UpperMatrix = new Array(MAXDIM); // Upper Matrix
var b = new Array(MAXDIM);
var ipvt = new Array(MAXDIM); // Vector for keeping track of permutations
for (var i = 0; i < MAXDIM; i++){ // Create the square Matrices
A[i] = new Array(MAXDIM);
PMatrix[i] = new Array(MAXDIM);
LowerMatrix[i] = new Array(MAXDIM);
UpperMatrix[i] = new Array(MAXDIM);
} // End of for i loop
// strPar is a dummy variable for passing the output string by reference
var strPar = new Object();
strPar.outmsgstr = "";
// inputPar is a dummy variable for passing input parameters by reference
var inputPar = new Object();
inputPar.mDim = 0;
inputPar.inEr = 0;
// outputPar is a dummy variable for passing output parameters by reference
var outputPar = new Object();
outputPar.rcond = 0; // The condition number
outputPar.outEr = 0; // Error code
// detOPar is a dummy variable for passing determinant parameters by reference
var detOPar = new Object();
detOPar.det1 = 1.0;
detOPar.det2 = 0.0;
document.getElementById('output').innerHTML = "";
textareaString = textareaString + dataFormElements[textareaIndex].value;
// Pass the raw array into the sub-routine tinabr for processing.
tinabr(textareaString, inputPar, A, b);
if (inputPar.inEr != 0) return;
MATRIXDIM = inputPar.mDim;
// *******************************************************************
// At this point, MATRIXDIM should be the matrix dimension
// and the A and b matrices should contain their appropriate values.
// ********************************************************************
saxbr(MATRIXDIM, A, b, ipvt, outputPar);
// *******************************************************************
// At this point, the original A matrix has been overwritten by
// coefficients of the LU decomposition and b contains the solution vector, x.
// ********************************************************************
strPar.outmsgstr = "
The x vector components follow:
";
realVecOut(MATRIXDIM, b, strPar);
strPar.outmsgstr = strPar.outmsgstr + "
Error Code = " + outputPar.outEr + "
";
strPar.outmsgstr = strPar.outmsgstr + " rcond = " + outputPar.rcond + "
";
// Initialize the P, L, and U Matrices
for (var i = 0; i < MATRIXDIM; i++){
for (var j = 0; j < MATRIXDIM; j++){
if (j >= i) {
UpperMatrix[i][j] = A[i][j];
if (j == i) PMatrix[i][j] = LowerMatrix[i][j] = 1.0;
else PMatrix[i][j] = LowerMatrix[i][j] = 0.0;
} // End if (j >= i)
else { // j < i
PMatrix[i][j] = UpperMatrix[i][j] = 0.0;
LowerMatrix[i][j] = -A[i][j];
} // End else j < i
} // End for j loop
} // End for i loop
if ((1.0 + outputPar.rcond) == 1.0) inverseAFlag = 1; // Compute determinant only
calcdetAr(MATRIXDIM, A, ipvt, detOPar, inverseAFlag);
strPar.outmsgstr = strPar.outmsgstr + " The determinant of [A] = " + (detOPar.det1)*Math.pow(10.0,(detOPar.det2)) + "
";
// The following code block is extra to SGEFS, to explicitly output the [P], [L], and [U] Matrices.
// ************************************************************************
// Rearrange the L Matrix according to ipvt
for (var i = 1; i < (MATRIXDIM - 1); i++){
if (ipvt[i] != i){
for (var j = 0; j < i; j++) {
dummy = LowerMatrix[i][j];
LowerMatrix[i][j] = LowerMatrix[ipvt[i]][j];
LowerMatrix[ipvt[i]][j] = dummy;
} // End for j loop
} // End if (ipvt[i] != i)
} // End for i loop
// Rearrange the P Matrix according to ipvt
for (var i = (MATRIXDIM - 1); i >= 0; i--){ // Make sure to do ONE LESS loop than matrix dimension
if (ipvt[i] != i){ // Swap the rows
for (var j = 0; j < MATRIXDIM; j++){
dummy = PMatrix[i][j];
PMatrix[i][j] = PMatrix[ipvt[i]][j];
PMatrix[ipvt[i]][j] = dummy;
} // End for j
} // End if (ipvt[i] != i)
} // End for i
// End of extra code block to explicitly define the [P][L][U] Matrices.
// ************************************************************************
strPar.outmsgstr = strPar.outmsgstr + "
The [U] Matrix components follow:
";
sqmrOut(MATRIXDIM, UpperMatrix, strPar);
strPar.outmsgstr = strPar.outmsgstr + "
The [L] Matrix components follow:
";
sqmrOut(MATRIXDIM, LowerMatrix, strPar);
strPar.outmsgstr = strPar.outmsgstr + "
The [P] Matrix components follow:
";
sqmrOut(MATRIXDIM, PMatrix, strPar);
if (inverseAFlag > 0){
strPar.outmsgstr = strPar.outmsgstr + "
rcond indicates A near singular so A-inverse not computed.
";
} //End if (inverseAFlag > 0)
else {
strPar.outmsgstr = strPar.outmsgstr + "
[A] inverse components follow:
";
sqmrOut(MATRIXDIM, A, strPar);
}
document.getElementById('output').innerHTML = strPar.outmsgstr;
return;
} //End of solaxbr
// end of JavaScript-->