3 * =========== DOCUMENTATION ===========
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
11 * SUBROUTINE STPT03( 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 * REAL RESID, SCALE, TSCAL
19 * .. Array Arguments ..
20 * REAL AP( * ), B( LDB, * ), CNORM( * ), WORK( * ),
30 *> STPT03 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 REAL 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.
94 *> The scaling factor s used in solving the triangular system.
99 *> CNORM is REAL array, dimension (N)
100 *> The 1-norms of the columns of A, not counting the diagonal.
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 REAL 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 REAL 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 REAL array, dimension (N)
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 single_lin
160 * =====================================================================
161 SUBROUTINE STPT03( 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 REAL RESID, SCALE, TSCAL
174 * .. Array Arguments ..
175 REAL AP( * ), B( LDB, * ), CNORM( * ), WORK( * ),
179 * =====================================================================
183 PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 )
185 * .. Local Scalars ..
187 REAL BIGNUM, EPS, ERR, SMLNUM, TNORM, XNORM, XSCAL
189 * .. External Functions ..
193 EXTERNAL LSAME, ISAMAX, SLAMCH
195 * .. External Subroutines ..
196 EXTERNAL SAXPY, SCOPY, SLABAD, SSCAL, STPMV
198 * .. Intrinsic Functions ..
199 INTRINSIC ABS, MAX, REAL
201 * .. Executable Statements ..
203 * Quick exit if N = 0.
205 IF( N.LE.0 .OR. NRHS.LE.0 ) THEN
209 EPS = SLAMCH( 'Epsilon' )
210 SMLNUM = SLAMCH( 'Safe minimum' )
211 BIGNUM = ONE / SMLNUM
212 CALL SLABAD( SMLNUM, BIGNUM )
214 * Compute the norm of the triangular matrix A using the column
215 * norms already computed by SLATPS.
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 SCOPY( N, X( 1, J ), 1, WORK, 1 )
244 IX = ISAMAX( N, WORK, 1 )
245 XNORM = MAX( ONE, ABS( X( IX, J ) ) )
246 XSCAL = ( ONE / XNORM ) / REAL( N )
247 CALL SSCAL( N, XSCAL, WORK, 1 )
248 CALL STPMV( UPLO, TRANS, DIAG, N, AP, WORK, 1 )
249 CALL SAXPY( N, -SCALE*XSCAL, B( 1, J ), 1, WORK, 1 )
250 IX = ISAMAX( N, WORK, 1 )
251 ERR = TSCAL*ABS( WORK( IX ) )
252 IX = ISAMAX( 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 )