LAPACK 3.3.1 Linear Algebra PACKage

# ctbt02.f

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```00001       SUBROUTINE CTBT02( UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB, X,
00002      \$                   LDX, B, LDB, WORK, 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          DIAG, TRANS, UPLO
00010       INTEGER            KD, LDAB, LDB, LDX, N, NRHS
00011       REAL               RESID
00012 *     ..
00013 *     .. Array Arguments ..
00014       REAL               RWORK( * )
00015       COMPLEX            AB( LDAB, * ), B( LDB, * ), WORK( * ),
00016      \$                   X( LDX, * )
00017 *     ..
00018 *
00019 *  Purpose
00020 *  =======
00021 *
00022 *  CTBT02 computes the residual for the computed solution to a
00023 *  triangular system of linear equations  A*x = b,  A**T *x = b,  or
00024 *  A**H *x = b  when A is a triangular band matrix.  Here A**T denotes
00025 *  the transpose of A, A**H denotes the conjugate transpose of A, and
00026 *  x and b are N by NRHS matrices.  The test ratio is the maximum over
00027 *  the number of right hand sides of
00028 *     norm(b - op(A)*x) / ( norm(op(A)) * norm(x) * EPS ),
00029 *  where op(A) denotes A, A**T, or A**H, and EPS is the machine epsilon.
00030 *
00031 *  Arguments
00032 *  =========
00033 *
00034 *  UPLO    (input) CHARACTER*1
00035 *          Specifies whether the matrix A is upper or lower triangular.
00036 *          = 'U':  Upper triangular
00037 *          = 'L':  Lower triangular
00038 *
00039 *  TRANS   (input) CHARACTER*1
00040 *          Specifies the operation applied to A.
00041 *          = 'N':  A *x = b     (No transpose)
00042 *          = 'T':  A**T *x = b  (Transpose)
00043 *          = 'C':  A**H *x = b  (Conjugate transpose)
00044 *
00045 *  DIAG    (input) CHARACTER*1
00046 *          Specifies whether or not the matrix A is unit triangular.
00047 *          = 'N':  Non-unit triangular
00048 *          = 'U':  Unit triangular
00049 *
00050 *  N       (input) INTEGER
00051 *          The order of the matrix A.  N >= 0.
00052 *
00053 *  KD      (input) INTEGER
00054 *          The number of superdiagonals or subdiagonals of the
00055 *          triangular band matrix A.  KD >= 0.
00056 *
00057 *  NRHS    (input) INTEGER
00058 *          The number of right hand sides, i.e., the number of columns
00059 *          of the matrices X and B.  NRHS >= 0.
00060 *
00061 *  AB      (input) COMPLEX array, dimension (LDA,N)
00062 *          The upper or lower triangular band matrix A, stored in the
00063 *          first kd+1 rows of the array. The j-th column of A is stored
00064 *          in the j-th column of the array AB as follows:
00065 *          if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
00066 *          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).
00067 *
00068 *  LDAB    (input) INTEGER
00069 *          The leading dimension of the array AB.  LDAB >= max(1,KD+1).
00070 *
00071 *  X       (input) COMPLEX array, dimension (LDX,NRHS)
00072 *          The computed solution vectors for the system of linear
00073 *          equations.
00074 *
00075 *  LDX     (input) INTEGER
00076 *          The leading dimension of the array X.  LDX >= max(1,N).
00077 *
00078 *  B       (input) COMPLEX array, dimension (LDB,NRHS)
00079 *          The right hand side vectors for the system of linear
00080 *          equations.
00081 *
00082 *  LDB     (input) INTEGER
00083 *          The leading dimension of the array B.  LDB >= max(1,N).
00084 *
00085 *  WORK    (workspace) COMPLEX array, dimension (N)
00086 *
00087 *  RWORK   (workspace) REAL array, dimension (N)
00088 *
00089 *  RESID   (output) REAL
00090 *          The maximum over the number of right hand sides of
00091 *          norm(op(A)*x - b) / ( norm(op(A)) * norm(x) * EPS ).
00092 *
00093 *  =====================================================================
00094 *
00095 *     .. Parameters ..
00096       REAL               ZERO, ONE
00097       PARAMETER          ( ZERO = 0.0E+0, ONE = 1.0E+0 )
00098 *     ..
00099 *     .. Local Scalars ..
00100       INTEGER            J
00101       REAL               ANORM, BNORM, EPS, XNORM
00102 *     ..
00103 *     .. External Functions ..
00104       LOGICAL            LSAME
00105       REAL               CLANTB, SCASUM, SLAMCH
00106       EXTERNAL           LSAME, CLANTB, SCASUM, SLAMCH
00107 *     ..
00108 *     .. External Subroutines ..
00109       EXTERNAL           CAXPY, CCOPY, CTBMV
00110 *     ..
00111 *     .. Intrinsic Functions ..
00112       INTRINSIC          CMPLX, MAX
00113 *     ..
00114 *     .. Executable Statements ..
00115 *
00116 *     Quick exit if N = 0 or NRHS = 0
00117 *
00118       IF( N.LE.0 .OR. NRHS.LE.0 ) THEN
00119          RESID = ZERO
00120          RETURN
00121       END IF
00122 *
00123 *     Compute the 1-norm of A or A'.
00124 *
00125       IF( LSAME( TRANS, 'N' ) ) THEN
00126          ANORM = CLANTB( '1', UPLO, DIAG, N, KD, AB, LDAB, RWORK )
00127       ELSE
00128          ANORM = CLANTB( 'I', UPLO, DIAG, N, KD, AB, LDAB, RWORK )
00129       END IF
00130 *
00131 *     Exit with RESID = 1/EPS if ANORM = 0.
00132 *
00133       EPS = SLAMCH( 'Epsilon' )
00134       IF( ANORM.LE.ZERO ) THEN
00135          RESID = ONE / EPS
00136          RETURN
00137       END IF
00138 *
00139 *     Compute the maximum over the number of right hand sides of
00140 *        norm(op(A)*x - b) / ( norm(op(A)) * norm(x) * EPS ).
00141 *
00142       RESID = ZERO
00143       DO 10 J = 1, NRHS
00144          CALL CCOPY( N, X( 1, J ), 1, WORK, 1 )
00145          CALL CTBMV( UPLO, TRANS, DIAG, N, KD, AB, LDAB, WORK, 1 )
00146          CALL CAXPY( N, CMPLX( -ONE ), B( 1, J ), 1, WORK, 1 )
00147          BNORM = SCASUM( N, WORK, 1 )
00148          XNORM = SCASUM( N, X( 1, J ), 1 )
00149          IF( XNORM.LE.ZERO ) THEN
00150             RESID = ONE / EPS
00151          ELSE
00152             RESID = MAX( RESID, ( ( BNORM / ANORM ) / XNORM ) / EPS )
00153          END IF
00154    10 CONTINUE
00155 *
00156       RETURN
00157 *
00158 *     End of CTBT02
00159 *
00160       END
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