org.netlib.lapack
Class Sgegs
java.lang.Object
org.netlib.lapack.Sgegs
public class Sgegs
- 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
* =======
*
* This routine is deprecated and has been replaced by routine SGGES.
*
* SGEGS computes for a pair of N-by-N 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 non-negative diagonal and A is block upper
* triangular with 1-by-1 and 2-by-2 blocks. 1-by-1 blocks correspond
* to real generalized eigenvalues, while 2-by-2 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 2-by-2 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 2-by-2
* diagonal blocks of the real Schur form of (A,B) were further
* reduced to triangular form using 2-by-2 complex unitary
* transformations. 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).
*
* 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 i-th 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 ..
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Constructor Summary |
Sgegs()
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Method Summary |
static void |
sgegs(java.lang.String jobvsl,
java.lang.String jobvsr,
int n,
float[] a,
int _a_offset,
int lda,
float[] b,
int _b_offset,
int ldb,
float[] alphar,
int _alphar_offset,
float[] alphai,
int _alphai_offset,
float[] beta,
int _beta_offset,
float[] vsl,
int _vsl_offset,
int ldvsl,
float[] vsr,
int _vsr_offset,
int ldvsr,
float[] 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 |
Sgegs
public Sgegs()
sgegs
public static void sgegs(java.lang.String jobvsl,
java.lang.String jobvsr,
int n,
float[] a,
int _a_offset,
int lda,
float[] b,
int _b_offset,
int ldb,
float[] alphar,
int _alphar_offset,
float[] alphai,
int _alphai_offset,
float[] beta,
int _beta_offset,
float[] vsl,
int _vsl_offset,
int ldvsl,
float[] vsr,
int _vsr_offset,
int ldvsr,
float[] work,
int _work_offset,
int lwork,
intW info)