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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief \b DGTT02 00002 * 00003 * =========== DOCUMENTATION =========== 00004 * 00005 * Online html documentation available at 00006 * http://www.netlib.org/lapack/explore-html/ 00007 * 00008 * Definition: 00009 * =========== 00010 * 00011 * SUBROUTINE DGTT02( TRANS, N, NRHS, DL, D, DU, X, LDX, B, LDB, 00012 * RESID ) 00013 * 00014 * .. Scalar Arguments .. 00015 * CHARACTER TRANS 00016 * INTEGER LDB, LDX, N, NRHS 00017 * DOUBLE PRECISION RESID 00018 * .. 00019 * .. Array Arguments .. 00020 * DOUBLE PRECISION B( LDB, * ), D( * ), DL( * ), DU( * ), 00021 * $ X( LDX, * ) 00022 * .. 00023 * 00024 * 00025 *> \par Purpose: 00026 * ============= 00027 *> 00028 *> \verbatim 00029 *> 00030 *> DGTT02 computes the residual for the solution to a tridiagonal 00031 *> system of equations: 00032 *> RESID = norm(B - op(A)*X) / (norm(A) * norm(X) * EPS), 00033 *> where EPS is the machine epsilon. 00034 *> \endverbatim 00035 * 00036 * Arguments: 00037 * ========== 00038 * 00039 *> \param[in] TRANS 00040 *> \verbatim 00041 *> TRANS is CHARACTER 00042 *> Specifies the form of the residual. 00043 *> = 'N': B - A * X (No transpose) 00044 *> = 'T': B - A'* X (Transpose) 00045 *> = 'C': B - A'* X (Conjugate transpose = Transpose) 00046 *> \endverbatim 00047 *> 00048 *> \param[in] N 00049 *> \verbatim 00050 *> N is INTEGTER 00051 *> The order of the matrix A. N >= 0. 00052 *> \endverbatim 00053 *> 00054 *> \param[in] NRHS 00055 *> \verbatim 00056 *> NRHS is INTEGER 00057 *> The number of right hand sides, i.e., the number of columns 00058 *> of the matrices B and X. NRHS >= 0. 00059 *> \endverbatim 00060 *> 00061 *> \param[in] DL 00062 *> \verbatim 00063 *> DL is DOUBLE PRECISION array, dimension (N-1) 00064 *> The (n-1) sub-diagonal elements of A. 00065 *> \endverbatim 00066 *> 00067 *> \param[in] D 00068 *> \verbatim 00069 *> D is DOUBLE PRECISION array, dimension (N) 00070 *> The diagonal elements of A. 00071 *> \endverbatim 00072 *> 00073 *> \param[in] DU 00074 *> \verbatim 00075 *> DU is DOUBLE PRECISION array, dimension (N-1) 00076 *> The (n-1) super-diagonal elements of A. 00077 *> \endverbatim 00078 *> 00079 *> \param[in] X 00080 *> \verbatim 00081 *> X is DOUBLE PRECISION array, dimension (LDX,NRHS) 00082 *> The computed solution vectors X. 00083 *> \endverbatim 00084 *> 00085 *> \param[in] LDX 00086 *> \verbatim 00087 *> LDX is INTEGER 00088 *> The leading dimension of the array X. LDX >= max(1,N). 00089 *> \endverbatim 00090 *> 00091 *> \param[in,out] B 00092 *> \verbatim 00093 *> B is DOUBLE PRECISION array, dimension (LDB,NRHS) 00094 *> On entry, the right hand side vectors for the system of 00095 *> linear equations. 00096 *> On exit, B is overwritten with the difference B - op(A)*X. 00097 *> \endverbatim 00098 *> 00099 *> \param[in] LDB 00100 *> \verbatim 00101 *> LDB is INTEGER 00102 *> The leading dimension of the array B. LDB >= max(1,N). 00103 *> \endverbatim 00104 *> 00105 *> \param[out] RESID 00106 *> \verbatim 00107 *> RESID is DOUBLE PRECISION 00108 *> norm(B - op(A)*X) / (norm(A) * norm(X) * EPS) 00109 *> \endverbatim 00110 * 00111 * Authors: 00112 * ======== 00113 * 00114 *> \author Univ. of Tennessee 00115 *> \author Univ. of California Berkeley 00116 *> \author Univ. of Colorado Denver 00117 *> \author NAG Ltd. 00118 * 00119 *> \date November 2011 00120 * 00121 *> \ingroup double_lin 00122 * 00123 * ===================================================================== 00124 SUBROUTINE DGTT02( TRANS, N, NRHS, DL, D, DU, X, LDX, B, LDB, 00125 $ RESID ) 00126 * 00127 * -- LAPACK test routine (version 3.4.0) -- 00128 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00129 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00130 * November 2011 00131 * 00132 * .. Scalar Arguments .. 00133 CHARACTER TRANS 00134 INTEGER LDB, LDX, N, NRHS 00135 DOUBLE PRECISION RESID 00136 * .. 00137 * .. Array Arguments .. 00138 DOUBLE PRECISION B( LDB, * ), D( * ), DL( * ), DU( * ), 00139 $ X( LDX, * ) 00140 * .. 00141 * 00142 * ===================================================================== 00143 * 00144 * .. Parameters .. 00145 DOUBLE PRECISION ONE, ZERO 00146 PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) 00147 * .. 00148 * .. Local Scalars .. 00149 INTEGER J 00150 DOUBLE PRECISION ANORM, BNORM, EPS, XNORM 00151 * .. 00152 * .. External Functions .. 00153 LOGICAL LSAME 00154 DOUBLE PRECISION DASUM, DLAMCH, DLANGT 00155 EXTERNAL LSAME, DASUM, DLAMCH, DLANGT 00156 * .. 00157 * .. External Subroutines .. 00158 EXTERNAL DLAGTM 00159 * .. 00160 * .. Intrinsic Functions .. 00161 INTRINSIC MAX 00162 * .. 00163 * .. Executable Statements .. 00164 * 00165 * Quick exit if N = 0 or NRHS = 0 00166 * 00167 RESID = ZERO 00168 IF( N.LE.0 .OR. NRHS.EQ.0 ) 00169 $ RETURN 00170 * 00171 * Compute the maximum over the number of right hand sides of 00172 * norm(B - op(A)*X) / ( norm(A) * norm(X) * EPS ). 00173 * 00174 IF( LSAME( TRANS, 'N' ) ) THEN 00175 ANORM = DLANGT( '1', N, DL, D, DU ) 00176 ELSE 00177 ANORM = DLANGT( 'I', N, DL, D, DU ) 00178 END IF 00179 * 00180 * Exit with RESID = 1/EPS if ANORM = 0. 00181 * 00182 EPS = DLAMCH( 'Epsilon' ) 00183 IF( ANORM.LE.ZERO ) THEN 00184 RESID = ONE / EPS 00185 RETURN 00186 END IF 00187 * 00188 * Compute B - op(A)*X. 00189 * 00190 CALL DLAGTM( TRANS, N, NRHS, -ONE, DL, D, DU, X, LDX, ONE, B, 00191 $ LDB ) 00192 * 00193 DO 10 J = 1, NRHS 00194 BNORM = DASUM( N, B( 1, J ), 1 ) 00195 XNORM = DASUM( N, X( 1, J ), 1 ) 00196 IF( XNORM.LE.ZERO ) THEN 00197 RESID = ONE / EPS 00198 ELSE 00199 RESID = MAX( RESID, ( ( BNORM / ANORM ) / XNORM ) / EPS ) 00200 END IF 00201 10 CONTINUE 00202 * 00203 RETURN 00204 * 00205 * End of DGTT02 00206 * 00207 END