3 * =========== DOCUMENTATION ===========
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
11 * SUBROUTINE DTPT03( UPLO, TRANS, DIAG, N, NRHS, AP, SCALE, CNORM,
12 * TSCAL, X, LDX, B, LDB, WORK, RESID )
14 * .. Scalar Arguments ..
15 * CHARACTER DIAG, TRANS, UPLO
16 * INTEGER LDB, LDX, N, NRHS
17 * DOUBLE PRECISION RESID, SCALE, TSCAL
19 * .. Array Arguments ..
20 * DOUBLE PRECISION AP( * ), B( LDB, * ), CNORM( * ), WORK( * ),
30 *> DTPT03 computes the residual for the solution to a scaled triangular
31 *> system of equations A*x = s*b or A'*x = s*b when the triangular
32 *> matrix A is stored in packed format. Here A' is the transpose of A,
33 *> s is a scalar, and x and b are N by NRHS matrices. The test ratio is
34 *> the maximum over the number of right hand sides of
35 *> norm(s*b - op(A)*x) / ( norm(op(A)) * norm(x) * EPS ),
36 *> where op(A) denotes A or A' and EPS is the machine epsilon.
44 *> UPLO is CHARACTER*1
45 *> Specifies whether the matrix A is upper or lower triangular.
46 *> = 'U': Upper triangular
47 *> = 'L': Lower triangular
52 *> TRANS is CHARACTER*1
53 *> Specifies the operation applied to A.
54 *> = 'N': A *x = s*b (No transpose)
55 *> = 'T': A'*x = s*b (Transpose)
56 *> = 'C': A'*x = s*b (Conjugate transpose = Transpose)
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
70 *> The order of the matrix A. N >= 0.
76 *> The number of right hand sides, i.e., the number of columns
77 *> of the matrices X and B. NRHS >= 0.
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
86 *> if UPLO = 'U', AP((j-1)*j/2 + i) = A(i,j) for 1<=i<=j;
88 *> AP((j-1)*(n-j) + j*(j+1)/2 + i-j) = A(i,j) for j<=i<=n.
93 *> SCALE is DOUBLE PRECISION
94 *> The scaling factor s used in solving the triangular system.
99 *> CNORM is DOUBLE PRECISION array, dimension (N)
100 *> The 1-norms of the columns of A, not counting the diagonal.
105 *> TSCAL is DOUBLE PRECISION
106 *> The scaling factor used in computing the 1-norms in CNORM.
107 *> CNORM actually contains the column norms of TSCAL*A.
112 *> X is DOUBLE PRECISION array, dimension (LDX,NRHS)
113 *> The computed solution vectors for the system of linear
120 *> The leading dimension of the array X. LDX >= max(1,N).
125 *> B is DOUBLE PRECISION array, dimension (LDB,NRHS)
126 *> The right hand side vectors for the system of linear
133 *> The leading dimension of the array B. LDB >= max(1,N).
138 *> WORK is DOUBLE PRECISION array, dimension (N)
143 *> RESID is DOUBLE PRECISION
144 *> The maximum over the number of right hand sides of
145 *> norm(op(A)*x - s*b) / ( norm(op(A)) * norm(x) * EPS ).
151 *> \author Univ. of Tennessee
152 *> \author Univ. of California Berkeley
153 *> \author Univ. of Colorado Denver
156 *> \date November 2011
158 *> \ingroup double_lin
160 * =====================================================================
161 SUBROUTINE DTPT03( UPLO, TRANS, DIAG, N, NRHS, AP, SCALE, CNORM,
162 $ TSCAL, X, LDX, B, LDB, WORK, RESID )
164 * -- LAPACK test routine (version 3.4.0) --
165 * -- LAPACK is a software package provided by Univ. of Tennessee, --
166 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
169 * .. Scalar Arguments ..
170 CHARACTER DIAG, TRANS, UPLO
171 INTEGER LDB, LDX, N, NRHS
172 DOUBLE PRECISION RESID, SCALE, TSCAL
174 * .. Array Arguments ..
175 DOUBLE PRECISION AP( * ), B( LDB, * ), CNORM( * ), WORK( * ),
179 * =====================================================================
182 DOUBLE PRECISION ONE, ZERO
183 PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
185 * .. Local Scalars ..
187 DOUBLE PRECISION BIGNUM, EPS, ERR, SMLNUM, TNORM, XNORM, XSCAL
189 * .. External Functions ..
192 DOUBLE PRECISION DLAMCH
193 EXTERNAL LSAME, IDAMAX, DLAMCH
195 * .. External Subroutines ..
196 EXTERNAL DAXPY, DCOPY, DLABAD, DSCAL, DTPMV
198 * .. Intrinsic Functions ..
199 INTRINSIC ABS, DBLE, MAX
201 * .. Executable Statements ..
203 * Quick exit if N = 0.
205 IF( N.LE.0 .OR. NRHS.LE.0 ) THEN
209 EPS = DLAMCH( 'Epsilon' )
210 SMLNUM = DLAMCH( 'Safe minimum' )
211 BIGNUM = ONE / SMLNUM
212 CALL DLABAD( SMLNUM, BIGNUM )
214 * Compute the norm of the triangular matrix A using the column
215 * norms already computed by DLATPS.
218 IF( LSAME( DIAG, 'N' ) ) THEN
219 IF( LSAME( UPLO, 'U' ) ) THEN
222 TNORM = MAX( TNORM, TSCAL*ABS( AP( JJ ) )+CNORM( J ) )
228 TNORM = MAX( TNORM, TSCAL*ABS( AP( JJ ) )+CNORM( J ) )
234 TNORM = MAX( TNORM, TSCAL+CNORM( J ) )
238 * Compute the maximum over the number of right hand sides of
239 * norm(op(A)*x - s*b) / ( norm(op(A)) * norm(x) * EPS ).
243 CALL DCOPY( N, X( 1, J ), 1, WORK, 1 )
244 IX = IDAMAX( N, WORK, 1 )
245 XNORM = MAX( ONE, ABS( X( IX, J ) ) )
246 XSCAL = ( ONE / XNORM ) / DBLE( N )
247 CALL DSCAL( N, XSCAL, WORK, 1 )
248 CALL DTPMV( UPLO, TRANS, DIAG, N, AP, WORK, 1 )
249 CALL DAXPY( N, -SCALE*XSCAL, B( 1, J ), 1, WORK, 1 )
250 IX = IDAMAX( N, WORK, 1 )
251 ERR = TSCAL*ABS( WORK( IX ) )
252 IX = IDAMAX( N, X( 1, J ), 1 )
253 XNORM = ABS( X( IX, J ) )
254 IF( ERR*SMLNUM.LE.XNORM ) THEN
261 IF( ERR*SMLNUM.LE.TNORM ) THEN
268 RESID = MAX( RESID, ERR )