1*> \brief \b DTPT02 2* 3* =========== DOCUMENTATION =========== 4* 5* Online html documentation available at 6* http://www.netlib.org/lapack/explore-html/ 7* 8* Definition: 9* =========== 10* 11* SUBROUTINE DTPT02( UPLO, TRANS, DIAG, N, NRHS, AP, X, LDX, B, LDB, 12* WORK, RESID ) 13* 14* .. Scalar Arguments .. 15* CHARACTER DIAG, TRANS, UPLO 16* INTEGER LDB, LDX, N, NRHS 17* DOUBLE PRECISION RESID 18* .. 19* .. Array Arguments .. 20* DOUBLE PRECISION AP( * ), B( LDB, * ), WORK( * ), X( LDX, * ) 21* .. 22* 23* 24*> \par Purpose: 25* ============= 26*> 27*> \verbatim 28*> 29*> DTPT02 computes the residual for the computed solution to a 30*> triangular system of linear equations A*x = b or A'*x = b when 31*> the triangular matrix A is stored in packed format. Here A' is the 32*> transpose of A and x and b are N by NRHS matrices. The test ratio is 33*> the maximum over the number of right hand sides of 34*> norm(b - op(A)*x) / ( norm(op(A)) * norm(x) * EPS ), 35*> where op(A) denotes A or A' and EPS is the machine epsilon. 36*> The norm used is the 1-norm. 37*> \endverbatim 38* 39* Arguments: 40* ========== 41* 42*> \param[in] UPLO 43*> \verbatim 44*> UPLO is CHARACTER*1 45*> Specifies whether the matrix A is upper or lower triangular. 46*> = 'U': Upper triangular 47*> = 'L': Lower triangular 48*> \endverbatim 49*> 50*> \param[in] TRANS 51*> \verbatim 52*> TRANS is CHARACTER*1 53*> Specifies the operation applied to A. 54*> = 'N': A *x = b (No transpose) 55*> = 'T': A'*x = b (Transpose) 56*> = 'C': A'*x = b (Conjugate transpose = Transpose) 57*> \endverbatim 58*> 59*> \param[in] DIAG 60*> \verbatim 61*> DIAG is CHARACTER*1 62*> Specifies whether or not the matrix A is unit triangular. 63*> = 'N': Non-unit triangular 64*> = 'U': Unit triangular 65*> \endverbatim 66*> 67*> \param[in] N 68*> \verbatim 69*> N is INTEGER 70*> The order of the matrix A. N >= 0. 71*> \endverbatim 72*> 73*> \param[in] NRHS 74*> \verbatim 75*> NRHS is INTEGER 76*> The number of right hand sides, i.e., the number of columns 77*> of the matrices X and B. NRHS >= 0. 78*> \endverbatim 79*> 80*> \param[in] AP 81*> \verbatim 82*> AP is DOUBLE PRECISION array, dimension (N*(N+1)/2) 83*> The upper or lower triangular matrix A, packed columnwise in 84*> a linear array. The j-th column of A is stored in the array 85*> AP as follows: 86*> if UPLO = 'U', AP((j-1)*j/2 + i) = A(i,j) for 1<=i<=j; 87*> if UPLO = 'L', 88*> AP((j-1)*(n-j) + j*(j+1)/2 + i-j) = A(i,j) for j<=i<=n. 89*> \endverbatim 90*> 91*> \param[in] X 92*> \verbatim 93*> X is DOUBLE PRECISION array, dimension (LDX,NRHS) 94*> The computed solution vectors for the system of linear 95*> equations. 96*> \endverbatim 97*> 98*> \param[in] LDX 99*> \verbatim 100*> LDX is INTEGER 101*> The leading dimension of the array X. LDX >= max(1,N). 102*> \endverbatim 103*> 104*> \param[in] B 105*> \verbatim 106*> B is DOUBLE PRECISION array, dimension (LDB,NRHS) 107*> The right hand side vectors for the system of linear 108*> equations. 109*> \endverbatim 110*> 111*> \param[in] LDB 112*> \verbatim 113*> LDB is INTEGER 114*> The leading dimension of the array B. LDB >= max(1,N). 115*> \endverbatim 116*> 117*> \param[out] WORK 118*> \verbatim 119*> WORK is DOUBLE PRECISION array, dimension (N) 120*> \endverbatim 121*> 122*> \param[out] RESID 123*> \verbatim 124*> RESID is DOUBLE PRECISION 125*> The maximum over the number of right hand sides of 126*> norm(op(A)*x - b) / ( norm(op(A)) * norm(x) * EPS ). 127*> \endverbatim 128* 129* Authors: 130* ======== 131* 132*> \author Univ. of Tennessee 133*> \author Univ. of California Berkeley 134*> \author Univ. of Colorado Denver 135*> \author NAG Ltd. 136* 137*> \ingroup double_lin 138* 139* ===================================================================== 140 SUBROUTINE DTPT02( UPLO, TRANS, DIAG, N, NRHS, AP, X, LDX, B, LDB, 141 $ WORK, RESID ) 142* 143* -- LAPACK test routine -- 144* -- LAPACK is a software package provided by Univ. of Tennessee, -- 145* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 146* 147* .. Scalar Arguments .. 148 CHARACTER DIAG, TRANS, UPLO 149 INTEGER LDB, LDX, N, NRHS 150 DOUBLE PRECISION RESID 151* .. 152* .. Array Arguments .. 153 DOUBLE PRECISION AP( * ), B( LDB, * ), WORK( * ), X( LDX, * ) 154* .. 155* 156* ===================================================================== 157* 158* .. Parameters .. 159 DOUBLE PRECISION ZERO, ONE 160 PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) 161* .. 162* .. Local Scalars .. 163 INTEGER J 164 DOUBLE PRECISION ANORM, BNORM, EPS, XNORM 165* .. 166* .. External Functions .. 167 LOGICAL LSAME 168 DOUBLE PRECISION DASUM, DLAMCH, DLANTP 169 EXTERNAL LSAME, DASUM, DLAMCH, DLANTP 170* .. 171* .. External Subroutines .. 172 EXTERNAL DAXPY, DCOPY, DTPMV 173* .. 174* .. Intrinsic Functions .. 175 INTRINSIC MAX 176* .. 177* .. Executable Statements .. 178* 179* Quick exit if N = 0 or NRHS = 0 180* 181 IF( N.LE.0 .OR. NRHS.LE.0 ) THEN 182 RESID = ZERO 183 RETURN 184 END IF 185* 186* Compute the 1-norm of A or A'. 187* 188 IF( LSAME( TRANS, 'N' ) ) THEN 189 ANORM = DLANTP( '1', UPLO, DIAG, N, AP, WORK ) 190 ELSE 191 ANORM = DLANTP( 'I', UPLO, DIAG, N, AP, WORK ) 192 END IF 193* 194* Exit with RESID = 1/EPS if ANORM = 0. 195* 196 EPS = DLAMCH( 'Epsilon' ) 197 IF( ANORM.LE.ZERO ) THEN 198 RESID = ONE / EPS 199 RETURN 200 END IF 201* 202* Compute the maximum over the number of right hand sides of 203* norm(op(A)*x - b) / ( norm(op(A)) * norm(x) * EPS ). 204* 205 RESID = ZERO 206 DO 10 J = 1, NRHS 207 CALL DCOPY( N, X( 1, J ), 1, WORK, 1 ) 208 CALL DTPMV( UPLO, TRANS, DIAG, N, AP, WORK, 1 ) 209 CALL DAXPY( N, -ONE, B( 1, J ), 1, WORK, 1 ) 210 BNORM = DASUM( N, WORK, 1 ) 211 XNORM = DASUM( N, X( 1, J ), 1 ) 212 IF( XNORM.LE.ZERO ) THEN 213 RESID = ONE / EPS 214 ELSE 215 RESID = MAX( RESID, ( ( BNORM / ANORM ) / XNORM ) / EPS ) 216 END IF 217 10 CONTINUE 218* 219 RETURN 220* 221* End of DTPT02 222* 223 END 224