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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief \b SPBT02 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 SPBT02( UPLO, N, KD, NRHS, A, LDA, X, LDX, B, LDB, 00012 * RWORK, RESID ) 00013 * 00014 * .. Scalar Arguments .. 00015 * CHARACTER UPLO 00016 * INTEGER KD, LDA, LDB, LDX, N, NRHS 00017 * REAL RESID 00018 * .. 00019 * .. Array Arguments .. 00020 * REAL A( LDA, * ), B( LDB, * ), RWORK( * ), 00021 * $ X( LDX, * ) 00022 * .. 00023 * 00024 * 00025 *> \par Purpose: 00026 * ============= 00027 *> 00028 *> \verbatim 00029 *> 00030 *> SPBT02 computes the residual for a solution of a symmetric banded 00031 *> system of equations A*x = b: 00032 *> RESID = norm( B - A*X ) / ( norm(A) * norm(X) * EPS) 00033 *> where EPS is the machine precision. 00034 *> \endverbatim 00035 * 00036 * Arguments: 00037 * ========== 00038 * 00039 *> \param[in] UPLO 00040 *> \verbatim 00041 *> UPLO is CHARACTER*1 00042 *> Specifies whether the upper or lower triangular part of the 00043 *> symmetric matrix A is stored: 00044 *> = 'U': Upper triangular 00045 *> = 'L': Lower triangular 00046 *> \endverbatim 00047 *> 00048 *> \param[in] N 00049 *> \verbatim 00050 *> N is INTEGER 00051 *> The number of rows and columns of the matrix A. N >= 0. 00052 *> \endverbatim 00053 *> 00054 *> \param[in] KD 00055 *> \verbatim 00056 *> KD is INTEGER 00057 *> The number of super-diagonals of the matrix A if UPLO = 'U', 00058 *> or the number of sub-diagonals if UPLO = 'L'. KD >= 0. 00059 *> \endverbatim 00060 *> 00061 *> \param[in] NRHS 00062 *> \verbatim 00063 *> NRHS is INTEGER 00064 *> The number of right hand sides. NRHS >= 0. 00065 *> \endverbatim 00066 *> 00067 *> \param[in] A 00068 *> \verbatim 00069 *> A is REAL array, dimension (LDA,N) 00070 *> The original symmetric band matrix A. If UPLO = 'U', the 00071 *> upper triangular part of A is stored as a band matrix; if 00072 *> UPLO = 'L', the lower triangular part of A is stored. The 00073 *> columns of the appropriate triangle are stored in the columns 00074 *> of A and the diagonals of the triangle are stored in the rows 00075 *> of A. See SPBTRF for further details. 00076 *> \endverbatim 00077 *> 00078 *> \param[in] LDA 00079 *> \verbatim 00080 *> LDA is INTEGER. 00081 *> The leading dimension of the array A. LDA >= max(1,KD+1). 00082 *> \endverbatim 00083 *> 00084 *> \param[in] X 00085 *> \verbatim 00086 *> X is REAL array, dimension (LDX,NRHS) 00087 *> The computed solution vectors for the system of linear 00088 *> equations. 00089 *> \endverbatim 00090 *> 00091 *> \param[in] LDX 00092 *> \verbatim 00093 *> LDX is INTEGER 00094 *> The leading dimension of the array X. LDX >= max(1,N). 00095 *> \endverbatim 00096 *> 00097 *> \param[in,out] B 00098 *> \verbatim 00099 *> B is REAL array, dimension (LDB,NRHS) 00100 *> On entry, the right hand side vectors for the system of 00101 *> linear equations. 00102 *> On exit, B is overwritten with the difference B - A*X. 00103 *> \endverbatim 00104 *> 00105 *> \param[in] LDB 00106 *> \verbatim 00107 *> LDB is INTEGER 00108 *> The leading dimension of the array B. LDB >= max(1,N). 00109 *> \endverbatim 00110 *> 00111 *> \param[out] RWORK 00112 *> \verbatim 00113 *> RWORK is REAL array, dimension (N) 00114 *> \endverbatim 00115 *> 00116 *> \param[out] RESID 00117 *> \verbatim 00118 *> RESID is REAL 00119 *> The maximum over the number of right hand sides of 00120 *> norm(B - A*X) / ( norm(A) * norm(X) * EPS ). 00121 *> \endverbatim 00122 * 00123 * Authors: 00124 * ======== 00125 * 00126 *> \author Univ. of Tennessee 00127 *> \author Univ. of California Berkeley 00128 *> \author Univ. of Colorado Denver 00129 *> \author NAG Ltd. 00130 * 00131 *> \date November 2011 00132 * 00133 *> \ingroup single_lin 00134 * 00135 * ===================================================================== 00136 SUBROUTINE SPBT02( UPLO, N, KD, NRHS, A, LDA, X, LDX, B, LDB, 00137 $ RWORK, RESID ) 00138 * 00139 * -- LAPACK test routine (version 3.4.0) -- 00140 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00141 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00142 * November 2011 00143 * 00144 * .. Scalar Arguments .. 00145 CHARACTER UPLO 00146 INTEGER KD, LDA, LDB, LDX, N, NRHS 00147 REAL RESID 00148 * .. 00149 * .. Array Arguments .. 00150 REAL A( LDA, * ), B( LDB, * ), RWORK( * ), 00151 $ X( LDX, * ) 00152 * .. 00153 * 00154 * ===================================================================== 00155 * 00156 * .. Parameters .. 00157 REAL ZERO, ONE 00158 PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 ) 00159 * .. 00160 * .. Local Scalars .. 00161 INTEGER J 00162 REAL ANORM, BNORM, EPS, XNORM 00163 * .. 00164 * .. External Functions .. 00165 REAL SASUM, SLAMCH, SLANSB 00166 EXTERNAL SASUM, SLAMCH, SLANSB 00167 * .. 00168 * .. External Subroutines .. 00169 EXTERNAL SSBMV 00170 * .. 00171 * .. Intrinsic Functions .. 00172 INTRINSIC MAX 00173 * .. 00174 * .. Executable Statements .. 00175 * 00176 * Quick exit if N = 0 or NRHS = 0. 00177 * 00178 IF( N.LE.0 .OR. NRHS.LE.0 ) THEN 00179 RESID = ZERO 00180 RETURN 00181 END IF 00182 * 00183 * Exit with RESID = 1/EPS if ANORM = 0. 00184 * 00185 EPS = SLAMCH( 'Epsilon' ) 00186 ANORM = SLANSB( '1', UPLO, N, KD, A, LDA, RWORK ) 00187 IF( ANORM.LE.ZERO ) THEN 00188 RESID = ONE / EPS 00189 RETURN 00190 END IF 00191 * 00192 * Compute B - A*X 00193 * 00194 DO 10 J = 1, NRHS 00195 CALL SSBMV( UPLO, N, KD, -ONE, A, LDA, X( 1, J ), 1, ONE, 00196 $ B( 1, J ), 1 ) 00197 10 CONTINUE 00198 * 00199 * Compute the maximum over the number of right hand sides of 00200 * norm( B - A*X ) / ( norm(A) * norm(X) * EPS ) 00201 * 00202 RESID = ZERO 00203 DO 20 J = 1, NRHS 00204 BNORM = SASUM( N, B( 1, J ), 1 ) 00205 XNORM = SASUM( N, X( 1, J ), 1 ) 00206 IF( XNORM.LE.ZERO ) THEN 00207 RESID = ONE / EPS 00208 ELSE 00209 RESID = MAX( RESID, ( ( BNORM / ANORM ) / XNORM ) / EPS ) 00210 END IF 00211 20 CONTINUE 00212 * 00213 RETURN 00214 * 00215 * End of SPBT02 00216 * 00217 END