strevc3.f(3)

NAME
strevc3.f

SYNOPSIS

  Functions/Subroutines
subroutine strevc3 (SIDE, HOWMNY, SELECT, N, T, LDT, VL, LDVL, VR, LDVR, MM, M, WORK, LWORK, INFO)
STREVC3

Function/Subroutine Documentation

  subroutine strevc3 (character SIDE, character HOWMNY, logical, dimension( * ) SELECT, integer N, real, dimension( ldt, * ) T, integer LDT, real, dimension( ldvl, * ) VL, integer LDVL, real, dimension( ldvr, * ) VR, integer LDVR, integer MM, integer M, real, dimension( * ) WORK, integer LWORK, integer INFO)

STREVC3

Purpose:

     STREVC3 computes some or all of the right and/or left eigenvectors of
     a real upper quasi-triangular matrix T.
     Matrices of this type are produced by the Schur factorization of
     a real general matrix:  A = Q*T*Q**T, as computed by SHSEQR.
     The right eigenvector x and the left eigenvector y of T corresponding
     to an eigenvalue w are defined by:
        T*x = w*x,     (y**H)*T = w*(y**H)
     where y**H denotes the conjugate transpose of y.
     The eigenvalues are not input to this routine, but are read directly
     from the diagonal blocks of T.
     This routine returns the matrices X and/or Y of right and left
     eigenvectors of T, or the products Q*X and/or Q*Y, where Q is an
     input matrix. If Q is the orthogonal factor that reduces a matrix
     A to Schur form T, then Q*X and Q*Y are the matrices of right and
     left eigenvectors of A.
     This uses a Level 3 BLAS version of the back transformation.

Parameters:
    SIDE

              SIDE is CHARACTER*1
              = 'R':  compute right eigenvectors only;
              = 'L':  compute left eigenvectors only;
              = 'B':  compute both right and left eigenvectors.

    HOWMNY

              HOWMNY is CHARACTER*1
              = 'A':  compute all right and/or left eigenvectors;
              = 'B':  compute all right and/or left eigenvectors,
                      backtransformed by the matrices in VR and/or VL;
              = 'S':  compute selected right and/or left eigenvectors,
                      as indicated by the logical array SELECT.

    SELECT

              SELECT is LOGICAL array, dimension (N)
              If HOWMNY = 'S', SELECT specifies the eigenvectors to be
              computed.
              If w(j) is a real eigenvalue, the corresponding real
              eigenvector is computed if SELECT(j) is .TRUE..
              If w(j) and w(j+1) are the real and imaginary parts of a
              complex eigenvalue, the corresponding complex eigenvector is
              computed if either SELECT(j) or SELECT(j+1) is .TRUE., and
              on exit SELECT(j) is set to .TRUE. and SELECT(j+1) is set to
              .FALSE..
              Not referenced if HOWMNY = 'A' or 'B'.

    N

              N is INTEGER
              The order of the matrix T. N >= 0.

    T

              T is REAL array, dimension (LDT,N)
              The upper quasi-triangular matrix T in Schur canonical form.

    LDT

              LDT is INTEGER
              The leading dimension of the array T. LDT >= max(1,N).

    VL

              VL is REAL array, dimension (LDVL,MM)
              On entry, if SIDE = 'L' or 'B' and HOWMNY = 'B', VL must
              contain 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;
              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.
              Not referenced if SIDE = 'R'.

    LDVL

              LDVL is INTEGER
              The leading dimension of the array VL.
              LDVL >= 1, and if SIDE = 'L' or 'B', LDVL >= N.

    VR

              VR is REAL array, dimension (LDVR,MM)
              On entry, if SIDE = 'R' or 'B' and HOWMNY = 'B', VR must
              contain 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;
              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 corresponding to a complex eigenvalue
              is stored in two consecutive columns, the first holding the
              real part and the second the imaginary part.
              Not referenced if SIDE = 'L'.

    LDVR

              LDVR is INTEGER
              The leading dimension of the array VR.
              LDVR >= 1, and if SIDE = 'R' or 'B', LDVR >= N.

    MM

              MM is INTEGER
              The number of columns in the arrays VL and/or VR. MM >= M.

    M

              M is INTEGER
              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

              WORK is REAL array, dimension (MAX(1,LWORK))

    LWORK

              LWORK is INTEGER
              The dimension of array WORK. LWORK >= max(1,3*N).
              For optimum performance, LWORK >= N + 2*N*NB, where NB is
              the optimal blocksize.
              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

              INFO is INTEGER
              = 0:  successful exit
              < 0:  if INFO = -i, the i-th argument had an illegal value

Author:
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Date:
    November 2017

Further Details:

      The algorithm used in this program is basically backward (forward)
      substitution, 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|.

Definition at line 241 of file strevc3.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.