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SUBROUTINE SCHKEQ( THRESH, NOUT )
* * -- LAPACK test routine (version 3.1) -- * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. * November 2006 * * .. Scalar Arguments .. INTEGER NOUT REAL THRESH * .. * * Purpose * ======= * * SCHKEQ tests SGEEQU, SGBEQU, SPOEQU, SPPEQU and SPBEQU * * Arguments * ========= * * THRESH (input) REAL * Threshold for testing routines. Should be between 2 and 10. * * NOUT (input) INTEGER * The unit number for output. * * ===================================================================== * * .. Parameters .. REAL ZERO, ONE, TEN PARAMETER ( ZERO = 0.0E0, ONE = 1.0E+0, TEN = 1.0E1 ) INTEGER NSZ, NSZB PARAMETER ( NSZ = 5, NSZB = 3*NSZ-2 ) INTEGER NSZP, NPOW PARAMETER ( NSZP = ( NSZ*( NSZ+1 ) ) / 2, $ NPOW = 2*NSZ+1 ) * .. * .. Local Scalars .. LOGICAL OK CHARACTER*3 PATH INTEGER I, INFO, J, KL, KU, M, N REAL CCOND, EPS, NORM, RATIO, RCMAX, RCMIN, RCOND * .. * .. Local Arrays .. REAL A( NSZ, NSZ ), AB( NSZB, NSZ ), AP( NSZP ), $ C( NSZ ), POW( NPOW ), R( NSZ ), RESLTS( 5 ), $ RPOW( NPOW ) * .. * .. External Functions .. REAL SLAMCH EXTERNAL SLAMCH * .. * .. External Subroutines .. EXTERNAL SGBEQU, SGEEQU, SPBEQU, SPOEQU, SPPEQU * .. * .. Intrinsic Functions .. INTRINSIC ABS, MAX, MIN * .. * .. Executable Statements .. * PATH( 1:1 ) = 'Single precision' PATH( 2:3 ) = 'EQ' * EPS = SLAMCH( 'P' ) DO 10 I = 1, 5 RESLTS( I ) = ZERO 10 CONTINUE DO 20 I = 1, NPOW POW( I ) = TEN**( I-1 ) RPOW( I ) = ONE / POW( I ) 20 CONTINUE * * Test SGEEQU * DO 80 N = 0, NSZ DO 70 M = 0, NSZ * DO 40 J = 1, NSZ DO 30 I = 1, NSZ IF( I.LE.M .AND. J.LE.N ) THEN A( I, J ) = POW( I+J+1 )*( -1 )**( I+J ) ELSE A( I, J ) = ZERO END IF 30 CONTINUE 40 CONTINUE * CALL SGEEQU( M, N, A, NSZ, R, C, RCOND, CCOND, NORM, INFO ) * IF( INFO.NE.0 ) THEN RESLTS( 1 ) = ONE ELSE IF( N.NE.0 .AND. M.NE.0 ) THEN RESLTS( 1 ) = MAX( RESLTS( 1 ), $ ABS( ( RCOND-RPOW( M ) ) / RPOW( M ) ) ) RESLTS( 1 ) = MAX( RESLTS( 1 ), $ ABS( ( CCOND-RPOW( N ) ) / RPOW( N ) ) ) RESLTS( 1 ) = MAX( RESLTS( 1 ), $ ABS( ( NORM-POW( N+M+1 ) ) / POW( N+M+ $ 1 ) ) ) DO 50 I = 1, M RESLTS( 1 ) = MAX( RESLTS( 1 ), $ ABS( ( R( I )-RPOW( I+N+1 ) ) / $ RPOW( I+N+1 ) ) ) 50 CONTINUE DO 60 J = 1, N RESLTS( 1 ) = MAX( RESLTS( 1 ), $ ABS( ( C( J )-POW( N-J+1 ) ) / $ POW( N-J+1 ) ) ) 60 CONTINUE END IF END IF * 70 CONTINUE 80 CONTINUE * * Test with zero rows and columns * DO 90 J = 1, NSZ A( MAX( NSZ-1, 1 ), J ) = ZERO 90 CONTINUE CALL SGEEQU( NSZ, NSZ, A, NSZ, R, C, RCOND, CCOND, NORM, INFO ) IF( INFO.NE.MAX( NSZ-1, 1 ) ) $ RESLTS( 1 ) = ONE * DO 100 J = 1, NSZ A( MAX( NSZ-1, 1 ), J ) = ONE 100 CONTINUE DO 110 I = 1, NSZ A( I, MAX( NSZ-1, 1 ) ) = ZERO 110 CONTINUE CALL SGEEQU( NSZ, NSZ, A, NSZ, R, C, RCOND, CCOND, NORM, INFO ) IF( INFO.NE.NSZ+MAX( NSZ-1, 1 ) ) $ RESLTS( 1 ) = ONE RESLTS( 1 ) = RESLTS( 1 ) / EPS * * Test SGBEQU * DO 250 N = 0, NSZ DO 240 M = 0, NSZ DO 230 KL = 0, MAX( M-1, 0 ) DO 220 KU = 0, MAX( N-1, 0 ) * DO 130 J = 1, NSZ DO 120 I = 1, NSZB AB( I, J ) = ZERO 120 CONTINUE 130 CONTINUE DO 150 J = 1, N DO 140 I = 1, M IF( I.LE.MIN( M, J+KL ) .AND. I.GE. $ MAX( 1, J-KU ) .AND. J.LE.N ) THEN AB( KU+1+I-J, J ) = POW( I+J+1 )* $ ( -1 )**( I+J ) END IF 140 CONTINUE 150 CONTINUE * CALL SGBEQU( M, N, KL, KU, AB, NSZB, R, C, RCOND, $ CCOND, NORM, INFO ) * IF( INFO.NE.0 ) THEN IF( .NOT.( ( N+KL.LT.M .AND. INFO.EQ.N+KL+1 ) .OR. $ ( M+KU.LT.N .AND. INFO.EQ.2*M+KU+1 ) ) ) THEN RESLTS( 2 ) = ONE END IF ELSE IF( N.NE.0 .AND. M.NE.0 ) THEN * RCMIN = R( 1 ) RCMAX = R( 1 ) DO 160 I = 1, M RCMIN = MIN( RCMIN, R( I ) ) RCMAX = MAX( RCMAX, R( I ) ) 160 CONTINUE RATIO = RCMIN / RCMAX RESLTS( 2 ) = MAX( RESLTS( 2 ), $ ABS( ( RCOND-RATIO ) / RATIO ) ) * RCMIN = C( 1 ) RCMAX = C( 1 ) DO 170 J = 1, N RCMIN = MIN( RCMIN, C( J ) ) RCMAX = MAX( RCMAX, C( J ) ) 170 CONTINUE RATIO = RCMIN / RCMAX RESLTS( 2 ) = MAX( RESLTS( 2 ), $ ABS( ( CCOND-RATIO ) / RATIO ) ) * RESLTS( 2 ) = MAX( RESLTS( 2 ), $ ABS( ( NORM-POW( N+M+1 ) ) / $ POW( N+M+1 ) ) ) DO 190 I = 1, M RCMAX = ZERO DO 180 J = 1, N IF( I.LE.J+KL .AND. I.GE.J-KU ) THEN RATIO = ABS( R( I )*POW( I+J+1 )* $ C( J ) ) RCMAX = MAX( RCMAX, RATIO ) END IF 180 CONTINUE RESLTS( 2 ) = MAX( RESLTS( 2 ), $ ABS( ONE-RCMAX ) ) 190 CONTINUE * DO 210 J = 1, N RCMAX = ZERO DO 200 I = 1, M IF( I.LE.J+KL .AND. I.GE.J-KU ) THEN RATIO = ABS( R( I )*POW( I+J+1 )* $ C( J ) ) RCMAX = MAX( RCMAX, RATIO ) END IF 200 CONTINUE RESLTS( 2 ) = MAX( RESLTS( 2 ), $ ABS( ONE-RCMAX ) ) 210 CONTINUE END IF END IF * 220 CONTINUE 230 CONTINUE 240 CONTINUE 250 CONTINUE RESLTS( 2 ) = RESLTS( 2 ) / EPS * * Test SPOEQU * DO 290 N = 0, NSZ * DO 270 I = 1, NSZ DO 260 J = 1, NSZ IF( I.LE.N .AND. J.EQ.I ) THEN A( I, J ) = POW( I+J+1 )*( -1 )**( I+J ) ELSE A( I, J ) = ZERO END IF 260 CONTINUE 270 CONTINUE * CALL SPOEQU( N, A, NSZ, R, RCOND, NORM, INFO ) * IF( INFO.NE.0 ) THEN RESLTS( 3 ) = ONE ELSE IF( N.NE.0 ) THEN RESLTS( 3 ) = MAX( RESLTS( 3 ), $ ABS( ( RCOND-RPOW( N ) ) / RPOW( N ) ) ) RESLTS( 3 ) = MAX( RESLTS( 3 ), $ ABS( ( NORM-POW( 2*N+1 ) ) / POW( 2*N+ $ 1 ) ) ) DO 280 I = 1, N RESLTS( 3 ) = MAX( RESLTS( 3 ), $ ABS( ( R( I )-RPOW( I+1 ) ) / RPOW( I+ $ 1 ) ) ) 280 CONTINUE END IF END IF 290 CONTINUE A( MAX( NSZ-1, 1 ), MAX( NSZ-1, 1 ) ) = -ONE CALL SPOEQU( NSZ, A, NSZ, R, RCOND, NORM, INFO ) IF( INFO.NE.MAX( NSZ-1, 1 ) ) $ RESLTS( 3 ) = ONE RESLTS( 3 ) = RESLTS( 3 ) / EPS * * Test SPPEQU * DO 360 N = 0, NSZ * * Upper triangular packed storage * DO 300 I = 1, ( N*( N+1 ) ) / 2 AP( I ) = ZERO 300 CONTINUE DO 310 I = 1, N AP( ( I*( I+1 ) ) / 2 ) = POW( 2*I+1 ) 310 CONTINUE * CALL SPPEQU( 'U', N, AP, R, RCOND, NORM, INFO ) * IF( INFO.NE.0 ) THEN RESLTS( 4 ) = ONE ELSE IF( N.NE.0 ) THEN RESLTS( 4 ) = MAX( RESLTS( 4 ), $ ABS( ( RCOND-RPOW( N ) ) / RPOW( N ) ) ) RESLTS( 4 ) = MAX( RESLTS( 4 ), $ ABS( ( NORM-POW( 2*N+1 ) ) / POW( 2*N+ $ 1 ) ) ) DO 320 I = 1, N RESLTS( 4 ) = MAX( RESLTS( 4 ), $ ABS( ( R( I )-RPOW( I+1 ) ) / RPOW( I+ $ 1 ) ) ) 320 CONTINUE END IF END IF * * Lower triangular packed storage * DO 330 I = 1, ( N*( N+1 ) ) / 2 AP( I ) = ZERO 330 CONTINUE J = 1 DO 340 I = 1, N AP( J ) = POW( 2*I+1 ) J = J + ( N-I+1 ) 340 CONTINUE * CALL SPPEQU( 'L', N, AP, R, RCOND, NORM, INFO ) * IF( INFO.NE.0 ) THEN RESLTS( 4 ) = ONE ELSE IF( N.NE.0 ) THEN RESLTS( 4 ) = MAX( RESLTS( 4 ), $ ABS( ( RCOND-RPOW( N ) ) / RPOW( N ) ) ) RESLTS( 4 ) = MAX( RESLTS( 4 ), $ ABS( ( NORM-POW( 2*N+1 ) ) / POW( 2*N+ $ 1 ) ) ) DO 350 I = 1, N RESLTS( 4 ) = MAX( RESLTS( 4 ), $ 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 |