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SUBROUTINE SCHKGT( DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR,
$ A, AF, B, X, XACT, WORK, RWORK, IWORK, NOUT ) * * -- LAPACK test routine (version 3.1) -- * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. * November 2006 * * .. Scalar Arguments .. LOGICAL TSTERR INTEGER NN, NNS, NOUT REAL THRESH * .. * .. Array Arguments .. LOGICAL DOTYPE( * ) INTEGER IWORK( * ), NSVAL( * ), NVAL( * ) REAL A( * ), AF( * ), B( * ), RWORK( * ), WORK( * ), $ X( * ), XACT( * ) * .. * * Purpose * ======= * * SCHKGT tests SGTTRF, -TRS, -RFS, and -CON * * Arguments * ========= * * DOTYPE (input) LOGICAL array, dimension (NTYPES) * The matrix types to be used for testing. Matrices of type j * (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) = * .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used. * * NN (input) INTEGER * The number of values of N contained in the vector NVAL. * * NVAL (input) INTEGER array, dimension (NN) * The values of the matrix dimension N. * * NNS (input) INTEGER * The number of values of NRHS contained in the vector NSVAL. * * NSVAL (input) INTEGER array, dimension (NNS) * The values of the number of right hand sides NRHS. * * THRESH (input) REAL * The threshold value for the test ratios. A result is * included in the output file if RESULT >= THRESH. To have * every test ratio printed, use THRESH = 0. * * TSTERR (input) LOGICAL * Flag that indicates whether error exits are to be tested. * * A (workspace) REAL array, dimension (NMAX*4) * * AF (workspace) REAL array, dimension (NMAX*4) * * B (workspace) REAL array, dimension (NMAX*NSMAX) * where NSMAX is the largest entry in NSVAL. * * X (workspace) REAL array, dimension (NMAX*NSMAX) * * XACT (workspace) REAL array, dimension (NMAX*NSMAX) * * WORK (workspace) REAL array, dimension * (NMAX*max(3,NSMAX)) * * RWORK (workspace) REAL array, dimension * (max(NMAX,2*NSMAX)) * * IWORK (workspace) INTEGER array, dimension (2*NMAX) * * NOUT (input) INTEGER * The unit number for output. * * ===================================================================== * * .. Parameters .. REAL ONE, ZERO PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 ) INTEGER NTYPES PARAMETER ( NTYPES = 12 ) INTEGER NTESTS PARAMETER ( NTESTS = 7 ) * .. * .. Local Scalars .. LOGICAL TRFCON, ZEROT CHARACTER DIST, NORM, TRANS, TYPE CHARACTER*3 PATH INTEGER I, IMAT, IN, INFO, IRHS, ITRAN, IX, IZERO, J, $ K, KL, KOFF, KU, LDA, M, MODE, N, NERRS, NFAIL, $ NIMAT, NRHS, NRUN REAL AINVNM, ANORM, COND, RCOND, RCONDC, RCONDI, $ RCONDO * .. * .. Local Arrays .. CHARACTER TRANSS( 3 ) INTEGER ISEED( 4 ), ISEEDY( 4 ) REAL RESULT( NTESTS ), Z( 3 ) * .. * .. External Functions .. REAL SASUM, SGET06, SLANGT EXTERNAL SASUM, SGET06, SLANGT * .. * .. External Subroutines .. EXTERNAL ALAERH, ALAHD, ALASUM, SCOPY, SERRGE, SGET04, $ SGTCON, SGTRFS, SGTT01, SGTT02, SGTT05, SGTTRF, $ SGTTRS, SLACPY, SLAGTM, SLARNV, SLATB4, SLATMS, $ SSCAL * .. * .. Intrinsic Functions .. INTRINSIC MAX * .. * .. Scalars in Common .. LOGICAL LERR, OK CHARACTER*32 SRNAMT INTEGER INFOT, NUNIT * .. * .. Common blocks .. COMMON / INFOC / INFOT, NUNIT, OK, LERR COMMON / SRNAMC / SRNAMT * .. * .. Data statements .. DATA ISEEDY / 0, 0, 0, 1 / , TRANSS / 'N', 'T', $ 'C' / * .. * .. Executable Statements .. * PATH( 1: 1 ) = 'Single precision' PATH( 2: 3 ) = 'GT' NRUN = 0 NFAIL = 0 NERRS = 0 DO 10 I = 1, 4 ISEED( I ) = ISEEDY( I ) 10 CONTINUE * * Test the error exits * IF( TSTERR ) $ CALL SERRGE( PATH, NOUT ) INFOT = 0 * DO 110 IN = 1, NN * * Do for each value of N in NVAL. * N = NVAL( IN ) M = MAX( N-1, 0 ) LDA = MAX( 1, N ) NIMAT = NTYPES IF( N.LE.0 ) $ NIMAT = 1 * DO 100 IMAT = 1, NIMAT * * Do the tests only if DOTYPE( IMAT ) is true. * IF( .NOT.DOTYPE( IMAT ) ) $ GO TO 100 * * Set up parameters with SLATB4. * CALL SLATB4( PATH, IMAT, N, N, TYPE, KL, KU, ANORM, MODE, $ COND, DIST ) * ZEROT = IMAT.GE.8 .AND. IMAT.LE.10 IF( IMAT.LE.6 ) THEN * * Types 1-6: generate matrices of known condition number. * KOFF = MAX( 2-KU, 3-MAX( 1, N ) ) SRNAMT = 'SLATMS' CALL SLATMS( N, N, DIST, ISEED, TYPE, RWORK, MODE, COND, $ ANORM, KL, KU, 'Z', AF( KOFF ), 3, WORK, $ INFO ) * * Check the error code from SLATMS. * IF( INFO.NE.0 ) THEN CALL ALAERH( PATH, 'SLATMS', INFO, 0, ' ', N, N, KL, $ KU, -1, IMAT, NFAIL, NERRS, NOUT ) GO TO 100 END IF IZERO = 0 * IF( N.GT.1 ) THEN CALL SCOPY( N-1, AF( 4 ), 3, A, 1 ) CALL SCOPY( N-1, AF( 3 ), 3, A( N+M+1 ), 1 ) END IF CALL SCOPY( N, AF( 2 ), 3, A( M+1 ), 1 ) ELSE * * Types 7-12: generate tridiagonal matrices with * unknown condition numbers. * IF( .NOT.ZEROT .OR. .NOT.DOTYPE( 7 ) ) THEN * * Generate a matrix with elements from [-1,1]. * CALL SLARNV( 2, ISEED, N+2*M, A ) IF( ANORM.NE.ONE ) $ CALL SSCAL( N+2*M, ANORM, A, 1 ) ELSE IF( IZERO.GT.0 ) THEN * * Reuse the last matrix by copying back the zeroed out * elements. * IF( IZERO.EQ.1 ) THEN A( N ) = Z( 2 ) IF( N.GT.1 ) $ A( 1 ) = Z( 3 ) ELSE IF( IZERO.EQ.N ) THEN A( 3*N-2 ) = Z( 1 ) A( 2*N-1 ) = Z( 2 ) ELSE A( 2*N-2+IZERO ) = Z( 1 ) A( N-1+IZERO ) = Z( 2 ) A( IZERO ) = Z( 3 ) END IF END IF * * If IMAT > 7, set one column of the matrix to 0. * IF( .NOT.ZEROT ) THEN IZERO = 0 ELSE IF( IMAT.EQ.8 ) THEN IZERO = 1 Z( 2 ) = A( N ) A( N ) = ZERO IF( N.GT.1 ) THEN Z( 3 ) = A( 1 ) A( 1 ) = ZERO END IF ELSE IF( IMAT.EQ.9 ) THEN IZERO = N Z( 1 ) = A( 3*N-2 ) Z( 2 ) = A( 2*N-1 ) A( 3*N-2 ) = ZERO A( 2*N-1 ) = ZERO ELSE IZERO = ( N+1 ) / 2 DO 20 I = IZERO, N - 1 A( 2*N-2+I ) = ZERO A( N-1+I ) = ZERO A( I ) = ZERO 20 CONTINUE A( 3*N-2 ) = ZERO A( 2*N-1 ) = ZERO END IF END IF * *+ TEST 1 * Factor A as L*U and compute the ratio * norm(L*U - A) / (n * norm(A) * EPS ) * CALL SCOPY( N+2*M, A, 1, AF, 1 ) SRNAMT = 'SGTTRF' CALL SGTTRF( N, AF, AF( M+1 ), AF( N+M+1 ), AF( N+2*M+1 ), $ IWORK, INFO ) * * Check error code from SGTTRF. * IF( INFO.NE.IZERO ) $ CALL ALAERH( PATH, 'SGTTRF', INFO, IZERO, ' ', N, N, 1, $ 1, -1, IMAT, NFAIL, NERRS, NOUT ) TRFCON = INFO.NE.0 * CALL SGTT01( N, A, A( M+1 ), A( N+M+1 ), AF, AF( M+1 ), $ AF( N+M+1 ), AF( N+2*M+1 ), IWORK, WORK, LDA, $ RWORK, RESULT( 1 ) ) * * Print the test ratio if it is .GE. THRESH. * IF( RESULT( 1 ).GE.THRESH ) THEN IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 ) $ CALL ALAHD( NOUT, PATH ) WRITE( NOUT, FMT = 9999 )N, IMAT, 1, RESULT( 1 ) NFAIL = NFAIL + 1 END IF NRUN = NRUN + 1 * DO 50 ITRAN = 1, 2 TRANS = TRANSS( ITRAN ) IF( ITRAN.EQ.1 ) THEN NORM = 'O' ELSE NORM = 'I' END IF ANORM = SLANGT( NORM, N, A, A( M+1 ), A( N+M+1 ) ) * IF( .NOT.TRFCON ) THEN * * Use SGTTRS to solve for one column at a time of inv(A) * or inv(A^T), computing the maximum column sum as we * go. * AINVNM = ZERO DO 40 I = 1, N DO 30 J = 1, N X( J ) = ZERO 30 CONTINUE X( I ) = ONE CALL SGTTRS( TRANS, N, 1, AF, AF( M+1 ), $ AF( N+M+1 ), AF( N+2*M+1 ), IWORK, X, $ LDA, INFO ) AINVNM = MAX( AINVNM, SASUM( N, X, 1 ) ) 40 CONTINUE * * Compute RCONDC = 1 / (norm(A) * norm(inv(A)) * IF( ANORM.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN RCONDC = ONE ELSE RCONDC = ( ONE / ANORM ) / AINVNM END IF IF( ITRAN.EQ.1 ) THEN RCONDO = RCONDC ELSE RCONDI = RCONDC END IF ELSE RCONDC = ZERO END IF * *+ TEST 7 * Estimate the reciprocal of the condition number of the * matrix. * SRNAMT = 'SGTCON' CALL SGTCON( NORM, N, AF, AF( M+1 ), AF( N+M+1 ), $ AF( N+2*M+1 ), IWORK, ANORM, RCOND, WORK, $ IWORK( N+1 ), INFO ) * * Check error code from SGTCON. * IF( INFO.NE.0 ) $ CALL ALAERH( PATH, 'SGTCON', INFO, 0, NORM, N, N, -1, $ -1, -1, IMAT, NFAIL, NERRS, NOUT ) * RESULT( 7 ) = SGET06( RCOND, RCONDC ) * * Print the test ratio if it is .GE. THRESH. * IF( RESULT( 7 ).GE.THRESH ) THEN IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 ) $ CALL ALAHD( NOUT, PATH ) WRITE( NOUT, FMT = 9997 )NORM, N, IMAT, 7, $ RESULT( 7 ) NFAIL = NFAIL + 1 END IF NRUN = NRUN + 1 50 CONTINUE * * Skip the remaining tests if the matrix is singular. * IF( TRFCON ) $ GO TO 100 * DO 90 IRHS = 1, NNS NRHS = NSVAL( IRHS ) * * Generate NRHS random solution vectors. * IX = 1 DO 60 J = 1, NRHS CALL SLARNV( 2, ISEED, N, XACT( IX ) ) IX = IX + LDA 60 CONTINUE * DO 80 ITRAN = 1, 3 TRANS = TRANSS( ITRAN ) IF( ITRAN.EQ.1 ) THEN RCONDC = RCONDO ELSE RCONDC = RCONDI END IF * * Set the right hand side. * CALL SLAGTM( TRANS, N, NRHS, ONE, A, A( M+1 ), $ A( N+M+1 ), XACT, LDA, ZERO, B, LDA ) * *+ TEST 2 * Solve op(A) * X = B and compute the residual. * CALL SLACPY( 'Full', N, NRHS, B, LDA, X, LDA ) SRNAMT = 'SGTTRS' CALL SGTTRS( TRANS, N, NRHS, AF, AF( M+1 ), $ AF( N+M+1 ), AF( N+2*M+1 ), IWORK, X, $ LDA, INFO ) * * Check error code from SGTTRS. * IF( INFO.NE.0 ) $ CALL ALAERH( PATH, 'SGTTRS', INFO, 0, TRANS, N, N, $ -1, -1, NRHS, IMAT, NFAIL, NERRS, $ NOUT ) * CALL SLACPY( 'Full', N, NRHS, B, LDA, WORK, LDA ) CALL SGTT02( TRANS, N, NRHS, A, A( M+1 ), A( N+M+1 ), $ X, LDA, WORK, LDA, RWORK, RESULT( 2 ) ) * *+ TEST 3 * Check solution from generated exact solution. * CALL SGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC, $ RESULT( 3 ) ) * *+ TESTS 4, 5, and 6 * Use iterative refinement to improve the solution. * SRNAMT = 'SGTRFS' CALL SGTRFS( TRANS, N, NRHS, A, A( M+1 ), A( N+M+1 ), $ AF, AF( M+1 ), AF( N+M+1 ), $ AF( N+2*M+1 ), IWORK, B, LDA, X, LDA, $ RWORK, RWORK( NRHS+1 ), WORK, $ IWORK( N+1 ), INFO ) * * Check error code from SGTRFS. * IF( INFO.NE.0 ) $ CALL ALAERH( PATH, 'SGTRFS', INFO, 0, TRANS, N, N, $ -1, -1, NRHS, IMAT, NFAIL, NERRS, $ NOUT ) * CALL SGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC, $ RESULT( 4 ) ) CALL SGTT05( TRANS, N, NRHS, A, A( M+1 ), A( N+M+1 ), $ B, LDA, X, LDA, XACT, LDA, RWORK, $ RWORK( NRHS+1 ), RESULT( 5 ) ) * * Print information about the tests that did not pass * the threshold. * DO 70 K = 2, 6 IF( RESULT( K ).GE.THRESH ) THEN IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 ) $ CALL ALAHD( NOUT, PATH ) WRITE( NOUT, FMT = 9998 )TRANS, N, NRHS, IMAT, $ K, RESULT( K ) NFAIL = NFAIL + 1 END IF 70 CONTINUE NRUN = NRUN + 5 80 CONTINUE 90 CONTINUE * 100 CONTINUE 110 CONTINUE * * Print a summary of the results. * CALL ALASUM( PATH, NOUT, NFAIL, NRUN, NERRS ) * 9999 FORMAT( 12X, 'N =', I5, ',', 10X, ' type ', I2, ', test(', I2, $ ') = ', G12.5 ) 9998 FORMAT( ' TRANS=''', A1, ''', N =', I5, ', NRHS=', I3, ', type ', $ I2, ', test(', I2, ') = ', G12.5 ) 9997 FORMAT( ' NORM =''', A1, ''', N =', I5, ',', 10X, ' type ', I2, $ ', test(', I2, ') = ', G12.5 ) RETURN * * End of SCHKGT * END |