--- rpl/lapack/lapack/dtgevc.f 2011/07/22 07:38:12 1.8
+++ rpl/lapack/lapack/dtgevc.f 2011/11/21 20:43:06 1.9
@@ -1,10 +1,304 @@
+*> \brief \b DTGEVC
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download DTGEVC + dependencies
+*>
+*> [TGZ]
+*>
+*> [ZIP]
+*>
+*> [TXT]
+*> \endhtmlonly
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE DTGEVC( SIDE, HOWMNY, SELECT, N, S, LDS, P, LDP, VL,
+* LDVL, VR, LDVR, MM, M, WORK, INFO )
+*
+* .. Scalar Arguments ..
+* CHARACTER HOWMNY, SIDE
+* INTEGER INFO, LDP, LDS, LDVL, LDVR, M, MM, N
+* ..
+* .. Array Arguments ..
+* LOGICAL SELECT( * )
+* DOUBLE PRECISION P( LDP, * ), S( LDS, * ), VL( LDVL, * ),
+* $ VR( LDVR, * ), WORK( * )
+* ..
+*
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> DTGEVC computes some or all of the right and/or left eigenvectors of
+*> a pair of real matrices (S,P), where S is a quasi-triangular matrix
+*> and P is upper triangular. Matrix pairs of this type are produced by
+*> the generalized Schur factorization of a matrix pair (A,B):
+*>
+*> A = Q*S*Z**T, B = Q*P*Z**T
+*>
+*> as computed by DGGHRD + DHGEQZ.
+*>
+*> The right eigenvector x and the left eigenvector y of (S,P)
+*> corresponding to an eigenvalue w are defined by:
+*>
+*> S*x = w*P*x, (y**H)*S = w*(y**H)*P,
+*>
+*> where y**H denotes the conjugate tranpose of y.
+*> The eigenvalues are not input to this routine, but are computed
+*> directly from the diagonal blocks of S and P.
+*>
+*> This routine returns the matrices X and/or Y of right and left
+*> eigenvectors of (S,P), or the products Z*X and/or Q*Y,
+*> where Z and Q are input matrices.
+*> If Q and Z are the orthogonal factors from the generalized Schur
+*> factorization of a matrix pair (A,B), then Z*X and Q*Y
+*> are the matrices of right and left eigenvectors of (A,B).
+*>
+*> \endverbatim
+*
+* Arguments:
+* ==========
+*
+*> \param[in] SIDE
+*> \verbatim
+*> SIDE is CHARACTER*1
+*> = 'R': compute right eigenvectors only;
+*> = 'L': compute left eigenvectors only;
+*> = 'B': compute both right and left eigenvectors.
+*> \endverbatim
+*>
+*> \param[in] HOWMNY
+*> \verbatim
+*> HOWMNY is 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,
+*> specified by the logical array SELECT.
+*> \endverbatim
+*>
+*> \param[in] SELECT
+*> \verbatim
+*> SELECT is 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'.
+*> \endverbatim
+*>
+*> \param[in] N
+*> \verbatim
+*> N is INTEGER
+*> The order of the matrices S and P. N >= 0.
+*> \endverbatim
+*>
+*> \param[in] S
+*> \verbatim
+*> S is DOUBLE PRECISION array, dimension (LDS,N)
+*> The upper quasi-triangular matrix S from a generalized Schur
+*> factorization, as computed by DHGEQZ.
+*> \endverbatim
+*>
+*> \param[in] LDS
+*> \verbatim
+*> LDS is INTEGER
+*> The leading dimension of array S. LDS >= max(1,N).
+*> \endverbatim
+*>
+*> \param[in] P
+*> \verbatim
+*> P is DOUBLE PRECISION array, dimension (LDP,N)
+*> The upper triangular matrix P from a generalized Schur
+*> factorization, as computed by DHGEQZ.
+*> 2-by-2 diagonal blocks of P corresponding to 2-by-2 blocks
+*> of S must be in positive diagonal form.
+*> \endverbatim
+*>
+*> \param[in] LDP
+*> \verbatim
+*> LDP is INTEGER
+*> The leading dimension of array P. LDP >= max(1,N).
+*> \endverbatim
+*>
+*> \param[in,out] VL
+*> \verbatim
+*> VL is DOUBLE PRECISION 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 left Schur vectors returned by DHGEQZ).
+*> On exit, if SIDE = 'L' or 'B', VL contains:
+*> if HOWMNY = 'A', the matrix Y of left eigenvectors of (S,P);
+*> if HOWMNY = 'B', the matrix Q*Y;
+*> if HOWMNY = 'S', the left eigenvectors of (S,P) 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'.
+*> \endverbatim
+*>
+*> \param[in] LDVL
+*> \verbatim
+*> LDVL is INTEGER
+*> The leading dimension of array VL. LDVL >= 1, and if
+*> SIDE = 'L' or 'B', LDVL >= N.
+*> \endverbatim
+*>
+*> \param[in,out] VR
+*> \verbatim
+*> VR is DOUBLE PRECISION array, dimension (LDVR,MM)
+*> On entry, if SIDE = 'R' or 'B' and HOWMNY = 'B', VR must
+*> contain an N-by-N matrix Z (usually the orthogonal matrix Z
+*> of right Schur vectors returned by DHGEQZ).
+*>
+*> On exit, if SIDE = 'R' or 'B', VR contains:
+*> if HOWMNY = 'A', the matrix X of right eigenvectors of (S,P);
+*> if HOWMNY = 'B' or 'b', the matrix Z*X;
+*> if HOWMNY = 'S' or 's', the right eigenvectors of (S,P)
+*> 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'.
+*> \endverbatim
+*>
+*> \param[in] LDVR
+*> \verbatim
+*> LDVR is INTEGER
+*> The leading dimension of the array VR. LDVR >= 1, and if
+*> SIDE = 'R' or 'B', LDVR >= N.
+*> \endverbatim
+*>
+*> \param[in] MM
+*> \verbatim
+*> MM is INTEGER
+*> The number of columns in the arrays VL and/or VR. MM >= M.
+*> \endverbatim
+*>
+*> \param[out] M
+*> \verbatim
+*> M is 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.
+*> \endverbatim
+*>
+*> \param[out] WORK
+*> \verbatim
+*> WORK is DOUBLE PRECISION array, dimension (6*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: the 2-by-2 block (INFO:INFO+1) does not have a complex
+*> eigenvalue.
+*> \endverbatim
+*
+* Authors:
+* ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \date November 2011
+*
+*> \ingroup doubleGEcomputational
+*
+*> \par Further Details:
+* =====================
+*>
+*> \verbatim
+*>
+*> Allocation of workspace:
+*> ---------- -- ---------
+*>
+*> WORK( j ) = 1-norm of j-th column of A, above the diagonal
+*> WORK( N+j ) = 1-norm of j-th column of B, above the diagonal
+*> WORK( 2*N+1:3*N ) = real part of eigenvector
+*> WORK( 3*N+1:4*N ) = imaginary part of eigenvector
+*> WORK( 4*N+1:5*N ) = real part of back-transformed eigenvector
+*> WORK( 5*N+1:6*N ) = imaginary part of back-transformed eigenvector
+*>
+*> Rowwise vs. columnwise solution methods:
+*> ------- -- ---------- -------- -------
+*>
+*> Finding a generalized eigenvector consists basically of solving the
+*> singular triangular system
+*>
+*> (A - w B) x = 0 (for right) or: (A - w B)**H y = 0 (for left)
+*>
+*> Consider finding the i-th right eigenvector (assume all eigenvalues
+*> are real). The equation to be solved is:
+*> n i
+*> 0 = sum C(j,k) v(k) = sum C(j,k) v(k) for j = i,. . .,1
+*> k=j k=j
+*>
+*> where C = (A - w B) (The components v(i+1:n) are 0.)
+*>
+*> The "rowwise" method is:
+*>
+*> (1) v(i) := 1
+*> for j = i-1,. . .,1:
+*> i
+*> (2) compute s = - sum C(j,k) v(k) and
+*> k=j+1
+*>
+*> (3) v(j) := s / C(j,j)
+*>
+*> Step 2 is sometimes called the "dot product" step, since it is an
+*> inner product between the j-th row and the portion of the eigenvector
+*> that has been computed so far.
+*>
+*> The "columnwise" method consists basically in doing the sums
+*> for all the rows in parallel. As each v(j) is computed, the
+*> contribution of v(j) times the j-th column of C is added to the
+*> partial sums. Since FORTRAN arrays are stored columnwise, this has
+*> the advantage that at each step, the elements of C that are accessed
+*> are adjacent to one another, whereas with the rowwise method, the
+*> elements accessed at a step are spaced LDS (and LDP) words apart.
+*>
+*> When finding left eigenvectors, the matrix in question is the
+*> transpose of the one in storage, so the rowwise method then
+*> actually accesses columns of A and B at each step, and so is the
+*> preferred method.
+*> \endverbatim
+*>
+* =====================================================================
SUBROUTINE DTGEVC( SIDE, HOWMNY, SELECT, N, S, LDS, P, LDP, VL,
$ LDVL, VR, LDVR, MM, M, WORK, INFO )
*
-* -- LAPACK routine (version 3.3.1) --
+* -- LAPACK computational 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 HOWMNY, SIDE
@@ -17,197 +311,6 @@
* ..
*
*
-* Purpose
-* =======
-*
-* DTGEVC computes some or all of the right and/or left eigenvectors of
-* a pair of real matrices (S,P), where S is a quasi-triangular matrix
-* and P is upper triangular. Matrix pairs of this type are produced by
-* the generalized Schur factorization of a matrix pair (A,B):
-*
-* A = Q*S*Z**T, B = Q*P*Z**T
-*
-* as computed by DGGHRD + DHGEQZ.
-*
-* The right eigenvector x and the left eigenvector y of (S,P)
-* corresponding to an eigenvalue w are defined by:
-*
-* S*x = w*P*x, (y**H)*S = w*(y**H)*P,
-*
-* where y**H denotes the conjugate tranpose of y.
-* The eigenvalues are not input to this routine, but are computed
-* directly from the diagonal blocks of S and P.
-*
-* This routine returns the matrices X and/or Y of right and left
-* eigenvectors of (S,P), or the products Z*X and/or Q*Y,
-* where Z and Q are input matrices.
-* If Q and Z are the orthogonal factors from the generalized Schur
-* factorization of a matrix pair (A,B), then Z*X and Q*Y
-* are the matrices of right and left eigenvectors of (A,B).
-*
-* 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,
-* specified by the logical array SELECT.
-*
-* SELECT (input) 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 matrices S and P. N >= 0.
-*
-* S (input) DOUBLE PRECISION array, dimension (LDS,N)
-* The upper quasi-triangular matrix S from a generalized Schur
-* factorization, as computed by DHGEQZ.
-*
-* LDS (input) INTEGER
-* The leading dimension of array S. LDS >= max(1,N).
-*
-* P (input) DOUBLE PRECISION array, dimension (LDP,N)
-* The upper triangular matrix P from a generalized Schur
-* factorization, as computed by DHGEQZ.
-* 2-by-2 diagonal blocks of P corresponding to 2-by-2 blocks
-* of S must be in positive diagonal form.
-*
-* LDP (input) INTEGER
-* The leading dimension of array P. LDP >= max(1,N).
-*
-* VL (input/output) DOUBLE PRECISION 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 left Schur vectors returned by DHGEQZ).
-* On exit, if SIDE = 'L' or 'B', VL contains:
-* if HOWMNY = 'A', the matrix Y of left eigenvectors of (S,P);
-* if HOWMNY = 'B', the matrix Q*Y;
-* if HOWMNY = 'S', the left eigenvectors of (S,P) 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 array VL. LDVL >= 1, and if
-* SIDE = 'L' or 'B', LDVL >= N.
-*
-* VR (input/output) DOUBLE PRECISION array, dimension (LDVR,MM)
-* On entry, if SIDE = 'R' or 'B' and HOWMNY = 'B', VR must
-* contain an N-by-N matrix Z (usually the orthogonal matrix Z
-* of right Schur vectors returned by DHGEQZ).
-*
-* On exit, if SIDE = 'R' or 'B', VR contains:
-* if HOWMNY = 'A', the matrix X of right eigenvectors of (S,P);
-* if HOWMNY = 'B' or 'b', the matrix Z*X;
-* if HOWMNY = 'S' or 's', the right eigenvectors of (S,P)
-* 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) DOUBLE PRECISION array, dimension (6*N)
-*
-* INFO (output) INTEGER
-* = 0: successful exit.
-* < 0: if INFO = -i, the i-th argument had an illegal value.
-* > 0: the 2-by-2 block (INFO:INFO+1) does not have a complex
-* eigenvalue.
-*
-* Further Details
-* ===============
-*
-* Allocation of workspace:
-* ---------- -- ---------
-*
-* WORK( j ) = 1-norm of j-th column of A, above the diagonal
-* WORK( N+j ) = 1-norm of j-th column of B, above the diagonal
-* WORK( 2*N+1:3*N ) = real part of eigenvector
-* WORK( 3*N+1:4*N ) = imaginary part of eigenvector
-* WORK( 4*N+1:5*N ) = real part of back-transformed eigenvector
-* WORK( 5*N+1:6*N ) = imaginary part of back-transformed eigenvector
-*
-* Rowwise vs. columnwise solution methods:
-* ------- -- ---------- -------- -------
-*
-* Finding a generalized eigenvector consists basically of solving the
-* singular triangular system
-*
-* (A - w B) x = 0 (for right) or: (A - w B)**H y = 0 (for left)
-*
-* Consider finding the i-th right eigenvector (assume all eigenvalues
-* are real). The equation to be solved is:
-* n i
-* 0 = sum C(j,k) v(k) = sum C(j,k) v(k) for j = i,. . .,1
-* k=j k=j
-*
-* where C = (A - w B) (The components v(i+1:n) are 0.)
-*
-* The "rowwise" method is:
-*
-* (1) v(i) := 1
-* for j = i-1,. . .,1:
-* i
-* (2) compute s = - sum C(j,k) v(k) and
-* k=j+1
-*
-* (3) v(j) := s / C(j,j)
-*
-* Step 2 is sometimes called the "dot product" step, since it is an
-* inner product between the j-th row and the portion of the eigenvector
-* that has been computed so far.
-*
-* The "columnwise" method consists basically in doing the sums
-* for all the rows in parallel. As each v(j) is computed, the
-* contribution of v(j) times the j-th column of C is added to the
-* partial sums. Since FORTRAN arrays are stored columnwise, this has
-* the advantage that at each step, the elements of C that are accessed
-* are adjacent to one another, whereas with the rowwise method, the
-* elements accessed at a step are spaced LDS (and LDP) words apart.
-*
-* When finding left eigenvectors, the matrix in question is the
-* transpose of the one in storage, so the rowwise method then
-* actually accesses columns of A and B at each step, and so is the
-* preferred method.
-*
* =====================================================================
*
* .. Parameters ..