---
name: "sort01.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/sort01.f"
---

# sort01.f(3)

## NAME

TESTING/EIG/sort01.f

## SYNOPSIS

### Functions/Subroutines

subroutine **sort01** (rowcol, m, n, u, ldu, work, lwork, resid)\
 **SORT01**

## Function/Subroutine Documentation

### subroutine sort01 (character rowcol, integer m, integer n, real, dimension( ldu, \* ) u, integer ldu, real, dimension( \* ) work, integer lwork, real resid)

**SORT01**

**Purpose:**

```
!>
!> SORT01 checks that the matrix U is orthogonal by computing the ratio
!>
!>    RESID = norm( I - U*U' ) / ( n * EPS ), if ROWCOL = 'R',
!> or
!>    RESID = norm( I - U'*U ) / ( m * EPS ), if ROWCOL = 'C'.
!>
!> Alternatively, if there isn't sufficient workspace to form
!> I - U*U' or I - U'*U, the ratio is computed as
!>
!>    RESID = abs( I - U*U' ) / ( n * EPS ), if ROWCOL = 'R',
!> or
!>    RESID = abs( I - U'*U ) / ( m * EPS ), if ROWCOL = 'C'.
!>
!> where EPS is the machine precision.  ROWCOL is used only if m = n;
!> if m > n, ROWCOL is assumed to be 'C', and if m < n, ROWCOL is
!> assumed to be 'R'.
!>
```

**Parameters**

*ROWCOL*

```
!>          ROWCOL is CHARACTER
!>          Specifies whether the rows or columns of U should be checked
!>          for orthogonality.  Used only if M = N.
!>          = 'R':  Check for orthogonal rows of U
!>          = 'C':  Check for orthogonal columns of U
!>
```

*M*

```
!>          M is INTEGER
!>          The number of rows of the matrix U.
!>
```

*N*

```
!>          N is INTEGER
!>          The number of columns of the matrix U.
!>
```

*U*

```
!>          U is REAL array, dimension (LDU,N)
!>          The orthogonal matrix U.  U is checked for orthogonal columns
!>          if m > n or if m = n and ROWCOL = 'C'.  U is checked for
!>          orthogonal rows if m < n or if m = n and ROWCOL = 'R'.
!>
```

*LDU*

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

*WORK*

```
!>          WORK is REAL array, dimension (LWORK)
!>
```

*LWORK*

```
!>          LWORK is INTEGER
!>          The length of the array WORK.  For best performance, LWORK
!>          should be at least N*(N+1) if ROWCOL = 'C' or M*(M+1) if
!>          ROWCOL = 'R', but the test will be done even if LWORK is 0.
!>
```

*RESID*

```
!>          RESID is REAL
!>          RESID = norm( I - U * U' ) / ( n * EPS ), if ROWCOL = 'R', or
!>          RESID = norm( I - U' * U ) / ( m * EPS ), if ROWCOL = 'C'.
!>
```

**Author**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **115** of file **sort01.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.