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java.lang.Object | +----org.netlib.lapack.Dgegs
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 * ======= * * DGEGS 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 DGEGV * 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) DOUBLE PRECISION 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) DOUBLE PRECISION 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) 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. 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) DOUBLE PRECISION 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) DOUBLE PRECISION 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) 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(1,4*N). * For good performance, LWORK must generally be larger. * To compute the optimal value of LWORK, call ILAENV to get * blocksizes (for DGEQRF, DORMQR, and DORGQR.) Then compute: * NB -- MAX of the blocksizes for DGEQRF, DORMQR, and DORGQR * The optimal LWORK is 2*N + N*(NB+1). * * 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 DGGBAL * =N+2: error return from DGEQRF * =N+3: error return from DORMQR * =N+4: error return from DORGQR * =N+5: error return from DGGHRD * =N+6: error return from DHGEQZ (other than failed * iteration) * =N+7: error return from DGGBAK (computing VSL) * =N+8: error return from DGGBAK (computing VSR) * =N+9: error return from DLASCL (various places) * * ===================================================================== * * .. Parameters ..
Dgegs()
dgegs(String, String, int, double[], int, int, double[], int, int, double[], int, double[], int, double[], int, double[], int, int, double[], int, int, double[], int, int, intW)
Dgegs
public Dgegs()
dgegs
public static void dgegs(String jobvsl,
String jobvsr,
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 vsl[],
int _vsl_offset,
int ldvsl,
double vsr[],
int _vsr_offset,
int ldvsr,
double work[],
int _work_offset,
int lwork,
intW info)
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