public class Shseqr
- 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 firstname.lastname@example.org with any questions.
* SHSEQR computes the eigenvalues of a real upper Hessenberg matrix H
* and, optionally, the matrices T and Z from the Schur decomposition
* H = Z T Z**T, where T is an upper quasi-triangular matrix (the Schur
* form), and Z is the orthogonal matrix of Schur vectors.
* Optionally Z may be postmultiplied into an input orthogonal matrix Q,
* so that this routine can give the Schur factorization of a matrix A
* which has been reduced to the Hessenberg form H by the orthogonal
* matrix Q: A = Q*H*Q**T = (QZ)*T*(QZ)**T.
* JOB (input) CHARACTER*1
* = 'E': compute eigenvalues only;
* = 'S': compute eigenvalues and the Schur form T.
* COMPZ (input) CHARACTER*1
* = 'N': no Schur vectors are computed;
* = 'I': Z is initialized to the unit matrix and the matrix Z
* of Schur vectors of H is returned;
* = 'V': Z must contain an orthogonal matrix Q on entry, and
* the product Q*Z is returned.
* N (input) INTEGER
* The order of the matrix H. N >= 0.
* ILO (input) INTEGER
* IHI (input) INTEGER
* It is assumed that H is already upper triangular in rows
* and columns 1:ILO-1 and IHI+1:N. ILO and IHI are normally
* set by a previous call to SGEBAL, and then passed to SGEHRD
* when the matrix output by SGEBAL is reduced to Hessenberg
* form. Otherwise ILO and IHI should be set to 1 and N
* 1 <= ILO <= IHI <= N, if N > 0; ILO=1 and IHI=0, if N=0.
* H (input/output) REAL array, dimension (LDH,N)
* On entry, the upper Hessenberg matrix H.
* On exit, if JOB = 'S', H contains the upper quasi-triangular
* matrix T from the Schur decomposition (the Schur form);
* 2-by-2 diagonal blocks (corresponding to complex conjugate
* pairs of eigenvalues) are returned in standard form, with
* H(i,i) = H(i+1,i+1) and H(i+1,i)*H(i,i+1) < 0. If JOB = 'E',
* the contents of H are unspecified on exit.
* LDH (input) INTEGER
* The leading dimension of the array H. LDH >= max(1,N).
* WR (output) REAL array, dimension (N)
* WI (output) REAL array, dimension (N)
* The real and imaginary parts, respectively, of the computed
* eigenvalues. If two eigenvalues are computed as a complex
* conjugate pair, they are stored in consecutive elements of
* WR and WI, say the i-th and (i+1)th, with WI(i) > 0 and
* WI(i+1) < 0. If JOB = 'S', the eigenvalues are stored in the
* same order as on the diagonal of the Schur form returned in
* H, with WR(i) = H(i,i) and, if H(i:i+1,i:i+1) is a 2-by-2
* diagonal block, WI(i) = sqrt(H(i+1,i)*H(i,i+1)) and
* WI(i+1) = -WI(i).
* Z (input/output) REAL array, dimension (LDZ,N)
* If COMPZ = 'N': Z is not referenced.
* If COMPZ = 'I': on entry, Z need not be set, and on exit, Z
* contains the orthogonal matrix Z of the Schur vectors of H.
* If COMPZ = 'V': on entry Z must contain an N-by-N matrix Q,
* which is assumed to be equal to the unit matrix except for
* the submatrix Z(ILO:IHI,ILO:IHI); on exit Z contains Q*Z.
* Normally Q is the orthogonal matrix generated by SORGHR after
* the call to SGEHRD which formed the Hessenberg matrix H.
* LDZ (input) INTEGER
* The leading dimension of the array Z.
* LDZ >= max(1,N) if COMPZ = 'I' or 'V'; LDZ >= 1 otherwise.
* WORK (workspace/output) REAL 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,N).
* 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
* > 0: if INFO = i, SHSEQR failed to compute all of the
* eigenvalues in a total of 30*(IHI-ILO+1) iterations;
* elements 1:ilo-1 and i+1:n of WR and WI contain those
* eigenvalues which have been successfully computed.
* .. Parameters ..
|Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
public static void shseqr(java.lang.String job,