---
name: "gesv_mixed"
section: "3"
platform: "linux"
package: "lapack-doc"
version: "3.12.1-2"
release: "Arch Linux 2026-11-01"
platforms: ["linux"]
url: "https://new.carta.tech/gesv_mixed"
---

# gesv\_mixed(3)

gesv: factor and solve, mixed precision

## NAME

gesv\_mixed - gesv: factor and solve, mixed precision

## SYNOPSIS

### Functions

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)  subroutine **zcgesv** (n, nrhs, a, lda, ipiv, b, ldb, x, ldx, work, swork, rwork, iter, info)\
  **ZCGESV computes the solution to system of linear equations A \* X = B for GE matrices** (mixed precision with iterative refinement)

## Detailed Description

## Function Documentation

### subroutine dsgesv (integer n, integer nrhs, double precision, dimension( lda, \* ) a, integer lda, integer, dimension( \* ) ipiv, double precision, dimension( ldb, \* ) b, integer ldb, double precision, dimension( ldx, \* ) x, integer ldx, double precision, dimension( n, \* ) work, real, dimension( \* ) swork, integer iter, integer info)

 **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 = 0 and ITER >= 0, see description below), then A is
!>          unchanged, if double precision factorization has been used
!>          (INFO = 0 and ITER < 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 = 0 and ITER >= 0) or the double precision
!>          factorization (if INFO = 0 and ITER < 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 successfully 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.

Definition at line **193** of file **dsgesv.f**.

### subroutine zcgesv (integer n, integer nrhs, complex\*16, dimension( lda, \* ) a, integer lda, integer, dimension( \* ) ipiv, complex\*16, dimension( ldb, \* ) b, integer ldb, complex\*16, dimension( ldx, \* ) x, integer ldx, complex\*16, dimension( n, \* ) work, complex, dimension( \* ) swork, double precision, dimension( \* ) rwork, integer iter, integer info)

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

**Purpose:**

```
!>
!> ZCGESV computes the solution to a complex system of linear equations
!>    A * X = B,
!> where A is an N-by-N matrix and X and B are N-by-NRHS matrices.
!>
!> ZCGESV first attempts to factorize the matrix in COMPLEX and use this
!> factorization within an iterative refinement procedure to produce a
!> solution with COMPLEX*16 normwise backward error quality (see below).
!> If the approach fails the method switches to a COMPLEX*16
!> factorization and solve.
!>
!> The iterative refinement is not going to be a winning strategy if
!> the ratio COMPLEX performance over COMPLEX*16 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 COMPLEX*16 array,
!>          dimension (LDA,N)
!>          On entry, the N-by-N coefficient matrix A.
!>          On exit, if iterative refinement has been successfully used
!>          (INFO = 0 and ITER >= 0, see description below), then A is
!>          unchanged, if double precision factorization has been used
!>          (INFO = 0 and ITER < 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 = 0 and ITER >= 0) or the double precision
!>          factorization (if INFO = 0 and ITER < 0).
!>
```

*B*

```
!>          B is COMPLEX*16 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 COMPLEX*16 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 COMPLEX*16 array, dimension (N,NRHS)
!>          This array is used to hold the residual vectors.
!>
```

*SWORK*

```
!>          SWORK is COMPLEX 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.
!>
```

*RWORK*

```
!>          RWORK is DOUBLE PRECISION array, dimension (N)
!>
```

*ITER*

```
!>          ITER is INTEGER
!>          < 0: iterative refinement has failed, COMPLEX*16
!>               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 CGETRF
!>               -31: stop the iterative refinement after the 30th
!>                    iterations
!>          > 0: iterative refinement has been successfully 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 COMPLEX*16 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.

Definition at line **199** of file **zcgesv.f**.

## Author

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