--- rpl/lapack/lapack/dlaed5.f 2010/04/21 13:45:16 1.2
+++ rpl/lapack/lapack/dlaed5.f 2023/08/07 08:38:53 1.18
@@ -1,9 +1,114 @@
+*> \brief \b DLAED5 used by DSTEDC. Solves the 2-by-2 secular equation.
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download DLAED5 + dependencies
+*>
+*> [TGZ]
+*>
+*> [ZIP]
+*>
+*> [TXT]
+*> \endhtmlonly
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE DLAED5( I, D, Z, DELTA, RHO, DLAM )
+*
+* .. Scalar Arguments ..
+* INTEGER I
+* DOUBLE PRECISION DLAM, RHO
+* ..
+* .. Array Arguments ..
+* DOUBLE PRECISION D( 2 ), DELTA( 2 ), Z( 2 )
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> This subroutine computes the I-th eigenvalue of a symmetric rank-one
+*> modification of a 2-by-2 diagonal matrix
+*>
+*> diag( D ) + RHO * Z * transpose(Z) .
+*>
+*> The diagonal elements in the array D are assumed to satisfy
+*>
+*> D(i) < D(j) for i < j .
+*>
+*> We also assume RHO > 0 and that the Euclidean norm of the vector
+*> Z is one.
+*> \endverbatim
+*
+* Arguments:
+* ==========
+*
+*> \param[in] I
+*> \verbatim
+*> I is INTEGER
+*> The index of the eigenvalue to be computed. I = 1 or I = 2.
+*> \endverbatim
+*>
+*> \param[in] D
+*> \verbatim
+*> D is DOUBLE PRECISION array, dimension (2)
+*> The original eigenvalues. We assume D(1) < D(2).
+*> \endverbatim
+*>
+*> \param[in] Z
+*> \verbatim
+*> Z is DOUBLE PRECISION array, dimension (2)
+*> The components of the updating vector.
+*> \endverbatim
+*>
+*> \param[out] DELTA
+*> \verbatim
+*> DELTA is DOUBLE PRECISION array, dimension (2)
+*> The vector DELTA contains the information necessary
+*> to construct the eigenvectors.
+*> \endverbatim
+*>
+*> \param[in] RHO
+*> \verbatim
+*> RHO is DOUBLE PRECISION
+*> The scalar in the symmetric updating formula.
+*> \endverbatim
+*>
+*> \param[out] DLAM
+*> \verbatim
+*> DLAM is DOUBLE PRECISION
+*> The computed lambda_I, the I-th updated eigenvalue.
+*> \endverbatim
+*
+* Authors:
+* ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \ingroup auxOTHERcomputational
+*
+*> \par Contributors:
+* ==================
+*>
+*> Ren-Cang Li, Computer Science Division, University of California
+*> at Berkeley, USA
+*>
+* =====================================================================
SUBROUTINE DLAED5( I, D, Z, DELTA, RHO, DLAM )
*
-* -- LAPACK routine (version 3.2) --
+* -- LAPACK computational 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 ..
INTEGER I
@@ -13,50 +118,6 @@
DOUBLE PRECISION D( 2 ), DELTA( 2 ), Z( 2 )
* ..
*
-* Purpose
-* =======
-*
-* This subroutine computes the I-th eigenvalue of a symmetric rank-one
-* modification of a 2-by-2 diagonal matrix
-*
-* diag( D ) + RHO * Z * transpose(Z) .
-*
-* The diagonal elements in the array D are assumed to satisfy
-*
-* D(i) < D(j) for i < j .
-*
-* We also assume RHO > 0 and that the Euclidean norm of the vector
-* Z is one.
-*
-* Arguments
-* =========
-*
-* I (input) INTEGER
-* The index of the eigenvalue to be computed. I = 1 or I = 2.
-*
-* D (input) DOUBLE PRECISION array, dimension (2)
-* The original eigenvalues. We assume D(1) < D(2).
-*
-* Z (input) DOUBLE PRECISION array, dimension (2)
-* The components of the updating vector.
-*
-* DELTA (output) DOUBLE PRECISION array, dimension (2)
-* The vector DELTA contains the information necessary
-* to construct the eigenvectors.
-*
-* RHO (input) DOUBLE PRECISION
-* The scalar in the symmetric updating formula.
-*
-* DLAM (output) DOUBLE PRECISION
-* The computed lambda_I, the I-th updated eigenvalue.
-*
-* Further Details
-* ===============
-*
-* Based on contributions by
-* Ren-Cang Li, Computer Science Division, University of California
-* at Berkeley, USA
-*
* =====================================================================
*
* .. Parameters ..
@@ -120,6 +181,6 @@
END IF
RETURN
*
-* End OF DLAED5
+* End of DLAED5
*
END