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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief \b SGBT02 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 SGBT02( TRANS, M, N, KL, KU, NRHS, A, LDA, X, LDX, B, 00012 * LDB, RESID ) 00013 * 00014 * .. Scalar Arguments .. 00015 * CHARACTER TRANS 00016 * INTEGER KL, KU, LDA, LDB, LDX, M, N, NRHS 00017 * REAL RESID 00018 * .. 00019 * .. Array Arguments .. 00020 * REAL A( LDA, * ), B( LDB, * ), X( LDX, * ) 00021 * .. 00022 * 00023 * 00024 *> \par Purpose: 00025 * ============= 00026 *> 00027 *> \verbatim 00028 *> 00029 *> SGBT02 computes the residual for a solution of a banded system of 00030 *> equations A*x = b or A'*x = b: 00031 *> RESID = norm( B - A*X ) / ( norm(A) * norm(X) * EPS). 00032 *> where EPS is the machine precision. 00033 *> \endverbatim 00034 * 00035 * Arguments: 00036 * ========== 00037 * 00038 *> \param[in] TRANS 00039 *> \verbatim 00040 *> TRANS is CHARACTER*1 00041 *> Specifies the form of the system of equations: 00042 *> = 'N': A *x = b 00043 *> = 'T': A'*x = b, where A' is the transpose of A 00044 *> = 'C': A'*x = b, where A' is the transpose of A 00045 *> \endverbatim 00046 *> 00047 *> \param[in] M 00048 *> \verbatim 00049 *> M is INTEGER 00050 *> The number of rows of the matrix A. M >= 0. 00051 *> \endverbatim 00052 *> 00053 *> \param[in] N 00054 *> \verbatim 00055 *> N is INTEGER 00056 *> The number of columns of the matrix A. N >= 0. 00057 *> \endverbatim 00058 *> 00059 *> \param[in] KL 00060 *> \verbatim 00061 *> KL is INTEGER 00062 *> The number of subdiagonals within the band of A. KL >= 0. 00063 *> \endverbatim 00064 *> 00065 *> \param[in] KU 00066 *> \verbatim 00067 *> KU is INTEGER 00068 *> The number of superdiagonals within the band of A. KU >= 0. 00069 *> \endverbatim 00070 *> 00071 *> \param[in] NRHS 00072 *> \verbatim 00073 *> NRHS is INTEGER 00074 *> The number of columns of B. NRHS >= 0. 00075 *> \endverbatim 00076 *> 00077 *> \param[in] A 00078 *> \verbatim 00079 *> A is REAL array, dimension (LDA,N) 00080 *> The original matrix A in band storage, stored in rows 1 to 00081 *> KL+KU+1. 00082 *> \endverbatim 00083 *> 00084 *> \param[in] LDA 00085 *> \verbatim 00086 *> LDA is INTEGER 00087 *> The leading dimension of the array A. LDA >= max(1,KL+KU+1). 00088 *> \endverbatim 00089 *> 00090 *> \param[in] X 00091 *> \verbatim 00092 *> X is REAL array, dimension (LDX,NRHS) 00093 *> The computed solution vectors for the system of linear 00094 *> equations. 00095 *> \endverbatim 00096 *> 00097 *> \param[in] LDX 00098 *> \verbatim 00099 *> LDX is INTEGER 00100 *> The leading dimension of the array X. If TRANS = 'N', 00101 *> LDX >= max(1,N); if TRANS = 'T' or 'C', LDX >= max(1,M). 00102 *> \endverbatim 00103 *> 00104 *> \param[in,out] B 00105 *> \verbatim 00106 *> B is REAL array, dimension (LDB,NRHS) 00107 *> On entry, the right hand side vectors for the system of 00108 *> linear equations. 00109 *> On exit, B is overwritten with the difference B - A*X. 00110 *> \endverbatim 00111 *> 00112 *> \param[in] LDB 00113 *> \verbatim 00114 *> LDB is INTEGER 00115 *> The leading dimension of the array B. IF TRANS = 'N', 00116 *> LDB >= max(1,M); if TRANS = 'T' or 'C', LDB >= max(1,N). 00117 *> \endverbatim 00118 *> 00119 *> \param[out] RESID 00120 *> \verbatim 00121 *> RESID is REAL 00122 *> The maximum over the number of right hand sides of 00123 *> norm(B - A*X) / ( norm(A) * norm(X) * EPS ). 00124 *> \endverbatim 00125 * 00126 * Authors: 00127 * ======== 00128 * 00129 *> \author Univ. of Tennessee 00130 *> \author Univ. of California Berkeley 00131 *> \author Univ. of Colorado Denver 00132 *> \author NAG Ltd. 00133 * 00134 *> \date November 2011 00135 * 00136 *> \ingroup single_lin 00137 * 00138 * ===================================================================== 00139 SUBROUTINE SGBT02( TRANS, M, N, KL, KU, NRHS, A, LDA, X, LDX, B, 00140 $ LDB, RESID ) 00141 * 00142 * -- LAPACK test routine (version 3.4.0) -- 00143 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00144 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00145 * November 2011 00146 * 00147 * .. Scalar Arguments .. 00148 CHARACTER TRANS 00149 INTEGER KL, KU, LDA, LDB, LDX, M, N, NRHS 00150 REAL RESID 00151 * .. 00152 * .. Array Arguments .. 00153 REAL A( LDA, * ), B( LDB, * ), X( LDX, * ) 00154 * .. 00155 * 00156 * ===================================================================== 00157 * 00158 * .. Parameters .. 00159 REAL ZERO, ONE 00160 PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 ) 00161 * .. 00162 * .. Local Scalars .. 00163 INTEGER I1, I2, J, KD, N1 00164 REAL ANORM, BNORM, EPS, XNORM 00165 * .. 00166 * .. External Functions .. 00167 LOGICAL LSAME 00168 REAL SASUM, SLAMCH 00169 EXTERNAL LSAME, SASUM, SLAMCH 00170 * .. 00171 * .. External Subroutines .. 00172 EXTERNAL SGBMV 00173 * .. 00174 * .. Intrinsic Functions .. 00175 INTRINSIC MAX, MIN 00176 * .. 00177 * .. Executable Statements .. 00178 * 00179 * Quick return if N = 0 pr NRHS = 0 00180 * 00181 IF( M.LE.0 .OR. N.LE.0 .OR. NRHS.LE.0 ) THEN 00182 RESID = ZERO 00183 RETURN 00184 END IF 00185 * 00186 * Exit with RESID = 1/EPS if ANORM = 0. 00187 * 00188 EPS = SLAMCH( 'Epsilon' ) 00189 KD = KU + 1 00190 ANORM = ZERO 00191 DO 10 J = 1, N 00192 I1 = MAX( KD+1-J, 1 ) 00193 I2 = MIN( KD+M-J, KL+KD ) 00194 ANORM = MAX( ANORM, SASUM( I2-I1+1, A( I1, J ), 1 ) ) 00195 10 CONTINUE 00196 IF( ANORM.LE.ZERO ) THEN 00197 RESID = ONE / EPS 00198 RETURN 00199 END IF 00200 * 00201 IF( LSAME( TRANS, 'T' ) .OR. LSAME( TRANS, 'C' ) ) THEN 00202 N1 = N 00203 ELSE 00204 N1 = M 00205 END IF 00206 * 00207 * Compute B - A*X (or B - A'*X ) 00208 * 00209 DO 20 J = 1, NRHS 00210 CALL SGBMV( TRANS, M, N, KL, KU, -ONE, A, LDA, X( 1, J ), 1, 00211 $ ONE, B( 1, J ), 1 ) 00212 20 CONTINUE 00213 * 00214 * Compute the maximum over the number of right hand sides of 00215 * norm(B - A*X) / ( norm(A) * norm(X) * EPS ). 00216 * 00217 RESID = ZERO 00218 DO 30 J = 1, NRHS 00219 BNORM = SASUM( N1, B( 1, J ), 1 ) 00220 XNORM = SASUM( N1, X( 1, J ), 1 ) 00221 IF( XNORM.LE.ZERO ) THEN 00222 RESID = ONE / EPS 00223 ELSE 00224 RESID = MAX( RESID, ( ( BNORM / ANORM ) / XNORM ) / EPS ) 00225 END IF 00226 30 CONTINUE 00227 * 00228 RETURN 00229 * 00230 * End of SGBT02 00231 * 00232 END