LAPACK  3.10.1 LAPACK: Linear Algebra PACKage
ztbt02.f
Go to the documentation of this file.
1 *> \brief \b ZTBT02
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 ZTBT02( UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB, X,
12 * LDX, B, LDB, WORK, RWORK, 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 RWORK( * )
21 * COMPLEX*16 AB( LDAB, * ), B( LDB, * ), WORK( * ),
22 * \$ X( LDX, * )
23 * ..
24 *
25 *
26 *> \par Purpose:
27 * =============
28 *>
29 *> \verbatim
30 *>
31 *> ZTBT02 computes the residual for the computed solution to a
32 *> triangular system of linear equations op(A)*X = B, when A is a
33 *> triangular band matrix. The test ratio is the maximum over
34 *> norm(b - op(A)*x) / ( ||op(A)||_1 * norm(x) * EPS ),
35 *> where op(A) = A, A**T, or A**H, b is the column of B, x is the
36 *> solution vector, and EPS is the machine epsilon.
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)
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 COMPLEX*16 array, dimension (LDA,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 >= max(1,KD+1).
101 *> \endverbatim
102 *>
103 *> \param[in] X
104 *> \verbatim
105 *> X is COMPLEX*16 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 COMPLEX*16 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 COMPLEX*16 array, dimension (N)
132 *> \endverbatim
133 *>
134 *> \param[out] RWORK
135 *> \verbatim
136 *> RWORK is DOUBLE PRECISION array, dimension (N)
137 *> \endverbatim
138 *>
139 *> \param[out] RESID
140 *> \verbatim
141 *> RESID is DOUBLE PRECISION
142 *> The maximum over the number of right hand sides of
143 *> norm(op(A)*x - b) / ( norm(op(A)) * norm(x) * EPS ).
144 *> \endverbatim
145 *
146 * Authors:
147 * ========
148 *
149 *> \author Univ. of Tennessee
150 *> \author Univ. of California Berkeley
151 *> \author Univ. of Colorado Denver
152 *> \author NAG Ltd.
153 *
154 *> \ingroup complex16_lin
155 *
156 * =====================================================================
157  SUBROUTINE ztbt02( UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB, X,
158  \$ LDX, B, LDB, WORK, RWORK, RESID )
159 *
160 * -- LAPACK test routine --
161 * -- LAPACK is a software package provided by Univ. of Tennessee, --
162 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
163 *
164 * .. Scalar Arguments ..
165  CHARACTER DIAG, TRANS, UPLO
166  INTEGER KD, LDAB, LDB, LDX, N, NRHS
167  DOUBLE PRECISION RESID
168 * ..
169 * .. Array Arguments ..
170  DOUBLE PRECISION RWORK( * )
171  COMPLEX*16 AB( LDAB, * ), B( LDB, * ), WORK( * ),
172  \$ x( ldx, * )
173 * ..
174 *
175 * =====================================================================
176 *
177 * .. Parameters ..
178  DOUBLE PRECISION ZERO, ONE
179  parameter( zero = 0.0d+0, one = 1.0d+0 )
180 * ..
181 * .. Local Scalars ..
182  INTEGER J
183  DOUBLE PRECISION ANORM, BNORM, EPS, XNORM
184 * ..
185 * .. External Functions ..
186  LOGICAL LSAME
187  DOUBLE PRECISION DLAMCH, DZASUM, ZLANTB
188  EXTERNAL lsame, dlamch, dzasum, zlantb
189 * ..
190 * .. External Subroutines ..
191  EXTERNAL zaxpy, zcopy, ztbmv
192 * ..
193 * .. Intrinsic Functions ..
194  INTRINSIC dcmplx, max
195 * ..
196 * .. Executable Statements ..
197 *
198 * Quick exit if N = 0 or NRHS = 0
199 *
200  IF( n.LE.0 .OR. nrhs.LE.0 ) THEN
201  resid = zero
202  RETURN
203  END IF
204 *
205 * Compute the 1-norm of op(A).
206 *
207  IF( lsame( trans, 'N' ) ) THEN
208  anorm = zlantb( '1', uplo, diag, n, kd, ab, ldab, rwork )
209  ELSE
210  anorm = zlantb( 'I', uplo, diag, n, kd, ab, ldab, rwork )
211  END IF
212 *
213 * Exit with RESID = 1/EPS if ANORM = 0.
214 *
215  eps = dlamch( 'Epsilon' )
216  IF( anorm.LE.zero ) THEN
217  resid = one / eps
218  RETURN
219  END IF
220 *
221 * Compute the maximum over the number of right hand sides of
222 * norm(op(A)*x - b) / ( norm(op(A)) * norm(x) * EPS ).
223 *
224  resid = zero
225  DO 10 j = 1, nrhs
226  CALL zcopy( n, x( 1, j ), 1, work, 1 )
227  CALL ztbmv( uplo, trans, diag, n, kd, ab, ldab, work, 1 )
228  CALL zaxpy( n, dcmplx( -one ), b( 1, j ), 1, work, 1 )
229  bnorm = dzasum( n, work, 1 )
230  xnorm = dzasum( n, x( 1, j ), 1 )
231  IF( xnorm.LE.zero ) THEN
232  resid = one / eps
233  ELSE
234  resid = max( resid, ( ( bnorm / anorm ) / xnorm ) / eps )
235  END IF
236  10 CONTINUE
237 *
238  RETURN
239 *
240 * End of ZTBT02
241 *
242  END
subroutine zaxpy(N, ZA, ZX, INCX, ZY, INCY)
ZAXPY
Definition: zaxpy.f:88
subroutine zcopy(N, ZX, INCX, ZY, INCY)
ZCOPY
Definition: zcopy.f:81
subroutine ztbmv(UPLO, TRANS, DIAG, N, K, A, LDA, X, INCX)
ZTBMV
Definition: ztbmv.f:186
subroutine ztbt02(UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB, X, LDX, B, LDB, WORK, RWORK, RESID)
ZTBT02
Definition: ztbt02.f:159