--- rpl/lapack/lapack/zgeevx.f 2010/12/21 13:53:43 1.7
+++ rpl/lapack/lapack/zgeevx.f 2011/11/21 20:43:08 1.8
@@ -1,11 +1,294 @@
+*> \brief ZGEEVX 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 ZGEEVX + dependencies
+*>
+*> [TGZ]
+*>
+*> [ZIP]
+*>
+*> [TXT]
+*> \endhtmlonly
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE ZGEEVX( BALANC, JOBVL, JOBVR, SENSE, N, A, LDA, W, VL,
+* LDVL, VR, LDVR, ILO, IHI, SCALE, ABNRM, RCONDE,
+* RCONDV, WORK, LWORK, RWORK, INFO )
+*
+* .. Scalar Arguments ..
+* CHARACTER BALANC, JOBVL, JOBVR, SENSE
+* INTEGER IHI, ILO, INFO, LDA, LDVL, LDVR, LWORK, N
+* DOUBLE PRECISION ABNRM
+* ..
+* .. Array Arguments ..
+* DOUBLE PRECISION RCONDE( * ), RCONDV( * ), RWORK( * ),
+* $ SCALE( * )
+* COMPLEX*16 A( LDA, * ), VL( LDVL, * ), VR( LDVR, * ),
+* $ W( * ), WORK( * )
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> ZGEEVX computes for an N-by-N complex 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, ie. 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 COMPLEX*16 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 Schur form of the balanced
+*> version of the matrix A.
+*> \endverbatim
+*>
+*> \param[in] LDA
+*> \verbatim
+*> LDA is INTEGER
+*> The leading dimension of the array A. LDA >= max(1,N).
+*> \endverbatim
+*>
+*> \param[out] W
+*> \verbatim
+*> W is COMPLEX*16 array, dimension (N)
+*> W contains the computed eigenvalues.
+*> \endverbatim
+*>
+*> \param[out] VL
+*> \verbatim
+*> VL is COMPLEX*16 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.
+*> u(j) = VL(:,j), the j-th column of VL.
+*> \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 COMPLEX*16 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.
+*> v(j) = VR(:,j), the j-th column of VR.
+*> \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] 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 COMPLEX*16 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 SENSE = 'V' or 'B',
+*> LWORK >= N*N+2*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] RWORK
+*> \verbatim
+*> RWORK is DOUBLE PRECISION array, dimension (2*N)
+*> \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 W
+*> 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 complex16GEeigen
+*
+* =====================================================================
SUBROUTINE ZGEEVX( BALANC, JOBVL, JOBVR, SENSE, N, A, LDA, W, VL,
$ LDVL, VR, LDVR, ILO, IHI, SCALE, ABNRM, RCONDE,
$ RCONDV, WORK, LWORK, RWORK, INFO )
*
-* -- LAPACK driver routine (version 3.2) --
+* -- 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..--
-* November 2006
+* November 2011
*
* .. Scalar Arguments ..
CHARACTER BALANC, JOBVL, JOBVR, SENSE
@@ -19,169 +302,6 @@
$ W( * ), WORK( * )
* ..
*
-* Purpose
-* =======
-*
-* ZGEEVX computes for an N-by-N complex 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, ie. 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) COMPLEX*16 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 Schur form of the balanced
-* version of the matrix A.
-*
-* LDA (input) INTEGER
-* The leading dimension of the array A. LDA >= max(1,N).
-*
-* W (output) COMPLEX*16 array, dimension (N)
-* W contains the computed eigenvalues.
-*
-* VL (output) COMPLEX*16 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.
-* u(j) = VL(:,j), the j-th column of VL.
-*
-* LDVL (input) INTEGER
-* The leading dimension of the array VL. LDVL >= 1; if
-* JOBVL = 'V', LDVL >= N.
-*
-* VR (output) COMPLEX*16 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.
-* v(j) = VR(:,j), the j-th column of VR.
-*
-* LDVR (input) INTEGER
-* The leading dimension of the array VR. LDVR >= 1; 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) COMPLEX*16 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 SENSE = 'V' or 'B',
-* LWORK >= N*N+2*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.
-*
-* RWORK (workspace) DOUBLE PRECISION array, dimension (2*N)
-*
-* 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 W
-* contain eigenvalues which have converged.
-*
* =====================================================================
*
* .. Parameters ..