LAPACK 3.11.0
LAPACK: Linear Algebra PACKage

◆ cget52()

subroutine cget52 ( logical  LEFT,
integer  N,
complex, dimension( lda, * )  A,
integer  LDA,
complex, dimension( ldb, * )  B,
integer  LDB,
complex, dimension( lde, * )  E,
integer  LDE,
complex, dimension( * )  ALPHA,
complex, dimension( * )  BETA,
complex, dimension( * )  WORK,
real, dimension( * )  RWORK,
real, dimension( 2 )  RESULT 
)

CGET52

Purpose:
 CGET52  does an eigenvector check for the generalized eigenvalue
 problem.

 The basic test for right eigenvectors is:

                           | b(i) A E(i) -  a(i) B E(i) |
         RESULT(1) = max   -------------------------------
                      i    n ulp max( |b(i) A|, |a(i) B| )

 using the 1-norm.  Here, a(i)/b(i) = w is the i-th generalized
 eigenvalue of A - w B, or, equivalently, b(i)/a(i) = m is the i-th
 generalized eigenvalue of m A - B.

                         H   H  _      _
 For left eigenvectors, A , B , a, and b  are used.

 CGET52 also tests the normalization of E.  Each eigenvector is
 supposed to be normalized so that the maximum "absolute value"
 of its elements is 1, where in this case, "absolute value"
 of a complex value x is  |Re(x)| + |Im(x)| ; let us call this
 maximum "absolute value" norm of a vector v  M(v).
 if a(i)=b(i)=0, then the eigenvector is set to be the jth coordinate
 vector. The normalization test is:

         RESULT(2) =      max       | M(v(i)) - 1 | / ( n ulp )
                    eigenvectors v(i)
Parameters
[in]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.
[in]N
          N is INTEGER
          The size of the matrices.  If it is zero, CGET52 does
          nothing.  It must be at least zero.
[in]A
          A is COMPLEX array, dimension (LDA, N)
          The matrix A.
[in]LDA
          LDA is INTEGER
          The leading dimension of A.  It must be at least 1
          and at least N.
[in]B
          B is COMPLEX array, dimension (LDB, N)
          The matrix B.
[in]LDB
          LDB is INTEGER
          The leading dimension of B.  It must be at least 1
          and at least N.
[in]E
          E is COMPLEX array, dimension (LDE, N)
          The matrix of eigenvectors.  It must be O( 1 ).
[in]LDE
          LDE is INTEGER
          The leading dimension of E.  It must be at least 1 and at
          least N.
[in]ALPHA
          ALPHA is COMPLEX array, dimension (N)
          The values a(i) as described above, which, along with b(i),
          define the generalized eigenvalues.
[in]BETA
          BETA is COMPLEX array, dimension (N)
          The values b(i) as described above, which, along with a(i),
          define the generalized eigenvalues.
[out]WORK
          WORK is COMPLEX array, dimension (N**2)
[out]RWORK
          RWORK is REAL array, dimension (N)
[out]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.