SRC/strevc3.f(3)

NAME
SRC/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**T)*T = w*(y**T)
    !>
    !> where y**T denotes the transpose of the vector 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.

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 235 of file strevc3.f.

Author

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