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PROGRAM TEST
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IMPLICIT NONE
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C
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INTEGER LDA, LDB, LDIWRK, LDWORK, LDX, N, NRHS
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INTEGER NDIAG
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PARAMETER (N = 4)
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PARAMETER (NDIAG = 1)
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PARAMETER (LDA = NDIAG + 1)
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PARAMETER (LDB = N)
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PARAMETER (LDIWRK = N)
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PARAMETER (LDWORK = 3 * N)
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PARAMETER (LDX = N)
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PARAMETER (NRHS = 1)
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C
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DOUBLE PRECISION A(LDA,N), B(LDB,NRHS), B1(LDB,NRHS)
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DOUBLE PRECISION BERR(NRHS), EPSLON, FERR(NRHS)
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DOUBLE PRECISION WORK(LDWORK), X(LDX,NRHS)
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INTEGER ICOL, INFO, IROW, IWORK(LDIWRK)
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C
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EXTERNAL DCOPY, DTBMV, DTBRFS, DTBTRS
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INTRINSIC MAX, SQRT
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C
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C Initialize the array A to store in banded form the matrix A
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C shown below. Initialize the array B to store the right hand
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C side vector b shown below.
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C
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C 0 3
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C A = 9 0 b = 5
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C 0.25 5 7
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C 7 0 11
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C
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DATA A / 0.0D0, 9.0D0, 0.0D0, 2.5D-1, 5.0D0, 7.0D0, 0.0D0,
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$ 8D8 /
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DATA B / 3.0D0, 5.0D0, 7.0D0, 1.1D1 /
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C
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C Add a small value to the elements of A on the diagonal
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C and on the subdiagonal. After this loop, A will contain
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C something similar to:
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C
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C e
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C A = 9+e e
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C 0.25+e 5+e
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C e 7+e
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C
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EPSLON = ((((2.0D0 / 3.0D0) + 2.0D0) - 2.0D0) -
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$ (2.0D0 / 3.0D0))
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DO 110, ICOL = 1, N
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DO 100, IROW = 1, NDIAG + 1
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A(IROW,ICOL) = A(IROW,ICOL) + EPSLON
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A(1,ICOL) = A(1,ICOL) + EPSLON
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100 CONTINUE
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110 CONTINUE
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A(LDA,N) = SQRT(-1.0D0)
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C
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C Print the A array.
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C
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PRINT 1000
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DO 120, IROW = 1, N
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PRINT 1010, (0.0D0, ICOL = 1, IROW - NDIAG - 1),
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$ (A(1 + IROW - ICOL, ICOL),
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$ ICOL = MAX(1,IROW - NDIAG), IROW),
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$ (0.0D0, ICOL = IROW + 1, N)
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120 CONTINUE
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PRINT 1020
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PRINT 1010, ((A(IROW,ICOL), ICOL = 1, N), IROW = 1, LDA)
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C
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C Make a copy of B and then print B.
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C
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CALL DCOPY (N, B, 1, X, 1)
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PRINT 1030
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PRINT 1040, B
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C
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C Solve Ax=b and print the solution.
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C
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CALL DTBTRS ('LOWER TRIANGULAR A', 'NO TRANSPOSE A',
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$ 'NOT UNIT DIAGONAL A', N, NDIAG, NRHS, A,
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$ LDA, X, LDX, INFO)
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IF (INFO .NE. 0) THEN
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PRINT 1060, INFO
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STOP 2
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END IF
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PRINT 1070
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PRINT 1080, X
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CALL DCOPY (N, X, 1, B1, 1)
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CALL DTBMV ('LOWER TRIANGULAR A', 'NO TRANSPOSE A',
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$ 'NOT UNIT DIAGONAL A', N, NDIAG, A, LDA, B1, 1)
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PRINT 1090
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PRINT 1040, B1
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C
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C Refine the initial solution and print the new solution.
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C
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CALL DTBRFS ('LOWER TRIANGULAR A', 'NO TRANSPOSE A',
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$ 'NOT UNIT TRIANGULAR A', N, NDIAG, NRHS,
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$ A, LDA, B, LDB, X, LDX, FERR, BERR, WORK,
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$ IWORK, INFO)
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IF (INFO .EQ. 0) THEN
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PRINT 1100, (IROW, BERR(IROW), IROW = 1, NRHS)
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PRINT 1110, (IROW, FERR(IROW), IROW = 1, NRHS)
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ELSE
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PRINT 1120, INFO
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STOP 3
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END IF
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C
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1000 FORMAT (1X, 'A in full form:')
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1010 FORMAT (4(2X, E14.8))
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1020 FORMAT (/1X, 'A in banded form: ("NaN" in unused elements)')
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1030 FORMAT (/1X, 'b:')
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1040 FORMAT (1X, F20.17)
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1050 FORMAT (1X, 'Error factoring A in DGBTRF, INFO = ', I5)
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1060 FORMAT (1X, 'Error solving Ax=b in DGBTRF, INFO = ', I5)
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1070 FORMAT (/1X, 'Initial solution for Ax=b:')
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1080 FORMAT (1X, E22.16)
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1090 FORMAT (/1X, 'Ax with initial x:')
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1110 FORMAT (/1X, 'Backward error bound for system #', I2, ' =',
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$ E15.8)
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1100 FORMAT (1X, 'Forward error bound for system #', I2, ' = ',
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$ E15.8)
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1120 FORMAT (1X, 'Error estimating error bounds, INFO = ', I5)
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C
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END
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