---
name: "zqrt16.f"
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/zqrt16.f"
---

# zqrt16.f(3)

## NAME

TESTING/LIN/zqrt16.f

## SYNOPSIS

### Functions/Subroutines

subroutine **zqrt16** (trans, m, n, nrhs, a, lda, x, ldx, b, ldb, rwork, resid)\
 **ZQRT16**

## Function/Subroutine Documentation

### subroutine zqrt16 (character trans, integer m, integer n, integer nrhs, complex\*16, dimension( lda, \* ) a, integer lda, complex\*16, dimension( ldx, \* ) x, integer ldx, complex\*16, dimension( ldb, \* ) b, integer ldb, double precision, dimension( \* ) rwork, double precision resid)

**ZQRT16**

**Purpose:**

```
!>
!> ZQRT16 computes the residual for a solution of a system of linear
!> equations  A*x = b  or  A'*x = b:
!>    RESID = norm(B - A*X) / ( max(m,n) * norm(A) * norm(X) * EPS ),
!> where EPS is the machine epsilon.
!>
```

**Parameters**

*TRANS*

```
!>          TRANS is CHARACTER*1
!>          Specifies the form of the system of equations:
!>          = 'N':  A *x = b
!>          = 'T':  A^T*x = b, where A^T is the transpose of A
!>          = 'C':  A^H*x = b, where A^H is the conjugate transpose of A
!>
```

*M*

```
!>          M is INTEGER
!>          The number of rows of the matrix A.  M >= 0.
!>
```

*N*

```
!>          N is INTEGER
!>          The number of columns of the matrix A.  N >= 0.
!>
```

*NRHS*

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

*A*

```
!>          A is COMPLEX*16 array, dimension (LDA,N)
!>          The original M x N matrix A.
!>
```

*LDA*

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

*X*

```
!>          X is COMPLEX*16 array, dimension (LDX,NRHS)
!>          The computed solution vectors for the system of linear
!>          equations.
!>
```

*LDX*

```
!>          LDX is INTEGER
!>          The leading dimension of the array X.  If TRANS = 'N',
!>          LDX >= max(1,N); if TRANS = 'T' or 'C', LDX >= max(1,M).
!>
```

*B*

```
!>          B is COMPLEX*16 array, dimension (LDB,NRHS)
!>          On entry, the right hand side vectors for the system of
!>          linear equations.
!>          On exit, B is overwritten with the difference B - A*X.
!>
```

*LDB*

```
!>          LDB is INTEGER
!>          The leading dimension of the array B.  IF TRANS = 'N',
!>          LDB >= max(1,M); if TRANS = 'T' or 'C', LDB >= max(1,N).
!>
```

*RWORK*

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

*RESID*

```
!>          RESID is DOUBLE PRECISION
!>          The maximum over the number of right hand sides of
!>          norm(B - A*X) / ( max(m,n) * norm(A) * norm(X) * EPS ).
!>
```

**Author**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **131** of file **zqrt16.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.