numeric-linalg
Educational material on the SciPy implementation of numerical linear algebra algorithms
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| lapack/TESTING/EIG/sget34.f | 15784B | -rw-r--r-- |
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*> \brief \b SGET34 * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE SGET34( RMAX, LMAX, NINFO, KNT ) * * .. Scalar Arguments .. * INTEGER KNT, LMAX * REAL RMAX * .. * .. Array Arguments .. * INTEGER NINFO( 2 ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> SGET34 tests SLAEXC, a routine for swapping adjacent blocks (either *> 1 by 1 or 2 by 2) on the diagonal of a matrix in real Schur form. *> Thus, SLAEXC computes an orthogonal matrix Q such that *> *> Q' * [ A B ] * Q = [ C1 B1 ] *> [ 0 C ] [ 0 A1 ] *> *> where C1 is similar to C and A1 is similar to A. Both A and C are *> assumed to be in standard form (equal diagonal entries and *> offdiagonal with differing signs) and A1 and C1 are returned with the *> same properties. *> *> The test code verifies these last last assertions, as well as that *> the residual in the above equation is small. *> \endverbatim * * Arguments: * ========== * *> \param[out] RMAX *> \verbatim *> RMAX is REAL *> Value of the largest test ratio. *> \endverbatim *> *> \param[out] LMAX *> \verbatim *> LMAX is INTEGER *> Example number where largest test ratio achieved. *> \endverbatim *> *> \param[out] NINFO *> \verbatim *> NINFO is INTEGER array, dimension (2) *> NINFO(J) is the number of examples where INFO=J occurred. *> \endverbatim *> *> \param[out] KNT *> \verbatim *> KNT is INTEGER *> Total number of examples tested. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \ingroup single_eig * * ===================================================================== SUBROUTINE SGET34( RMAX, LMAX, NINFO, KNT ) * * -- LAPACK test routine -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * * .. Scalar Arguments .. INTEGER KNT, LMAX REAL RMAX * .. * .. Array Arguments .. INTEGER NINFO( 2 ) * .. * * ===================================================================== * * .. Parameters .. REAL ZERO, HALF, ONE PARAMETER ( ZERO = 0.0E0, HALF = 0.5E0, ONE = 1.0E0 ) REAL TWO, THREE PARAMETER ( TWO = 2.0E0, THREE = 3.0E0 ) INTEGER LWORK PARAMETER ( LWORK = 32 ) * .. * .. Local Scalars .. INTEGER I, IA, IA11, IA12, IA21, IA22, IAM, IB, IC, $ IC11, IC12, IC21, IC22, ICM, INFO, J REAL BIGNUM, EPS, RES, SMLNUM, TNRM * .. * .. Local Arrays .. REAL Q( 4, 4 ), RESULT( 2 ), T( 4, 4 ), T1( 4, 4 ), $ VAL( 9 ), VM( 2 ), WORK( LWORK ) * .. * .. External Functions .. REAL SLAMCH EXTERNAL SLAMCH * .. * .. External Subroutines .. EXTERNAL SCOPY, SLAEXC * .. * .. Intrinsic Functions .. INTRINSIC ABS, MAX, REAL, SIGN, SQRT * .. * .. Executable Statements .. * * Get machine parameters * EPS = SLAMCH( 'P' ) SMLNUM = SLAMCH( 'S' ) / EPS BIGNUM = ONE / SMLNUM * * Set up test case parameters * VAL( 1 ) = ZERO VAL( 2 ) = SQRT( SMLNUM ) VAL( 3 ) = ONE VAL( 4 ) = TWO VAL( 5 ) = SQRT( BIGNUM ) VAL( 6 ) = -SQRT( SMLNUM ) VAL( 7 ) = -ONE VAL( 8 ) = -TWO VAL( 9 ) = -SQRT( BIGNUM ) VM( 1 ) = ONE VM( 2 ) = ONE + TWO*EPS CALL SCOPY( 16, VAL( 4 ), 0, T( 1, 1 ), 1 ) * NINFO( 1 ) = 0 NINFO( 2 ) = 0 KNT = 0 LMAX = 0 RMAX = ZERO * * Begin test loop * DO 40 IA = 1, 9 DO 30 IAM = 1, 2 DO 20 IB = 1, 9 DO 10 IC = 1, 9 T( 1, 1 ) = VAL( IA )*VM( IAM ) T( 2, 2 ) = VAL( IC ) T( 1, 2 ) = VAL( IB ) T( 2, 1 ) = ZERO TNRM = MAX( ABS( T( 1, 1 ) ), ABS( T( 2, 2 ) ), $ ABS( T( 1, 2 ) ) ) CALL SCOPY( 16, T, 1, T1, 1 ) CALL SCOPY( 16, VAL( 1 ), 0, Q, 1 ) CALL SCOPY( 4, VAL( 3 ), 0, Q, 5 ) CALL SLAEXC( .TRUE., 2, T, 4, Q, 4, 1, 1, 1, WORK, $ INFO ) IF( INFO.NE.0 ) $ NINFO( INFO ) = NINFO( INFO ) + 1 CALL SHST01( 2, 1, 2, T1, 4, T, 4, Q, 4, WORK, LWORK, $ RESULT ) RES = RESULT( 1 ) + RESULT( 2 ) IF( INFO.NE.0 ) $ RES = RES + ONE / EPS IF( T( 1, 1 ).NE.T1( 2, 2 ) ) $ RES = RES + ONE / EPS IF( T( 2, 2 ).NE.T1( 1, 1 ) ) $ RES = RES + ONE / EPS IF( T( 2, 1 ).NE.ZERO ) $ RES = RES + ONE / EPS KNT = KNT + 1 IF( RES.GT.RMAX ) THEN LMAX = KNT RMAX = RES END IF 10 CONTINUE 20 CONTINUE 30 CONTINUE 40 CONTINUE * DO 110 IA = 1, 5 DO 100 IAM = 1, 2 DO 90 IB = 1, 5 DO 80 IC11 = 1, 5 DO 70 IC12 = 2, 5 DO 60 IC21 = 2, 4 DO 50 IC22 = -1, 1, 2 T( 1, 1 ) = VAL( IA )*VM( IAM ) T( 1, 2 ) = VAL( IB ) T( 1, 3 ) = -TWO*VAL( IB ) T( 2, 1 ) = ZERO T( 2, 2 ) = VAL( IC11 ) T( 2, 3 ) = VAL( IC12 ) T( 3, 1 ) = ZERO T( 3, 2 ) = -VAL( IC21 ) T( 3, 3 ) = VAL( IC11 )*REAL( IC22 ) TNRM = MAX( ABS( T( 1, 1 ) ), $ ABS( T( 1, 2 ) ), ABS( T( 1, 3 ) ), $ ABS( T( 2, 2 ) ), ABS( T( 2, 3 ) ), $ ABS( T( 3, 2 ) ), ABS( T( 3, 3 ) ) ) CALL SCOPY( 16, T, 1, T1, 1 ) CALL SCOPY( 16, VAL( 1 ), 0, Q, 1 ) CALL SCOPY( 4, VAL( 3 ), 0, Q, 5 ) CALL SLAEXC( .TRUE., 3, T, 4, Q, 4, 1, 1, 2, $ WORK, INFO ) IF( INFO.NE.0 ) $ NINFO( INFO ) = NINFO( INFO ) + 1 CALL SHST01( 3, 1, 3, T1, 4, T, 4, Q, 4, $ WORK, LWORK, RESULT ) RES = RESULT( 1 ) + RESULT( 2 ) IF( INFO.EQ.0 ) THEN IF( T1( 1, 1 ).NE.T( 3, 3 ) ) $ RES = RES + ONE / EPS IF( T( 3, 1 ).NE.ZERO ) $ RES = RES + ONE / EPS IF( T( 3, 2 ).NE.ZERO ) $ RES = RES + ONE / EPS IF( T( 2, 1 ).NE.0 .AND. $ ( T( 1, 1 ).NE.T( 2, $ 2 ) .OR. SIGN( ONE, T( 1, $ 2 ) ).EQ.SIGN( ONE, T( 2, 1 ) ) ) ) $ RES = RES + ONE / EPS END IF KNT = KNT + 1 IF( RES.GT.RMAX ) THEN LMAX = KNT RMAX = RES END IF 50 CONTINUE 60 CONTINUE 70 CONTINUE 80 CONTINUE 90 CONTINUE 100 CONTINUE 110 CONTINUE * DO 180 IA11 = 1, 5 DO 170 IA12 = 2, 5 DO 160 IA21 = 2, 4 DO 150 IA22 = -1, 1, 2 DO 140 ICM = 1, 2 DO 130 IB = 1, 5 DO 120 IC = 1, 5 T( 1, 1 ) = VAL( IA11 ) T( 1, 2 ) = VAL( IA12 ) T( 1, 3 ) = -TWO*VAL( IB ) T( 2, 1 ) = -VAL( IA21 ) T( 2, 2 ) = VAL( IA11 )*REAL( IA22 ) T( 2, 3 ) = VAL( IB ) T( 3, 1 ) = ZERO T( 3, 2 ) = ZERO T( 3, 3 ) = VAL( IC )*VM( ICM ) TNRM = MAX( ABS( T( 1, 1 ) ), $ ABS( T( 1, 2 ) ), ABS( T( 1, 3 ) ), $ ABS( T( 2, 2 ) ), ABS( T( 2, 3 ) ), $ ABS( T( 3, 2 ) ), ABS( T( 3, 3 ) ) ) CALL SCOPY( 16, T, 1, T1, 1 ) CALL SCOPY( 16, VAL( 1 ), 0, Q, 1 ) CALL SCOPY( 4, VAL( 3 ), 0, Q, 5 ) CALL SLAEXC( .TRUE., 3, T, 4, Q, 4, 1, 2, 1, $ WORK, INFO ) IF( INFO.NE.0 ) $ NINFO( INFO ) = NINFO( INFO ) + 1 CALL SHST01( 3, 1, 3, T1, 4, T, 4, Q, 4, $ WORK, LWORK, RESULT ) RES = RESULT( 1 ) + RESULT( 2 ) IF( INFO.EQ.0 ) THEN IF( T1( 3, 3 ).NE.T( 1, 1 ) ) $ RES = RES + ONE / EPS IF( T( 2, 1 ).NE.ZERO ) $ RES = RES + ONE / EPS IF( T( 3, 1 ).NE.ZERO ) $ RES = RES + ONE / EPS IF( T( 3, 2 ).NE.0 .AND. $ ( T( 2, 2 ).NE.T( 3, $ 3 ) .OR. SIGN( ONE, T( 2, $ 3 ) ).EQ.SIGN( ONE, T( 3, 2 ) ) ) ) $ RES = RES + ONE / EPS END IF KNT = KNT + 1 IF( RES.GT.RMAX ) THEN LMAX = KNT RMAX = RES END IF 120 CONTINUE 130 CONTINUE 140 CONTINUE 150 CONTINUE 160 CONTINUE 170 CONTINUE 180 CONTINUE * DO 300 IA11 = 1, 5 DO 290 IA12 = 2, 5 DO 280 IA21 = 2, 4 DO 270 IA22 = -1, 1, 2 DO 260 IB = 1, 5 DO 250 IC11 = 3, 4 DO 240 IC12 = 3, 4 DO 230 IC21 = 3, 4 DO 220 IC22 = -1, 1, 2 DO 210 ICM = 5, 7 IAM = 1 T( 1, 1 ) = VAL( IA11 )*VM( IAM ) T( 1, 2 ) = VAL( IA12 )*VM( IAM ) T( 1, 3 ) = -TWO*VAL( IB ) T( 1, 4 ) = HALF*VAL( IB ) T( 2, 1 ) = -T( 1, 2 )*VAL( IA21 ) T( 2, 2 ) = VAL( IA11 )* $ REAL( IA22 )*VM( IAM ) T( 2, 3 ) = VAL( IB ) T( 2, 4 ) = THREE*VAL( IB ) T( 3, 1 ) = ZERO T( 3, 2 ) = ZERO T( 3, 3 ) = VAL( IC11 )* $ ABS( VAL( ICM ) ) T( 3, 4 ) = VAL( IC12 )* $ ABS( VAL( ICM ) ) T( 4, 1 ) = ZERO T( 4, 2 ) = ZERO T( 4, 3 ) = -T( 3, 4 )*VAL( IC21 )* $ ABS( VAL( ICM ) ) T( 4, 4 ) = VAL( IC11 )* $ REAL( IC22 )* $ ABS( VAL( ICM ) ) TNRM = ZERO DO 200 I = 1, 4 DO 190 J = 1, 4 TNRM = MAX( TNRM, $ ABS( T( I, J ) ) ) 190 CONTINUE 200 CONTINUE CALL SCOPY( 16, T, 1, T1, 1 ) CALL SCOPY( 16, VAL( 1 ), 0, Q, 1 ) CALL SCOPY( 4, VAL( 3 ), 0, Q, 5 ) CALL SLAEXC( .TRUE., 4, T, 4, Q, 4, $ 1, 2, 2, WORK, INFO ) IF( INFO.NE.0 ) $ NINFO( INFO ) = NINFO( INFO ) + 1 CALL SHST01( 4, 1, 4, T1, 4, T, 4, $ Q, 4, WORK, LWORK, $ RESULT ) RES = RESULT( 1 ) + RESULT( 2 ) IF( INFO.EQ.0 ) THEN IF( T( 3, 1 ).NE.ZERO ) $ RES = RES + ONE / EPS IF( T( 4, 1 ).NE.ZERO ) $ RES = RES + ONE / EPS IF( T( 3, 2 ).NE.ZERO ) $ RES = RES + ONE / EPS IF( T( 4, 2 ).NE.ZERO ) $ RES = RES + ONE / EPS IF( T( 2, 1 ).NE.0 .AND. $ ( T( 1, 1 ).NE.T( 2, $ 2 ) .OR. SIGN( ONE, T( 1, $ 2 ) ).EQ.SIGN( ONE, T( 2, $ 1 ) ) ) )RES = RES + $ ONE / EPS IF( T( 4, 3 ).NE.0 .AND. $ ( T( 3, 3 ).NE.T( 4, $ 4 ) .OR. SIGN( ONE, T( 3, $ 4 ) ).EQ.SIGN( ONE, T( 4, $ 3 ) ) ) )RES = RES + $ ONE / EPS END IF KNT = KNT + 1 IF( RES.GT.RMAX ) THEN LMAX = KNT RMAX = RES END IF 210 CONTINUE 220 CONTINUE 230 CONTINUE 240 CONTINUE 250 CONTINUE 260 CONTINUE 270 CONTINUE 280 CONTINUE 290 CONTINUE 300 CONTINUE * RETURN * * End of SGET34 * END