LAPACK 3.3.1 Linear Algebra PACKage

# dpbt02.f

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```00001       SUBROUTINE DPBT02( UPLO, N, KD, NRHS, A, LDA, X, LDX, B, LDB,
00002      \$                   RWORK, RESID )
00003 *
00004 *  -- LAPACK test routine (version 3.1) --
00005 *     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
00006 *     November 2006
00007 *
00008 *     .. Scalar Arguments ..
00009       CHARACTER          UPLO
00010       INTEGER            KD, LDA, LDB, LDX, N, NRHS
00011       DOUBLE PRECISION   RESID
00012 *     ..
00013 *     .. Array Arguments ..
00014       DOUBLE PRECISION   A( LDA, * ), B( LDB, * ), RWORK( * ),
00015      \$                   X( LDX, * )
00016 *     ..
00017 *
00018 *  Purpose
00019 *  =======
00020 *
00021 *  DPBT02 computes the residual for a solution of a symmetric banded
00022 *  system of equations  A*x = b:
00023 *     RESID = norm( B - A*X ) / ( norm(A) * norm(X) * EPS)
00024 *  where EPS is the machine precision.
00025 *
00026 *  Arguments
00027 *  =========
00028 *
00029 *  UPLO    (input) CHARACTER*1
00030 *          Specifies whether the upper or lower triangular part of the
00031 *          symmetric matrix A is stored:
00032 *          = 'U':  Upper triangular
00033 *          = 'L':  Lower triangular
00034 *
00035 *  N       (input) INTEGER
00036 *          The number of rows and columns of the matrix A.  N >= 0.
00037 *
00038 *  KD      (input) INTEGER
00039 *          The number of super-diagonals of the matrix A if UPLO = 'U',
00040 *          or the number of sub-diagonals if UPLO = 'L'.  KD >= 0.
00041 *
00042 *  A       (input) DOUBLE PRECISION array, dimension (LDA,N)
00043 *          The original symmetric band matrix A.  If UPLO = 'U', the
00044 *          upper triangular part of A is stored as a band matrix; if
00045 *          UPLO = 'L', the lower triangular part of A is stored.  The
00046 *          columns of the appropriate triangle are stored in the columns
00047 *          of A and the diagonals of the triangle are stored in the rows
00048 *          of A.  See DPBTRF for further details.
00049 *
00050 *  LDA     (input) INTEGER.
00051 *          The leading dimension of the array A.  LDA >= max(1,KD+1).
00052 *
00053 *  X       (input) DOUBLE PRECISION array, dimension (LDX,NRHS)
00054 *          The computed solution vectors for the system of linear
00055 *          equations.
00056 *
00057 *  LDX     (input) INTEGER
00058 *          The leading dimension of the array X.   LDX >= max(1,N).
00059 *
00060 *  B       (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS)
00061 *          On entry, the right hand side vectors for the system of
00062 *          linear equations.
00063 *          On exit, B is overwritten with the difference B - A*X.
00064 *
00065 *  LDB     (input) INTEGER
00066 *          The leading dimension of the array B.  LDB >= max(1,N).
00067 *
00068 *  RWORK   (workspace) DOUBLE PRECISION array, dimension (N)
00069 *
00070 *  RESID   (output) DOUBLE PRECISION
00071 *          The maximum over the number of right hand sides of
00072 *          norm(B - A*X) / ( norm(A) * norm(X) * EPS ).
00073 *
00074 *  =====================================================================
00075 *
00076 *     .. Parameters ..
00077       DOUBLE PRECISION   ZERO, ONE
00078       PARAMETER          ( ZERO = 0.0D+0, ONE = 1.0D+0 )
00079 *     ..
00080 *     .. Local Scalars ..
00081       INTEGER            J
00082       DOUBLE PRECISION   ANORM, BNORM, EPS, XNORM
00083 *     ..
00084 *     .. External Functions ..
00085       DOUBLE PRECISION   DASUM, DLAMCH, DLANSB
00086       EXTERNAL           DASUM, DLAMCH, DLANSB
00087 *     ..
00088 *     .. External Subroutines ..
00089       EXTERNAL           DSBMV
00090 *     ..
00091 *     .. Intrinsic Functions ..
00092       INTRINSIC          MAX
00093 *     ..
00094 *     .. Executable Statements ..
00095 *
00096 *     Quick exit if N = 0 or NRHS = 0.
00097 *
00098       IF( N.LE.0 .OR. NRHS.LE.0 ) THEN
00099          RESID = ZERO
00100          RETURN
00101       END IF
00102 *
00103 *     Exit with RESID = 1/EPS if ANORM = 0.
00104 *
00105       EPS = DLAMCH( 'Epsilon' )
00106       ANORM = DLANSB( '1', UPLO, N, KD, A, LDA, RWORK )
00107       IF( ANORM.LE.ZERO ) THEN
00108          RESID = ONE / EPS
00109          RETURN
00110       END IF
00111 *
00112 *     Compute  B - A*X
00113 *
00114       DO 10 J = 1, NRHS
00115          CALL DSBMV( UPLO, N, KD, -ONE, A, LDA, X( 1, J ), 1, ONE,
00116      \$               B( 1, J ), 1 )
00117    10 CONTINUE
00118 *
00119 *     Compute the maximum over the number of right hand sides of
00120 *          norm( B - A*X ) / ( norm(A) * norm(X) * EPS )
00121 *
00122       RESID = ZERO
00123       DO 20 J = 1, NRHS
00124          BNORM = DASUM( N, B( 1, J ), 1 )
00125          XNORM = DASUM( N, X( 1, J ), 1 )
00126          IF( XNORM.LE.ZERO ) THEN
00127             RESID = ONE / EPS
00128          ELSE
00129             RESID = MAX( RESID, ( ( BNORM / ANORM ) / XNORM ) / EPS )
00130          END IF
00131    20 CONTINUE
00132 *
00133       RETURN
00134 *
00135 *     End of DPBT02
00136 *
00137       END
```