Provided by: liblapack-doc_3.12.0-3build1.1_all bug

NAME

       larrv - larrv: eig tridiagonal, step in stemr & stegr

SYNOPSIS

   Functions
       subroutine clarrv (n, vl, vu, d, l, pivmin, isplit, m, dol, dou, minrgp, rtol1, rtol2, w,
           werr, wgap, iblock, indexw, gers, z, ldz, isuppz, work, iwork, info)
           CLARRV computes the eigenvectors of the tridiagonal matrix T = L D LT given L, D and
           the eigenvalues of L D LT.
       subroutine dlarrv (n, vl, vu, d, l, pivmin, isplit, m, dol, dou, minrgp, rtol1, rtol2, w,
           werr, wgap, iblock, indexw, gers, z, ldz, isuppz, work, iwork, info)
           DLARRV computes the eigenvectors of the tridiagonal matrix T = L D LT given L, D and
           the eigenvalues of L D LT.
       subroutine slarrv (n, vl, vu, d, l, pivmin, isplit, m, dol, dou, minrgp, rtol1, rtol2, w,
           werr, wgap, iblock, indexw, gers, z, ldz, isuppz, work, iwork, info)
           SLARRV computes the eigenvectors of the tridiagonal matrix T = L D LT given L, D and
           the eigenvalues of L D LT.
       subroutine zlarrv (n, vl, vu, d, l, pivmin, isplit, m, dol, dou, minrgp, rtol1, rtol2, w,
           werr, wgap, iblock, indexw, gers, z, ldz, isuppz, work, iwork, info)
           ZLARRV computes the eigenvectors of the tridiagonal matrix T = L D LT given L, D and
           the eigenvalues of L D LT.

Detailed Description

Function Documentation

   subroutine clarrv (integer n, real vl, real vu, real, dimension( * ) d, real, dimension( * )
       l, real pivmin, integer, dimension( * ) isplit, integer m, integer dol, integer dou, real
       minrgp, real rtol1, real rtol2, real, dimension( * ) w, real, dimension( * ) werr, real,
       dimension( * ) wgap, integer, dimension( * ) iblock, integer, dimension( * ) indexw, real,
       dimension( * ) gers, complex, dimension( ldz, * ) z, integer ldz, integer, dimension( * )
       isuppz, real, dimension( * ) work, integer, dimension( * ) iwork, integer info)
       CLARRV computes the eigenvectors of the tridiagonal matrix T = L D LT given L, D and the
       eigenvalues of L D LT.

       Purpose:

            CLARRV computes the eigenvectors of the tridiagonal matrix
            T = L D L**T given L, D and APPROXIMATIONS to the eigenvalues of L D L**T.
            The input eigenvalues should have been computed by SLARRE.

       Parameters
           N

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

           VL

                     VL is REAL
                     Lower bound of the interval that contains the desired
                     eigenvalues. VL < VU. Needed to compute gaps on the left or right
                     end of the extremal eigenvalues in the desired RANGE.

           VU

                     VU is REAL
                     Upper bound of the interval that contains the desired
                     eigenvalues. VL < VU. Needed to compute gaps on the left or right
                     end of the extremal eigenvalues in the desired RANGE.

           D

                     D is REAL array, dimension (N)
                     On entry, the N diagonal elements of the diagonal matrix D.
                     On exit, D may be overwritten.

           L

                     L is REAL array, dimension (N)
                     On entry, the (N-1) subdiagonal elements of the unit
                     bidiagonal matrix L are in elements 1 to N-1 of L
                     (if the matrix is not split.) At the end of each block
                     is stored the corresponding shift as given by SLARRE.
                     On exit, L is overwritten.

           PIVMIN

                     PIVMIN is REAL
                     The minimum pivot allowed in the Sturm sequence.

           ISPLIT

                     ISPLIT is INTEGER array, dimension (N)
                     The splitting points, at which T breaks up into blocks.
                     The first block consists of rows/columns 1 to
                     ISPLIT( 1 ), the second of rows/columns ISPLIT( 1 )+1
                     through ISPLIT( 2 ), etc.

           M

                     M is INTEGER
                     The total number of input eigenvalues.  0 <= M <= N.

           DOL

                     DOL is INTEGER

           DOU

                     DOU is INTEGER
                     If the user wants to compute only selected eigenvectors from all
                     the eigenvalues supplied, he can specify an index range DOL:DOU.
                     Or else the setting DOL=1, DOU=M should be applied.
                     Note that DOL and DOU refer to the order in which the eigenvalues
                     are stored in W.
                     If the user wants to compute only selected eigenpairs, then
                     the columns DOL-1 to DOU+1 of the eigenvector space Z contain the
                     computed eigenvectors. All other columns of Z are set to zero.

           MINRGP

                     MINRGP is REAL

           RTOL1

                     RTOL1 is REAL

           RTOL2

                     RTOL2 is REAL
                      Parameters for bisection.
                      An interval [LEFT,RIGHT] has converged if
                      RIGHT-LEFT < MAX( RTOL1*GAP, RTOL2*MAX(|LEFT|,|RIGHT|) )

           W

                     W is REAL array, dimension (N)
                     The first M elements of W contain the APPROXIMATE eigenvalues for
                     which eigenvectors are to be computed.  The eigenvalues
                     should be grouped by split-off block and ordered from
                     smallest to largest within the block ( The output array
                     W from SLARRE is expected here ). Furthermore, they are with
                     respect to the shift of the corresponding root representation
                     for their block. On exit, W holds the eigenvalues of the
                     UNshifted matrix.

           WERR

                     WERR is REAL array, dimension (N)
                     The first M elements contain the semiwidth of the uncertainty
                     interval of the corresponding eigenvalue in W

           WGAP

                     WGAP is REAL array, dimension (N)
                     The separation from the right neighbor eigenvalue in W.

           IBLOCK

                     IBLOCK is INTEGER array, dimension (N)
                     The indices of the blocks (submatrices) associated with the
                     corresponding eigenvalues in W; IBLOCK(i)=1 if eigenvalue
                     W(i) belongs to the first block from the top, =2 if W(i)
                     belongs to the second block, etc.

           INDEXW

                     INDEXW is INTEGER array, dimension (N)
                     The indices of the eigenvalues within each block (submatrix);
                     for example, INDEXW(i)= 10 and IBLOCK(i)=2 imply that the
                     i-th eigenvalue W(i) is the 10-th eigenvalue in the second block.

           GERS

                     GERS is REAL array, dimension (2*N)
                     The N Gerschgorin intervals (the i-th Gerschgorin interval
                     is (GERS(2*i-1), GERS(2*i)). The Gerschgorin intervals should
                     be computed from the original UNshifted matrix.

           Z

                     Z is COMPLEX array, dimension (LDZ, max(1,M) )
                     If INFO = 0, the first M columns of Z contain the
                     orthonormal eigenvectors of the matrix T
                     corresponding to the input eigenvalues, with the i-th
                     column of Z holding the eigenvector associated with W(i).
                     Note: the user must ensure that at least max(1,M) columns are
                     supplied in the array Z.

           LDZ

                     LDZ is INTEGER
                     The leading dimension of the array Z.  LDZ >= 1, and if
                     JOBZ = 'V', LDZ >= max(1,N).

           ISUPPZ

                     ISUPPZ is INTEGER array, dimension ( 2*max(1,M) )
                     The support of the eigenvectors in Z, i.e., the indices
                     indicating the nonzero elements in Z. The I-th eigenvector
                     is nonzero only in elements ISUPPZ( 2*I-1 ) through
                     ISUPPZ( 2*I ).

           WORK

                     WORK is REAL array, dimension (12*N)

           IWORK

                     IWORK is INTEGER array, dimension (7*N)

           INFO

                     INFO is INTEGER
                     = 0:  successful exit

                     > 0:  A problem occurred in CLARRV.
                     < 0:  One of the called subroutines signaled an internal problem.
                           Needs inspection of the corresponding parameter IINFO
                           for further information.

                     =-1:  Problem in SLARRB when refining a child's eigenvalues.
                     =-2:  Problem in SLARRF when computing the RRR of a child.
                           When a child is inside a tight cluster, it can be difficult
                           to find an RRR. A partial remedy from the user's point of
                           view is to make the parameter MINRGP smaller and recompile.
                           However, as the orthogonality of the computed vectors is
                           proportional to 1/MINRGP, the user should be aware that
                           he might be trading in precision when he decreases MINRGP.
                     =-3:  Problem in SLARRB when refining a single eigenvalue
                           after the Rayleigh correction was rejected.
                     = 5:  The Rayleigh Quotient Iteration failed to converge to
                           full accuracy in MAXITR steps.

       Author
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Contributors:
           Beresford Parlett, University of California, Berkeley, USA
            Jim Demmel, University of California, Berkeley, USA
            Inderjit Dhillon, University of Texas, Austin, USA
            Osni Marques, LBNL/NERSC, USA
            Christof Voemel, University of California, Berkeley, USA

   subroutine dlarrv (integer n, double precision vl, double precision vu, double precision,
       dimension( * ) d, double precision, dimension( * ) l, double precision pivmin, integer,
       dimension( * ) isplit, integer m, integer dol, integer dou, double precision minrgp,
       double precision rtol1, double precision rtol2, double precision, dimension( * ) w, double
       precision, dimension( * ) werr, double precision, dimension( * ) wgap, integer, dimension(
       * ) iblock, integer, dimension( * ) indexw, double precision, dimension( * ) gers, double
       precision, dimension( ldz, * ) z, integer ldz, integer, dimension( * ) isuppz, double
       precision, dimension( * ) work, integer, dimension( * ) iwork, integer info)
       DLARRV computes the eigenvectors of the tridiagonal matrix T = L D LT given L, D and the
       eigenvalues of L D LT.

       Purpose:

            DLARRV computes the eigenvectors of the tridiagonal matrix
            T = L D L**T given L, D and APPROXIMATIONS to the eigenvalues of L D L**T.
            The input eigenvalues should have been computed by DLARRE.

       Parameters
           N

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

           VL

                     VL is DOUBLE PRECISION
                     Lower bound of the interval that contains the desired
                     eigenvalues. VL < VU. Needed to compute gaps on the left or right
                     end of the extremal eigenvalues in the desired RANGE.

           VU

                     VU is DOUBLE PRECISION
                     Upper bound of the interval that contains the desired
                     eigenvalues. VL < VU.
                     Note: VU is currently not used by this implementation of DLARRV, VU is
                     passed to DLARRV because it could be used compute gaps on the right end
                     of the extremal eigenvalues. However, with not much initial accuracy in
                     LAMBDA and VU, the formula can lead to an overestimation of the right gap
                     and thus to inadequately early RQI 'convergence'. This is currently
                     prevented this by forcing a small right gap. And so it turns out that VU
                     is currently not used by this implementation of DLARRV.

           D

                     D is DOUBLE PRECISION array, dimension (N)
                     On entry, the N diagonal elements of the diagonal matrix D.
                     On exit, D may be overwritten.

           L

                     L is DOUBLE PRECISION array, dimension (N)
                     On entry, the (N-1) subdiagonal elements of the unit
                     bidiagonal matrix L are in elements 1 to N-1 of L
                     (if the matrix is not split.) At the end of each block
                     is stored the corresponding shift as given by DLARRE.
                     On exit, L is overwritten.

           PIVMIN

                     PIVMIN is DOUBLE PRECISION
                     The minimum pivot allowed in the Sturm sequence.

           ISPLIT

                     ISPLIT is INTEGER array, dimension (N)
                     The splitting points, at which T breaks up into blocks.
                     The first block consists of rows/columns 1 to
                     ISPLIT( 1 ), the second of rows/columns ISPLIT( 1 )+1
                     through ISPLIT( 2 ), etc.

           M

                     M is INTEGER
                     The total number of input eigenvalues.  0 <= M <= N.

           DOL

                     DOL is INTEGER

           DOU

                     DOU is INTEGER
                     If the user wants to compute only selected eigenvectors from all
                     the eigenvalues supplied, he can specify an index range DOL:DOU.
                     Or else the setting DOL=1, DOU=M should be applied.
                     Note that DOL and DOU refer to the order in which the eigenvalues
                     are stored in W.
                     If the user wants to compute only selected eigenpairs, then
                     the columns DOL-1 to DOU+1 of the eigenvector space Z contain the
                     computed eigenvectors. All other columns of Z are set to zero.

           MINRGP

                     MINRGP is DOUBLE PRECISION

           RTOL1

                     RTOL1 is DOUBLE PRECISION

           RTOL2

                     RTOL2 is DOUBLE PRECISION
                      Parameters for bisection.
                      An interval [LEFT,RIGHT] has converged if
                      RIGHT-LEFT < MAX( RTOL1*GAP, RTOL2*MAX(|LEFT|,|RIGHT|) )

           W

                     W is DOUBLE PRECISION array, dimension (N)
                     The first M elements of W contain the APPROXIMATE eigenvalues for
                     which eigenvectors are to be computed.  The eigenvalues
                     should be grouped by split-off block and ordered from
                     smallest to largest within the block ( The output array
                     W from DLARRE is expected here ). Furthermore, they are with
                     respect to the shift of the corresponding root representation
                     for their block. On exit, W holds the eigenvalues of the
                     UNshifted matrix.

           WERR

                     WERR is DOUBLE PRECISION array, dimension (N)
                     The first M elements contain the semiwidth of the uncertainty
                     interval of the corresponding eigenvalue in W

           WGAP

                     WGAP is DOUBLE PRECISION array, dimension (N)
                     The separation from the right neighbor eigenvalue in W.

           IBLOCK

                     IBLOCK is INTEGER array, dimension (N)
                     The indices of the blocks (submatrices) associated with the
                     corresponding eigenvalues in W; IBLOCK(i)=1 if eigenvalue
                     W(i) belongs to the first block from the top, =2 if W(i)
                     belongs to the second block, etc.

           INDEXW

                     INDEXW is INTEGER array, dimension (N)
                     The indices of the eigenvalues within each block (submatrix);
                     for example, INDEXW(i)= 10 and IBLOCK(i)=2 imply that the
                     i-th eigenvalue W(i) is the 10-th eigenvalue in the second block.

           GERS

                     GERS is DOUBLE PRECISION array, dimension (2*N)
                     The N Gerschgorin intervals (the i-th Gerschgorin interval
                     is (GERS(2*i-1), GERS(2*i)). The Gerschgorin intervals should
                     be computed from the original UNshifted matrix.

           Z

                     Z is DOUBLE PRECISION array, dimension (LDZ, max(1,M) )
                     If INFO = 0, the first M columns of Z contain the
                     orthonormal eigenvectors of the matrix T
                     corresponding to the input eigenvalues, with the i-th
                     column of Z holding the eigenvector associated with W(i).
                     Note: the user must ensure that at least max(1,M) columns are
                     supplied in the array Z.

           LDZ

                     LDZ is INTEGER
                     The leading dimension of the array Z.  LDZ >= 1, and if
                     JOBZ = 'V', LDZ >= max(1,N).

           ISUPPZ

                     ISUPPZ is INTEGER array, dimension ( 2*max(1,M) )
                     The support of the eigenvectors in Z, i.e., the indices
                     indicating the nonzero elements in Z. The I-th eigenvector
                     is nonzero only in elements ISUPPZ( 2*I-1 ) through
                     ISUPPZ( 2*I ).

           WORK

                     WORK is DOUBLE PRECISION array, dimension (12*N)

           IWORK

                     IWORK is INTEGER array, dimension (7*N)

           INFO

                     INFO is INTEGER
                     = 0:  successful exit

                     > 0:  A problem occurred in DLARRV.
                     < 0:  One of the called subroutines signaled an internal problem.
                           Needs inspection of the corresponding parameter IINFO
                           for further information.

                     =-1:  Problem in DLARRB when refining a child's eigenvalues.
                     =-2:  Problem in DLARRF when computing the RRR of a child.
                           When a child is inside a tight cluster, it can be difficult
                           to find an RRR. A partial remedy from the user's point of
                           view is to make the parameter MINRGP smaller and recompile.
                           However, as the orthogonality of the computed vectors is
                           proportional to 1/MINRGP, the user should be aware that
                           he might be trading in precision when he decreases MINRGP.
                     =-3:  Problem in DLARRB when refining a single eigenvalue
                           after the Rayleigh correction was rejected.
                     = 5:  The Rayleigh Quotient Iteration failed to converge to
                           full accuracy in MAXITR steps.

       Author
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Contributors:
           Beresford Parlett, University of California, Berkeley, USA
            Jim Demmel, University of California, Berkeley, USA
            Inderjit Dhillon, University of Texas, Austin, USA
            Osni Marques, LBNL/NERSC, USA
            Christof Voemel, University of California, Berkeley, USA

   subroutine slarrv (integer n, real vl, real vu, real, dimension( * ) d, real, dimension( * )
       l, real pivmin, integer, dimension( * ) isplit, integer m, integer dol, integer dou, real
       minrgp, real rtol1, real rtol2, real, dimension( * ) w, real, dimension( * ) werr, real,
       dimension( * ) wgap, integer, dimension( * ) iblock, integer, dimension( * ) indexw, real,
       dimension( * ) gers, real, dimension( ldz, * ) z, integer ldz, integer, dimension( * )
       isuppz, real, dimension( * ) work, integer, dimension( * ) iwork, integer info)
       SLARRV computes the eigenvectors of the tridiagonal matrix T = L D LT given L, D and the
       eigenvalues of L D LT.

       Purpose:

            SLARRV computes the eigenvectors of the tridiagonal matrix
            T = L D L**T given L, D and APPROXIMATIONS to the eigenvalues of L D L**T.
            The input eigenvalues should have been computed by SLARRE.

       Parameters
           N

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

           VL

                     VL is REAL
                     Lower bound of the interval that contains the desired
                     eigenvalues. VL < VU. Needed to compute gaps on the left or right
                     end of the extremal eigenvalues in the desired RANGE.

           VU

                     VU is REAL
                     Upper bound of the interval that contains the desired
                     eigenvalues. VL < VU.
                     Note: VU is currently not used by this implementation of SLARRV, VU is
                     passed to SLARRV because it could be used compute gaps on the right end
                     of the extremal eigenvalues. However, with not much initial accuracy in
                     LAMBDA and VU, the formula can lead to an overestimation of the right gap
                     and thus to inadequately early RQI 'convergence'. This is currently
                     prevented this by forcing a small right gap. And so it turns out that VU
                     is currently not used by this implementation of SLARRV.

           D

                     D is REAL array, dimension (N)
                     On entry, the N diagonal elements of the diagonal matrix D.
                     On exit, D may be overwritten.

           L

                     L is REAL array, dimension (N)
                     On entry, the (N-1) subdiagonal elements of the unit
                     bidiagonal matrix L are in elements 1 to N-1 of L
                     (if the matrix is not split.) At the end of each block
                     is stored the corresponding shift as given by SLARRE.
                     On exit, L is overwritten.

           PIVMIN

                     PIVMIN is REAL
                     The minimum pivot allowed in the Sturm sequence.

           ISPLIT

                     ISPLIT is INTEGER array, dimension (N)
                     The splitting points, at which T breaks up into blocks.
                     The first block consists of rows/columns 1 to
                     ISPLIT( 1 ), the second of rows/columns ISPLIT( 1 )+1
                     through ISPLIT( 2 ), etc.

           M

                     M is INTEGER
                     The total number of input eigenvalues.  0 <= M <= N.

           DOL

                     DOL is INTEGER

           DOU

                     DOU is INTEGER
                     If the user wants to compute only selected eigenvectors from all
                     the eigenvalues supplied, he can specify an index range DOL:DOU.
                     Or else the setting DOL=1, DOU=M should be applied.
                     Note that DOL and DOU refer to the order in which the eigenvalues
                     are stored in W.
                     If the user wants to compute only selected eigenpairs, then
                     the columns DOL-1 to DOU+1 of the eigenvector space Z contain the
                     computed eigenvectors. All other columns of Z are set to zero.

           MINRGP

                     MINRGP is REAL

           RTOL1

                     RTOL1 is REAL

           RTOL2

                     RTOL2 is REAL
                      Parameters for bisection.
                      An interval [LEFT,RIGHT] has converged if
                      RIGHT-LEFT < MAX( RTOL1*GAP, RTOL2*MAX(|LEFT|,|RIGHT|) )

           W

                     W is REAL array, dimension (N)
                     The first M elements of W contain the APPROXIMATE eigenvalues for
                     which eigenvectors are to be computed.  The eigenvalues
                     should be grouped by split-off block and ordered from
                     smallest to largest within the block ( The output array
                     W from SLARRE is expected here ). Furthermore, they are with
                     respect to the shift of the corresponding root representation
                     for their block. On exit, W holds the eigenvalues of the
                     UNshifted matrix.

           WERR

                     WERR is REAL array, dimension (N)
                     The first M elements contain the semiwidth of the uncertainty
                     interval of the corresponding eigenvalue in W

           WGAP

                     WGAP is REAL array, dimension (N)
                     The separation from the right neighbor eigenvalue in W.

           IBLOCK

                     IBLOCK is INTEGER array, dimension (N)
                     The indices of the blocks (submatrices) associated with the
                     corresponding eigenvalues in W; IBLOCK(i)=1 if eigenvalue
                     W(i) belongs to the first block from the top, =2 if W(i)
                     belongs to the second block, etc.

           INDEXW

                     INDEXW is INTEGER array, dimension (N)
                     The indices of the eigenvalues within each block (submatrix);
                     for example, INDEXW(i)= 10 and IBLOCK(i)=2 imply that the
                     i-th eigenvalue W(i) is the 10-th eigenvalue in the second block.

           GERS

                     GERS is REAL array, dimension (2*N)
                     The N Gerschgorin intervals (the i-th Gerschgorin interval
                     is (GERS(2*i-1), GERS(2*i)). The Gerschgorin intervals should
                     be computed from the original UNshifted matrix.

           Z

                     Z is REAL array, dimension (LDZ, max(1,M) )
                     If INFO = 0, the first M columns of Z contain the
                     orthonormal eigenvectors of the matrix T
                     corresponding to the input eigenvalues, with the i-th
                     column of Z holding the eigenvector associated with W(i).
                     Note: the user must ensure that at least max(1,M) columns are
                     supplied in the array Z.

           LDZ

                     LDZ is INTEGER
                     The leading dimension of the array Z.  LDZ >= 1, and if
                     JOBZ = 'V', LDZ >= max(1,N).

           ISUPPZ

                     ISUPPZ is INTEGER array, dimension ( 2*max(1,M) )
                     The support of the eigenvectors in Z, i.e., the indices
                     indicating the nonzero elements in Z. The I-th eigenvector
                     is nonzero only in elements ISUPPZ( 2*I-1 ) through
                     ISUPPZ( 2*I ).

           WORK

                     WORK is REAL array, dimension (12*N)

           IWORK

                     IWORK is INTEGER array, dimension (7*N)

           INFO

                     INFO is INTEGER
                     = 0:  successful exit

                     > 0:  A problem occurred in SLARRV.
                     < 0:  One of the called subroutines signaled an internal problem.
                           Needs inspection of the corresponding parameter IINFO
                           for further information.

                     =-1:  Problem in SLARRB when refining a child's eigenvalues.
                     =-2:  Problem in SLARRF when computing the RRR of a child.
                           When a child is inside a tight cluster, it can be difficult
                           to find an RRR. A partial remedy from the user's point of
                           view is to make the parameter MINRGP smaller and recompile.
                           However, as the orthogonality of the computed vectors is
                           proportional to 1/MINRGP, the user should be aware that
                           he might be trading in precision when he decreases MINRGP.
                     =-3:  Problem in SLARRB when refining a single eigenvalue
                           after the Rayleigh correction was rejected.
                     = 5:  The Rayleigh Quotient Iteration failed to converge to
                           full accuracy in MAXITR steps.

       Author
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Contributors:
           Beresford Parlett, University of California, Berkeley, USA
            Jim Demmel, University of California, Berkeley, USA
            Inderjit Dhillon, University of Texas, Austin, USA
            Osni Marques, LBNL/NERSC, USA
            Christof Voemel, University of California, Berkeley, USA

   subroutine zlarrv (integer n, double precision vl, double precision vu, double precision,
       dimension( * ) d, double precision, dimension( * ) l, double precision pivmin, integer,
       dimension( * ) isplit, integer m, integer dol, integer dou, double precision minrgp,
       double precision rtol1, double precision rtol2, double precision, dimension( * ) w, double
       precision, dimension( * ) werr, double precision, dimension( * ) wgap, integer, dimension(
       * ) iblock, integer, dimension( * ) indexw, double precision, dimension( * ) gers,
       complex*16, dimension( ldz, * ) z, integer ldz, integer, dimension( * ) isuppz, double
       precision, dimension( * ) work, integer, dimension( * ) iwork, integer info)
       ZLARRV computes the eigenvectors of the tridiagonal matrix T = L D LT given L, D and the
       eigenvalues of L D LT.

       Purpose:

            ZLARRV computes the eigenvectors of the tridiagonal matrix
            T = L D L**T given L, D and APPROXIMATIONS to the eigenvalues of L D L**T.
            The input eigenvalues should have been computed by DLARRE.

       Parameters
           N

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

           VL

                     VL is DOUBLE PRECISION
                     Lower bound of the interval that contains the desired
                     eigenvalues. VL < VU. Needed to compute gaps on the left or right
                     end of the extremal eigenvalues in the desired RANGE.

           VU

                     VU is DOUBLE PRECISION
                     Upper bound of the interval that contains the desired
                     eigenvalues. VL < VU. Needed to compute gaps on the left or right
                     end of the extremal eigenvalues in the desired RANGE.

           D

                     D is DOUBLE PRECISION array, dimension (N)
                     On entry, the N diagonal elements of the diagonal matrix D.
                     On exit, D may be overwritten.

           L

                     L is DOUBLE PRECISION array, dimension (N)
                     On entry, the (N-1) subdiagonal elements of the unit
                     bidiagonal matrix L are in elements 1 to N-1 of L
                     (if the matrix is not split.) At the end of each block
                     is stored the corresponding shift as given by DLARRE.
                     On exit, L is overwritten.

           PIVMIN

                     PIVMIN is DOUBLE PRECISION
                     The minimum pivot allowed in the Sturm sequence.

           ISPLIT

                     ISPLIT is INTEGER array, dimension (N)
                     The splitting points, at which T breaks up into blocks.
                     The first block consists of rows/columns 1 to
                     ISPLIT( 1 ), the second of rows/columns ISPLIT( 1 )+1
                     through ISPLIT( 2 ), etc.

           M

                     M is INTEGER
                     The total number of input eigenvalues.  0 <= M <= N.

           DOL

                     DOL is INTEGER

           DOU

                     DOU is INTEGER
                     If the user wants to compute only selected eigenvectors from all
                     the eigenvalues supplied, he can specify an index range DOL:DOU.
                     Or else the setting DOL=1, DOU=M should be applied.
                     Note that DOL and DOU refer to the order in which the eigenvalues
                     are stored in W.
                     If the user wants to compute only selected eigenpairs, then
                     the columns DOL-1 to DOU+1 of the eigenvector space Z contain the
                     computed eigenvectors. All other columns of Z are set to zero.

           MINRGP

                     MINRGP is DOUBLE PRECISION

           RTOL1

                     RTOL1 is DOUBLE PRECISION

           RTOL2

                     RTOL2 is DOUBLE PRECISION
                      Parameters for bisection.
                      An interval [LEFT,RIGHT] has converged if
                      RIGHT-LEFT < MAX( RTOL1*GAP, RTOL2*MAX(|LEFT|,|RIGHT|) )

           W

                     W is DOUBLE PRECISION array, dimension (N)
                     The first M elements of W contain the APPROXIMATE eigenvalues for
                     which eigenvectors are to be computed.  The eigenvalues
                     should be grouped by split-off block and ordered from
                     smallest to largest within the block ( The output array
                     W from DLARRE is expected here ). Furthermore, they are with
                     respect to the shift of the corresponding root representation
                     for their block. On exit, W holds the eigenvalues of the
                     UNshifted matrix.

           WERR

                     WERR is DOUBLE PRECISION array, dimension (N)
                     The first M elements contain the semiwidth of the uncertainty
                     interval of the corresponding eigenvalue in W

           WGAP

                     WGAP is DOUBLE PRECISION array, dimension (N)
                     The separation from the right neighbor eigenvalue in W.

           IBLOCK

                     IBLOCK is INTEGER array, dimension (N)
                     The indices of the blocks (submatrices) associated with the
                     corresponding eigenvalues in W; IBLOCK(i)=1 if eigenvalue
                     W(i) belongs to the first block from the top, =2 if W(i)
                     belongs to the second block, etc.

           INDEXW

                     INDEXW is INTEGER array, dimension (N)
                     The indices of the eigenvalues within each block (submatrix);
                     for example, INDEXW(i)= 10 and IBLOCK(i)=2 imply that the
                     i-th eigenvalue W(i) is the 10-th eigenvalue in the second block.

           GERS

                     GERS is DOUBLE PRECISION array, dimension (2*N)
                     The N Gerschgorin intervals (the i-th Gerschgorin interval
                     is (GERS(2*i-1), GERS(2*i)). The Gerschgorin intervals should
                     be computed from the original UNshifted matrix.

           Z

                     Z is COMPLEX*16 array, dimension (LDZ, max(1,M) )
                     If INFO = 0, the first M columns of Z contain the
                     orthonormal eigenvectors of the matrix T
                     corresponding to the input eigenvalues, with the i-th
                     column of Z holding the eigenvector associated with W(i).
                     Note: the user must ensure that at least max(1,M) columns are
                     supplied in the array Z.

           LDZ

                     LDZ is INTEGER
                     The leading dimension of the array Z.  LDZ >= 1, and if
                     JOBZ = 'V', LDZ >= max(1,N).

           ISUPPZ

                     ISUPPZ is INTEGER array, dimension ( 2*max(1,M) )
                     The support of the eigenvectors in Z, i.e., the indices
                     indicating the nonzero elements in Z. The I-th eigenvector
                     is nonzero only in elements ISUPPZ( 2*I-1 ) through
                     ISUPPZ( 2*I ).

           WORK

                     WORK is DOUBLE PRECISION array, dimension (12*N)

           IWORK

                     IWORK is INTEGER array, dimension (7*N)

           INFO

                     INFO is INTEGER
                     = 0:  successful exit

                     > 0:  A problem occurred in ZLARRV.
                     < 0:  One of the called subroutines signaled an internal problem.
                           Needs inspection of the corresponding parameter IINFO
                           for further information.

                     =-1:  Problem in DLARRB when refining a child's eigenvalues.
                     =-2:  Problem in DLARRF when computing the RRR of a child.
                           When a child is inside a tight cluster, it can be difficult
                           to find an RRR. A partial remedy from the user's point of
                           view is to make the parameter MINRGP smaller and recompile.
                           However, as the orthogonality of the computed vectors is
                           proportional to 1/MINRGP, the user should be aware that
                           he might be trading in precision when he decreases MINRGP.
                     =-3:  Problem in DLARRB when refining a single eigenvalue
                           after the Rayleigh correction was rejected.
                     = 5:  The Rayleigh Quotient Iteration failed to converge to
                           full accuracy in MAXITR steps.

       Author
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Contributors:
           Beresford Parlett, University of California, Berkeley, USA
            Jim Demmel, University of California, Berkeley, USA
            Inderjit Dhillon, University of Texas, Austin, USA
            Osni Marques, LBNL/NERSC, USA
            Christof Voemel, University of California, Berkeley, USA

Author

       Generated automatically by Doxygen for LAPACK from the source code.