◆ _dgesv()

(Simple driver) Solution to system of linear equations AX = B for a general matrix

Purpose: This routine computes the solution to a real system of linear equations
A * X = B

where A is an n x n matrix and X and B are n x nrhs matrices.

The LU decomposition with partial pivoting and row interchanges is used to factor A as
A = P * L * U

where P is a permutation matrix, L is unit lower triangular, and U is upper triangular. The factored form of A is then used to solve the system of equations A * X = B.

Parameters

[in]	n	Number of linear equations, i.e., order of the matrix A. (n >= 0) (if n = 0, returns without computation)
[in]	nrhs	Number of right hand sides, i.e., number of columns of the matrix B. (nrhs >= 0) (if nrhs = 0, returns without computation)
[in]	lda	Leading dimension of the two dimensional array a[][]. (lda >= max(1, n))
[in,out]	a[][]	Array a[la][lda] (la >= n) [in] n x n coefficient matrix A. [out] Factors L and U from the factorization A = PLU; the unit diagonal elements of L are not stored.
[out]	ipiv[]	Array ipiv[lipiv] (lipiv >= n) Pivot indices that define the permutation matrix P; row i of the matrix was interchanged with row ipiv[i-1].
[in]	ldb	Leading dimension of the two dimensional array b[][]. (ldb >= max(1, n))
[in,out]	b[][]	Array b[lb][ldb] (lb >= nrhs) [in] n x nrhs matrix of right hand side matrix B. [out] If info = 0, n x nrhs solution matrix X.
[out]	info	= 0: Successful exit = -1: The argument n had an illegal value (n < 0) = -2: The argument nrhs had an illegal value (nrhs < 0) = -3: The argument lda had an illegal value (lda < max(1, n)) = -6: The argument ldb had an illegal value (ldb < max(1, n)) = i > 0: The i-th diagonal element of the factor U is exactly zero. The factorization has been completed, but the factor U is exactly singular, so the solution could not be computed.