--- rpl/lapack/lapack/dtrevc.f 2011/07/22 07:38:13 1.8
+++ rpl/lapack/lapack/dtrevc.f 2011/11/21 20:43:06 1.9
@@ -1,10 +1,231 @@
+*> \brief \b DTREVC
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download DTREVC + dependencies
+*>
+*> [TGZ]
+*>
+*> [ZIP]
+*>
+*> [TXT]
+*> \endhtmlonly
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE DTREVC( SIDE, HOWMNY, SELECT, N, T, LDT, VL, LDVL, VR,
+* LDVR, MM, M, WORK, INFO )
+*
+* .. Scalar Arguments ..
+* CHARACTER HOWMNY, SIDE
+* INTEGER INFO, LDT, LDVL, LDVR, M, MM, N
+* ..
+* .. Array Arguments ..
+* LOGICAL SELECT( * )
+* DOUBLE PRECISION T( LDT, * ), VL( LDVL, * ), VR( LDVR, * ),
+* $ WORK( * )
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> DTREVC computes some or all of the right and/or left eigenvectors of
+*> a real upper quasi-triangular matrix T.
+*> Matrices of this type are produced by the Schur factorization of
+*> a real general matrix: A = Q*T*Q**T, as computed by DHSEQR.
+*>
+*> The right eigenvector x and the left eigenvector y of T corresponding
+*> to an eigenvalue w are defined by:
+*>
+*> T*x = w*x, (y**T)*T = w*(y**T)
+*>
+*> where y**T denotes the transpose of y.
+*> The eigenvalues are not input to this routine, but are read directly
+*> from the diagonal blocks of T.
+*>
+*> This routine returns the matrices X and/or Y of right and left
+*> eigenvectors of T, or the products Q*X and/or Q*Y, where Q is an
+*> input matrix. If Q is the orthogonal factor that reduces a matrix
+*> A to Schur form T, then Q*X and Q*Y are the matrices of right and
+*> left eigenvectors of A.
+*> \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,
+*> as indicated by the logical array SELECT.
+*> \endverbatim
+*>
+*> \param[in,out] 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 matrix T. N >= 0.
+*> \endverbatim
+*>
+*> \param[in] T
+*> \verbatim
+*> T is DOUBLE PRECISION array, dimension (LDT,N)
+*> The upper quasi-triangular matrix T in Schur canonical form.
+*> \endverbatim
+*>
+*> \param[in] LDT
+*> \verbatim
+*> LDT is INTEGER
+*> The leading dimension of the array T. LDT >= 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 Schur vectors returned by DHSEQR).
+*> On exit, if SIDE = 'L' or 'B', VL contains:
+*> if HOWMNY = 'A', the matrix Y of left eigenvectors of T;
+*> if HOWMNY = 'B', the matrix Q*Y;
+*> if HOWMNY = 'S', the left eigenvectors of T 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 the 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 Q (usually the orthogonal matrix Q
+*> of Schur vectors returned by DHSEQR).
+*> On exit, if SIDE = 'R' or 'B', VR contains:
+*> if HOWMNY = 'A', the matrix X of right eigenvectors of T;
+*> if HOWMNY = 'B', the matrix Q*X;
+*> if HOWMNY = 'S', the right eigenvectors of T 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 (3*N)
+*> \endverbatim
+*>
+*> \param[out] INFO
+*> \verbatim
+*> INFO is INTEGER
+*> = 0: successful exit
+*> < 0: if INFO = -i, the i-th argument had an illegal value
+*> \endverbatim
+*
+* Authors:
+* ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \date November 2011
+*
+*> \ingroup doubleOTHERcomputational
+*
+*> \par Further Details:
+* =====================
+*>
+*> \verbatim
+*>
+*> The algorithm used in this program is basically backward (forward)
+*> substitution, with scaling to make the the code robust against
+*> possible overflow.
+*>
+*> Each eigenvector is normalized so that the element of largest
+*> magnitude has magnitude 1; here the magnitude of a complex number
+*> (x,y) is taken to be |x| + |y|.
+*> \endverbatim
+*>
+* =====================================================================
SUBROUTINE DTREVC( SIDE, HOWMNY, SELECT, N, T, LDT, 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
@@ -16,132 +237,6 @@
$ WORK( * )
* ..
*
-* Purpose
-* =======
-*
-* DTREVC computes some or all of the right and/or left eigenvectors of
-* a real upper quasi-triangular matrix T.
-* Matrices of this type are produced by the Schur factorization of
-* a real general matrix: A = Q*T*Q**T, as computed by DHSEQR.
-*
-* The right eigenvector x and the left eigenvector y of T corresponding
-* to an eigenvalue w are defined by:
-*
-* T*x = w*x, (y**T)*T = w*(y**T)
-*
-* where y**T denotes the transpose of y.
-* The eigenvalues are not input to this routine, but are read directly
-* from the diagonal blocks of T.
-*
-* This routine returns the matrices X and/or Y of right and left
-* eigenvectors of T, or the products Q*X and/or Q*Y, where Q is an
-* input matrix. If Q is the orthogonal factor that reduces a matrix
-* A to Schur form T, then Q*X and Q*Y are the matrices of right and
-* left eigenvectors of A.
-*
-* 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,
-* as indicated by the logical array SELECT.
-*
-* SELECT (input/output) 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 matrix T. N >= 0.
-*
-* T (input) DOUBLE PRECISION array, dimension (LDT,N)
-* The upper quasi-triangular matrix T in Schur canonical form.
-*
-* LDT (input) INTEGER
-* The leading dimension of the array T. LDT >= 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 Schur vectors returned by DHSEQR).
-* On exit, if SIDE = 'L' or 'B', VL contains:
-* if HOWMNY = 'A', the matrix Y of left eigenvectors of T;
-* if HOWMNY = 'B', the matrix Q*Y;
-* if HOWMNY = 'S', the left eigenvectors of T 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 the 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 Q (usually the orthogonal matrix Q
-* of Schur vectors returned by DHSEQR).
-* On exit, if SIDE = 'R' or 'B', VR contains:
-* if HOWMNY = 'A', the matrix X of right eigenvectors of T;
-* if HOWMNY = 'B', the matrix Q*X;
-* if HOWMNY = 'S', the right eigenvectors of T 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 (3*N)
-*
-* INFO (output) INTEGER
-* = 0: successful exit
-* < 0: if INFO = -i, the i-th argument had an illegal value
-*
-* Further Details
-* ===============
-*
-* The algorithm used in this program is basically backward (forward)
-* substitution, with scaling to make the the code robust against
-* possible overflow.
-*
-* Each eigenvector is normalized so that the element of largest
-* magnitude has magnitude 1; here the magnitude of a complex number
-* (x,y) is taken to be |x| + |y|.
-*
* =====================================================================
*
* .. Parameters ..