Provided by: liblapack-doc_3.3.1-1_all bug

NAME

       LAPACK-3  -  computes  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      HOWMNY, SIDE

           INTEGER        INFO, LDT, LDVL, LDVR, M, MM, N

           LOGICAL        SELECT( * )

           REAL           T( LDT, * ), VL( LDVL, * ), VR( LDVR, * ), WORK( * )

PURPOSE

       STREVC  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 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.

ARGUMENTS

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

        HOWMNY  (input) 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  (input/output) 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       (input) INTEGER
                The order of the matrix T. N >= 0.

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

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

        VL      (input/output) 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    (input) INTEGER
                The leading dimension of the array VL.  LDVL >= 1, and if
                SIDE = 'L' or 'B', LDVL >= N.

        VR      (input/output) 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    (input) INTEGER
                The leading dimension of the array VR.  LDVR >= 1, and if
                SIDE = 'R' or 'B', LDVR >= N.

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

        M       (output) 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    (workspace) REAL array, dimension (3*N)

        INFO    (output) INTEGER
                = 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)
        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|.

 LAPACK routine (version 3.3.1)             April 2011                            STREVC(3lapack)