1*> \brief \b ZTPT03 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 ZTPT03( UPLO, TRANS, DIAG, N, NRHS, AP, SCALE, CNORM, 12* TSCAL, X, LDX, B, LDB, WORK, RESID ) 13* 14* .. Scalar Arguments .. 15* CHARACTER DIAG, TRANS, UPLO 16* INTEGER LDB, LDX, N, NRHS 17* DOUBLE PRECISION RESID, SCALE, TSCAL 18* .. 19* .. Array Arguments .. 20* DOUBLE PRECISION CNORM( * ) 21* COMPLEX*16 AP( * ), B( LDB, * ), WORK( * ), X( LDX, * ) 22* .. 23* 24* 25*> \par Purpose: 26* ============= 27*> 28*> \verbatim 29*> 30*> ZTPT03 computes the residual for the solution to a scaled triangular 31*> system of equations A*x = s*b, A**T *x = s*b, or A**H *x = s*b, 32*> when the triangular matrix A is stored in packed format. Here A**T 33*> denotes the transpose of A, A**H denotes the conjugate transpose of 34*> A, s is a scalar, and x and b are N by NRHS matrices. The test ratio 35*> is the maximum over the number of right hand sides of 36*> norm(s*b - op(A)*x) / ( norm(op(A)) * norm(x) * EPS ), 37*> where op(A) denotes A, A**T, or A**H, and EPS is the machine epsilon. 38*> \endverbatim 39* 40* Arguments: 41* ========== 42* 43*> \param[in] UPLO 44*> \verbatim 45*> UPLO is CHARACTER*1 46*> Specifies whether the matrix A is upper or lower triangular. 47*> = 'U': Upper triangular 48*> = 'L': Lower triangular 49*> \endverbatim 50*> 51*> \param[in] TRANS 52*> \verbatim 53*> TRANS is CHARACTER*1 54*> Specifies the operation applied to A. 55*> = 'N': A *x = s*b (No transpose) 56*> = 'T': A**T *x = s*b (Transpose) 57*> = 'C': A**H *x = s*b (Conjugate transpose) 58*> \endverbatim 59*> 60*> \param[in] DIAG 61*> \verbatim 62*> DIAG is CHARACTER*1 63*> Specifies whether or not the matrix A is unit triangular. 64*> = 'N': Non-unit triangular 65*> = 'U': Unit triangular 66*> \endverbatim 67*> 68*> \param[in] N 69*> \verbatim 70*> N is INTEGER 71*> The order of the matrix A. N >= 0. 72*> \endverbatim 73*> 74*> \param[in] NRHS 75*> \verbatim 76*> NRHS is INTEGER 77*> The number of right hand sides, i.e., the number of columns 78*> of the matrices X and B. NRHS >= 0. 79*> \endverbatim 80*> 81*> \param[in] AP 82*> \verbatim 83*> AP is COMPLEX*16 array, dimension (N*(N+1)/2) 84*> The upper or lower triangular matrix A, packed columnwise in 85*> a linear array. The j-th column of A is stored in the array 86*> AP as follows: 87*> if UPLO = 'U', AP((j-1)*j/2 + i) = A(i,j) for 1<=i<=j; 88*> if UPLO = 'L', 89*> AP((j-1)*(n-j) + j*(j+1)/2 + i-j) = A(i,j) for j<=i<=n. 90*> \endverbatim 91*> 92*> \param[in] SCALE 93*> \verbatim 94*> SCALE is DOUBLE PRECISION 95*> The scaling factor s used in solving the triangular system. 96*> \endverbatim 97*> 98*> \param[in] CNORM 99*> \verbatim 100*> CNORM is DOUBLE PRECISION array, dimension (N) 101*> The 1-norms of the columns of A, not counting the diagonal. 102*> \endverbatim 103*> 104*> \param[in] TSCAL 105*> \verbatim 106*> TSCAL is DOUBLE PRECISION 107*> The scaling factor used in computing the 1-norms in CNORM. 108*> CNORM actually contains the column norms of TSCAL*A. 109*> \endverbatim 110*> 111*> \param[in] X 112*> \verbatim 113*> X is COMPLEX*16 array, dimension (LDX,NRHS) 114*> The computed solution vectors for the system of linear 115*> equations. 116*> \endverbatim 117*> 118*> \param[in] LDX 119*> \verbatim 120*> LDX is INTEGER 121*> The leading dimension of the array X. LDX >= max(1,N). 122*> \endverbatim 123*> 124*> \param[in] B 125*> \verbatim 126*> B is COMPLEX*16 array, dimension (LDB,NRHS) 127*> The right hand side vectors for the system of linear 128*> equations. 129*> \endverbatim 130*> 131*> \param[in] LDB 132*> \verbatim 133*> LDB is INTEGER 134*> The leading dimension of the array B. LDB >= max(1,N). 135*> \endverbatim 136*> 137*> \param[out] WORK 138*> \verbatim 139*> WORK is COMPLEX*16 array, dimension (N) 140*> \endverbatim 141*> 142*> \param[out] RESID 143*> \verbatim 144*> RESID is DOUBLE PRECISION 145*> The maximum over the number of right hand sides of 146*> norm(op(A)*x - s*b) / ( norm(op(A)) * norm(x) * EPS ). 147*> \endverbatim 148* 149* Authors: 150* ======== 151* 152*> \author Univ. of Tennessee 153*> \author Univ. of California Berkeley 154*> \author Univ. of Colorado Denver 155*> \author NAG Ltd. 156* 157*> \date November 2011 158* 159*> \ingroup complex16_lin 160* 161* ===================================================================== 162 SUBROUTINE ZTPT03( UPLO, TRANS, DIAG, N, NRHS, AP, SCALE, CNORM, 163 $ TSCAL, X, LDX, B, LDB, WORK, RESID ) 164* 165* -- LAPACK test routine (version 3.4.0) -- 166* -- LAPACK is a software package provided by Univ. of Tennessee, -- 167* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 168* November 2011 169* 170* .. Scalar Arguments .. 171 CHARACTER DIAG, TRANS, UPLO 172 INTEGER LDB, LDX, N, NRHS 173 DOUBLE PRECISION RESID, SCALE, TSCAL 174* .. 175* .. Array Arguments .. 176 DOUBLE PRECISION CNORM( * ) 177 COMPLEX*16 AP( * ), B( LDB, * ), WORK( * ), X( LDX, * ) 178* .. 179* 180* ===================================================================== 181* 182* .. Parameters .. 183 DOUBLE PRECISION ONE, ZERO 184 PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) 185* .. 186* .. Local Scalars .. 187 INTEGER IX, J, JJ 188 DOUBLE PRECISION EPS, ERR, SMLNUM, TNORM, XNORM, XSCAL 189* .. 190* .. External Functions .. 191 LOGICAL LSAME 192 INTEGER IZAMAX 193 DOUBLE PRECISION DLAMCH 194 EXTERNAL LSAME, IZAMAX, DLAMCH 195* .. 196* .. External Subroutines .. 197 EXTERNAL ZAXPY, ZCOPY, ZDSCAL, ZTPMV 198* .. 199* .. Intrinsic Functions .. 200 INTRINSIC ABS, DBLE, DCMPLX, MAX 201* .. 202* .. Executable Statements .. 203* 204* Quick exit if N = 0. 205* 206 IF( N.LE.0 .OR. NRHS.LE.0 ) THEN 207 RESID = ZERO 208 RETURN 209 END IF 210 EPS = DLAMCH( 'Epsilon' ) 211 SMLNUM = DLAMCH( 'Safe minimum' ) 212* 213* Compute the norm of the triangular matrix A using the column 214* norms already computed by ZLATPS. 215* 216 TNORM = 0.D0 217 IF( LSAME( DIAG, 'N' ) ) THEN 218 IF( LSAME( UPLO, 'U' ) ) THEN 219 JJ = 1 220 DO 10 J = 1, N 221 TNORM = MAX( TNORM, TSCAL*ABS( AP( JJ ) )+CNORM( J ) ) 222 JJ = JJ + J 223 10 CONTINUE 224 ELSE 225 JJ = 1 226 DO 20 J = 1, N 227 TNORM = MAX( TNORM, TSCAL*ABS( AP( JJ ) )+CNORM( J ) ) 228 JJ = JJ + N - J + 1 229 20 CONTINUE 230 END IF 231 ELSE 232 DO 30 J = 1, N 233 TNORM = MAX( TNORM, TSCAL+CNORM( J ) ) 234 30 CONTINUE 235 END IF 236* 237* Compute the maximum over the number of right hand sides of 238* norm(op(A)*x - s*b) / ( norm(A) * norm(x) * EPS ). 239* 240 RESID = ZERO 241 DO 40 J = 1, NRHS 242 CALL ZCOPY( N, X( 1, J ), 1, WORK, 1 ) 243 IX = IZAMAX( N, WORK, 1 ) 244 XNORM = MAX( ONE, ABS( X( IX, J ) ) ) 245 XSCAL = ( ONE / XNORM ) / DBLE( N ) 246 CALL ZDSCAL( N, XSCAL, WORK, 1 ) 247 CALL ZTPMV( UPLO, TRANS, DIAG, N, AP, WORK, 1 ) 248 CALL ZAXPY( N, DCMPLX( -SCALE*XSCAL ), B( 1, J ), 1, WORK, 1 ) 249 IX = IZAMAX( N, WORK, 1 ) 250 ERR = TSCAL*ABS( WORK( IX ) ) 251 IX = IZAMAX( N, X( 1, J ), 1 ) 252 XNORM = ABS( X( IX, J ) ) 253 IF( ERR*SMLNUM.LE.XNORM ) THEN 254 IF( XNORM.GT.ZERO ) 255 $ ERR = ERR / XNORM 256 ELSE 257 IF( ERR.GT.ZERO ) 258 $ ERR = ONE / EPS 259 END IF 260 IF( ERR*SMLNUM.LE.TNORM ) THEN 261 IF( TNORM.GT.ZERO ) 262 $ ERR = ERR / TNORM 263 ELSE 264 IF( ERR.GT.ZERO ) 265 $ ERR = ONE / EPS 266 END IF 267 RESID = MAX( RESID, ERR ) 268 40 CONTINUE 269* 270 RETURN 271* 272* End of ZTPT03 273* 274 END 275