version 1.9, 2011/11/21 20:42:56
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version 1.20, 2023/08/07 08:38:55
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*> \brief \b DLANV2 |
*> \brief \b DLANV2 computes the Schur factorization of a real 2-by-2 nonsymmetric matrix in standard form. |
* |
* |
* =========== DOCUMENTATION =========== |
* =========== DOCUMENTATION =========== |
* |
* |
* Online html documentation available at |
* Online html documentation available at |
* http://www.netlib.org/lapack/explore-html/ |
* http://www.netlib.org/lapack/explore-html/ |
* |
* |
*> \htmlonly |
*> \htmlonly |
*> Download DLANV2 + dependencies |
*> Download DLANV2 + dependencies |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlanv2.f"> |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlanv2.f"> |
*> [TGZ]</a> |
*> [TGZ]</a> |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlanv2.f"> |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlanv2.f"> |
*> [ZIP]</a> |
*> [ZIP]</a> |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlanv2.f"> |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlanv2.f"> |
*> [TXT]</a> |
*> [TXT]</a> |
*> \endhtmlonly |
*> \endhtmlonly |
* |
* |
* Definition: |
* Definition: |
* =========== |
* =========== |
* |
* |
* SUBROUTINE DLANV2( A, B, C, D, RT1R, RT1I, RT2R, RT2I, CS, SN ) |
* SUBROUTINE DLANV2( A, B, C, D, RT1R, RT1I, RT2R, RT2I, CS, SN ) |
* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
* DOUBLE PRECISION A, B, C, CS, D, RT1I, RT1R, RT2I, RT2R, SN |
* DOUBLE PRECISION A, B, C, CS, D, RT1I, RT1R, RT2I, RT2R, SN |
* .. |
* .. |
* |
* |
* |
* |
*> \par Purpose: |
*> \par Purpose: |
* ============= |
* ============= |
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* Authors: |
* Authors: |
* ======== |
* ======== |
* |
* |
*> \author Univ. of Tennessee |
*> \author Univ. of Tennessee |
*> \author Univ. of California Berkeley |
*> \author Univ. of California Berkeley |
*> \author Univ. of Colorado Denver |
*> \author Univ. of Colorado Denver |
*> \author NAG Ltd. |
*> \author NAG Ltd. |
* |
|
*> \date November 2011 |
|
* |
* |
*> \ingroup doubleOTHERauxiliary |
*> \ingroup doubleOTHERauxiliary |
* |
* |
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* ===================================================================== |
* ===================================================================== |
SUBROUTINE DLANV2( A, B, C, D, RT1R, RT1I, RT2R, RT2I, CS, SN ) |
SUBROUTINE DLANV2( A, B, C, D, RT1R, RT1I, RT2R, RT2I, CS, SN ) |
* |
* |
* -- LAPACK auxiliary routine (version 3.4.0) -- |
* -- LAPACK auxiliary routine -- |
* -- LAPACK is a software package provided by Univ. of Tennessee, -- |
* -- LAPACK is a software package provided by Univ. of Tennessee, -- |
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
* November 2011 |
|
* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
DOUBLE PRECISION A, B, C, CS, D, RT1I, RT1R, RT2I, RT2R, SN |
DOUBLE PRECISION A, B, C, CS, D, RT1I, RT1R, RT2I, RT2R, SN |
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* ===================================================================== |
* ===================================================================== |
* |
* |
* .. Parameters .. |
* .. Parameters .. |
DOUBLE PRECISION ZERO, HALF, ONE |
DOUBLE PRECISION ZERO, HALF, ONE, TWO |
PARAMETER ( ZERO = 0.0D+0, HALF = 0.5D+0, ONE = 1.0D+0 ) |
PARAMETER ( ZERO = 0.0D+0, HALF = 0.5D+0, ONE = 1.0D+0, |
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$ TWO = 2.0D0 ) |
DOUBLE PRECISION MULTPL |
DOUBLE PRECISION MULTPL |
PARAMETER ( MULTPL = 4.0D+0 ) |
PARAMETER ( MULTPL = 4.0D+0 ) |
* .. |
* .. |
* .. Local Scalars .. |
* .. Local Scalars .. |
DOUBLE PRECISION AA, BB, BCMAX, BCMIS, CC, CS1, DD, EPS, P, SAB, |
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, |
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$ SAFMN2, SAFMX2 |
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INTEGER COUNT |
* .. |
* .. |
* .. External Functions .. |
* .. External Functions .. |
DOUBLE PRECISION DLAMCH, DLAPY2 |
DOUBLE PRECISION DLAMCH, DLAPY2 |
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* .. |
* .. |
* .. Executable Statements .. |
* .. Executable Statements .. |
* |
* |
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SAFMIN = DLAMCH( 'S' ) |
EPS = DLAMCH( 'P' ) |
EPS = DLAMCH( 'P' ) |
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SAFMN2 = DLAMCH( 'B' )**INT( LOG( SAFMIN / EPS ) / |
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$ LOG( DLAMCH( 'B' ) ) / TWO ) |
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SAFMX2 = ONE / SAFMN2 |
IF( C.EQ.ZERO ) THEN |
IF( C.EQ.ZERO ) THEN |
CS = ONE |
CS = ONE |
SN = ZERO |
SN = ZERO |
GO TO 10 |
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* |
* |
ELSE IF( B.EQ.ZERO ) THEN |
ELSE IF( B.EQ.ZERO ) THEN |
* |
* |
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A = TEMP |
A = TEMP |
B = -C |
B = -C |
C = ZERO |
C = ZERO |
GO TO 10 |
* |
ELSE IF( ( A-D ).EQ.ZERO .AND. SIGN( ONE, B ).NE.SIGN( ONE, C ) ) |
ELSE IF( ( A-D ).EQ.ZERO .AND. SIGN( ONE, B ).NE.SIGN( ONE, C ) ) |
$ THEN |
$ THEN |
CS = ONE |
CS = ONE |
SN = ZERO |
SN = ZERO |
GO TO 10 |
* |
ELSE |
ELSE |
* |
* |
TEMP = A - D |
TEMP = A - D |
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SN = C / TAU |
SN = C / TAU |
B = B - C |
B = B - C |
C = ZERO |
C = ZERO |
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* |
ELSE |
ELSE |
* |
* |
* Complex eigenvalues, or real (almost) equal eigenvalues. |
* Complex eigenvalues, or real (almost) equal eigenvalues. |
* Make diagonal elements equal. |
* Make diagonal elements equal. |
* |
* |
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COUNT = 0 |
SIGMA = B + C |
SIGMA = B + C |
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10 CONTINUE |
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COUNT = COUNT + 1 |
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SCALE = MAX( ABS(TEMP), ABS(SIGMA) ) |
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IF( SCALE.GE.SAFMX2 ) THEN |
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SIGMA = SIGMA * SAFMN2 |
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TEMP = TEMP * SAFMN2 |
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IF (COUNT .LE. 20) |
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$ GOTO 10 |
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END IF |
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IF( SCALE.LE.SAFMN2 ) THEN |
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SIGMA = SIGMA * SAFMX2 |
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TEMP = TEMP * SAFMX2 |
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IF (COUNT .LE. 20) |
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$ GOTO 10 |
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END IF |
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P = HALF*TEMP |
TAU = DLAPY2( SIGMA, TEMP ) |
TAU = DLAPY2( SIGMA, TEMP ) |
CS = SQRT( HALF*( ONE+ABS( SIGMA ) / TAU ) ) |
CS = SQRT( HALF*( ONE+ABS( SIGMA ) / TAU ) ) |
SN = -( P / ( TAU*CS ) )*SIGN( ONE, SIGMA ) |
SN = -( P / ( TAU*CS ) )*SIGN( ONE, SIGMA ) |
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* |
* |
END IF |
END IF |
* |
* |
10 CONTINUE |
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* |
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* Store eigenvalues in (RT1R,RT1I) and (RT2R,RT2I). |
* Store eigenvalues in (RT1R,RT1I) and (RT2R,RT2I). |
* |
* |
RT1R = A |
RT1R = A |