---
name: "ctrt05.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/ctrt05.f"
---

# ctrt05.f(3)

## NAME

TESTING/LIN/ctrt05.f

## SYNOPSIS

### Functions/Subroutines

subroutine **ctrt05** (uplo, trans, diag, n, nrhs, a, lda, b, ldb, x, ldx, xact, ldxact, ferr, berr, reslts)\
 **CTRT05**

## Function/Subroutine Documentation

### subroutine ctrt05 (character uplo, character trans, character diag, integer n, integer nrhs, complex, dimension( lda, \* ) a, integer lda, complex, dimension( ldb, \* ) b, integer ldb, complex, dimension( ldx, \* ) x, integer ldx, complex, dimension( ldxact, \* ) xact, integer ldxact, real, dimension( \* ) ferr, real, dimension( \* ) berr, real, dimension( \* ) reslts)

**CTRT05**

**Purpose:**

```
!>
!> CTRT05 tests the error bounds from iterative refinement for the
!> computed solution to a system of equations A*X = B, where A is a
!> triangular n by n matrix.
!>
!> RESLTS(1) = test of the error bound
!>           = norm(X - XACT) / ( norm(X) * FERR )
!>
!> A large value is returned if this ratio is not less than one.
!>
!> RESLTS(2) = residual from the iterative refinement routine
!>           = the maximum of BERR / ( (n+1)*EPS + (*) ), where
!>             (*) = (n+1)*UNFL / (min_i (abs(A)*abs(X) +abs(b))_i )
!>
```

**Parameters**

*UPLO*

```
!>          UPLO is CHARACTER*1
!>          Specifies whether the matrix A is upper or lower triangular.
!>          = 'U':  Upper triangular
!>          = 'L':  Lower triangular
!>
```

*TRANS*

```
!>          TRANS is CHARACTER*1
!>          Specifies the form of the system of equations.
!>          = 'N':  A * X = B  (No transpose)
!>          = 'T':  A'* X = B  (Transpose)
!>          = 'C':  A'* X = B  (Conjugate transpose = Transpose)
!>
```

*DIAG*

```
!>          DIAG is CHARACTER*1
!>          Specifies whether or not the matrix A is unit triangular.
!>          = 'N':  Non-unit triangular
!>          = 'U':  Unit triangular
!>
```

*N*

```
!>          N is INTEGER
!>          The number of rows of the matrices X, B, and XACT, and the
!>          order of the matrix A.  N >= 0.
!>
```

*NRHS*

```
!>          NRHS is INTEGER
!>          The number of columns of the matrices X, B, and XACT.
!>          NRHS >= 0.
!>
```

*A*

```
!>          A is COMPLEX array, dimension (LDA,N)
!>          The triangular matrix A.  If UPLO = 'U', the leading n by n
!>          upper triangular part of the array A contains the upper
!>          triangular matrix, and the strictly lower triangular part of
!>          A is not referenced.  If UPLO = 'L', the leading n by n lower
!>          triangular part of the array A contains the lower triangular
!>          matrix, and the strictly upper triangular part of A is not
!>          referenced.  If DIAG = 'U', the diagonal elements of A are
!>          also not referenced and are assumed to be 1.
!>
```

*LDA*

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

*B*

```
!>          B is COMPLEX array, dimension (LDB,NRHS)
!>          The right hand side vectors for the system of linear
!>          equations.
!>
```

*LDB*

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

*X*

```
!>          X is COMPLEX array, dimension (LDX,NRHS)
!>          The computed solution vectors.  Each vector is stored as a
!>          column of the matrix X.
!>
```

*LDX*

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

*XACT*

```
!>          XACT is COMPLEX array, dimension (LDX,NRHS)
!>          The exact solution vectors.  Each vector is stored as a
!>          column of the matrix XACT.
!>
```

*LDXACT*

```
!>          LDXACT is INTEGER
!>          The leading dimension of the array XACT.  LDXACT >= max(1,N).
!>
```

*FERR*

```
!>          FERR is REAL array, dimension (NRHS)
!>          The estimated forward error bounds for each solution vector
!>          X.  If XTRUE is the true solution, FERR bounds the magnitude
!>          of the largest entry in (X - XTRUE) divided by the magnitude
!>          of the largest entry in X.
!>
```

*BERR*

```
!>          BERR is REAL array, dimension (NRHS)
!>          The componentwise relative backward error of each solution
!>          vector (i.e., the smallest relative change in any entry of A
!>          or B that makes X an exact solution).
!>
```

*RESLTS*

```
!>          RESLTS is REAL array, dimension (2)
!>          The maximum over the NRHS solution vectors of the ratios:
!>          RESLTS(1) = norm(X - XACT) / ( norm(X) * FERR )
!>          RESLTS(2) = BERR / ( (n+1)*EPS + (*) )
!>
```

**Author**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **180** of file **ctrt05.f**.

## Author

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