strevc - compute some or all of the right and/or left eigenvectors of a real upper quasi-triangular matrix T
SUBROUTINE STREVC(SIDE, HOWMNY, SELECT, N, T, LDT, VL, LDVL, VR, LDVR, MM, M, WORK, INFO) CHARACTER*1 SIDE, HOWMNY INTEGER N, LDT, LDVL, LDVR, MM, M, INFO LOGICAL SELECT(*) REAL T(LDT,*), VL(LDVL,*), VR(LDVR,*), WORK(*) SUBROUTINE STREVC_64(SIDE, HOWMNY, SELECT, N, T, LDT, VL, LDVL, VR, LDVR, MM, M, WORK, INFO) CHARACTER*1 SIDE, HOWMNY INTEGER*8 N, LDT, LDVL, LDVR, MM, M, INFO LOGICAL*8 SELECT(*) REAL T(LDT,*), VL(LDVL,*), VR(LDVR,*), WORK(*) F95 INTERFACE SUBROUTINE TREVC(SIDE, HOWMNY, SELECT, N, T, LDT, VL, LDVL, VR, LDVR, MM, M, WORK, INFO) CHARACTER(LEN=1) :: SIDE, HOWMNY INTEGER :: N, LDT, LDVL, LDVR, MM, M, INFO LOGICAL, DIMENSION(:) :: SELECT REAL, DIMENSION(:) :: WORK REAL, DIMENSION(:,:) :: T, VL, VR SUBROUTINE TREVC_64(SIDE, HOWMNY, SELECT, N, T, LDT, VL, LDVL, VR, LDVR, MM, M, WORK, INFO) CHARACTER(LEN=1) :: SIDE, HOWMNY INTEGER(8) :: N, LDT, LDVL, LDVR, MM, M, INFO LOGICAL(8), DIMENSION(:) :: SELECT REAL, DIMENSION(:) :: WORK REAL, DIMENSION(:,:) :: T, VL, VR C INTERFACE #include <sunperf.h> void strevc(char side, char howmny, int *select, int n, float *t, int ldt, float *vl, int ldvl, float *vr, int ldvr, int mm, int *m, int *info); void strevc_64(char side, char howmny, long *select, long n, float *t, long ldt, float *vl, long ldvl, float *vr, long ldvr, long mm, long *m, long *info);
Oracle Solaris Studio Performance Library strevc(3P) NAME strevc - compute some or all of the right and/or left eigenvectors of a real upper quasi-triangular matrix T SYNOPSIS SUBROUTINE STREVC(SIDE, HOWMNY, SELECT, N, T, LDT, VL, LDVL, VR, LDVR, MM, M, WORK, INFO) CHARACTER*1 SIDE, HOWMNY INTEGER N, LDT, LDVL, LDVR, MM, M, INFO LOGICAL SELECT(*) REAL T(LDT,*), VL(LDVL,*), VR(LDVR,*), WORK(*) SUBROUTINE STREVC_64(SIDE, HOWMNY, SELECT, N, T, LDT, VL, LDVL, VR, LDVR, MM, M, WORK, INFO) CHARACTER*1 SIDE, HOWMNY INTEGER*8 N, LDT, LDVL, LDVR, MM, M, INFO LOGICAL*8 SELECT(*) REAL T(LDT,*), VL(LDVL,*), VR(LDVR,*), WORK(*) F95 INTERFACE SUBROUTINE TREVC(SIDE, HOWMNY, SELECT, N, T, LDT, VL, LDVL, VR, LDVR, MM, M, WORK, INFO) CHARACTER(LEN=1) :: SIDE, HOWMNY INTEGER :: N, LDT, LDVL, LDVR, MM, M, INFO LOGICAL, DIMENSION(:) :: SELECT REAL, DIMENSION(:) :: WORK REAL, DIMENSION(:,:) :: T, VL, VR SUBROUTINE TREVC_64(SIDE, HOWMNY, SELECT, N, T, LDT, VL, LDVL, VR, LDVR, MM, M, WORK, INFO) CHARACTER(LEN=1) :: SIDE, HOWMNY INTEGER(8) :: N, LDT, LDVL, LDVR, MM, M, INFO LOGICAL(8), DIMENSION(:) :: SELECT REAL, DIMENSION(:) :: WORK REAL, DIMENSION(:,:) :: T, VL, VR C INTERFACE #include <sunperf.h> void strevc(char side, char howmny, int *select, int n, float *t, int ldt, float *vl, int ldvl, float *vr, int ldvr, int mm, int *m, int *info); void strevc_64(char side, char howmny, long *select, long n, float *t, long ldt, float *vl, long ldvl, float *vr, long ldvr, long mm, long *m, long *info); PURPOSE strevc computes some or all of the right and/or left eigenvectors of a real upper quasi-triangular matrix T. The right eigenvector x and the left eigenvector y of T corresponding to an eigenvalue w are defined by: T*x = w*x, y'*T = w*y' where y' denotes the conjugate transpose of the vector y. If all eigenvectors are requested, the routine may either return the matrices X and/or Y of right or left eigenvectors of T, or the products Q*X and/or Q*Y, where Q is an input orthogonal matrix. If T was obtained from the real-Schur factorization of an orig- inal matrix A = Q*T*Q', then Q*X and Q*Y are the matrices of right or left eigenvectors of A. T must be in Schur canonical form (as returned by SHSEQR), that is, block upper triangular with 1-by-1 and 2-by-2 diagonal blocks; each 2-by-2 diagonal block has its diagonal elements equal and its off-diag- onal elements of opposite sign. Corresponding to each 2-by-2 diagonal block is a complex conjugate pair of eigenvalues and eigenvectors; only one eigenvector of the pair is computed, namely the one corresponding to the eigenvalue with positive imaginary part. ARGUMENTS SIDE (input) = 'R': compute right eigenvectors only; = 'L': compute left eigenvectors only; = 'B': compute both right and left eigenvectors. HOWMNY (input) = 'A': compute all right and/or left eigenvectors; = 'B': compute all right and/or left eigenvectors, and back- transform them using the input matrices supplied in VR and/or VL; = 'S': compute selected right and/or left eigenvectors, specified by the logical array SELECT. SELECT (input/output) If HOWMNY = 'S', SELECT specifies the eigenvectors to be com- puted. If HOWMNY = 'A' or 'B', SELECT is not referenced. To select the real eigenvector corresponding to a real eigenval- ue w(j), SELECT(j) must be set to .TRUE.. To select the com- plex eigenvector corresponding to a complex conjugate pair w(j) and w(j+1), either SELECT(j) or SELECT(j+1) must be set to .TRUE.; then on exit SELECT(j) is .TRUE. and SELECT(j+1) is .FALSE.. N (input) The order of the matrix T. N >= 0. T (input/output) The upper quasi-triangular matrix T in Schur canonical form. LDT (input) The leading dimension of the array T. LDT >= max(1,N). VL (input/output) On entry, if SIDE = 'L' or 'B' and HOWMNY = 'B', VL must con- tain an N-by-N matrix Q (usually the orthogonal matrix Q of Schur vectors returned by SHSEQR). On exit, if SIDE = 'L' or 'B', VL contains: if HOWMNY = 'A', the matrix Y of left eigenvectors of T; VL has the same quasi-lower triangular form as T'. If T(i,i) is a real eigenvalue, then the i-th column VL(i) of VL is its corresponding eigenvector. If T(i:i+1,i:i+1) is a 2-by-2 block whose eigenvalues are com- plex-conjugate eigenvalues of T, then VL(i)+sqrt(-1)*VL(i+1) is the complex eigenvector corresponding to the eigenvalue with positive real part. if HOWMNY = 'B', the matrix Q*Y; if HOWMNY = 'S', the left eigenvectors of T specified by SELECT, stored consecutively in the columns of VL, in the same order as their eigenvalues. A complex eigenvector corresponding to a complex eigenvalue is stored in two consecutive columns, the first holding the real part, and the second the imaginary part. If SIDE = 'R', VL is not referenced. LDVL (input) The leading dimension of the array VL. LDVL >= max(1,N) if SIDE = 'L' or 'B'; LDVL >= 1 otherwise. VR (input/output) On entry, if SIDE = 'R' or 'B' and HOWMNY = 'B', VR must con- tain an N-by-N matrix Q (usually the orthogonal matrix Q of Schur vectors returned by SHSEQR). On exit, if SIDE = 'R' or 'B', VR contains: if HOWMNY = 'A', the matrix X of right eigenvectors of T; VR has the same quasi-upper triangular form as T. If T(i,i) is a real eigenvalue, then the i-th col- umn VR(i) of VR is its corresponding eigenvector. If T(i:i+1,i:i+1) is a 2-by-2 block whose eigenvalues are com- plex-conjugate eigenvalues of T, then VR(i)+sqrt(-1)*VR(i+1) is the complex eigenvector corresponding to the eigenvalue with positive real part. if HOWMNY = 'B', the matrix Q*X; if HOWMNY = 'S', the right eigenvectors of T specified by SELECT, stored consecutively in the columns of VR, in the same order as their eigenvalues. A complex eigenvector cor- responding to a complex eigenvalue is stored in two consecu- tive columns, the first holding the real part and the second the imaginary part. If SIDE = 'L', VR is not referenced. LDVR (input) The leading dimension of the array VR. LDVR >= max(1,N) if SIDE = 'R' or 'B'; LDVR >= 1 otherwise. MM (input) The number of columns in the arrays VL and/or VR. MM >= M. M (output) The number of columns in the arrays VL and/or VR actually used to store the eigenvectors. If HOWMNY = 'A' or 'B', M is set to N. Each selected real eigenvector occupies one column and each selected complex eigenvector occupies two columns. WORK (workspace) dimension(3*N) INFO (output) = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value FURTHER DETAILS The algorithm used in this program is basically backward (forward) sub- stitution, with scaling to make the the code robust against possible overflow. Each eigenvector is normalized so that the element of largest magnitude has magnitude 1; here the magnitude of a complex number (x,y) is taken to be |x| + |y|. 7 Nov 2015 strevc(3P)