---
name: "dort03.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/dort03.f"
---

# dort03.f(3)

## NAME

TESTING/EIG/dort03.f

## SYNOPSIS

### Functions/Subroutines

subroutine **dort03** (rc, mu, mv, n, k, u, ldu, v, ldv, work, lwork, result, info)\
 **DORT03**

## Function/Subroutine Documentation

### subroutine dort03 (character\*( \* ) rc, integer mu, integer mv, integer n, integer k, double precision, dimension( ldu, \* ) u, integer ldu, double precision, dimension( ldv, \* ) v, integer ldv, double precision, dimension( \* ) work, integer lwork, double precision result, integer info)

**DORT03**

**Purpose:**

```
!>
!> DORT03 compares two orthogonal matrices U and V to see if their
!> corresponding rows or columns span the same spaces.  The rows are
!> checked if RC = 'R', and the columns are checked if RC = 'C'.
!>
!> RESULT is the maximum of
!>
!>    | V*V' - I | / ( MV ulp ), if RC = 'R', or
!>
!>    | V'*V - I | / ( MV ulp ), if RC = 'C',
!>
!> and the maximum over rows (or columns) 1 to K of
!>
!>    | U(i) - S*V(i) |/ ( N ulp )
!>
!> where S is +-1 (chosen to minimize the expression), U(i) is the i-th
!> row (column) of U, and V(i) is the i-th row (column) of V.
!>
```

**Parameters**

*RC*

```
!>          RC is CHARACTER*1
!>          If RC = 'R' the rows of U and V are to be compared.
!>          If RC = 'C' the columns of U and V are to be compared.
!>
```

*MU*

```
!>          MU is INTEGER
!>          The number of rows of U if RC = 'R', and the number of
!>          columns if RC = 'C'.  If MU = 0 DORT03 does nothing.
!>          MU must be at least zero.
!>
```

*MV*

```
!>          MV is INTEGER
!>          The number of rows of V if RC = 'R', and the number of
!>          columns if RC = 'C'.  If MV = 0 DORT03 does nothing.
!>          MV must be at least zero.
!>
```

*N*

```
!>          N is INTEGER
!>          If RC = 'R', the number of columns in the matrices U and V,
!>          and if RC = 'C', the number of rows in U and V.  If N = 0
!>          DORT03 does nothing.  N must be at least zero.
!>
```

*K*

```
!>          K is INTEGER
!>          The number of rows or columns of U and V to compare.
!>          0 <= K <= max(MU,MV).
!>
```

*U*

```
!>          U is DOUBLE PRECISION array, dimension (LDU,N)
!>          The first matrix to compare.  If RC = 'R', U is MU by N, and
!>          if RC = 'C', U is N by MU.
!>
```

*LDU*

```
!>          LDU is INTEGER
!>          The leading dimension of U.  If RC = 'R', LDU >= max(1,MU),
!>          and if RC = 'C', LDU >= max(1,N).
!>
```

*V*

```
!>          V is DOUBLE PRECISION array, dimension (LDV,N)
!>          The second matrix to compare.  If RC = 'R', V is MV by N, and
!>          if RC = 'C', V is N by MV.
!>
```

*LDV*

```
!>          LDV is INTEGER
!>          The leading dimension of V.  If RC = 'R', LDV >= max(1,MV),
!>          and if RC = 'C', LDV >= max(1,N).
!>
```

*WORK*

```
!>          WORK is DOUBLE PRECISION array, dimension (LWORK)
!>
```

*LWORK*

```
!>          LWORK is INTEGER
!>          The length of the array WORK.  For best performance, LWORK
!>          should be at least N*N if RC = 'C' or M*M if RC = 'R', but
!>          the tests will be done even if LWORK is 0.
!>
```

*RESULT*

```
!>          RESULT is DOUBLE PRECISION
!>          The value computed by the test described above.  RESULT is
!>          limited to 1/ulp to avoid overflow.
!>
```

*INFO*

```
!>          INFO is INTEGER
!>          0  indicates a successful exit
!>          -k indicates the k-th parameter had an illegal value
!>
```

**Author**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **154** of file **dort03.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.