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---
:name: dgesv
:md5sum: 8ab66d02ed18d053ba3faf7a6a1d1ad2
:category: :subroutine
:arguments:
- n:
:type: integer
:intent: input
- nrhs:
:type: integer
:intent: input
- a:
:type: doublereal
:intent: input/output
:dims:
- lda
- n
- lda:
:type: integer
:intent: input
- ipiv:
:type: integer
:intent: output
:dims:
- n
- b:
:type: doublereal
:intent: input/output
:dims:
- ldb
- nrhs
- ldb:
:type: integer
:intent: input
- info:
:type: integer
:intent: output
:substitutions: {}
:fortran_help: " SUBROUTINE DGESV( N, NRHS, A, LDA, IPIV, B, LDB, INFO )\n\n\
* Purpose\n\
* =======\n\
*\n\
* DGESV computes the solution to a real system of linear equations\n\
* A * X = B,\n\
* where A is an N-by-N matrix and X and B are N-by-NRHS matrices.\n\
*\n\
* The LU decomposition with partial pivoting and row interchanges is\n\
* used to factor A as\n\
* A = P * L * U,\n\
* where P is a permutation matrix, L is unit lower triangular, and U is\n\
* upper triangular. The factored form of A is then used to solve the\n\
* system of equations A * X = B.\n\
*\n\n\
* Arguments\n\
* =========\n\
*\n\
* N (input) INTEGER\n\
* The number of linear equations, i.e., the order of the\n\
* matrix A. N >= 0.\n\
*\n\
* NRHS (input) INTEGER\n\
* The number of right hand sides, i.e., the number of columns\n\
* of the matrix B. NRHS >= 0.\n\
*\n\
* A (input/output) DOUBLE PRECISION array, dimension (LDA,N)\n\
* On entry, the N-by-N coefficient matrix A.\n\
* On exit, the factors L and U from the factorization\n\
* A = P*L*U; the unit diagonal elements of L are not stored.\n\
*\n\
* LDA (input) INTEGER\n\
* The leading dimension of the array A. LDA >= max(1,N).\n\
*\n\
* IPIV (output) INTEGER array, dimension (N)\n\
* The pivot indices that define the permutation matrix P;\n\
* row i of the matrix was interchanged with row IPIV(i).\n\
*\n\
* B (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS)\n\
* On entry, the N-by-NRHS matrix of right hand side matrix B.\n\
* On exit, if INFO = 0, the N-by-NRHS solution matrix X.\n\
*\n\
* LDB (input) INTEGER\n\
* The leading dimension of the array B. LDB >= max(1,N).\n\
*\n\
* INFO (output) INTEGER\n\
* = 0: successful exit\n\
* < 0: if INFO = -i, the i-th argument had an illegal value\n\
* > 0: if INFO = i, U(i,i) is exactly zero. The factorization\n\
* has been completed, but the factor U is exactly\n\
* singular, so the solution could not be computed.\n\
*\n\n\
* =====================================================================\n\
*\n\
* .. External Subroutines ..\n EXTERNAL DGETRF, DGETRS, XERBLA\n\
* ..\n\
* .. Intrinsic Functions ..\n INTRINSIC MAX\n\
* ..\n"
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