--- rpl/lapack/lapack/dlanv2.f 2010/08/13 21:03:50 1.7
+++ rpl/lapack/lapack/dlanv2.f 2023/08/07 08:38:55 1.20
@@ -1,69 +1,152 @@
+*> \brief \b DLANV2 computes the Schur factorization of a real 2-by-2 nonsymmetric matrix in standard form.
+*
+* =========== DOCUMENTATION ===========
+*
+* Online html documentation available at
+* http://www.netlib.org/lapack/explore-html/
+*
+*> \htmlonly
+*> Download DLANV2 + dependencies
+*>
+*> [TGZ]
+*>
+*> [ZIP]
+*>
+*> [TXT]
+*> \endhtmlonly
+*
+* Definition:
+* ===========
+*
+* SUBROUTINE DLANV2( A, B, C, D, RT1R, RT1I, RT2R, RT2I, CS, SN )
+*
+* .. Scalar Arguments ..
+* DOUBLE PRECISION A, B, C, CS, D, RT1I, RT1R, RT2I, RT2R, SN
+* ..
+*
+*
+*> \par Purpose:
+* =============
+*>
+*> \verbatim
+*>
+*> DLANV2 computes the Schur factorization of a real 2-by-2 nonsymmetric
+*> matrix in standard form:
+*>
+*> [ A B ] = [ CS -SN ] [ AA BB ] [ CS SN ]
+*> [ C D ] [ SN CS ] [ CC DD ] [-SN CS ]
+*>
+*> where either
+*> 1) CC = 0 so that AA and DD are real eigenvalues of the matrix, or
+*> 2) AA = DD and BB*CC < 0, so that AA + or - sqrt(BB*CC) are complex
+*> conjugate eigenvalues.
+*> \endverbatim
+*
+* Arguments:
+* ==========
+*
+*> \param[in,out] A
+*> \verbatim
+*> A is DOUBLE PRECISION
+*> \endverbatim
+*>
+*> \param[in,out] B
+*> \verbatim
+*> B is DOUBLE PRECISION
+*> \endverbatim
+*>
+*> \param[in,out] C
+*> \verbatim
+*> C is DOUBLE PRECISION
+*> \endverbatim
+*>
+*> \param[in,out] D
+*> \verbatim
+*> D is DOUBLE PRECISION
+*> On entry, the elements of the input matrix.
+*> On exit, they are overwritten by the elements of the
+*> standardised Schur form.
+*> \endverbatim
+*>
+*> \param[out] RT1R
+*> \verbatim
+*> RT1R is DOUBLE PRECISION
+*> \endverbatim
+*>
+*> \param[out] RT1I
+*> \verbatim
+*> RT1I is DOUBLE PRECISION
+*> \endverbatim
+*>
+*> \param[out] RT2R
+*> \verbatim
+*> RT2R is DOUBLE PRECISION
+*> \endverbatim
+*>
+*> \param[out] RT2I
+*> \verbatim
+*> RT2I is DOUBLE PRECISION
+*> The real and imaginary parts of the eigenvalues. If the
+*> eigenvalues are a complex conjugate pair, RT1I > 0.
+*> \endverbatim
+*>
+*> \param[out] CS
+*> \verbatim
+*> CS is DOUBLE PRECISION
+*> \endverbatim
+*>
+*> \param[out] SN
+*> \verbatim
+*> SN is DOUBLE PRECISION
+*> Parameters of the rotation matrix.
+*> \endverbatim
+*
+* Authors:
+* ========
+*
+*> \author Univ. of Tennessee
+*> \author Univ. of California Berkeley
+*> \author Univ. of Colorado Denver
+*> \author NAG Ltd.
+*
+*> \ingroup doubleOTHERauxiliary
+*
+*> \par Further Details:
+* =====================
+*>
+*> \verbatim
+*>
+*> Modified by V. Sima, Research Institute for Informatics, Bucharest,
+*> Romania, to reduce the risk of cancellation errors,
+*> when computing real eigenvalues, and to ensure, if possible, that
+*> abs(RT1R) >= abs(RT2R).
+*> \endverbatim
+*>
+* =====================================================================
SUBROUTINE DLANV2( A, B, C, D, RT1R, RT1I, RT2R, RT2I, CS, SN )
*
-* -- LAPACK auxiliary routine (version 3.2.2) --
+* -- LAPACK auxiliary routine --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
-* June 2010
*
* .. Scalar Arguments ..
DOUBLE PRECISION A, B, C, CS, D, RT1I, RT1R, RT2I, RT2R, SN
* ..
*
-* Purpose
-* =======
-*
-* DLANV2 computes the Schur factorization of a real 2-by-2 nonsymmetric
-* matrix in standard form:
-*
-* [ A B ] = [ CS -SN ] [ AA BB ] [ CS SN ]
-* [ C D ] [ SN CS ] [ CC DD ] [-SN CS ]
-*
-* where either
-* 1) CC = 0 so that AA and DD are real eigenvalues of the matrix, or
-* 2) AA = DD and BB*CC < 0, so that AA + or - sqrt(BB*CC) are complex
-* conjugate eigenvalues.
-*
-* Arguments
-* =========
-*
-* A (input/output) DOUBLE PRECISION
-* B (input/output) DOUBLE PRECISION
-* C (input/output) DOUBLE PRECISION
-* D (input/output) DOUBLE PRECISION
-* On entry, the elements of the input matrix.
-* On exit, they are overwritten by the elements of the
-* standardised Schur form.
-*
-* RT1R (output) DOUBLE PRECISION
-* RT1I (output) DOUBLE PRECISION
-* RT2R (output) DOUBLE PRECISION
-* RT2I (output) DOUBLE PRECISION
-* The real and imaginary parts of the eigenvalues. If the
-* eigenvalues are a complex conjugate pair, RT1I > 0.
-*
-* CS (output) DOUBLE PRECISION
-* SN (output) DOUBLE PRECISION
-* Parameters of the rotation matrix.
-*
-* Further Details
-* ===============
-*
-* Modified by V. Sima, Research Institute for Informatics, Bucharest,
-* Romania, to reduce the risk of cancellation errors,
-* when computing real eigenvalues, and to ensure, if possible, that
-* abs(RT1R) >= abs(RT2R).
-*
* =====================================================================
*
* .. Parameters ..
- DOUBLE PRECISION ZERO, HALF, ONE
- PARAMETER ( ZERO = 0.0D+0, HALF = 0.5D+0, ONE = 1.0D+0 )
+ DOUBLE PRECISION ZERO, HALF, ONE, TWO
+ PARAMETER ( ZERO = 0.0D+0, HALF = 0.5D+0, ONE = 1.0D+0,
+ $ TWO = 2.0D0 )
DOUBLE PRECISION MULTPL
PARAMETER ( MULTPL = 4.0D+0 )
* ..
* .. Local Scalars ..
DOUBLE PRECISION AA, BB, BCMAX, BCMIS, CC, CS1, DD, EPS, P, SAB,
- $ SAC, SCALE, SIGMA, SN1, TAU, TEMP, Z
+ $ SAC, SCALE, SIGMA, SN1, TAU, TEMP, Z, SAFMIN,
+ $ SAFMN2, SAFMX2
+ INTEGER COUNT
* ..
* .. External Functions ..
DOUBLE PRECISION DLAMCH, DLAPY2
@@ -74,11 +157,14 @@
* ..
* .. Executable Statements ..
*
+ SAFMIN = DLAMCH( 'S' )
EPS = DLAMCH( 'P' )
+ SAFMN2 = DLAMCH( 'B' )**INT( LOG( SAFMIN / EPS ) /
+ $ LOG( DLAMCH( 'B' ) ) / TWO )
+ SAFMX2 = ONE / SAFMN2
IF( C.EQ.ZERO ) THEN
CS = ONE
SN = ZERO
- GO TO 10
*
ELSE IF( B.EQ.ZERO ) THEN
*
@@ -91,12 +177,12 @@
A = TEMP
B = -C
C = ZERO
- GO TO 10
+*
ELSE IF( ( A-D ).EQ.ZERO .AND. SIGN( ONE, B ).NE.SIGN( ONE, C ) )
$ THEN
CS = ONE
SN = ZERO
- GO TO 10
+*
ELSE
*
TEMP = A - D
@@ -124,12 +210,30 @@
SN = C / TAU
B = B - C
C = ZERO
+*
ELSE
*
* Complex eigenvalues, or real (almost) equal eigenvalues.
* Make diagonal elements equal.
*
+ COUNT = 0
SIGMA = B + C
+ 10 CONTINUE
+ COUNT = COUNT + 1
+ SCALE = MAX( ABS(TEMP), ABS(SIGMA) )
+ IF( SCALE.GE.SAFMX2 ) THEN
+ SIGMA = SIGMA * SAFMN2
+ TEMP = TEMP * SAFMN2
+ IF (COUNT .LE. 20)
+ $ GOTO 10
+ END IF
+ IF( SCALE.LE.SAFMN2 ) THEN
+ SIGMA = SIGMA * SAFMX2
+ TEMP = TEMP * SAFMX2
+ IF (COUNT .LE. 20)
+ $ GOTO 10
+ END IF
+ P = HALF*TEMP
TAU = DLAPY2( SIGMA, TEMP )
CS = SQRT( HALF*( ONE+ABS( SIGMA ) / TAU ) )
SN = -( P / ( TAU*CS ) )*SIGN( ONE, SIGMA )
@@ -186,8 +290,6 @@
*
END IF
*
- 10 CONTINUE
-*
* Store eigenvalues in (RT1R,RT1I) and (RT2R,RT2I).
*
RT1R = A