--- rpl/lapack/lapack/dgeevx.f 2010/12/21 13:53:25 1.7
+++ rpl/lapack/lapack/dgeevx.f 2023/08/07 08:38:48 1.20
@@ -1,11 +1,313 @@
+*> \brief DGEEVX computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE matrices
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download DGEEVX + dependencies
+*>
+*> [TGZ]
+*>
+*> [ZIP]
+*>
+*> [TXT]
+*> \endhtmlonly
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE DGEEVX( BALANC, JOBVL, JOBVR, SENSE, N, A, LDA, WR, WI,
+* VL, LDVL, VR, LDVR, ILO, IHI, SCALE, ABNRM,
+* RCONDE, RCONDV, WORK, LWORK, IWORK, INFO )
+*
+* .. Scalar Arguments ..
+* CHARACTER BALANC, JOBVL, JOBVR, SENSE
+* INTEGER IHI, ILO, INFO, LDA, LDVL, LDVR, LWORK, N
+* DOUBLE PRECISION ABNRM
+* ..
+* .. Array Arguments ..
+* INTEGER IWORK( * )
+* DOUBLE PRECISION A( LDA, * ), RCONDE( * ), RCONDV( * ),
+* $ SCALE( * ), VL( LDVL, * ), VR( LDVR, * ),
+* $ WI( * ), WORK( * ), WR( * )
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> DGEEVX computes for an N-by-N real nonsymmetric matrix A, the
+*> eigenvalues and, optionally, the left and/or right eigenvectors.
+*>
+*> Optionally also, it computes a balancing transformation to improve
+*> the conditioning of the eigenvalues and eigenvectors (ILO, IHI,
+*> SCALE, and ABNRM), reciprocal condition numbers for the eigenvalues
+*> (RCONDE), and reciprocal condition numbers for the right
+*> eigenvectors (RCONDV).
+*>
+*> The right eigenvector v(j) of A satisfies
+*> A * v(j) = lambda(j) * v(j)
+*> where lambda(j) is its eigenvalue.
+*> The left eigenvector u(j) of A satisfies
+*> u(j)**H * A = lambda(j) * u(j)**H
+*> where u(j)**H denotes the conjugate-transpose of u(j).
+*>
+*> The computed eigenvectors are normalized to have Euclidean norm
+*> equal to 1 and largest component real.
+*>
+*> Balancing a matrix means permuting the rows and columns to make it
+*> more nearly upper triangular, and applying a diagonal similarity
+*> transformation D * A * D**(-1), where D is a diagonal matrix, to
+*> make its rows and columns closer in norm and the condition numbers
+*> of its eigenvalues and eigenvectors smaller. The computed
+*> reciprocal condition numbers correspond to the balanced matrix.
+*> Permuting rows and columns will not change the condition numbers
+*> (in exact arithmetic) but diagonal scaling will. For further
+*> explanation of balancing, see section 4.10.2 of the LAPACK
+*> Users' Guide.
+*> \endverbatim
+*
+* Arguments:
+* ==========
+*
+*> \param[in] BALANC
+*> \verbatim
+*> BALANC is CHARACTER*1
+*> Indicates how the input matrix should be diagonally scaled
+*> and/or permuted to improve the conditioning of its
+*> eigenvalues.
+*> = 'N': Do not diagonally scale or permute;
+*> = 'P': Perform permutations to make the matrix more nearly
+*> upper triangular. Do not diagonally scale;
+*> = 'S': Diagonally scale the matrix, i.e. replace A by
+*> D*A*D**(-1), where D is a diagonal matrix chosen
+*> to make the rows and columns of A more equal in
+*> norm. Do not permute;
+*> = 'B': Both diagonally scale and permute A.
+*>
+*> Computed reciprocal condition numbers will be for the matrix
+*> after balancing and/or permuting. Permuting does not change
+*> condition numbers (in exact arithmetic), but balancing does.
+*> \endverbatim
+*>
+*> \param[in] JOBVL
+*> \verbatim
+*> JOBVL is CHARACTER*1
+*> = 'N': left eigenvectors of A are not computed;
+*> = 'V': left eigenvectors of A are computed.
+*> If SENSE = 'E' or 'B', JOBVL must = 'V'.
+*> \endverbatim
+*>
+*> \param[in] JOBVR
+*> \verbatim
+*> JOBVR is CHARACTER*1
+*> = 'N': right eigenvectors of A are not computed;
+*> = 'V': right eigenvectors of A are computed.
+*> If SENSE = 'E' or 'B', JOBVR must = 'V'.
+*> \endverbatim
+*>
+*> \param[in] SENSE
+*> \verbatim
+*> SENSE is CHARACTER*1
+*> Determines which reciprocal condition numbers are computed.
+*> = 'N': None are computed;
+*> = 'E': Computed for eigenvalues only;
+*> = 'V': Computed for right eigenvectors only;
+*> = 'B': Computed for eigenvalues and right eigenvectors.
+*>
+*> If SENSE = 'E' or 'B', both left and right eigenvectors
+*> must also be computed (JOBVL = 'V' and JOBVR = 'V').
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*> N is INTEGER
+*> The order of the matrix A. N >= 0.
+*> \endverbatim
+*>
+*> \param[in,out] A
+*> \verbatim
+*> A is DOUBLE PRECISION array, dimension (LDA,N)
+*> On entry, the N-by-N matrix A.
+*> On exit, A has been overwritten. If JOBVL = 'V' or
+*> JOBVR = 'V', A contains the real Schur form of the balanced
+*> version of the input matrix A.
+*> \endverbatim
+*>
+*> \param[in] LDA
+*> \verbatim
+*> LDA is INTEGER
+*> The leading dimension of the array A. LDA >= max(1,N).
+*> \endverbatim
+*>
+*> \param[out] WR
+*> \verbatim
+*> WR is DOUBLE PRECISION array, dimension (N)
+*> \endverbatim
+*>
+*> \param[out] WI
+*> \verbatim
+*> WI is DOUBLE PRECISION array, dimension (N)
+*> WR and WI contain the real and imaginary parts,
+*> respectively, of the computed eigenvalues. Complex
+*> conjugate pairs of eigenvalues will appear consecutively
+*> with the eigenvalue having the positive imaginary part
+*> first.
+*> \endverbatim
+*>
+*> \param[out] VL
+*> \verbatim
+*> VL is DOUBLE PRECISION array, dimension (LDVL,N)
+*> If JOBVL = 'V', the left eigenvectors u(j) are stored one
+*> after another in the columns of VL, in the same order
+*> as their eigenvalues.
+*> If JOBVL = 'N', VL is not referenced.
+*> If the j-th eigenvalue is real, then u(j) = VL(:,j),
+*> the j-th column of VL.
+*> If the j-th and (j+1)-st eigenvalues form a complex
+*> conjugate pair, then u(j) = VL(:,j) + i*VL(:,j+1) and
+*> u(j+1) = VL(:,j) - i*VL(:,j+1).
+*> \endverbatim
+*>
+*> \param[in] LDVL
+*> \verbatim
+*> LDVL is INTEGER
+*> The leading dimension of the array VL. LDVL >= 1; if
+*> JOBVL = 'V', LDVL >= N.
+*> \endverbatim
+*>
+*> \param[out] VR
+*> \verbatim
+*> VR is DOUBLE PRECISION array, dimension (LDVR,N)
+*> If JOBVR = 'V', the right eigenvectors v(j) are stored one
+*> after another in the columns of VR, in the same order
+*> as their eigenvalues.
+*> If JOBVR = 'N', VR is not referenced.
+*> If the j-th eigenvalue is real, then v(j) = VR(:,j),
+*> the j-th column of VR.
+*> If the j-th and (j+1)-st eigenvalues form a complex
+*> conjugate pair, then v(j) = VR(:,j) + i*VR(:,j+1) and
+*> v(j+1) = VR(:,j) - i*VR(:,j+1).
+*> \endverbatim
+*>
+*> \param[in] LDVR
+*> \verbatim
+*> LDVR is INTEGER
+*> The leading dimension of the array VR. LDVR >= 1, and if
+*> JOBVR = 'V', LDVR >= N.
+*> \endverbatim
+*>
+*> \param[out] ILO
+*> \verbatim
+*> ILO is INTEGER
+*> \endverbatim
+*>
+*> \param[out] IHI
+*> \verbatim
+*> IHI is INTEGER
+*> ILO and IHI are integer values determined when A was
+*> balanced. The balanced A(i,j) = 0 if I > J and
+*> J = 1,...,ILO-1 or I = IHI+1,...,N.
+*> \endverbatim
+*>
+*> \param[out] SCALE
+*> \verbatim
+*> SCALE is DOUBLE PRECISION array, dimension (N)
+*> Details of the permutations and scaling factors applied
+*> when balancing A. If P(j) is the index of the row and column
+*> interchanged with row and column j, and D(j) is the scaling
+*> factor applied to row and column j, then
+*> SCALE(J) = P(J), for J = 1,...,ILO-1
+*> = D(J), for J = ILO,...,IHI
+*> = P(J) for J = IHI+1,...,N.
+*> The order in which the interchanges are made is N to IHI+1,
+*> then 1 to ILO-1.
+*> \endverbatim
+*>
+*> \param[out] ABNRM
+*> \verbatim
+*> ABNRM is DOUBLE PRECISION
+*> The one-norm of the balanced matrix (the maximum
+*> of the sum of absolute values of elements of any column).
+*> \endverbatim
+*>
+*> \param[out] RCONDE
+*> \verbatim
+*> RCONDE is DOUBLE PRECISION array, dimension (N)
+*> RCONDE(j) is the reciprocal condition number of the j-th
+*> eigenvalue.
+*> \endverbatim
+*>
+*> \param[out] RCONDV
+*> \verbatim
+*> RCONDV is DOUBLE PRECISION array, dimension (N)
+*> RCONDV(j) is the reciprocal condition number of the j-th
+*> right eigenvector.
+*> \endverbatim
+*>
+*> \param[out] WORK
+*> \verbatim
+*> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
+*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
+*> \endverbatim
+*>
+*> \param[in] LWORK
+*> \verbatim
+*> LWORK is INTEGER
+*> The dimension of the array WORK. If SENSE = 'N' or 'E',
+*> LWORK >= max(1,2*N), and if JOBVL = 'V' or JOBVR = 'V',
+*> LWORK >= 3*N. If SENSE = 'V' or 'B', LWORK >= N*(N+6).
+*> For good performance, LWORK must generally be larger.
+*>
+*> 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.
+*> \endverbatim
+*>
+*> \param[out] IWORK
+*> \verbatim
+*> IWORK is INTEGER array, dimension (2*N-2)
+*> If SENSE = 'N' or 'E', not referenced.
+*> \endverbatim
+*>
+*> \param[out] INFO
+*> \verbatim
+*> INFO is INTEGER
+*> = 0: successful exit
+*> < 0: if INFO = -i, the i-th argument had an illegal value.
+*> > 0: if INFO = i, the QR algorithm failed to compute all the
+*> eigenvalues, and no eigenvectors or condition numbers
+*> have been computed; elements 1:ILO-1 and i+1:N of WR
+*> and WI contain eigenvalues which have converged.
+*> \endverbatim
+*
+* Authors:
+* ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*
+* @precisions fortran d -> s
+*
+*> \ingroup doubleGEeigen
+*
+* =====================================================================
SUBROUTINE DGEEVX( BALANC, JOBVL, JOBVR, SENSE, N, A, LDA, WR, WI,
$ VL, LDVL, VR, LDVR, ILO, IHI, SCALE, ABNRM,
$ RCONDE, RCONDV, WORK, LWORK, IWORK, INFO )
+ implicit none
*
-* -- LAPACK driver routine (version 3.2) --
+* -- LAPACK driver routine --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-* November 2006
*
* .. Scalar Arguments ..
CHARACTER BALANC, JOBVL, JOBVR, SENSE
@@ -19,183 +321,6 @@
$ WI( * ), WORK( * ), WR( * )
* ..
*
-* Purpose
-* =======
-*
-* DGEEVX computes for an N-by-N real nonsymmetric matrix A, the
-* eigenvalues and, optionally, the left and/or right eigenvectors.
-*
-* Optionally also, it computes a balancing transformation to improve
-* the conditioning of the eigenvalues and eigenvectors (ILO, IHI,
-* SCALE, and ABNRM), reciprocal condition numbers for the eigenvalues
-* (RCONDE), and reciprocal condition numbers for the right
-* eigenvectors (RCONDV).
-*
-* The right eigenvector v(j) of A satisfies
-* A * v(j) = lambda(j) * v(j)
-* where lambda(j) is its eigenvalue.
-* The left eigenvector u(j) of A satisfies
-* u(j)**H * A = lambda(j) * u(j)**H
-* where u(j)**H denotes the conjugate transpose of u(j).
-*
-* The computed eigenvectors are normalized to have Euclidean norm
-* equal to 1 and largest component real.
-*
-* Balancing a matrix means permuting the rows and columns to make it
-* more nearly upper triangular, and applying a diagonal similarity
-* transformation D * A * D**(-1), where D is a diagonal matrix, to
-* make its rows and columns closer in norm and the condition numbers
-* of its eigenvalues and eigenvectors smaller. The computed
-* reciprocal condition numbers correspond to the balanced matrix.
-* Permuting rows and columns will not change the condition numbers
-* (in exact arithmetic) but diagonal scaling will. For further
-* explanation of balancing, see section 4.10.2 of the LAPACK
-* Users' Guide.
-*
-* Arguments
-* =========
-*
-* BALANC (input) CHARACTER*1
-* Indicates how the input matrix should be diagonally scaled
-* and/or permuted to improve the conditioning of its
-* eigenvalues.
-* = 'N': Do not diagonally scale or permute;
-* = 'P': Perform permutations to make the matrix more nearly
-* upper triangular. Do not diagonally scale;
-* = 'S': Diagonally scale the matrix, i.e. replace A by
-* D*A*D**(-1), where D is a diagonal matrix chosen
-* to make the rows and columns of A more equal in
-* norm. Do not permute;
-* = 'B': Both diagonally scale and permute A.
-*
-* Computed reciprocal condition numbers will be for the matrix
-* after balancing and/or permuting. Permuting does not change
-* condition numbers (in exact arithmetic), but balancing does.
-*
-* JOBVL (input) CHARACTER*1
-* = 'N': left eigenvectors of A are not computed;
-* = 'V': left eigenvectors of A are computed.
-* If SENSE = 'E' or 'B', JOBVL must = 'V'.
-*
-* JOBVR (input) CHARACTER*1
-* = 'N': right eigenvectors of A are not computed;
-* = 'V': right eigenvectors of A are computed.
-* If SENSE = 'E' or 'B', JOBVR must = 'V'.
-*
-* SENSE (input) CHARACTER*1
-* Determines which reciprocal condition numbers are computed.
-* = 'N': None are computed;
-* = 'E': Computed for eigenvalues only;
-* = 'V': Computed for right eigenvectors only;
-* = 'B': Computed for eigenvalues and right eigenvectors.
-*
-* If SENSE = 'E' or 'B', both left and right eigenvectors
-* must also be computed (JOBVL = 'V' and JOBVR = 'V').
-*
-* N (input) INTEGER
-* The order of the matrix A. N >= 0.
-*
-* A (input/output) DOUBLE PRECISION array, dimension (LDA,N)
-* On entry, the N-by-N matrix A.
-* On exit, A has been overwritten. If JOBVL = 'V' or
-* JOBVR = 'V', A contains the real Schur form of the balanced
-* version of the input matrix A.
-*
-* LDA (input) INTEGER
-* The leading dimension of the array A. LDA >= max(1,N).
-*
-* WR (output) DOUBLE PRECISION array, dimension (N)
-* WI (output) DOUBLE PRECISION array, dimension (N)
-* WR and WI contain the real and imaginary parts,
-* respectively, of the computed eigenvalues. Complex
-* conjugate pairs of eigenvalues will appear consecutively
-* with the eigenvalue having the positive imaginary part
-* first.
-*
-* VL (output) DOUBLE PRECISION array, dimension (LDVL,N)
-* If JOBVL = 'V', the left eigenvectors u(j) are stored one
-* after another in the columns of VL, in the same order
-* as their eigenvalues.
-* If JOBVL = 'N', VL is not referenced.
-* If the j-th eigenvalue is real, then u(j) = VL(:,j),
-* the j-th column of VL.
-* If the j-th and (j+1)-st eigenvalues form a complex
-* conjugate pair, then u(j) = VL(:,j) + i*VL(:,j+1) and
-* u(j+1) = VL(:,j) - i*VL(:,j+1).
-*
-* LDVL (input) INTEGER
-* The leading dimension of the array VL. LDVL >= 1; if
-* JOBVL = 'V', LDVL >= N.
-*
-* VR (output) DOUBLE PRECISION array, dimension (LDVR,N)
-* If JOBVR = 'V', the right eigenvectors v(j) are stored one
-* after another in the columns of VR, in the same order
-* as their eigenvalues.
-* If JOBVR = 'N', VR is not referenced.
-* If the j-th eigenvalue is real, then v(j) = VR(:,j),
-* the j-th column of VR.
-* If the j-th and (j+1)-st eigenvalues form a complex
-* conjugate pair, then v(j) = VR(:,j) + i*VR(:,j+1) and
-* v(j+1) = VR(:,j) - i*VR(:,j+1).
-*
-* LDVR (input) INTEGER
-* The leading dimension of the array VR. LDVR >= 1, and if
-* JOBVR = 'V', LDVR >= N.
-*
-* ILO (output) INTEGER
-* IHI (output) INTEGER
-* ILO and IHI are integer values determined when A was
-* balanced. The balanced A(i,j) = 0 if I > J and
-* J = 1,...,ILO-1 or I = IHI+1,...,N.
-*
-* SCALE (output) DOUBLE PRECISION array, dimension (N)
-* Details of the permutations and scaling factors applied
-* when balancing A. If P(j) is the index of the row and column
-* interchanged with row and column j, and D(j) is the scaling
-* factor applied to row and column j, then
-* SCALE(J) = P(J), for J = 1,...,ILO-1
-* = D(J), for J = ILO,...,IHI
-* = P(J) for J = IHI+1,...,N.
-* The order in which the interchanges are made is N to IHI+1,
-* then 1 to ILO-1.
-*
-* ABNRM (output) DOUBLE PRECISION
-* The one-norm of the balanced matrix (the maximum
-* of the sum of absolute values of elements of any column).
-*
-* RCONDE (output) DOUBLE PRECISION array, dimension (N)
-* RCONDE(j) is the reciprocal condition number of the j-th
-* eigenvalue.
-*
-* RCONDV (output) DOUBLE PRECISION array, dimension (N)
-* RCONDV(j) is the reciprocal condition number of the j-th
-* right eigenvector.
-*
-* WORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK))
-* On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
-*
-* LWORK (input) INTEGER
-* The dimension of the array WORK. If SENSE = 'N' or 'E',
-* LWORK >= max(1,2*N), and if JOBVL = 'V' or JOBVR = 'V',
-* LWORK >= 3*N. If SENSE = 'V' or 'B', LWORK >= N*(N+6).
-* For good performance, LWORK must generally be larger.
-*
-* 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.
-*
-* IWORK (workspace) INTEGER array, dimension (2*N-2)
-* If SENSE = 'N' or 'E', not referenced.
-*
-* INFO (output) INTEGER
-* = 0: successful exit
-* < 0: if INFO = -i, the i-th argument had an illegal value.
-* > 0: if INFO = i, the QR algorithm failed to compute all the
-* eigenvalues, and no eigenvectors or condition numbers
-* have been computed; elements 1:ILO-1 and i+1:N of WR
-* and WI contain eigenvalues which have converged.
-*
* =====================================================================
*
* .. Parameters ..
@@ -206,8 +331,8 @@
LOGICAL LQUERY, SCALEA, WANTVL, WANTVR, WNTSNB, WNTSNE,
$ WNTSNN, WNTSNV
CHARACTER JOB, SIDE
- INTEGER HSWORK, I, ICOND, IERR, ITAU, IWRK, K, MAXWRK,
- $ MINWRK, NOUT
+ INTEGER HSWORK, I, ICOND, IERR, ITAU, IWRK, K,
+ $ LWORK_TREVC, MAXWRK, MINWRK, NOUT
DOUBLE PRECISION ANRM, BIGNUM, CS, CSCALE, EPS, R, SCL, SMLNUM,
$ SN
* ..
@@ -217,7 +342,7 @@
* ..
* .. External Subroutines ..
EXTERNAL DGEBAK, DGEBAL, DGEHRD, DHSEQR, DLABAD, DLACPY,
- $ DLARTG, DLASCL, DORGHR, DROT, DSCAL, DTREVC,
+ $ DLARTG, DLASCL, DORGHR, DROT, DSCAL, DTREVC3,
$ DTRSNA, XERBLA
* ..
* .. External Functions ..
@@ -242,8 +367,8 @@
WNTSNE = LSAME( SENSE, 'E' )
WNTSNV = LSAME( SENSE, 'V' )
WNTSNB = LSAME( SENSE, 'B' )
- IF( .NOT.( LSAME( BALANC, 'N' ) .OR. LSAME( BALANC,
- $ 'S' ) .OR. LSAME( BALANC, 'P' ) .OR. LSAME( BALANC, 'B' ) ) )
+ IF( .NOT.( LSAME( BALANC, 'N' ) .OR. LSAME( BALANC, 'S' )
+ $ .OR. LSAME( BALANC, 'P' ) .OR. LSAME( BALANC, 'B' ) ) )
$ THEN
INFO = -1
ELSE IF( ( .NOT.WANTVL ) .AND. ( .NOT.LSAME( JOBVL, 'N' ) ) ) THEN
@@ -282,9 +407,19 @@
MAXWRK = N + N*ILAENV( 1, 'DGEHRD', ' ', N, 1, N, 0 )
*
IF( WANTVL ) THEN
+ CALL DTREVC3( 'L', 'B', SELECT, N, A, LDA,
+ $ VL, LDVL, VR, LDVR,
+ $ N, NOUT, WORK, -1, IERR )
+ LWORK_TREVC = INT( WORK(1) )
+ MAXWRK = MAX( MAXWRK, N + LWORK_TREVC )
CALL DHSEQR( 'S', 'V', N, 1, N, A, LDA, WR, WI, VL, LDVL,
$ WORK, -1, INFO )
ELSE IF( WANTVR ) THEN
+ CALL DTREVC3( 'R', 'B', SELECT, N, A, LDA,
+ $ VL, LDVL, VR, LDVR,
+ $ N, NOUT, WORK, -1, IERR )
+ LWORK_TREVC = INT( WORK(1) )
+ MAXWRK = MAX( MAXWRK, N + LWORK_TREVC )
CALL DHSEQR( 'S', 'V', N, 1, N, A, LDA, WR, WI, VR, LDVR,
$ WORK, -1, INFO )
ELSE
@@ -296,7 +431,7 @@
$ LDVR, WORK, -1, INFO )
END IF
END IF
- HSWORK = WORK( 1 )
+ HSWORK = INT( WORK(1) )
*
IF( ( .NOT.WANTVL ) .AND. ( .NOT.WANTVR ) ) THEN
MINWRK = 2*N
@@ -448,18 +583,18 @@
$ WORK( IWRK ), LWORK-IWRK+1, INFO )
END IF
*
-* If INFO > 0 from DHSEQR, then quit
+* If INFO .NE. 0 from DHSEQR, then quit
*
- IF( INFO.GT.0 )
+ IF( INFO.NE.0 )
$ GO TO 50
*
IF( WANTVL .OR. WANTVR ) THEN
*
* Compute left and/or right eigenvectors
-* (Workspace: need 3*N)
+* (Workspace: need 3*N, prefer N + 2*N*NB)
*
- CALL DTREVC( SIDE, 'B', SELECT, N, A, LDA, VL, LDVL, VR, LDVR,
- $ N, NOUT, WORK( IWRK ), IERR )
+ CALL DTREVC3( SIDE, 'B', SELECT, N, A, LDA, VL, LDVL, VR, LDVR,
+ $ N, NOUT, WORK( IWRK ), LWORK-IWRK+1, IERR )
END IF
*
* Compute condition numbers if desired