org.netlib.lapack
Class Strevc
java.lang.Object
org.netlib.lapack.Strevc
public class Strevc
- 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
* =======
*
* STREVC computes some or all of the right and/or left eigenvectors of
* a real upper quasi-triangular matrix T.
*
* The right eigenvector x and the left eigenvector y of T corresponding
* to an eigenvalue w are defined by:
*
* T*x = w*x, y'*T = w*y'
*
* where y' denotes the conjugate transpose of the vector y.
*
* If all eigenvectors are requested, the routine may either return the
* matrices X and/or Y of right or left eigenvectors of T, or the
* products Q*X and/or Q*Y, where Q is an input orthogonal
* matrix. If T was obtained from the real-Schur factorization of an
* original matrix A = Q*T*Q', then Q*X and Q*Y are the matrices of
* right or left eigenvectors of A.
*
* T must be in Schur canonical form (as returned by SHSEQR), that is,
* block upper triangular with 1-by-1 and 2-by-2 diagonal blocks; each
* 2-by-2 diagonal block has its diagonal elements equal and its
* off-diagonal elements of opposite sign. Corresponding to each 2-by-2
* diagonal block is a complex conjugate pair of eigenvalues and
* eigenvectors; only one eigenvector of the pair is computed, namely
* the one corresponding to the eigenvalue with positive imaginary part.
*
* Arguments
* =========
*
* SIDE (input) CHARACTER*1
* = 'R': compute right eigenvectors only;
* = 'L': compute left eigenvectors only;
* = 'B': compute both right and left eigenvectors.
*
* HOWMNY (input) CHARACTER*1
* = 'A': compute all right and/or left eigenvectors;
* = 'B': compute all right and/or left eigenvectors,
* and backtransform them using the input matrices
* supplied in VR and/or VL;
* = 'S': compute selected right and/or left eigenvectors,
* specified by the logical array SELECT.
*
* SELECT (input/output) LOGICAL array, dimension (N)
* If HOWMNY = 'S', SELECT specifies the eigenvectors to be
* computed.
* If HOWMNY = 'A' or 'B', SELECT is not referenced.
* To select the real eigenvector corresponding to a real
* eigenvalue w(j), SELECT(j) must be set to .TRUE.. To select
* the complex eigenvector corresponding to a complex conjugate
* pair w(j) and w(j+1), either SELECT(j) or SELECT(j+1) must be
* set to .TRUE.; then on exit SELECT(j) is .TRUE. and
* SELECT(j+1) is .FALSE..
*
* N (input) INTEGER
* The order of the matrix T. N >= 0.
*
* T (input) REAL array, dimension (LDT,N)
* The upper quasi-triangular matrix T in Schur canonical form.
*
* LDT (input) INTEGER
* The leading dimension of the array T. LDT >= max(1,N).
*
* VL (input/output) REAL array, dimension (LDVL,MM)
* On entry, if SIDE = 'L' or 'B' and HOWMNY = 'B', VL must
* contain an N-by-N matrix Q (usually the orthogonal matrix Q
* of Schur vectors returned by SHSEQR).
* On exit, if SIDE = 'L' or 'B', VL contains:
* if HOWMNY = 'A', the matrix Y of left eigenvectors of T;
* VL has the same quasi-lower triangular form
* as T'. If T(i,i) is a real eigenvalue, then
* the i-th column VL(i) of VL is its
* corresponding eigenvector. If T(i:i+1,i:i+1)
* is a 2-by-2 block whose eigenvalues are
* complex-conjugate eigenvalues of T, then
* VL(i)+sqrt(-1)*VL(i+1) is the complex
* eigenvector corresponding to the eigenvalue
* with positive real part.
* if HOWMNY = 'B', the matrix Q*Y;
* if HOWMNY = 'S', the left eigenvectors of T specified by
* SELECT, stored consecutively in the columns
* of VL, in the same order as their
* eigenvalues.
* A complex eigenvector corresponding to a complex eigenvalue
* is stored in two consecutive columns, the first holding the
* real part, and the second the imaginary part.
* If SIDE = 'R', VL is not referenced.
*
* LDVL (input) INTEGER
* The leading dimension of the array VL. LDVL >= max(1,N) if
* SIDE = 'L' or 'B'; LDVL >= 1 otherwise.
*
* VR (input/output) REAL array, dimension (LDVR,MM)
* On entry, if SIDE = 'R' or 'B' and HOWMNY = 'B', VR must
* contain an N-by-N matrix Q (usually the orthogonal matrix Q
* of Schur vectors returned by SHSEQR).
* On exit, if SIDE = 'R' or 'B', VR contains:
* if HOWMNY = 'A', the matrix X of right eigenvectors of T;
* VR has the same quasi-upper triangular form
* as T. If T(i,i) is a real eigenvalue, then
* the i-th column VR(i) of VR is its
* corresponding eigenvector. If T(i:i+1,i:i+1)
* is a 2-by-2 block whose eigenvalues are
* complex-conjugate eigenvalues of T, then
* VR(i)+sqrt(-1)*VR(i+1) is the complex
* eigenvector corresponding to the eigenvalue
* with positive real part.
* if HOWMNY = 'B', the matrix Q*X;
* if HOWMNY = 'S', the right eigenvectors of T specified by
* SELECT, stored consecutively in the columns
* of VR, in the same order as their
* eigenvalues.
* A complex eigenvector corresponding to a complex eigenvalue
* is stored in two consecutive columns, the first holding the
* real part and the second the imaginary part.
* If SIDE = 'L', VR is not referenced.
*
* LDVR (input) INTEGER
* The leading dimension of the array VR. LDVR >= max(1,N) if
* SIDE = 'R' or 'B'; LDVR >= 1 otherwise.
*
* MM (input) INTEGER
* The number of columns in the arrays VL and/or VR. MM >= M.
*
* M (output) INTEGER
* The number of columns in the arrays VL and/or VR actually
* used to store the eigenvectors.
* If HOWMNY = 'A' or 'B', M is set to N.
* Each selected real eigenvector occupies one column and each
* selected complex eigenvector occupies two columns.
*
* WORK (workspace) REAL array, dimension (3*N)
*
* INFO (output) INTEGER
* = 0: successful exit
* < 0: if INFO = -i, the i-th argument had an illegal value
*
* Further Details
* ===============
*
* The algorithm used in this program is basically backward (forward)
* substitution, with scaling to make the the code robust against
* possible overflow.
*
* Each eigenvector is normalized so that the element of largest
* magnitude has magnitude 1; here the magnitude of a complex number
* (x,y) is taken to be |x| + |y|.
*
* =====================================================================
*
* .. Parameters ..
|
Method Summary |
static void |
strevc(java.lang.String side,
java.lang.String howmny,
boolean[] select,
int _select_offset,
int n,
float[] t,
int _t_offset,
int ldt,
float[] vl,
int _vl_offset,
int ldvl,
float[] vr,
int _vr_offset,
int ldvr,
int mm,
intW m,
float[] work,
int _work_offset,
intW info)
|
| Methods inherited from class java.lang.Object |
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait |
Strevc
public Strevc()
strevc
public static void strevc(java.lang.String side,
java.lang.String howmny,
boolean[] select,
int _select_offset,
int n,
float[] t,
int _t_offset,
int ldt,
float[] vl,
int _vl_offset,
int ldvl,
float[] vr,
int _vr_offset,
int ldvr,
int mm,
intW m,
float[] work,
int _work_offset,
intW info)