---
name: "sget52.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/sget52.f"
---

# sget52.f(3)

## NAME

TESTING/EIG/sget52.f

## SYNOPSIS

### Functions/Subroutines

subroutine **sget52** (left, n, a, lda, b, ldb, e, **lde**, alphar, alphai, beta, work, result)\
 **SGET52**

## Function/Subroutine Documentation

### subroutine sget52 (logical left, integer n, real, dimension( lda, \* ) a, integer lda, real, dimension( ldb, \* ) b, integer ldb, real, dimension( lde, \* ) e, integer lde, real, dimension( \* ) alphar, real, dimension( \* ) alphai, real, dimension( \* ) beta, real, dimension( \* ) work, real, dimension( 2 ) result)

**SGET52**

**Purpose:**

```
!>
!> SGET52  does an eigenvector check for the generalized eigenvalue
!> problem.
!>
!> The basic test for right eigenvectors is:
!>
!>                           | b(j) A E(j) -  a(j) B E(j) |
!>         RESULT(1) = max   -------------------------------
!>                      j    n ulp max( |b(j) A|, |a(j) B| )
!>
!> using the 1-norm.  Here, a(j)/b(j) = w is the j-th generalized
!> eigenvalue of A - w B, or, equivalently, b(j)/a(j) = m is the j-th
!> generalized eigenvalue of m A - B.
!>
!> For real eigenvalues, the test is straightforward.  For complex
!> eigenvalues, E(j) and a(j) are complex, represented by
!> Er(j) + i*Ei(j) and ar(j) + i*ai(j), resp., so the test for that
!> eigenvector becomes
!>
!>                 max( |Wr|, |Wi| )
!>     --------------------------------------------
!>     n ulp max( |b(j) A|, (|ar(j)|+|ai(j)|) |B| )
!>
!> where
!>
!>     Wr = b(j) A Er(j) - ar(j) B Er(j) + ai(j) B Ei(j)
!>
!>     Wi = b(j) A Ei(j) - ai(j) B Er(j) - ar(j) B Ei(j)
!>
!>                         T   T  _
!> For left eigenvectors, A , B , a, and b  are used.
!>
!> SGET52 also tests the normalization of E.  Each eigenvector is
!> supposed to be normalized so that the maximum
!> of its elements is 1, where in this case,
!> of a complex value x is  |Re(x)| + |Im(x)| ; let us call this
!> maximum  norm of a vector v  M(v).
!> if a(j)=b(j)=0, then the eigenvector is set to be the jth coordinate
!> vector.  The normalization test is:
!>
!>         RESULT(2) =      max       | M(v(j)) - 1 | / ( n ulp )
!>                    eigenvectors v(j)
!>
```

**Parameters**

*LEFT*

```
!>          LEFT is LOGICAL
!>          =.TRUE.:  The eigenvectors in the columns of E are assumed
!>                    to be *left* eigenvectors.
!>          =.FALSE.: The eigenvectors in the columns of E are assumed
!>                    to be *right* eigenvectors.
!>
```

*N*

```
!>          N is INTEGER
!>          The size of the matrices.  If it is zero, SGET52 does
!>          nothing.  It must be at least zero.
!>
```

*A*

```
!>          A is REAL array, dimension (LDA, N)
!>          The matrix A.
!>
```

*LDA*

```
!>          LDA is INTEGER
!>          The leading dimension of A.  It must be at least 1
!>          and at least N.
!>
```

*B*

```
!>          B is REAL array, dimension (LDB, N)
!>          The matrix B.
!>
```

*LDB*

```
!>          LDB is INTEGER
!>          The leading dimension of B.  It must be at least 1
!>          and at least N.
!>
```

*E*

```
!>          E is REAL array, dimension (LDE, N)
!>          The matrix of eigenvectors.  It must be O( 1 ).  Complex
!>          eigenvalues and eigenvectors always come in pairs, the
!>          eigenvalue and its conjugate being stored in adjacent
!>          elements of ALPHAR, ALPHAI, and BETA.  Thus, if a(j)/b(j)
!>          and a(j+1)/b(j+1) are a complex conjugate pair of
!>          generalized eigenvalues, then E(,j) contains the real part
!>          of the eigenvector and E(,j+1) contains the imaginary part.
!>          Note that whether E(,j) is a real eigenvector or part of a
!>          complex one is specified by whether ALPHAI(j) is zero or not.
!>
```

*LDE*

```
!>          LDE is INTEGER
!>          The leading dimension of E.  It must be at least 1 and at
!>          least N.
!>
```

*ALPHAR*

```
!>          ALPHAR is REAL array, dimension (N)
!>          The real parts of the values a(j) as described above, which,
!>          along with b(j), define the generalized eigenvalues.
!>          Complex eigenvalues always come in complex conjugate pairs
!>          a(j)/b(j) and a(j+1)/b(j+1), which are stored in adjacent
!>          elements in ALPHAR, ALPHAI, and BETA.  Thus, if the j-th
!>          and (j+1)-st eigenvalues form a pair, ALPHAR(j+1)/BETA(j+1)
!>          is assumed to be equal to ALPHAR(j)/BETA(j).
!>
```

*ALPHAI*

```
!>          ALPHAI is REAL array, dimension (N)
!>          The imaginary parts of the values a(j) as described above,
!>          which, along with b(j), define the generalized eigenvalues.
!>          If ALPHAI(j)=0, then the eigenvalue is real, otherwise it
!>          is part of a complex conjugate pair.  Complex eigenvalues
!>          always come in complex conjugate pairs a(j)/b(j) and
!>          a(j+1)/b(j+1), which are stored in adjacent elements in
!>          ALPHAR, ALPHAI, and BETA.  Thus, if the j-th and (j+1)-st
!>          eigenvalues form a pair, ALPHAI(j+1)/BETA(j+1) is assumed to
!>          be equal to  -ALPHAI(j)/BETA(j).  Also, nonzero values in
!>          ALPHAI are assumed to always come in adjacent pairs.
!>
```

*BETA*

```
!>          BETA is REAL array, dimension (N)
!>          The values b(j) as described above, which, along with a(j),
!>          define the generalized eigenvalues.
!>
```

*WORK*

```
!>          WORK is REAL array, dimension (N**2+N)
!>
```

*RESULT*

```
!>          RESULT is REAL array, dimension (2)
!>          The values computed by the test described above.  If A E or
!>          B E is likely to overflow, then RESULT(1:2) is set to
!>          10 / ulp.
!>
```

**Author**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **197** of file **sget52.f**.

## Author

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