org.netlib.lapack
Class Dggev
java.lang.Object
org.netlib.lapack.Dggev
public class Dggev
- extends java.lang.Object
Following is the description from the original
Fortran source. For each array argument, the Java
version will include an integer offset parameter, so
the arguments may not match the description exactly.
Contact seymour@cs.utk.edu with any questions.
* ..
*
* Purpose
* =======
*
* DGGEV computes for a pair of N-by-N real nonsymmetric matrices (A,B)
* the generalized eigenvalues, and optionally, the left and/or right
* generalized eigenvectors.
*
* A generalized eigenvalue for a pair of matrices (A,B) is a scalar
* lambda or a ratio alpha/beta = lambda, such that A - lambda*B is
* singular. It is usually represented as the pair (alpha,beta), as
* there is a reasonable interpretation for beta=0, and even for both
* being zero.
*
* The right eigenvector v(j) corresponding to the eigenvalue lambda(j)
* of (A,B) satisfies
*
* A * v(j) = lambda(j) * B * v(j).
*
* The left eigenvector u(j) corresponding to the eigenvalue lambda(j)
* of (A,B) satisfies
*
* u(j)**H * A = lambda(j) * u(j)**H * B .
*
* where u(j)**H is the conjugate-transpose of u(j).
*
*
* Arguments
* =========
*
* JOBVL (input) CHARACTER*1
* = 'N': do not compute the left generalized eigenvectors;
* = 'V': compute the left generalized eigenvectors.
*
* JOBVR (input) CHARACTER*1
* = 'N': do not compute the right generalized eigenvectors;
* = 'V': compute the right generalized eigenvectors.
*
* N (input) INTEGER
* The order of the matrices A, B, VL, and VR. N >= 0.
*
* A (input/output) DOUBLE PRECISION array, dimension (LDA, N)
* On entry, the matrix A in the pair (A,B).
* On exit, A has been overwritten.
*
* LDA (input) INTEGER
* The leading dimension of A. LDA >= max(1,N).
*
* B (input/output) DOUBLE PRECISION array, dimension (LDB, N)
* On entry, the matrix B in the pair (A,B).
* On exit, B has been overwritten.
*
* LDB (input) INTEGER
* The leading dimension of B. LDB >= max(1,N).
*
* ALPHAR (output) DOUBLE PRECISION array, dimension (N)
* ALPHAI (output) DOUBLE PRECISION array, dimension (N)
* BETA (output) DOUBLE PRECISION array, dimension (N)
* On exit, (ALPHAR(j) + ALPHAI(j)*i)/BETA(j), j=1,...,N, will
* be the generalized eigenvalues. If ALPHAI(j) is zero, then
* the j-th eigenvalue is real; if positive, then the j-th and
* (j+1)-st eigenvalues are a complex conjugate pair, with
* ALPHAI(j+1) negative.
*
* Note: the quotients ALPHAR(j)/BETA(j) and ALPHAI(j)/BETA(j)
* may easily over- or underflow, and BETA(j) may even be zero.
* Thus, the user should avoid naively computing the ratio
* alpha/beta. However, ALPHAR and ALPHAI will be always less
* than and usually comparable with norm(A) in magnitude, and
* BETA always less than and usually comparable with norm(B).
*
* VL (output) DOUBLE PRECISION array, dimension (LDVL,N)
* If JOBVL = 'V', the left eigenvectors u(j) are stored one
* after another in the columns of VL, in the same order as
* their eigenvalues. If the j-th eigenvalue is real, then
* u(j) = VL(:,j), the j-th column of VL. If the j-th and
* (j+1)-th eigenvalues form a complex conjugate pair, then
* u(j) = VL(:,j)+i*VL(:,j+1) and u(j+1) = VL(:,j)-i*VL(:,j+1).
* Each eigenvector will be scaled so the largest component have
* abs(real part)+abs(imag. part)=1.
* Not referenced if JOBVL = 'N'.
*
* LDVL (input) INTEGER
* The leading dimension of the matrix VL. LDVL >= 1, and
* if JOBVL = 'V', LDVL >= N.
*
* VR (output) DOUBLE PRECISION array, dimension (LDVR,N)
* If JOBVR = 'V', the right eigenvectors v(j) are stored one
* after another in the columns of VR, in the same order as
* their eigenvalues. If the j-th eigenvalue is real, then
* v(j) = VR(:,j), the j-th column of VR. If the j-th and
* (j+1)-th eigenvalues form a complex conjugate pair, then
* v(j) = VR(:,j)+i*VR(:,j+1) and v(j+1) = VR(:,j)-i*VR(:,j+1).
* Each eigenvector will be scaled so the largest component have
* abs(real part)+abs(imag. part)=1.
* Not referenced if JOBVR = 'N'.
*
* LDVR (input) INTEGER
* The leading dimension of the matrix VR. LDVR >= 1, and
* if JOBVR = 'V', LDVR >= N.
*
* WORK (workspace/output) DOUBLE PRECISION array, dimension (LWORK)
* On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
*
* LWORK (input) INTEGER
* The dimension of the array WORK. LWORK >= max(1,8*N).
* For good performance, LWORK must generally be larger.
*
* If LWORK = -1, then a workspace query is assumed; the routine
* only calculates the optimal size of the WORK array, returns
* this value as the first entry of the WORK array, and no error
* message related to LWORK is issued by XERBLA.
*
* INFO (output) INTEGER
* = 0: successful exit
* < 0: if INFO = -i, the i-th argument had an illegal value.
* = 1,...,N:
* The QZ iteration failed. No eigenvectors have been
* calculated, but ALPHAR(j), ALPHAI(j), and BETA(j)
* should be correct for j=INFO+1,...,N.
* > N: =N+1: other than QZ iteration failed in DHGEQZ.
* =N+2: error return from DTGEVC.
*
* =====================================================================
*
* .. Parameters ..
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Constructor Summary |
Dggev()
|
|
Method Summary |
static void |
dggev(java.lang.String jobvl,
java.lang.String jobvr,
int n,
double[] a,
int _a_offset,
int lda,
double[] b,
int _b_offset,
int ldb,
double[] alphar,
int _alphar_offset,
double[] alphai,
int _alphai_offset,
double[] beta,
int _beta_offset,
double[] vl,
int _vl_offset,
int ldvl,
double[] vr,
int _vr_offset,
int ldvr,
double[] work,
int _work_offset,
int lwork,
intW info)
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| Methods inherited from class java.lang.Object |
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait |
Dggev
public Dggev()
dggev
public static void dggev(java.lang.String jobvl,
java.lang.String jobvr,
int n,
double[] a,
int _a_offset,
int lda,
double[] b,
int _b_offset,
int ldb,
double[] alphar,
int _alphar_offset,
double[] alphai,
int _alphai_offset,
double[] beta,
int _beta_offset,
double[] vl,
int _vl_offset,
int ldvl,
double[] vr,
int _vr_offset,
int ldvr,
double[] work,
int _work_offset,
int lwork,
intW info)