# DSGESV (3) - Linux Man Pages

dsgesv.f -

## SYNOPSIS

### Functions/Subroutines

subroutine dsgesv (N, NRHS, A, LDA, IPIV, B, LDB, X, LDX, WORK, SWORK, ITER, INFO)
DSGESV computes the solution to system of linear equations A * X = B for GE matrices (mixed precision with iterative refinement)

## Function/Subroutine Documentation

### subroutine dsgesv (integerN, integerNRHS, double precision, dimension( lda, * )A, integerLDA, integer, dimension( * )IPIV, double precision, dimension( ldb, * )B, integerLDB, double precision, dimension( ldx, * )X, integerLDX, double precision, dimension( n, * )WORK, real, dimension( * )SWORK, integerITER, integerINFO)

DSGESV computes the solution to system of linear equations A * X = B for GE matrices (mixed precision with iterative refinement)

Purpose:

``` DSGESV computes the solution to a real system of linear equations
A * X = B,
where A is an N-by-N matrix and X and B are N-by-NRHS matrices.

DSGESV first attempts to factorize the matrix in SINGLE PRECISION
and use this factorization within an iterative refinement procedure
to produce a solution with DOUBLE PRECISION normwise backward error
quality (see below). If the approach fails the method switches to a
DOUBLE PRECISION factorization and solve.

The iterative refinement is not going to be a winning strategy if
the ratio SINGLE PRECISION performance over DOUBLE PRECISION
performance is too small. A reasonable strategy should take the
number of right-hand sides and the size of the matrix into account.
This might be done with a call to ILAENV in the future. Up to now, we
always try iterative refinement.

The iterative refinement process is stopped if
ITER > ITERMAX
or for all the RHS we have:
RNRM < SQRT(N)*XNRM*ANRM*EPS*BWDMAX
where
o ITER is the number of the current iteration in the iterative
refinement process
o RNRM is the infinity-norm of the residual
o XNRM is the infinity-norm of the solution
o ANRM is the infinity-operator-norm of the matrix A
o EPS is the machine epsilon returned by DLAMCH('Epsilon')
The value ITERMAX and BWDMAX are fixed to 30 and 1.0D+00
respectively.
```

Parameters:

N

```          N is INTEGER
The number of linear equations, i.e., the order of the
matrix A.  N >= 0.
```

NRHS

```          NRHS is INTEGER
The number of right hand sides, i.e., the number of columns
of the matrix B.  NRHS >= 0.
```

A

```          A is DOUBLE PRECISION array,
dimension (LDA,N)
On entry, the N-by-N coefficient matrix A.
On exit, if iterative refinement has been successfully used
(INFO.EQ.0 and ITER.GE.0, see description below), then A is
unchanged, if double precision factorization has been used
(INFO.EQ.0 and ITER.LT.0, see description below), then the
array A contains the factors L and U from the factorization
A = P*L*U; the unit diagonal elements of L are not stored.
```

LDA

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

IPIV

```          IPIV is INTEGER array, dimension (N)
The pivot indices that define the permutation matrix P;
row i of the matrix was interchanged with row IPIV(i).
Corresponds either to the single precision factorization
(if INFO.EQ.0 and ITER.GE.0) or the double precision
factorization (if INFO.EQ.0 and ITER.LT.0).
```

B

```          B is DOUBLE PRECISION array, dimension (LDB,NRHS)
The N-by-NRHS right hand side matrix B.
```

LDB

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

X

```          X is DOUBLE PRECISION array, dimension (LDX,NRHS)
If INFO = 0, the N-by-NRHS solution matrix X.
```

LDX

```          LDX is INTEGER
The leading dimension of the array X.  LDX >= max(1,N).
```

WORK

```          WORK is DOUBLE PRECISION array, dimension (N,NRHS)
This array is used to hold the residual vectors.
```

SWORK

```          SWORK is REAL array, dimension (N*(N+NRHS))
This array is used to use the single precision matrix and the
right-hand sides or solutions in single precision.
```

ITER

```          ITER is INTEGER
< 0: iterative refinement has failed, double precision
factorization has been performed
-1 : the routine fell back to full precision for
implementation- or machine-specific reasons
-2 : narrowing the precision induced an overflow,
the routine fell back to full precision
-3 : failure of SGETRF
-31: stop the iterative refinement after the 30th
iterations
> 0: iterative refinement has been sucessfully used.
Returns the number of iterations
```

INFO

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

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

November 2011

Definition at line 195 of file dsgesv.f.

## Author

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