BackSub
Advanced Analysis Library Only
AnalysisLibErrType BackSub (void *inputMatrixA, double knownVectory[], ssize_t arraySizes, double outputVectorx[]);
Purpose
Solves linear equations AX=Y using backward substitution. BackSub assumes that A is an upper triangular matrix whose diagonal elements are all ones. BackSub obtains X using the following formulas:
The input matrix must be an upper triangular matrix or a matrix obtained from LU decomposition.
BackSub can perform the operation in place; that is, the input and output arrays can be the same. Use BackSub in conjunction with LU and ForwSub to solve linear equations.
Example Code
/* to solve a linear equation A*x = y */
double A[10][10], x[10], y[10];
int p[10]; /* permutation vector */
int sign, n;
n = 10;
LU(A, n, p, &sign); /* LU decomposition of A */
ForwSub(A, y, n, x, p); /* forward substitution */
BackSub(A, x, n, x); /* backward substitution */
Parameters
| Input | ||
| Name | Type | Description |
| inputMatrix_A | void * | Input square matrix. inputMatrixA can be either an upper triangular matrix or a matrix from the LU decomposition. This matrix must be an array of doubles. |
| knownVector_y | double [] | The array that represents the set of known vector coefficients. |
| arraySizes | ssize_t | The number of rows and columns in the square input matrix and the number of elements in the known vector array. The size of knownVectory must be arraySizes. |
| Output | ||
| Name | Type | Description |
| outputVector_x | double [] | The solution vector. outputVectorx can be NULL or knownVectory to perform in place operation. |
Return Value
| Name | Type | Description |
| status | AnalysisLibErrType | A value that specifies the type of error that occurred. Refer to analysis.h for definitions of these constants. |
Additional Information
Library: Advanced Analysis Library
Include file: analysis.h
LabWindows/CVI compatibility: LabWindows/CVI 3.1 and later