---
name: "ctrt01.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/ctrt01.f"
---

# ctrt01.f(3)

## NAME

TESTING/LIN/ctrt01.f

## SYNOPSIS

### Functions/Subroutines

subroutine **ctrt01** (uplo, diag, n, a, lda, ainv, ldainv, rcond, rwork, resid)\
 **CTRT01**

## Function/Subroutine Documentation

### subroutine ctrt01 (character uplo, character diag, integer n, complex, dimension( lda, \* ) a, integer lda, complex, dimension( ldainv, \* ) ainv, integer ldainv, real rcond, real, dimension( \* ) rwork, real resid)

**CTRT01**

**Purpose:**

```
!>
!> CTRT01 computes the residual for a triangular matrix A times its
!> inverse:
!>    RESID = norm( A*AINV - I ) / ( N * norm(A) * norm(AINV) * EPS ),
!> where EPS is the machine epsilon.
!>
```

**Parameters**

*UPLO*

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

*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 order of the matrix A.  N >= 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).
!>
```

*AINV*

```
!>          AINV is COMPLEX array, dimension (LDAINV,N)
!>          On entry, the (triangular) inverse of the matrix A, in the
!>          same storage format as A.
!>          On exit, the contents of AINV are destroyed.
!>
```

*LDAINV*

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

*RCOND*

```
!>          RCOND is REAL
!>          The reciprocal condition number of A, computed as
!>          1/(norm(A) * norm(AINV)).
!>
```

*RWORK*

```
!>          RWORK is REAL array, dimension (N)
!>
```

*RESID*

```
!>          RESID is REAL
!>          norm(A*AINV - I) / ( N * norm(A) * norm(AINV) * EPS )
!>
```

**Author**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **123** of file **ctrt01.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.