--- rpl/lapack/lapack/dgeev.f 2011/07/22 07:38:04 1.8
+++ rpl/lapack/lapack/dgeev.f 2011/11/21 20:42:50 1.9
@@ -1,10 +1,198 @@
+*> \brief DGEEV 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 DGEEV + dependencies
+*>
+*> [TGZ]
+*>
+*> [ZIP]
+*>
+*> [TXT]
+*> \endhtmlonly
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE DGEEV( JOBVL, JOBVR, N, A, LDA, WR, WI, VL, LDVL, VR,
+* LDVR, WORK, LWORK, INFO )
+*
+* .. Scalar Arguments ..
+* CHARACTER JOBVL, JOBVR
+* INTEGER INFO, LDA, LDVL, LDVR, LWORK, N
+* ..
+* .. Array Arguments ..
+* DOUBLE PRECISION A( LDA, * ), VL( LDVL, * ), VR( LDVR, * ),
+* $ WI( * ), WORK( * ), WR( * )
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> DGEEV computes for an N-by-N real nonsymmetric matrix A, the
+*> eigenvalues and, optionally, the left and/or right eigenvectors.
+*>
+*> 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)**T * A = lambda(j) * u(j)**T
+*> where u(j)**T denotes the transpose of u(j).
+*>
+*> The computed eigenvectors are normalized to have Euclidean norm
+*> equal to 1 and largest component real.
+*> \endverbatim
+*
+* Arguments:
+* ==========
+*
+*> \param[in] JOBVL
+*> \verbatim
+*> JOBVL is CHARACTER*1
+*> = 'N': left eigenvectors of A are not computed;
+*> = 'V': left eigenvectors of A are computed.
+*> \endverbatim
+*>
+*> \param[in] JOBVR
+*> \verbatim
+*> JOBVR is CHARACTER*1
+*> = 'N': right eigenvectors of A are not computed;
+*> = 'V': right eigenvectors of A are computed.
+*> \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.
+*> \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 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; if
+*> JOBVR = 'V', LDVR >= N.
+*> \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. LWORK >= max(1,3*N), and
+*> if JOBVL = 'V' or JOBVR = 'V', LWORK >= 4*N. 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] 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 have been computed;
+*> elements 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.
+*
+*> \date November 2011
+*
+*> \ingroup doubleGEeigen
+*
+* =====================================================================
SUBROUTINE DGEEV( JOBVL, JOBVR, N, A, LDA, WR, WI, VL, LDVL, VR,
$ LDVR, WORK, LWORK, INFO )
*
-* -- LAPACK driver routine (version 3.3.1) --
+* -- LAPACK driver routine (version 3.4.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-* -- April 2011 --
+* November 2011
*
* .. Scalar Arguments ..
CHARACTER JOBVL, JOBVR
@@ -15,102 +203,6 @@
$ WI( * ), WORK( * ), WR( * )
* ..
*
-* Purpose
-* =======
-*
-* DGEEV computes for an N-by-N real nonsymmetric matrix A, the
-* eigenvalues and, optionally, the left and/or right eigenvectors.
-*
-* 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)**T * A = lambda(j) * u(j)**T
-* where u(j)**T denotes the transpose of u(j).
-*
-* The computed eigenvectors are normalized to have Euclidean norm
-* equal to 1 and largest component real.
-*
-* Arguments
-* =========
-*
-* JOBVL (input) CHARACTER*1
-* = 'N': left eigenvectors of A are not computed;
-* = 'V': left eigenvectors of A are computed.
-*
-* JOBVR (input) CHARACTER*1
-* = 'N': right eigenvectors of A are not computed;
-* = 'V': right eigenvectors of A are computed.
-*
-* 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.
-*
-* 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 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; if
-* JOBVR = 'V', LDVR >= N.
-*
-* 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. LWORK >= max(1,3*N), and
-* if JOBVL = 'V' or JOBVR = 'V', LWORK >= 4*N. 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.
-*
-* 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 have been computed;
-* elements i+1:N of WR and WI contain eigenvalues which
-* have converged.
-*
* =====================================================================
*
* .. Parameters ..