dgegs - routine is deprecated and has been replaced by routine DGGES
SUBROUTINE DGEGS(JOBVSL, JOBVSR, N, A, LDA, B, LDB, ALPHAR, ALPHAI, BETA, VSL, LDVSL, VSR, LDVSR, WORK, LDWORK, INFO) CHARACTER*1 JOBVSL, JOBVSR INTEGER N, LDA, LDB, LDVSL, LDVSR, LDWORK, INFO DOUBLE PRECISION A(LDA,*), B(LDB,*), ALPHAR(*), ALPHAI(*), BETA(*), VSL(LDVSL,*), VSR(LDVSR,*), WORK(*) SUBROUTINE DGEGS_64(JOBVSL, JOBVSR, N, A, LDA, B, LDB, ALPHAR, ALPHAI, BETA, VSL, LDVSL, VSR, LDVSR, WORK, LDWORK, INFO) CHARACTER*1 JOBVSL, JOBVSR INTEGER*8 N, LDA, LDB, LDVSL, LDVSR, LDWORK, INFO DOUBLE PRECISION A(LDA,*), B(LDB,*), ALPHAR(*), ALPHAI(*), BETA(*), VSL(LDVSL,*), VSR(LDVSR,*), WORK(*) F95 INTERFACE SUBROUTINE GEGS(JOBVSL, JOBVSR, N, A, LDA, B, LDB, ALPHAR, ALPHAI, BETA, VSL, LDVSL, VSR, LDVSR, WORK, LDWORK, INFO) CHARACTER(LEN=1) :: JOBVSL, JOBVSR INTEGER :: N, LDA, LDB, LDVSL, LDVSR, LDWORK, INFO REAL(8), DIMENSION(:) :: ALPHAR, ALPHAI, BETA, WORK REAL(8), DIMENSION(:,:) :: A, B, VSL, VSR SUBROUTINE GEGS_64(JOBVSL, JOBVSR, N, A, LDA, B, LDB, ALPHAR, ALPHAI, BETA, VSL, LDVSL, VSR, LDVSR, WORK, LDWORK, INFO) CHARACTER(LEN=1) :: JOBVSL, JOBVSR INTEGER(8) :: N, LDA, LDB, LDVSL, LDVSR, LDWORK, INFO REAL(8), DIMENSION(:) :: ALPHAR, ALPHAI, BETA, WORK REAL(8), DIMENSION(:,:) :: A, B, VSL, VSR C INTERFACE #include <sunperf.h> void dgegs(char jobvsl, char jobvsr, int n, double *a, int lda, double *b, int ldb, double *alphar, double *alphai, double *beta, double *vsl, int ldvsl, double *vsr, int ldvsr, int *info); void dgegs_64(char jobvsl, char jobvsr, long n, double *a, long lda, double *b, long ldb, double *alphar, double *alphai, double *beta, double *vsl, long ldvsl, double *vsr, long ldvsr, long *info);
Oracle Solaris Studio Performance Library dgegs(3P) NAME dgegs - routine is deprecated and has been replaced by routine DGGES SYNOPSIS SUBROUTINE DGEGS(JOBVSL, JOBVSR, N, A, LDA, B, LDB, ALPHAR, ALPHAI, BETA, VSL, LDVSL, VSR, LDVSR, WORK, LDWORK, INFO) CHARACTER*1 JOBVSL, JOBVSR INTEGER N, LDA, LDB, LDVSL, LDVSR, LDWORK, INFO DOUBLE PRECISION A(LDA,*), B(LDB,*), ALPHAR(*), ALPHAI(*), BETA(*), VSL(LDVSL,*), VSR(LDVSR,*), WORK(*) SUBROUTINE DGEGS_64(JOBVSL, JOBVSR, N, A, LDA, B, LDB, ALPHAR, ALPHAI, BETA, VSL, LDVSL, VSR, LDVSR, WORK, LDWORK, INFO) CHARACTER*1 JOBVSL, JOBVSR INTEGER*8 N, LDA, LDB, LDVSL, LDVSR, LDWORK, INFO DOUBLE PRECISION A(LDA,*), B(LDB,*), ALPHAR(*), ALPHAI(*), BETA(*), VSL(LDVSL,*), VSR(LDVSR,*), WORK(*) F95 INTERFACE SUBROUTINE GEGS(JOBVSL, JOBVSR, N, A, LDA, B, LDB, ALPHAR, ALPHAI, BETA, VSL, LDVSL, VSR, LDVSR, WORK, LDWORK, INFO) CHARACTER(LEN=1) :: JOBVSL, JOBVSR INTEGER :: N, LDA, LDB, LDVSL, LDVSR, LDWORK, INFO REAL(8), DIMENSION(:) :: ALPHAR, ALPHAI, BETA, WORK REAL(8), DIMENSION(:,:) :: A, B, VSL, VSR SUBROUTINE GEGS_64(JOBVSL, JOBVSR, N, A, LDA, B, LDB, ALPHAR, ALPHAI, BETA, VSL, LDVSL, VSR, LDVSR, WORK, LDWORK, INFO) CHARACTER(LEN=1) :: JOBVSL, JOBVSR INTEGER(8) :: N, LDA, LDB, LDVSL, LDVSR, LDWORK, INFO REAL(8), DIMENSION(:) :: ALPHAR, ALPHAI, BETA, WORK REAL(8), DIMENSION(:,:) :: A, B, VSL, VSR C INTERFACE #include <sunperf.h> void dgegs(char jobvsl, char jobvsr, int n, double *a, int lda, double *b, int ldb, double *alphar, double *alphai, double *beta, double *vsl, int ldvsl, double *vsr, int ldvsr, int *info); void dgegs_64(char jobvsl, char jobvsr, long n, double *a, long lda, double *b, long ldb, double *alphar, double *alphai, double *beta, double *vsl, long ldvsl, double *vsr, long ldvsr, long *info); PURPOSE dgegs routine is deprecated and has been replaced by routine DGGES. 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 matri- ces 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 gener- alized 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 com- plex 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) = 'N': do not compute the left Schur vectors; = 'V': compute the left Schur vectors. JOBVSR (input) = 'N': do not compute the right Schur vectors; = 'V': compute the right Schur vectors. N (input) The order of the matrices A, B, VSL, and VSR. N >= 0. A (input/output) On entry, the first of the pair of matrices whose generalized eigenvalues and (optionally) Schur vectors are to be com- puted. 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) The leading dimension of A. LDA >= max(1,N). B (input/output) On entry, the second of the pair of matrices whose general- ized 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) The leading dimension of B. LDB >= max(1,N). ALPHAR (output) 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 eigen- value is real; if positive, then the j-th and (j+1)-st eigen- values are a complex conjugate pair, with ALPHAI(j+1) nega- tive. 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). ALPHAI (output) See the description for ALPHAR. BETA (output) See the description for ALPHAR. VSL (output) If JOBVSL = 'V', VSL will contain the left Schur vectors. (See "Purpose", above.) Not referenced if JOBVSL = 'N'. LDVSL (output) The leading dimension of the matrix VSL. LDVSL >=1, and if JOBVSL = 'V', LDVSL >= N. VSR (input) If JOBVSR = 'V', VSR will contain the right Schur vectors. (See "Purpose", above.) Not referenced if JOBVSR = 'N'. LDVSR (input) The leading dimension of the matrix VSR. LDVSR >= 1, and if JOBVSR = 'V', LDVSR >= N. WORK (workspace) On exit, if INFO = 0, WORK(1) returns the optimal LDWORK. LDWORK (input) The dimension of the array WORK. LDWORK >= max(1,4*N). For good performance, LDWORK must generally be larger. To com- pute the optimal value of LDWORK, call ILAENV to get block- sizes (for DGEQRF, DORMQR, and DORGQR.) Then compute: NB -- MAX of the blocksizes for DGEQRF, DORMQR, and DORGQR The optimal LDWORK is 2*N + N*(NB+1). If LDWORK = -1, then a workspace query is assumed; the rou- tine 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 LDWORK is issued by XERBLA. INFO (output) = 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 SLASCL (various places) 7 Nov 2015 dgegs(3P)