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LAPACK
3.7.0
LAPACK: Linear Algebra PACKage
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subroutine zget52 | ( | logical | LEFT, |
integer | N, | ||
complex*16, dimension( lda, * ) | A, | ||
integer | LDA, | ||
complex*16, dimension( ldb, * ) | B, | ||
integer | LDB, | ||
complex*16, dimension( lde, * ) | E, | ||
integer | LDE, | ||
complex*16, dimension( * ) | ALPHA, | ||
complex*16, dimension( * ) | BETA, | ||
complex*16, dimension( * ) | WORK, | ||
double precision, dimension( * ) | RWORK, | ||
double precision, dimension( 2 ) | RESULT | ||
) |
ZGET52
ZGET52 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. ZGET52 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)
[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, ZGET52 does nothing. It must be at least zero. |
[in] | A | A is COMPLEX*16 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*16 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*16 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*16 array, dimension (N) The values a(i) as described above, which, along with b(i), define the generalized eigenvalues. |
[in] | BETA | BETA is COMPLEX*16 array, dimension (N) The values b(i) as described above, which, along with a(i), define the generalized eigenvalues. |
[out] | WORK | WORK is COMPLEX*16 array, dimension (N**2) |
[out] | RWORK | RWORK is DOUBLE PRECISION array, dimension (N) |
[out] | RESULT | RESULT is DOUBLE PRECISION 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. |
Definition at line 164 of file zget52.f.