org.netlib.lapack
Class SGEGS
java.lang.Object
org.netlib.lapack.SGEGS
public class SGEGS
 extends java.lang.Object
SGEGS is a simplified interface to the JLAPACK routine sgegs.
This interface converts Javastyle 2D rowmajor arrays into
the 1D columnmajor linearized arrays expected by the lower
level JLAPACK routines. Using this interface also allows you
to omit offset and leading dimension arguments. However, because
of these conversions, these routines will be slower than the low
level ones. Following is the description from the original Fortran
source. Contact seymour@cs.utk.edu with any questions.
* ..
*
* Purpose
* =======
*
* This routine is deprecated and has been replaced by routine SGGES.
*
* SGEGS computes for a pair of NbyN real nonsymmetric matrices A, B:
* the generalized eigenvalues (alphar +/ alphai*i, beta), the real
* Schur form (A, B), and optionally left and/or right Schur vectors
* (VSL and VSR).
*
* (If only the generalized eigenvalues are needed, use the driver SGEGV
* instead.)
*
* A generalized eigenvalue for a pair of matrices (A,B) is, roughly
* speaking, a scalar w or a ratio alpha/beta = w, such that A  w*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. A good beginning reference is the book, "Matrix
* Computations", by G. Golub & C. van Loan (Johns Hopkins U. Press)
*
* The (generalized) Schur form of a pair of matrices is the result of
* multiplying both matrices on the left by one orthogonal matrix and
* both on the right by another orthogonal matrix, these two orthogonal
* matrices being chosen so as to bring the pair of matrices into
* (real) Schur form.
*
* A pair of matrices A, B is in generalized real Schur form if B is
* upper triangular with nonnegative diagonal and A is block upper
* triangular with 1by1 and 2by2 blocks. 1by1 blocks correspond
* to real generalized eigenvalues, while 2by2 blocks of A will be
* "standardized" by making the corresponding elements of B have the
* form:
* [ a 0 ]
* [ 0 b ]
*
* and the pair of corresponding 2by2 blocks in A and B will
* have a complex conjugate pair of generalized eigenvalues.
*
* The left and right Schur vectors are the columns of VSL and VSR,
* respectively, where VSL and VSR are the orthogonal matrices
* which reduce A and B to Schur form:
*
* Schur form of (A,B) = ( (VSL)**T A (VSR), (VSL)**T B (VSR) )
*
* Arguments
* =========
*
* JOBVSL (input) CHARACTER*1
* = 'N': do not compute the left Schur vectors;
* = 'V': compute the left Schur vectors.
*
* JOBVSR (input) CHARACTER*1
* = 'N': do not compute the right Schur vectors;
* = 'V': compute the right Schur vectors.
*
* N (input) INTEGER
* The order of the matrices A, B, VSL, and VSR. N >= 0.
*
* A (input/output) REAL array, dimension (LDA, N)
* On entry, the first of the pair of matrices whose generalized
* eigenvalues and (optionally) Schur vectors are to be
* computed.
* On exit, the generalized Schur form of A.
* Note: to avoid overflow, the Frobenius norm of the matrix
* A should be less than the overflow threshold.
*
* LDA (input) INTEGER
* The leading dimension of A. LDA >= max(1,N).
*
* B (input/output) REAL array, dimension (LDB, N)
* On entry, the second of the pair of matrices whose
* generalized eigenvalues and (optionally) Schur vectors are
* to be computed.
* On exit, the generalized Schur form of B.
* Note: to avoid overflow, the Frobenius norm of the matrix
* B should be less than the overflow threshold.
*
* LDB (input) INTEGER
* The leading dimension of B. LDB >= max(1,N).
*
* ALPHAR (output) REAL array, dimension (N)
* ALPHAI (output) REAL array, dimension (N)
* BETA (output) REAL array, dimension (N)
* On exit, (ALPHAR(j) + ALPHAI(j)*i)/BETA(j), j=1,...,N, will
* be the generalized eigenvalues. ALPHAR(j) + ALPHAI(j)*i,
* j=1,...,N and BETA(j),j=1,...,N are the diagonals of the
* complex Schur form (A,B) that would result if the 2by2
* diagonal blocks of the real Schur form of (A,B) were further
* reduced to triangular form using 2by2 complex unitary
* transformations. If ALPHAI(j) is zero, then the jth
* eigenvalue is real; if positive, then the jth 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).
*
* VSL (output) REAL array, dimension (LDVSL,N)
* If JOBVSL = 'V', VSL will contain the left Schur vectors.
* (See "Purpose", above.)
* Not referenced if JOBVSL = 'N'.
*
* LDVSL (input) INTEGER
* The leading dimension of the matrix VSL. LDVSL >=1, and
* if JOBVSL = 'V', LDVSL >= N.
*
* VSR (output) REAL array, dimension (LDVSR,N)
* If JOBVSR = 'V', VSR will contain the right Schur vectors.
* (See "Purpose", above.)
* Not referenced if JOBVSR = 'N'.
*
* LDVSR (input) INTEGER
* The leading dimension of the matrix VSR. LDVSR >= 1, and
* if JOBVSR = 'V', LDVSR >= N.
*
* 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(1,4*N).
* For good performance, LWORK must generally be larger.
* To compute the optimal value of LWORK, call ILAENV to get
* blocksizes (for SGEQRF, SORMQR, and SORGQR.) Then compute:
* NB  MAX of the blocksizes for SGEQRF, SORMQR, and SORGQR
* The optimal LWORK is 2*N + N*(NB+1).
*
* 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 ith argument had an illegal value.
* = 1,...,N:
* The QZ iteration failed. (A,B) are not in Schur
* form, but ALPHAR(j), ALPHAI(j), and BETA(j) should
* be correct for j=INFO+1,...,N.
* > N: errors that usually indicate LAPACK problems:
* =N+1: error return from SGGBAL
* =N+2: error return from SGEQRF
* =N+3: error return from SORMQR
* =N+4: error return from SORGQR
* =N+5: error return from SGGHRD
* =N+6: error return from SHGEQZ (other than failed
* iteration)
* =N+7: error return from SGGBAK (computing VSL)
* =N+8: error return from SGGBAK (computing VSR)
* =N+9: error return from SLASCL (various places)
*
* =====================================================================
*
* .. Parameters ..
Constructor Summary 
SGEGS()

Method Summary 
static void 
SGEGS(java.lang.String jobvsl,
java.lang.String jobvsr,
int n,
float[][] a,
float[][] b,
float[] alphar,
float[] alphai,
float[] beta,
float[][] vsl,
float[][] vsr,
float[] work,
int lwork,
intW info)

Methods inherited from class java.lang.Object 
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait 
SGEGS
public SGEGS()
SGEGS
public static void SGEGS(java.lang.String jobvsl,
java.lang.String jobvsr,
int n,
float[][] a,
float[][] b,
float[] alphar,
float[] alphai,
float[] beta,
float[][] vsl,
float[][] vsr,
float[] work,
int lwork,
intW info)