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SUBROUTINE SDRVGT( DOTYPE, NN, NVAL, NRHS, 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, NOUT, NRHS REAL THRESH * .. * .. Array Arguments .. LOGICAL DOTYPE( * ) INTEGER IWORK( * ), NVAL( * ) REAL A( * ), AF( * ), B( * ), RWORK( * ), WORK( * ), $ X( * ), XACT( * ) * .. * * Purpose * ======= * * SDRVGT tests SGTSV and -SVX. * * 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. * * 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*NRHS) * * X (workspace) REAL array, dimension (NMAX*NRHS) * * XACT (workspace) REAL array, dimension (NMAX*NRHS) * * WORK (workspace) REAL array, dimension * (NMAX*max(3,NRHS)) * * RWORK (workspace) REAL array, dimension * (max(NMAX,2*NRHS)) * * 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 = 6 ) * .. * .. Local Scalars .. LOGICAL TRFCON, ZEROT CHARACTER DIST, FACT, TRANS, TYPE CHARACTER*3 PATH INTEGER I, IFACT, IMAT, IN, INFO, ITRAN, IX, IZERO, J, $ K, K1, KL, KOFF, KU, LDA, M, MODE, N, NERRS, $ NFAIL, NIMAT, NRUN, NT REAL AINVNM, ANORM, ANORMI, ANORMO, 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 ALADHD, ALAERH, ALASVM, SCOPY, SERRVX, SGET04, $ SGTSV, SGTSVX, SGTT01, SGTT02, SGTT05, SGTTRF, $ SGTTRS, SLACPY, SLAGTM, SLARNV, SLASET, 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 SERRVX( PATH, NOUT ) INFOT = 0 * DO 140 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 130 IMAT = 1, NIMAT * * Do the tests only if DOTYPE( IMAT ) is true. * IF( .NOT.DOTYPE( IMAT ) ) $ GO TO 130 * * 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 130 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 * DO 120 IFACT = 1, 2 IF( IFACT.EQ.1 ) THEN FACT = 'F' ELSE FACT = 'N' END IF * * Compute the condition number for comparison with * the value returned by SGTSVX. * IF( ZEROT ) THEN IF( IFACT.EQ.1 ) $ GO TO 120 RCONDO = ZERO RCONDI = ZERO * ELSE IF( IFACT.EQ.1 ) THEN CALL SCOPY( N+2*M, A, 1, AF, 1 ) * * Compute the 1-norm and infinity-norm of A. * ANORMO = SLANGT( '1', N, A, A( M+1 ), A( N+M+1 ) ) ANORMI = SLANGT( 'I', N, A, A( M+1 ), A( N+M+1 ) ) * * Factor the matrix A. * CALL SGTTRF( N, AF, AF( M+1 ), AF( N+M+1 ), $ AF( N+2*M+1 ), IWORK, INFO ) * * Use SGTTRS to solve for one column at a time of * inv(A), 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( 'No transpose', 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 the 1-norm condition number of A. * IF( ANORMO.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN RCONDO = ONE ELSE RCONDO = ( ONE / ANORMO ) / AINVNM END IF * * Use SGTTRS to solve for one column at a time of * inv(A'), computing the maximum column sum as we go. * AINVNM = ZERO DO 60 I = 1, N DO 50 J = 1, N X( J ) = ZERO 50 CONTINUE X( I ) = ONE CALL SGTTRS( 'Transpose', 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 ) ) 60 CONTINUE * * Compute the infinity-norm condition number of A. * IF( ANORMI.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN RCONDI = ONE ELSE RCONDI = ( ONE / ANORMI ) / AINVNM END IF END IF * DO 110 ITRAN = 1, 3 TRANS = TRANSS( ITRAN ) IF( ITRAN.EQ.1 ) THEN RCONDC = RCONDO ELSE RCONDC = RCONDI END IF * * Generate NRHS random solution vectors. * IX = 1 DO 70 J = 1, NRHS CALL SLARNV( 2, ISEED, N, XACT( IX ) ) IX = IX + LDA 70 CONTINUE * * Set the right hand side. * CALL SLAGTM( TRANS, N, NRHS, ONE, A, A( M+1 ), $ A( N+M+1 ), XACT, LDA, ZERO, B, LDA ) * IF( IFACT.EQ.2 .AND. ITRAN.EQ.1 ) THEN * * --- Test SGTSV --- * * Solve the system using Gaussian elimination with * partial pivoting. * CALL SCOPY( N+2*M, A, 1, AF, 1 ) CALL SLACPY( 'Full', N, NRHS, B, LDA, X, LDA ) * SRNAMT = 'SGTSV ' CALL SGTSV( N, NRHS, AF, AF( M+1 ), AF( N+M+1 ), X, $ LDA, INFO ) * * Check error code from SGTSV . * IF( INFO.NE.IZERO ) $ CALL ALAERH( PATH, 'SGTSV ', INFO, IZERO, ' ', $ N, N, 1, 1, NRHS, IMAT, NFAIL, $ NERRS, NOUT ) NT = 1 IF( IZERO.EQ.0 ) THEN * * Check residual of computed solution. * 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 ) ) * * Check solution from generated exact solution. * CALL SGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC, $ RESULT( 3 ) ) NT = 3 END IF * * Print information about the tests that did not pass * the threshold. * DO 80 K = 2, NT IF( RESULT( K ).GE.THRESH ) THEN IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 ) $ CALL ALADHD( NOUT, PATH ) WRITE( NOUT, FMT = 9999 )'SGTSV ', N, IMAT, $ K, RESULT( K ) NFAIL = NFAIL + 1 END IF 80 CONTINUE NRUN = NRUN + NT - 1 END IF * * --- Test SGTSVX --- * IF( IFACT.GT.1 ) THEN * * Initialize AF to zero. * DO 90 I = 1, 3*N - 2 AF( I ) = ZERO 90 CONTINUE END IF CALL SLASET( 'Full', N, NRHS, ZERO, ZERO, X, LDA ) * * Solve the system and compute the condition number and * error bounds using SGTSVX. * SRNAMT = 'SGTSVX' CALL SGTSVX( FACT, 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, $ RCOND, RWORK, RWORK( NRHS+1 ), WORK, $ IWORK( N+1 ), INFO ) * * Check the error code from SGTSVX. * IF( INFO.NE.IZERO ) $ CALL ALAERH( PATH, 'SGTSVX', INFO, IZERO, $ FACT // TRANS, N, N, 1, 1, NRHS, IMAT, $ NFAIL, NERRS, NOUT ) * IF( IFACT.GE.2 ) THEN * * Reconstruct matrix from factors and compute * residual. * 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 ) ) K1 = 1 ELSE K1 = 2 END IF * IF( INFO.EQ.0 ) THEN TRFCON = .FALSE. * * Check residual of computed solution. * 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 ) ) * * Check solution from generated exact solution. * CALL SGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC, $ RESULT( 3 ) ) * * Check the error bounds from iterative refinement. * CALL SGTT05( TRANS, N, NRHS, A, A( M+1 ), $ A( N+M+1 ), B, LDA, X, LDA, XACT, LDA, $ RWORK, RWORK( NRHS+1 ), RESULT( 4 ) ) NT = 5 END IF * * Print information about the tests that did not pass * the threshold. * DO 100 K = K1, NT IF( RESULT( K ).GE.THRESH ) THEN IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 ) $ CALL ALADHD( NOUT, PATH ) WRITE( NOUT, FMT = 9998 )'SGTSVX', FACT, TRANS, $ N, IMAT, K, RESULT( K ) NFAIL = NFAIL + 1 END IF 100 CONTINUE * * Check the reciprocal of the condition number. * RESULT( 6 ) = SGET06( RCOND, RCONDC ) IF( RESULT( 6 ).GE.THRESH ) THEN IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 ) $ CALL ALADHD( NOUT, PATH ) WRITE( NOUT, FMT = 9998 )'SGTSVX', FACT, TRANS, N, $ IMAT, K, RESULT( K ) NFAIL = NFAIL + 1 END IF NRUN = NRUN + NT - K1 + 2 * 110 CONTINUE 120 CONTINUE 130 CONTINUE 140 CONTINUE * * Print a summary of the results. * CALL ALASVM( PATH, NOUT, NFAIL, NRUN, NERRS ) * 9999 FORMAT( 1X, A, ', N =', I5, ', type ', I2, ', test ', I2, $ ', ratio = ', G12.5 ) 9998 FORMAT( 1X, A, ', FACT=''', A1, ''', TRANS=''', A1, ''', N =', $ I5, ', type ', I2, ', test ', I2, ', ratio = ', G12.5 ) RETURN * * End of SDRVGT * END |