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# sgesv

```
NAME
SGESV - compute the solution to a real system of linear
equations  A * X = B,

SYNOPSIS
SUBROUTINE SGESV( N, NRHS, A, LDA, IPIV, B, LDB, INFO )

INTEGER       INFO, LDA, LDB, N, NRHS

INTEGER       IPIV( * )

REAL          A( LDA, * ), B( LDB, * )

PURPOSE
SGESV computes the solution to a real system of linear equa-
tions
A * X = B, where A is an N-by-N matrix and X and B are
N-by-NRHS matrices.

The LU decomposition with partial pivoting and row inter-
changes 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.

ARGUMENTS
N       (input) INTEGER
The number of linear equations, i.e., the order of
the matrix A.  N >= 0.

NRHS    (input) INTEGER
The number of right hand sides, i.e., the number of
columns of the matrix B.  NRHS >= 0.

A       (input/output) REAL array, dimension (LDA,N)
On entry, the N-by-N coefficient matrix A.  On exit,
the factors L and U from the factorization A =
P*L*U; the unit diagonal elements of L are not
stored.

LDA     (input) INTEGER
The leading dimension of the array A.  LDA >=
max(1,N).

IPIV    (output) INTEGER array, dimension (N)
The pivot indices that define the permutation matrix
P; row i of the matrix was interchanged with row
IPIV(i).

B       (input/output) REAL array, dimension (LDB,NRHS)

On entry, the N-by-NRHS matrix of right hand side
matrix B.  On exit, if INFO = 0, the N-by-NRHS solu-
tion matrix X.

LDB     (input) INTEGER
The leading dimension of the array B.  LDB >=
max(1,N).

INFO    (output) INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal
value
> 0:  if INFO = i, U(i,i) is exactly zero.  The fac-
torization has been completed, but the factor U is
exactly singular, so the solution could not be com-
puted.
```