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488 lines
16 KiB
488 lines
16 KiB
2 years ago
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*> \brief \b SCHKEQ
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*
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* =========== DOCUMENTATION ===========
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*
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* Online html documentation available at
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* http://www.netlib.org/lapack/explore-html/
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*
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* Definition:
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* ===========
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*
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* SUBROUTINE SCHKEQ( THRESH, NOUT )
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*
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* .. Scalar Arguments ..
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* INTEGER NOUT
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* REAL THRESH
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* ..
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*
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*
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*> \par Purpose:
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* =============
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*>
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*> \verbatim
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*>
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*> SCHKEQ tests SGEEQU, SGBEQU, SPOEQU, SPPEQU and SPBEQU
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*> \endverbatim
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*
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* Arguments:
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* ==========
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*
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*> \param[in] THRESH
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*> \verbatim
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*> THRESH is REAL
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*> Threshold for testing routines. Should be between 2 and 10.
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*> \endverbatim
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*>
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*> \param[in] NOUT
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*> \verbatim
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*> NOUT is INTEGER
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*> The unit number for output.
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*> \endverbatim
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*
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* Authors:
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* ========
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*
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*> \author Univ. of Tennessee
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*> \author Univ. of California Berkeley
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*> \author Univ. of Colorado Denver
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*> \author NAG Ltd.
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*
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*> \ingroup single_lin
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*
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* =====================================================================
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SUBROUTINE SCHKEQ( THRESH, NOUT )
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*
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* -- LAPACK test routine --
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* -- LAPACK is a software package provided by Univ. of Tennessee, --
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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*
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* .. Scalar Arguments ..
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INTEGER NOUT
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REAL THRESH
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* ..
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*
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* =====================================================================
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*
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* .. Parameters ..
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REAL ZERO, ONE, TEN
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PARAMETER ( ZERO = 0.0E0, ONE = 1.0E+0, TEN = 1.0E1 )
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INTEGER NSZ, NSZB
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PARAMETER ( NSZ = 5, NSZB = 3*NSZ-2 )
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INTEGER NSZP, NPOW
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PARAMETER ( NSZP = ( NSZ*( NSZ+1 ) ) / 2,
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$ NPOW = 2*NSZ+1 )
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* ..
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* .. Local Scalars ..
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LOGICAL OK
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CHARACTER*3 PATH
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INTEGER I, INFO, J, KL, KU, M, N
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REAL CCOND, EPS, NORM, RATIO, RCMAX, RCMIN, RCOND
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* ..
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* .. Local Arrays ..
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REAL A( NSZ, NSZ ), AB( NSZB, NSZ ), AP( NSZP ),
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$ C( NSZ ), POW( NPOW ), R( NSZ ), RESLTS( 5 ),
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$ RPOW( NPOW )
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* ..
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* .. External Functions ..
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REAL SLAMCH
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EXTERNAL SLAMCH
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* ..
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* .. External Subroutines ..
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EXTERNAL SGBEQU, SGEEQU, SPBEQU, SPOEQU, SPPEQU
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC ABS, MAX, MIN
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* ..
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* .. Executable Statements ..
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*
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PATH( 1:1 ) = 'Single precision'
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PATH( 2:3 ) = 'EQ'
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*
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EPS = SLAMCH( 'P' )
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DO 10 I = 1, 5
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RESLTS( I ) = ZERO
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10 CONTINUE
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DO 20 I = 1, NPOW
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POW( I ) = TEN**( I-1 )
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RPOW( I ) = ONE / POW( I )
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20 CONTINUE
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*
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* Test SGEEQU
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*
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DO 80 N = 0, NSZ
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DO 70 M = 0, NSZ
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*
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DO 40 J = 1, NSZ
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DO 30 I = 1, NSZ
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IF( I.LE.M .AND. J.LE.N ) THEN
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A( I, J ) = POW( I+J+1 )*( -1 )**( I+J )
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ELSE
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A( I, J ) = ZERO
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END IF
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30 CONTINUE
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40 CONTINUE
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*
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CALL SGEEQU( M, N, A, NSZ, R, C, RCOND, CCOND, NORM, INFO )
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*
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IF( INFO.NE.0 ) THEN
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RESLTS( 1 ) = ONE
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ELSE
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IF( N.NE.0 .AND. M.NE.0 ) THEN
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RESLTS( 1 ) = MAX( RESLTS( 1 ),
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$ ABS( ( RCOND-RPOW( M ) ) / RPOW( M ) ) )
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RESLTS( 1 ) = MAX( RESLTS( 1 ),
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$ ABS( ( CCOND-RPOW( N ) ) / RPOW( N ) ) )
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RESLTS( 1 ) = MAX( RESLTS( 1 ),
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$ ABS( ( NORM-POW( N+M+1 ) ) / POW( N+M+
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$ 1 ) ) )
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DO 50 I = 1, M
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RESLTS( 1 ) = MAX( RESLTS( 1 ),
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$ ABS( ( R( I )-RPOW( I+N+1 ) ) /
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$ RPOW( I+N+1 ) ) )
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50 CONTINUE
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DO 60 J = 1, N
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RESLTS( 1 ) = MAX( RESLTS( 1 ),
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$ ABS( ( C( J )-POW( N-J+1 ) ) /
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$ POW( N-J+1 ) ) )
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60 CONTINUE
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END IF
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END IF
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*
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70 CONTINUE
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80 CONTINUE
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*
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* Test with zero rows and columns
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*
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DO 90 J = 1, NSZ
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A( MAX( NSZ-1, 1 ), J ) = ZERO
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90 CONTINUE
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CALL SGEEQU( NSZ, NSZ, A, NSZ, R, C, RCOND, CCOND, NORM, INFO )
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IF( INFO.NE.MAX( NSZ-1, 1 ) )
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$ RESLTS( 1 ) = ONE
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*
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DO 100 J = 1, NSZ
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A( MAX( NSZ-1, 1 ), J ) = ONE
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100 CONTINUE
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DO 110 I = 1, NSZ
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A( I, MAX( NSZ-1, 1 ) ) = ZERO
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110 CONTINUE
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CALL SGEEQU( NSZ, NSZ, A, NSZ, R, C, RCOND, CCOND, NORM, INFO )
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IF( INFO.NE.NSZ+MAX( NSZ-1, 1 ) )
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$ RESLTS( 1 ) = ONE
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RESLTS( 1 ) = RESLTS( 1 ) / EPS
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*
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* Test SGBEQU
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*
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DO 250 N = 0, NSZ
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DO 240 M = 0, NSZ
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DO 230 KL = 0, MAX( M-1, 0 )
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DO 220 KU = 0, MAX( N-1, 0 )
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*
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DO 130 J = 1, NSZ
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DO 120 I = 1, NSZB
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AB( I, J ) = ZERO
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120 CONTINUE
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130 CONTINUE
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DO 150 J = 1, N
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DO 140 I = 1, M
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IF( I.LE.MIN( M, J+KL ) .AND. I.GE.
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$ MAX( 1, J-KU ) .AND. J.LE.N ) THEN
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AB( KU+1+I-J, J ) = POW( I+J+1 )*
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$ ( -1 )**( I+J )
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END IF
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140 CONTINUE
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150 CONTINUE
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*
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CALL SGBEQU( M, N, KL, KU, AB, NSZB, R, C, RCOND,
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$ CCOND, NORM, INFO )
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*
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IF( INFO.NE.0 ) THEN
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IF( .NOT.( ( N+KL.LT.M .AND. INFO.EQ.N+KL+1 ) .OR.
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$ ( M+KU.LT.N .AND. INFO.EQ.2*M+KU+1 ) ) ) THEN
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RESLTS( 2 ) = ONE
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END IF
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ELSE
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IF( N.NE.0 .AND. M.NE.0 ) THEN
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*
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RCMIN = R( 1 )
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RCMAX = R( 1 )
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DO 160 I = 1, M
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RCMIN = MIN( RCMIN, R( I ) )
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RCMAX = MAX( RCMAX, R( I ) )
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160 CONTINUE
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RATIO = RCMIN / RCMAX
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RESLTS( 2 ) = MAX( RESLTS( 2 ),
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$ ABS( ( RCOND-RATIO ) / RATIO ) )
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*
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RCMIN = C( 1 )
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RCMAX = C( 1 )
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DO 170 J = 1, N
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RCMIN = MIN( RCMIN, C( J ) )
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RCMAX = MAX( RCMAX, C( J ) )
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170 CONTINUE
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RATIO = RCMIN / RCMAX
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RESLTS( 2 ) = MAX( RESLTS( 2 ),
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$ ABS( ( CCOND-RATIO ) / RATIO ) )
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*
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RESLTS( 2 ) = MAX( RESLTS( 2 ),
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$ ABS( ( NORM-POW( N+M+1 ) ) /
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$ POW( N+M+1 ) ) )
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DO 190 I = 1, M
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RCMAX = ZERO
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DO 180 J = 1, N
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IF( I.LE.J+KL .AND. I.GE.J-KU ) THEN
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RATIO = ABS( R( I )*POW( I+J+1 )*
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$ C( J ) )
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RCMAX = MAX( RCMAX, RATIO )
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END IF
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180 CONTINUE
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RESLTS( 2 ) = MAX( RESLTS( 2 ),
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$ ABS( ONE-RCMAX ) )
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190 CONTINUE
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*
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DO 210 J = 1, N
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RCMAX = ZERO
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DO 200 I = 1, M
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IF( I.LE.J+KL .AND. I.GE.J-KU ) THEN
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RATIO = ABS( R( I )*POW( I+J+1 )*
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$ C( J ) )
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RCMAX = MAX( RCMAX, RATIO )
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END IF
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200 CONTINUE
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RESLTS( 2 ) = MAX( RESLTS( 2 ),
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$ ABS( ONE-RCMAX ) )
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210 CONTINUE
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END IF
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END IF
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*
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220 CONTINUE
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230 CONTINUE
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240 CONTINUE
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250 CONTINUE
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RESLTS( 2 ) = RESLTS( 2 ) / EPS
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*
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* Test SPOEQU
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*
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DO 290 N = 0, NSZ
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*
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DO 270 I = 1, NSZ
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DO 260 J = 1, NSZ
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IF( I.LE.N .AND. J.EQ.I ) THEN
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A( I, J ) = POW( I+J+1 )*( -1 )**( I+J )
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ELSE
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A( I, J ) = ZERO
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END IF
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260 CONTINUE
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270 CONTINUE
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*
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CALL SPOEQU( N, A, NSZ, R, RCOND, NORM, INFO )
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*
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IF( INFO.NE.0 ) THEN
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RESLTS( 3 ) = ONE
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ELSE
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IF( N.NE.0 ) THEN
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RESLTS( 3 ) = MAX( RESLTS( 3 ),
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$ ABS( ( RCOND-RPOW( N ) ) / RPOW( N ) ) )
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RESLTS( 3 ) = MAX( RESLTS( 3 ),
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$ ABS( ( NORM-POW( 2*N+1 ) ) / POW( 2*N+
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$ 1 ) ) )
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DO 280 I = 1, N
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RESLTS( 3 ) = MAX( RESLTS( 3 ),
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$ ABS( ( R( I )-RPOW( I+1 ) ) / RPOW( I+
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$ 1 ) ) )
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280 CONTINUE
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END IF
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END IF
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290 CONTINUE
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A( MAX( NSZ-1, 1 ), MAX( NSZ-1, 1 ) ) = -ONE
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CALL SPOEQU( NSZ, A, NSZ, R, RCOND, NORM, INFO )
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IF( INFO.NE.MAX( NSZ-1, 1 ) )
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$ RESLTS( 3 ) = ONE
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RESLTS( 3 ) = RESLTS( 3 ) / EPS
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*
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* Test SPPEQU
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*
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DO 360 N = 0, NSZ
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*
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* Upper triangular packed storage
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*
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DO 300 I = 1, ( N*( N+1 ) ) / 2
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AP( I ) = ZERO
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300 CONTINUE
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DO 310 I = 1, N
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AP( ( I*( I+1 ) ) / 2 ) = POW( 2*I+1 )
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310 CONTINUE
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*
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CALL SPPEQU( 'U', N, AP, R, RCOND, NORM, INFO )
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*
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IF( INFO.NE.0 ) THEN
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RESLTS( 4 ) = ONE
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ELSE
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IF( N.NE.0 ) THEN
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RESLTS( 4 ) = MAX( RESLTS( 4 ),
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$ ABS( ( RCOND-RPOW( N ) ) / RPOW( N ) ) )
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RESLTS( 4 ) = MAX( RESLTS( 4 ),
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$ ABS( ( NORM-POW( 2*N+1 ) ) / POW( 2*N+
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$ 1 ) ) )
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DO 320 I = 1, N
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RESLTS( 4 ) = MAX( RESLTS( 4 ),
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$ ABS( ( R( I )-RPOW( I+1 ) ) / RPOW( I+
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$ 1 ) ) )
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320 CONTINUE
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END IF
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END IF
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*
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* Lower triangular packed storage
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*
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DO 330 I = 1, ( N*( N+1 ) ) / 2
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AP( I ) = ZERO
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330 CONTINUE
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J = 1
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DO 340 I = 1, N
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AP( J ) = POW( 2*I+1 )
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J = J + ( N-I+1 )
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340 CONTINUE
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*
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CALL SPPEQU( 'L', N, AP, R, RCOND, NORM, INFO )
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*
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IF( INFO.NE.0 ) THEN
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RESLTS( 4 ) = ONE
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ELSE
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IF( N.NE.0 ) THEN
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RESLTS( 4 ) = MAX( RESLTS( 4 ),
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$ ABS( ( RCOND-RPOW( N ) ) / RPOW( N ) ) )
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RESLTS( 4 ) = MAX( RESLTS( 4 ),
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$ ABS( ( NORM-POW( 2*N+1 ) ) / POW( 2*N+
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$ 1 ) ) )
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DO 350 I = 1, N
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RESLTS( 4 ) = MAX( RESLTS( 4 ),
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$ ABS( ( R( I )-RPOW( I+1 ) ) / RPOW( I+
|
||
|
|
$ 1 ) ) )
|
||
|
|
350 CONTINUE
|
||
|
|
END IF
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
360 CONTINUE
|
||
|
|
I = ( NSZ*( NSZ+1 ) ) / 2 - 2
|
||
|
|
AP( I ) = -ONE
|
||
|
|
CALL SPPEQU( 'L', NSZ, AP, R, RCOND, NORM, INFO )
|
||
|
|
IF( INFO.NE.MAX( NSZ-1, 1 ) )
|
||
|
|
$ RESLTS( 4 ) = ONE
|
||
|
|
RESLTS( 4 ) = RESLTS( 4 ) / EPS
|
||
|
|
*
|
||
|
|
* Test SPBEQU
|
||
|
|
*
|
||
|
|
DO 460 N = 0, NSZ
|
||
|
|
DO 450 KL = 0, MAX( N-1, 0 )
|
||
|
|
*
|
||
|
|
* Test upper triangular storage
|
||
|
|
*
|
||
|
|
DO 380 J = 1, NSZ
|
||
|
|
DO 370 I = 1, NSZB
|
||
|
|
AB( I, J ) = ZERO
|
||
|
|
370 CONTINUE
|
||
|
|
380 CONTINUE
|
||
|
|
DO 390 J = 1, N
|
||
|
|
AB( KL+1, J ) = POW( 2*J+1 )
|
||
|
|
390 CONTINUE
|
||
|
|
*
|
||
|
|
CALL SPBEQU( 'U', N, KL, AB, NSZB, R, RCOND, NORM, INFO )
|
||
|
|
*
|
||
|
|
IF( INFO.NE.0 ) THEN
|
||
|
|
RESLTS( 5 ) = ONE
|
||
|
|
ELSE
|
||
|
|
IF( N.NE.0 ) THEN
|
||
|
|
RESLTS( 5 ) = MAX( RESLTS( 5 ),
|
||
|
|
$ ABS( ( RCOND-RPOW( N ) ) / RPOW( N ) ) )
|
||
|
|
RESLTS( 5 ) = MAX( RESLTS( 5 ),
|
||
|
|
$ ABS( ( NORM-POW( 2*N+1 ) ) / POW( 2*N+
|
||
|
|
$ 1 ) ) )
|
||
|
|
DO 400 I = 1, N
|
||
|
|
RESLTS( 5 ) = MAX( RESLTS( 5 ),
|
||
|
|
$ ABS( ( R( I )-RPOW( I+1 ) ) /
|
||
|
|
$ RPOW( I+1 ) ) )
|
||
|
|
400 CONTINUE
|
||
|
|
END IF
|
||
|
|
END IF
|
||
|
|
IF( N.NE.0 ) THEN
|
||
|
|
AB( KL+1, MAX( N-1, 1 ) ) = -ONE
|
||
|
|
CALL SPBEQU( 'U', N, KL, AB, NSZB, R, RCOND, NORM, INFO )
|
||
|
|
IF( INFO.NE.MAX( N-1, 1 ) )
|
||
|
|
$ RESLTS( 5 ) = ONE
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* Test lower triangular storage
|
||
|
|
*
|
||
|
|
DO 420 J = 1, NSZ
|
||
|
|
DO 410 I = 1, NSZB
|
||
|
|
AB( I, J ) = ZERO
|
||
|
|
410 CONTINUE
|
||
|
|
420 CONTINUE
|
||
|
|
DO 430 J = 1, N
|
||
|
|
AB( 1, J ) = POW( 2*J+1 )
|
||
|
|
430 CONTINUE
|
||
|
|
*
|
||
|
|
CALL SPBEQU( 'L', N, KL, AB, NSZB, R, RCOND, NORM, INFO )
|
||
|
|
*
|
||
|
|
IF( INFO.NE.0 ) THEN
|
||
|
|
RESLTS( 5 ) = ONE
|
||
|
|
ELSE
|
||
|
|
IF( N.NE.0 ) THEN
|
||
|
|
RESLTS( 5 ) = MAX( RESLTS( 5 ),
|
||
|
|
$ ABS( ( RCOND-RPOW( N ) ) / RPOW( N ) ) )
|
||
|
|
RESLTS( 5 ) = MAX( RESLTS( 5 ),
|
||
|
|
$ ABS( ( NORM-POW( 2*N+1 ) ) / POW( 2*N+
|
||
|
|
$ 1 ) ) )
|
||
|
|
DO 440 I = 1, N
|
||
|
|
RESLTS( 5 ) = MAX( RESLTS( 5 ),
|
||
|
|
$ ABS( ( R( I )-RPOW( I+1 ) ) /
|
||
|
|
$ RPOW( I+1 ) ) )
|
||
|
|
440 CONTINUE
|
||
|
|
END IF
|
||
|
|
END IF
|
||
|
|
IF( N.NE.0 ) THEN
|
||
|
|
AB( 1, MAX( N-1, 1 ) ) = -ONE
|
||
|
|
CALL SPBEQU( 'L', N, KL, AB, NSZB, R, RCOND, NORM, INFO )
|
||
|
|
IF( INFO.NE.MAX( N-1, 1 ) )
|
||
|
|
$ RESLTS( 5 ) = ONE
|
||
|
|
END IF
|
||
|
|
450 CONTINUE
|
||
|
|
460 CONTINUE
|
||
|
|
RESLTS( 5 ) = RESLTS( 5 ) / EPS
|
||
|
|
OK = ( RESLTS( 1 ).LE.THRESH ) .AND.
|
||
|
|
$ ( RESLTS( 2 ).LE.THRESH ) .AND.
|
||
|
|
$ ( RESLTS( 3 ).LE.THRESH ) .AND.
|
||
|
|
$ ( RESLTS( 4 ).LE.THRESH ) .AND. ( RESLTS( 5 ).LE.THRESH )
|
||
|
|
WRITE( NOUT, FMT = * )
|
||
|
|
IF( OK ) THEN
|
||
|
|
WRITE( NOUT, FMT = 9999 )PATH
|
||
|
|
ELSE
|
||
|
|
IF( RESLTS( 1 ).GT.THRESH )
|
||
|
|
$ WRITE( NOUT, FMT = 9998 )RESLTS( 1 ), THRESH
|
||
|
|
IF( RESLTS( 2 ).GT.THRESH )
|
||
|
|
$ WRITE( NOUT, FMT = 9997 )RESLTS( 2 ), THRESH
|
||
|
|
IF( RESLTS( 3 ).GT.THRESH )
|
||
|
|
$ WRITE( NOUT, FMT = 9996 )RESLTS( 3 ), THRESH
|
||
|
|
IF( RESLTS( 4 ).GT.THRESH )
|
||
|
|
$ WRITE( NOUT, FMT = 9995 )RESLTS( 4 ), THRESH
|
||
|
|
IF( RESLTS( 5 ).GT.THRESH )
|
||
|
|
$ WRITE( NOUT, FMT = 9994 )RESLTS( 5 ), THRESH
|
||
|
|
END IF
|
||
|
|
9999 FORMAT( 1X, 'All tests for ', A3,
|
||
|
|
$ ' routines passed the threshold' )
|
||
|
|
9998 FORMAT( ' SGEEQU failed test with value ', E10.3, ' exceeding',
|
||
|
|
$ ' threshold ', E10.3 )
|
||
|
|
9997 FORMAT( ' SGBEQU failed test with value ', E10.3, ' exceeding',
|
||
|
|
$ ' threshold ', E10.3 )
|
||
|
|
9996 FORMAT( ' SPOEQU failed test with value ', E10.3, ' exceeding',
|
||
|
|
$ ' threshold ', E10.3 )
|
||
|
|
9995 FORMAT( ' SPPEQU failed test with value ', E10.3, ' exceeding',
|
||
|
|
$ ' threshold ', E10.3 )
|
||
|
|
9994 FORMAT( ' SPBEQU failed test with value ', E10.3, ' exceeding',
|
||
|
|
$ ' threshold ', E10.3 )
|
||
|
|
RETURN
|
||
|
|
*
|
||
|
|
* End of SCHKEQ
|
||
|
|
*
|
||
|
|
END
|