LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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dtbt02.f
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1*> \brief \b DTBT02
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 DTBT02( UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB, X,
12* LDX, B, LDB, WORK, RESID )
13*
14* .. Scalar Arguments ..
15* CHARACTER DIAG, TRANS, UPLO
16* INTEGER KD, LDAB, LDB, LDX, N, NRHS
17* DOUBLE PRECISION RESID
18* ..
19* .. Array Arguments ..
20* DOUBLE PRECISION AB( LDAB, * ), B( LDB, * ), WORK( * ),
21* $ X( LDX, * )
22* ..
23*
24*
25*> \par Purpose:
26* =============
27*>
28*> \verbatim
29*>
30*> DTBT02 computes the residual for the computed solution to a
31*> triangular system of linear equations op(A)*X = B, when A is a
32*> triangular band matrix. The test ratio is the maximum over
33*> norm(b - op(A)*x) / ( ||op(A)||_1 * norm(x) * EPS ),
34*> where op(A) = A or A**T, b is the column of B, x is the solution
35*> vector, 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**T * X = B (Transpose)
56*> = 'C': A**H * 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] KD
74*> \verbatim
75*> KD is INTEGER
76*> The number of superdiagonals or subdiagonals of the
77*> triangular band matrix A. KD >= 0.
78*> \endverbatim
79*>
80*> \param[in] NRHS
81*> \verbatim
82*> NRHS is INTEGER
83*> The number of right hand sides, i.e., the number of columns
84*> of the matrices X and B. NRHS >= 0.
85*> \endverbatim
86*>
87*> \param[in] AB
88*> \verbatim
89*> AB is DOUBLE PRECISION array, dimension (LDAB,N)
90*> The upper or lower triangular band matrix A, stored in the
91*> first kd+1 rows of the array. The j-th column of A is stored
92*> in the j-th column of the array AB as follows:
93*> if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
94*> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).
95*> \endverbatim
96*>
97*> \param[in] LDAB
98*> \verbatim
99*> LDAB is INTEGER
100*> The leading dimension of the array AB. LDAB >= KD+1.
101*> \endverbatim
102*>
103*> \param[in] X
104*> \verbatim
105*> X is DOUBLE PRECISION array, dimension (LDX,NRHS)
106*> The computed solution vectors for the system of linear
107*> equations.
108*> \endverbatim
109*>
110*> \param[in] LDX
111*> \verbatim
112*> LDX is INTEGER
113*> The leading dimension of the array X. LDX >= max(1,N).
114*> \endverbatim
115*>
116*> \param[in] B
117*> \verbatim
118*> B is DOUBLE PRECISION array, dimension (LDB,NRHS)
119*> The right hand side vectors for the system of linear
120*> equations.
121*> \endverbatim
122*>
123*> \param[in] LDB
124*> \verbatim
125*> LDB is INTEGER
126*> The leading dimension of the array B. LDB >= max(1,N).
127*> \endverbatim
128*>
129*> \param[out] WORK
130*> \verbatim
131*> WORK is DOUBLE PRECISION array, dimension (N)
132*> \endverbatim
133*>
134*> \param[out] RESID
135*> \verbatim
136*> RESID is DOUBLE PRECISION
137*> The maximum over the number of right hand sides of
138*> norm(op(A)*x - b) / ( norm(op(A)) * norm(x) * EPS ).
139*> \endverbatim
140*
141* Authors:
142* ========
143*
144*> \author Univ. of Tennessee
145*> \author Univ. of California Berkeley
146*> \author Univ. of Colorado Denver
147*> \author NAG Ltd.
148*
149*> \ingroup double_lin
150*
151* =====================================================================
152 SUBROUTINE dtbt02( UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB, X,
153 $ LDX, B, LDB, WORK, RESID )
154*
155* -- LAPACK test routine --
156* -- LAPACK is a software package provided by Univ. of Tennessee, --
157* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
158*
159* .. Scalar Arguments ..
160 CHARACTER DIAG, TRANS, UPLO
161 INTEGER KD, LDAB, LDB, LDX, N, NRHS
162 DOUBLE PRECISION RESID
163* ..
164* .. Array Arguments ..
165 DOUBLE PRECISION AB( LDAB, * ), B( LDB, * ), WORK( * ),
166 $ x( ldx, * )
167* ..
168*
169* =====================================================================
170*
171* .. Parameters ..
172 DOUBLE PRECISION ZERO, ONE
173 parameter( zero = 0.0d+0, one = 1.0d+0 )
174* ..
175* .. Local Scalars ..
176 INTEGER J
177 DOUBLE PRECISION ANORM, BNORM, EPS, XNORM
178* ..
179* .. External Functions ..
180 LOGICAL LSAME
181 DOUBLE PRECISION DASUM, DLAMCH, DLANTB
182 EXTERNAL lsame, dasum, dlamch, dlantb
183* ..
184* .. External Subroutines ..
185 EXTERNAL daxpy, dcopy, dtbmv
186* ..
187* .. Intrinsic Functions ..
188 INTRINSIC max
189* ..
190* .. Executable Statements ..
191*
192* Quick exit if N = 0 or NRHS = 0
193*
194 IF( n.LE.0 .OR. nrhs.LE.0 ) THEN
195 resid = zero
196 RETURN
197 END IF
198*
199* Compute the 1-norm of op(A).
200*
201 IF( lsame( trans, 'N' ) ) THEN
202 anorm = dlantb( '1', uplo, diag, n, kd, ab, ldab, work )
203 ELSE
204 anorm = dlantb( 'I', uplo, diag, n, kd, ab, ldab, work )
205 END IF
206*
207* Exit with RESID = 1/EPS if ANORM = 0.
208*
209 eps = dlamch( 'Epsilon' )
210 IF( anorm.LE.zero ) THEN
211 resid = one / eps
212 RETURN
213 END IF
214*
215* Compute the maximum over the number of right hand sides of
216* norm(op(A)*x - b) / ( norm(op(A)) * norm(x) * EPS ).
217*
218 resid = zero
219 DO 10 j = 1, nrhs
220 CALL dcopy( n, x( 1, j ), 1, work, 1 )
221 CALL dtbmv( uplo, trans, diag, n, kd, ab, ldab, work, 1 )
222 CALL daxpy( n, -one, b( 1, j ), 1, work, 1 )
223 bnorm = dasum( n, work, 1 )
224 xnorm = dasum( n, x( 1, j ), 1 )
225 IF( xnorm.LE.zero ) THEN
226 resid = one / eps
227 ELSE
228 resid = max( resid, ( ( bnorm / anorm ) / xnorm ) / eps )
229 END IF
230 10 CONTINUE
231*
232 RETURN
233*
234* End of DTBT02
235*
236 END
subroutine dtbt02(uplo, trans, diag, n, kd, nrhs, ab, ldab, x, ldx, b, ldb, work, resid)
DTBT02
Definition dtbt02.f:154
subroutine daxpy(n, da, dx, incx, dy, incy)
DAXPY
Definition daxpy.f:89
subroutine dcopy(n, dx, incx, dy, incy)
DCOPY
Definition dcopy.f:82
subroutine dtbmv(uplo, trans, diag, n, k, a, lda, x, incx)
DTBMV
Definition dtbmv.f:186