LAPACK  3.10.1 LAPACK: Linear Algebra PACKage
dtpt02.f
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1 *> \brief \b DTPT02
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 DTPT02( UPLO, TRANS, DIAG, N, NRHS, AP, X, LDX, B, LDB,
12 * WORK, 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 AP( * ), B( LDB, * ), WORK( * ), X( LDX, * )
21 * ..
22 *
23 *
24 *> \par Purpose:
25 * =============
26 *>
27 *> \verbatim
28 *>
29 *> DTPT02 computes the residual for the computed solution to a
30 *> triangular system of linear equations op(A)*X = B, when the
31 *> triangular matrix A is stored in packed format. The test ratio is
32 *> 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] 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 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
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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (N)
120 *> \endverbatim
121 *>
122 *> \param[out] RESID
123 *> \verbatim
124 *> RESID is DOUBLE PRECISION
125 *> The maximum over the number of right hand sides of
126 *> norm(op(A)*X - B) / ( norm(op(A)) * norm(X) * EPS ).
127 *> \endverbatim
128 *
129 * Authors:
130 * ========
131 *
132 *> \author Univ. of Tennessee
133 *> \author Univ. of California Berkeley
134 *> \author Univ. of Colorado Denver
135 *> \author NAG Ltd.
136 *
137 *> \ingroup double_lin
138 *
139 * =====================================================================
140  SUBROUTINE dtpt02( UPLO, TRANS, DIAG, N, NRHS, AP, X, LDX, B, LDB,
141  \$ WORK, RESID )
142 *
143 * -- LAPACK test routine --
144 * -- LAPACK is a software package provided by Univ. of Tennessee, --
145 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
146 *
147 * .. Scalar Arguments ..
148  CHARACTER DIAG, TRANS, UPLO
149  INTEGER LDB, LDX, N, NRHS
150  DOUBLE PRECISION RESID
151 * ..
152 * .. Array Arguments ..
153  DOUBLE PRECISION AP( * ), B( LDB, * ), WORK( * ), X( LDX, * )
154 * ..
155 *
156 * =====================================================================
157 *
158 * .. Parameters ..
159  DOUBLE PRECISION ZERO, ONE
160  parameter( zero = 0.0d+0, one = 1.0d+0 )
161 * ..
162 * .. Local Scalars ..
163  INTEGER J
164  DOUBLE PRECISION ANORM, BNORM, EPS, XNORM
165 * ..
166 * .. External Functions ..
167  LOGICAL LSAME
168  DOUBLE PRECISION DASUM, DLAMCH, DLANTP
169  EXTERNAL lsame, dasum, dlamch, dlantp
170 * ..
171 * .. External Subroutines ..
172  EXTERNAL daxpy, dcopy, dtpmv
173 * ..
174 * .. Intrinsic Functions ..
175  INTRINSIC max
176 * ..
177 * .. Executable Statements ..
178 *
179 * Quick exit if N = 0 or NRHS = 0
180 *
181  IF( n.LE.0 .OR. nrhs.LE.0 ) THEN
182  resid = zero
183  RETURN
184  END IF
185 *
186 * Compute the 1-norm of op(A).
187 *
188  IF( lsame( trans, 'N' ) ) THEN
189  anorm = dlantp( '1', uplo, diag, n, ap, work )
190  ELSE
191  anorm = dlantp( 'I', uplo, diag, n, ap, work )
192  END IF
193 *
194 * Exit with RESID = 1/EPS if ANORM = 0.
195 *
196  eps = dlamch( 'Epsilon' )
197  IF( anorm.LE.zero ) THEN
198  resid = one / eps
199  RETURN
200  END IF
201 *
202 * Compute the maximum over the number of right hand sides of
203 * norm(op(A)*X - B) / ( norm(op(A)) * norm(X) * EPS ).
204 *
205  resid = zero
206  DO 10 j = 1, nrhs
207  CALL dcopy( n, x( 1, j ), 1, work, 1 )
208  CALL dtpmv( uplo, trans, diag, n, ap, work, 1 )
209  CALL daxpy( n, -one, b( 1, j ), 1, work, 1 )
210  bnorm = dasum( n, work, 1 )
211  xnorm = dasum( n, x( 1, j ), 1 )
212  IF( xnorm.LE.zero ) THEN
213  resid = one / eps
214  ELSE
215  resid = max( resid, ( ( bnorm / anorm ) / xnorm ) / eps )
216  END IF
217  10 CONTINUE
218 *
219  RETURN
220 *
221 * End of DTPT02
222 *
223  END
subroutine dcopy(N, DX, INCX, DY, INCY)
DCOPY
Definition: dcopy.f:82
subroutine daxpy(N, DA, DX, INCX, DY, INCY)
DAXPY
Definition: daxpy.f:89
subroutine dtpmv(UPLO, TRANS, DIAG, N, AP, X, INCX)
DTPMV
Definition: dtpmv.f:142
subroutine dtpt02(UPLO, TRANS, DIAG, N, NRHS, AP, X, LDX, B, LDB, WORK, RESID)
DTPT02
Definition: dtpt02.f:142