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---
:name: dsgesv
:md5sum: 37507bbdfd1407291f8640470f411a6e
: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
:dims:
- ldb
- nrhs
- ldb:
:type: integer
:intent: input
- x:
:type: doublereal
:intent: output
:dims:
- ldx
- nrhs
- ldx:
:type: integer
:intent: input
- work:
:type: doublereal
:intent: workspace
:dims:
- n
- nrhs
- swork:
:type: real
:intent: workspace
:dims:
- n*(n+nrhs)
- iter:
:type: integer
:intent: output
- info:
:type: integer
:intent: output
:substitutions:
ldx: MAX(1,n)
:fortran_help: " SUBROUTINE DSGESV( N, NRHS, A, LDA, IPIV, B, LDB, X, LDX, WORK, SWORK, ITER, INFO )\n\n\
* Purpose\n\
* =======\n\
*\n\
* DSGESV 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\
* DSGESV first attempts to factorize the matrix in SINGLE PRECISION\n\
* and use this factorization within an iterative refinement procedure\n\
* to produce a solution with DOUBLE PRECISION normwise backward error\n\
* quality (see below). If the approach fails the method switches to a\n\
* DOUBLE PRECISION factorization and solve.\n\
*\n\
* The iterative refinement is not going to be a winning strategy if\n\
* the ratio SINGLE PRECISION performance over DOUBLE PRECISION\n\
* performance is too small. A reasonable strategy should take the\n\
* number of right-hand sides and the size of the matrix into account.\n\
* This might be done with a call to ILAENV in the future. Up to now, we\n\
* always try iterative refinement.\n\
*\n\
* The iterative refinement process is stopped if\n\
* ITER > ITERMAX\n\
* or for all the RHS we have:\n\
* RNRM < SQRT(N)*XNRM*ANRM*EPS*BWDMAX\n\
* where\n\
* o ITER is the number of the current iteration in the iterative\n\
* refinement process\n\
* o RNRM is the infinity-norm of the residual\n\
* o XNRM is the infinity-norm of the solution\n\
* o ANRM is the infinity-operator-norm of the matrix A\n\
* o EPS is the machine epsilon returned by DLAMCH('Epsilon')\n\
* The value ITERMAX and BWDMAX are fixed to 30 and 1.0D+00\n\
* respectively.\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,\n\
* dimension (LDA,N)\n\
* On entry, the N-by-N coefficient matrix A.\n\
* On exit, if iterative refinement has been successfully used\n\
* (INFO.EQ.0 and ITER.GE.0, see description below), then A is\n\
* unchanged, if double precision factorization has been used\n\
* (INFO.EQ.0 and ITER.LT.0, see description below), then the\n\
* array A contains 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\
* Corresponds either to the single precision factorization\n\
* (if INFO.EQ.0 and ITER.GE.0) or the double precision\n\
* factorization (if INFO.EQ.0 and ITER.LT.0).\n\
*\n\
* B (input) DOUBLE PRECISION array, dimension (LDB,NRHS)\n\
* The N-by-NRHS right hand side matrix B.\n\
*\n\
* LDB (input) INTEGER\n\
* The leading dimension of the array B. LDB >= max(1,N).\n\
*\n\
* X (output) DOUBLE PRECISION array, dimension (LDX,NRHS)\n\
* If INFO = 0, the N-by-NRHS solution matrix X.\n\
*\n\
* LDX (input) INTEGER\n\
* The leading dimension of the array X. LDX >= max(1,N).\n\
*\n\
* WORK (workspace) DOUBLE PRECISION array, dimension (N,NRHS)\n\
* This array is used to hold the residual vectors.\n\
*\n\
* SWORK (workspace) REAL array, dimension (N*(N+NRHS))\n\
* This array is used to use the single precision matrix and the\n\
* right-hand sides or solutions in single precision.\n\
*\n\
* ITER (output) INTEGER\n\
* < 0: iterative refinement has failed, double precision\n\
* factorization has been performed\n\
* -1 : the routine fell back to full precision for\n\
* implementation- or machine-specific reasons\n\
* -2 : narrowing the precision induced an overflow,\n\
* the routine fell back to full precision\n\
* -3 : failure of SGETRF\n\
* -31: stop the iterative refinement after the 30th\n\
* iterations\n\
* > 0: iterative refinement has been successfully used.\n\
* Returns the number of iterations\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) computed in DOUBLE PRECISION is\n\
* exactly zero. The factorization has been completed,\n\
* but the factor U is exactly singular, so the solution\n\
* could not be computed.\n\
*\n\
* =========\n\
*\n"
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