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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief \b ZTBT02 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 ZTBT02( UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB, X, 00012 * LDX, B, LDB, WORK, RWORK, RESID ) 00013 * 00014 * .. Scalar Arguments .. 00015 * CHARACTER DIAG, TRANS, UPLO 00016 * INTEGER KD, LDAB, LDB, LDX, N, NRHS 00017 * DOUBLE PRECISION RESID 00018 * .. 00019 * .. Array Arguments .. 00020 * DOUBLE PRECISION RWORK( * ) 00021 * COMPLEX*16 AB( LDAB, * ), B( LDB, * ), WORK( * ), 00022 * $ X( LDX, * ) 00023 * .. 00024 * 00025 * 00026 *> \par Purpose: 00027 * ============= 00028 *> 00029 *> \verbatim 00030 *> 00031 *> ZTBT02 computes the residual for the computed solution to a 00032 *> triangular system of linear equations A*x = b, A**T *x = b, or 00033 *> A**H *x = b when A is a triangular band matrix. Here A**T denotes 00034 *> the transpose of A, A**H denotes the conjugate transpose of A, and 00035 *> x and b are N by NRHS matrices. The test ratio is the maximum over 00036 *> the number of right hand sides of 00037 *> norm(b - op(A)*x) / ( norm(op(A)) * norm(x) * EPS ), 00038 *> where op(A) denotes A, A**T, or A**H, and EPS is the machine epsilon. 00039 *> \endverbatim 00040 * 00041 * Arguments: 00042 * ========== 00043 * 00044 *> \param[in] UPLO 00045 *> \verbatim 00046 *> UPLO is CHARACTER*1 00047 *> Specifies whether the matrix A is upper or lower triangular. 00048 *> = 'U': Upper triangular 00049 *> = 'L': Lower triangular 00050 *> \endverbatim 00051 *> 00052 *> \param[in] TRANS 00053 *> \verbatim 00054 *> TRANS is CHARACTER*1 00055 *> Specifies the operation applied to A. 00056 *> = 'N': A *x = b (No transpose) 00057 *> = 'T': A**T *x = b (Transpose) 00058 *> = 'C': A**H *x = b (Conjugate transpose) 00059 *> \endverbatim 00060 *> 00061 *> \param[in] DIAG 00062 *> \verbatim 00063 *> DIAG is CHARACTER*1 00064 *> Specifies whether or not the matrix A is unit triangular. 00065 *> = 'N': Non-unit triangular 00066 *> = 'U': Unit triangular 00067 *> \endverbatim 00068 *> 00069 *> \param[in] N 00070 *> \verbatim 00071 *> N is INTEGER 00072 *> The order of the matrix A. N >= 0. 00073 *> \endverbatim 00074 *> 00075 *> \param[in] KD 00076 *> \verbatim 00077 *> KD is INTEGER 00078 *> The number of superdiagonals or subdiagonals of the 00079 *> triangular band matrix A. KD >= 0. 00080 *> \endverbatim 00081 *> 00082 *> \param[in] NRHS 00083 *> \verbatim 00084 *> NRHS is INTEGER 00085 *> The number of right hand sides, i.e., the number of columns 00086 *> of the matrices X and B. NRHS >= 0. 00087 *> \endverbatim 00088 *> 00089 *> \param[in] AB 00090 *> \verbatim 00091 *> AB is COMPLEX*16 array, dimension (LDA,N) 00092 *> The upper or lower triangular band matrix A, stored in the 00093 *> first kd+1 rows of the array. The j-th column of A is stored 00094 *> in the j-th column of the array AB as follows: 00095 *> if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; 00096 *> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd). 00097 *> \endverbatim 00098 *> 00099 *> \param[in] LDAB 00100 *> \verbatim 00101 *> LDAB is INTEGER 00102 *> The leading dimension of the array AB. LDAB >= max(1,KD+1). 00103 *> \endverbatim 00104 *> 00105 *> \param[in] X 00106 *> \verbatim 00107 *> X is COMPLEX*16 array, dimension (LDX,NRHS) 00108 *> The computed solution vectors for the system of linear 00109 *> equations. 00110 *> \endverbatim 00111 *> 00112 *> \param[in] LDX 00113 *> \verbatim 00114 *> LDX is INTEGER 00115 *> The leading dimension of the array X. LDX >= max(1,N). 00116 *> \endverbatim 00117 *> 00118 *> \param[in] B 00119 *> \verbatim 00120 *> B is COMPLEX*16 array, dimension (LDB,NRHS) 00121 *> The right hand side vectors for the system of linear 00122 *> equations. 00123 *> \endverbatim 00124 *> 00125 *> \param[in] LDB 00126 *> \verbatim 00127 *> LDB is INTEGER 00128 *> The leading dimension of the array B. LDB >= max(1,N). 00129 *> \endverbatim 00130 *> 00131 *> \param[out] WORK 00132 *> \verbatim 00133 *> WORK is COMPLEX*16 array, dimension (N) 00134 *> \endverbatim 00135 *> 00136 *> \param[out] RWORK 00137 *> \verbatim 00138 *> RWORK is DOUBLE PRECISION array, dimension (N) 00139 *> \endverbatim 00140 *> 00141 *> \param[out] RESID 00142 *> \verbatim 00143 *> RESID is DOUBLE PRECISION 00144 *> The maximum over the number of right hand sides of 00145 *> norm(op(A)*x - b) / ( norm(op(A)) * norm(x) * EPS ). 00146 *> \endverbatim 00147 * 00148 * Authors: 00149 * ======== 00150 * 00151 *> \author Univ. of Tennessee 00152 *> \author Univ. of California Berkeley 00153 *> \author Univ. of Colorado Denver 00154 *> \author NAG Ltd. 00155 * 00156 *> \date November 2011 00157 * 00158 *> \ingroup complex16_lin 00159 * 00160 * ===================================================================== 00161 SUBROUTINE ZTBT02( UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB, X, 00162 $ LDX, B, LDB, WORK, RWORK, RESID ) 00163 * 00164 * -- LAPACK test routine (version 3.4.0) -- 00165 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00166 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00167 * November 2011 00168 * 00169 * .. Scalar Arguments .. 00170 CHARACTER DIAG, TRANS, UPLO 00171 INTEGER KD, LDAB, LDB, LDX, N, NRHS 00172 DOUBLE PRECISION RESID 00173 * .. 00174 * .. Array Arguments .. 00175 DOUBLE PRECISION RWORK( * ) 00176 COMPLEX*16 AB( LDAB, * ), B( LDB, * ), WORK( * ), 00177 $ X( LDX, * ) 00178 * .. 00179 * 00180 * ===================================================================== 00181 * 00182 * .. Parameters .. 00183 DOUBLE PRECISION ZERO, ONE 00184 PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) 00185 * .. 00186 * .. Local Scalars .. 00187 INTEGER J 00188 DOUBLE PRECISION ANORM, BNORM, EPS, XNORM 00189 * .. 00190 * .. External Functions .. 00191 LOGICAL LSAME 00192 DOUBLE PRECISION DLAMCH, DZASUM, ZLANTB 00193 EXTERNAL LSAME, DLAMCH, DZASUM, ZLANTB 00194 * .. 00195 * .. External Subroutines .. 00196 EXTERNAL ZAXPY, ZCOPY, ZTBMV 00197 * .. 00198 * .. Intrinsic Functions .. 00199 INTRINSIC DCMPLX, MAX 00200 * .. 00201 * .. Executable Statements .. 00202 * 00203 * Quick exit if N = 0 or NRHS = 0 00204 * 00205 IF( N.LE.0 .OR. NRHS.LE.0 ) THEN 00206 RESID = ZERO 00207 RETURN 00208 END IF 00209 * 00210 * Compute the 1-norm of A or A'. 00211 * 00212 IF( LSAME( TRANS, 'N' ) ) THEN 00213 ANORM = ZLANTB( '1', UPLO, DIAG, N, KD, AB, LDAB, RWORK ) 00214 ELSE 00215 ANORM = ZLANTB( 'I', UPLO, DIAG, N, KD, AB, LDAB, RWORK ) 00216 END IF 00217 * 00218 * Exit with RESID = 1/EPS if ANORM = 0. 00219 * 00220 EPS = DLAMCH( 'Epsilon' ) 00221 IF( ANORM.LE.ZERO ) THEN 00222 RESID = ONE / EPS 00223 RETURN 00224 END IF 00225 * 00226 * Compute the maximum over the number of right hand sides of 00227 * norm(op(A)*x - b) / ( norm(op(A)) * norm(x) * EPS ). 00228 * 00229 RESID = ZERO 00230 DO 10 J = 1, NRHS 00231 CALL ZCOPY( N, X( 1, J ), 1, WORK, 1 ) 00232 CALL ZTBMV( UPLO, TRANS, DIAG, N, KD, AB, LDAB, WORK, 1 ) 00233 CALL ZAXPY( N, DCMPLX( -ONE ), B( 1, J ), 1, WORK, 1 ) 00234 BNORM = DZASUM( N, WORK, 1 ) 00235 XNORM = DZASUM( N, X( 1, J ), 1 ) 00236 IF( XNORM.LE.ZERO ) THEN 00237 RESID = ONE / EPS 00238 ELSE 00239 RESID = MAX( RESID, ( ( BNORM / ANORM ) / XNORM ) / EPS ) 00240 END IF 00241 10 CONTINUE 00242 * 00243 RETURN 00244 * 00245 * End of ZTBT02 00246 * 00247 END