LAPACK  3.10.1
LAPACK: Linear Algebra PACKage
ztpt02.f
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1 *> \brief \b ZTPT02
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 ZTPT02( UPLO, TRANS, DIAG, N, NRHS, AP, X, LDX, B, LDB,
12 * WORK, RWORK, RESID )
13 *
14 * .. Scalar Arguments ..
15 * CHARACTER DIAG, TRANS, UPLO
16 * INTEGER LDB, LDX, N, NRHS
17 * DOUBLE PRECISION RESID
18 * ..
19 * .. Array Arguments ..
20 * DOUBLE PRECISION RWORK( * )
21 * COMPLEX*16 AP( * ), B( LDB, * ), WORK( * ), X( LDX, * )
22 * ..
23 *
24 *
25 *> \par Purpose:
26 * =============
27 *>
28 *> \verbatim
29 *>
30 *> ZTPT02 computes the residual for the computed solution to a
31 *> triangular system of linear equations op(A)*X = B, when the
32 *> triangular matrix A is stored in packed format. The test ratio is
33 *> 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] NRHS
74 *> \verbatim
75 *> NRHS is INTEGER
76 *> The number of right hand sides, i.e., the number of columns
77 *> of the matrices X and B. NRHS >= 0.
78 *> \endverbatim
79 *>
80 *> \param[in] AP
81 *> \verbatim
82 *> AP is COMPLEX*16 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
85 *> AP as follows:
86 *> if UPLO = 'U', AP((j-1)*j/2 + i) = A(i,j) for 1<=i<=j;
87 *> if UPLO = 'L',
88 *> AP((j-1)*(n-j) + j*(j+1)/2 + i-j) = A(i,j) for j<=i<=n.
89 *> \endverbatim
90 *>
91 *> \param[in] X
92 *> \verbatim
93 *> X is COMPLEX*16 array, dimension (LDX,NRHS)
94 *> The computed solution vectors for the system of linear
95 *> equations.
96 *> \endverbatim
97 *>
98 *> \param[in] LDX
99 *> \verbatim
100 *> LDX is INTEGER
101 *> The leading dimension of the array X. LDX >= max(1,N).
102 *> \endverbatim
103 *>
104 *> \param[in] B
105 *> \verbatim
106 *> B is COMPLEX*16 array, dimension (LDB,NRHS)
107 *> The right hand side vectors for the system of linear
108 *> equations.
109 *> \endverbatim
110 *>
111 *> \param[in] LDB
112 *> \verbatim
113 *> LDB is INTEGER
114 *> The leading dimension of the array B. LDB >= max(1,N).
115 *> \endverbatim
116 *>
117 *> \param[out] WORK
118 *> \verbatim
119 *> WORK is COMPLEX*16 array, dimension (N)
120 *> \endverbatim
121 *>
122 *> \param[out] RWORK
123 *> \verbatim
124 *> RWORK is DOUBLE PRECISION array, dimension (N)
125 *> \endverbatim
126 *>
127 *> \param[out] RESID
128 *> \verbatim
129 *> RESID is DOUBLE PRECISION
130 *> The maximum over the number of right hand sides of
131 *> norm(op(A)*X - B) / ( norm(op(A)) * norm(X) * EPS ).
132 *> \endverbatim
133 *
134 * Authors:
135 * ========
136 *
137 *> \author Univ. of Tennessee
138 *> \author Univ. of California Berkeley
139 *> \author Univ. of Colorado Denver
140 *> \author NAG Ltd.
141 *
142 *> \ingroup complex16_lin
143 *
144 * =====================================================================
145  SUBROUTINE ztpt02( UPLO, TRANS, DIAG, N, NRHS, AP, X, LDX, B, LDB,
146  $ WORK, RWORK, RESID )
147 *
148 * -- LAPACK test routine --
149 * -- LAPACK is a software package provided by Univ. of Tennessee, --
150 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
151 *
152 * .. Scalar Arguments ..
153  CHARACTER DIAG, TRANS, UPLO
154  INTEGER LDB, LDX, N, NRHS
155  DOUBLE PRECISION RESID
156 * ..
157 * .. Array Arguments ..
158  DOUBLE PRECISION RWORK( * )
159  COMPLEX*16 AP( * ), B( LDB, * ), WORK( * ), X( LDX, * )
160 * ..
161 *
162 * =====================================================================
163 *
164 * .. Parameters ..
165  DOUBLE PRECISION ZERO, ONE
166  parameter( zero = 0.0d+0, one = 1.0d+0 )
167 * ..
168 * .. Local Scalars ..
169  INTEGER J
170  DOUBLE PRECISION ANORM, BNORM, EPS, XNORM
171 * ..
172 * .. External Functions ..
173  LOGICAL LSAME
174  DOUBLE PRECISION DLAMCH, DZASUM, ZLANTP
175  EXTERNAL lsame, dlamch, dzasum, zlantp
176 * ..
177 * .. External Subroutines ..
178  EXTERNAL zaxpy, zcopy, ztpmv
179 * ..
180 * .. Intrinsic Functions ..
181  INTRINSIC dcmplx, max
182 * ..
183 * .. Executable Statements ..
184 *
185 * Quick exit if N = 0 or NRHS = 0
186 *
187  IF( n.LE.0 .OR. nrhs.LE.0 ) THEN
188  resid = zero
189  RETURN
190  END IF
191 *
192 * Compute the 1-norm of op(A).
193 *
194  IF( lsame( trans, 'N' ) ) THEN
195  anorm = zlantp( '1', uplo, diag, n, ap, rwork )
196  ELSE
197  anorm = zlantp( 'I', uplo, diag, n, ap, rwork )
198  END IF
199 *
200 * Exit with RESID = 1/EPS if ANORM = 0.
201 *
202  eps = dlamch( 'Epsilon' )
203  IF( anorm.LE.zero ) THEN
204  resid = one / eps
205  RETURN
206  END IF
207 *
208 * Compute the maximum over the number of right hand sides of
209 * norm(op(A)*X - B) / ( norm(op(A)) * norm(X) * EPS ).
210 *
211  resid = zero
212  DO 10 j = 1, nrhs
213  CALL zcopy( n, x( 1, j ), 1, work, 1 )
214  CALL ztpmv( uplo, trans, diag, n, ap, work, 1 )
215  CALL zaxpy( n, dcmplx( -one ), b( 1, j ), 1, work, 1 )
216  bnorm = dzasum( n, work, 1 )
217  xnorm = dzasum( n, x( 1, j ), 1 )
218  IF( xnorm.LE.zero ) THEN
219  resid = one / eps
220  ELSE
221  resid = max( resid, ( ( bnorm / anorm ) / xnorm ) / eps )
222  END IF
223  10 CONTINUE
224 *
225  RETURN
226 *
227 * End of ZTPT02
228 *
229  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 ztpmv(UPLO, TRANS, DIAG, N, AP, X, INCX)
ZTPMV
Definition: ztpmv.f:142
subroutine ztpt02(UPLO, TRANS, DIAG, N, NRHS, AP, X, LDX, B, LDB, WORK, RWORK, RESID)
ZTPT02
Definition: ztpt02.f:147