LAPACK  3.10.1
LAPACK: Linear Algebra PACKage
ctpt03.f
Go to the documentation of this file.
1 *> \brief \b CTPT03
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 CTPT03( UPLO, TRANS, DIAG, N, NRHS, AP, SCALE, CNORM,
12 * TSCAL, X, LDX, B, LDB, WORK, RESID )
13 *
14 * .. Scalar Arguments ..
15 * CHARACTER DIAG, TRANS, UPLO
16 * INTEGER LDB, LDX, N, NRHS
17 * REAL RESID, SCALE, TSCAL
18 * ..
19 * .. Array Arguments ..
20 * REAL CNORM( * )
21 * COMPLEX AP( * ), B( LDB, * ), WORK( * ), X( LDX, * )
22 * ..
23 *
24 *
25 *> \par Purpose:
26 * =============
27 *>
28 *> \verbatim
29 *>
30 *> CTPT03 computes the residual for the solution to a scaled triangular
31 *> system of equations A*x = s*b, A**T *x = s*b, or A**H *x = s*b,
32 *> when the triangular matrix A is stored in packed format. Here A**T
33 *> denotes the transpose of A, A**H denotes the conjugate transpose of
34 *> A, s is a scalar, and x and b are N by NRHS matrices. The test ratio
35 *> is the maximum over the number of right hand sides of
36 *> norm(s*b - op(A)*x) / ( norm(op(A)) * norm(x) * EPS ),
37 *> where op(A) denotes A, A**T, or A**H, and EPS is the machine epsilon.
38 *> \endverbatim
39 *
40 * Arguments:
41 * ==========
42 *
43 *> \param[in] UPLO
44 *> \verbatim
45 *> UPLO is CHARACTER*1
46 *> Specifies whether the matrix A is upper or lower triangular.
47 *> = 'U': Upper triangular
48 *> = 'L': Lower triangular
49 *> \endverbatim
50 *>
51 *> \param[in] TRANS
52 *> \verbatim
53 *> TRANS is CHARACTER*1
54 *> Specifies the operation applied to A.
55 *> = 'N': A *x = s*b (No transpose)
56 *> = 'T': A**T *x = s*b (Transpose)
57 *> = 'C': A**H *x = s*b (Conjugate transpose)
58 *> \endverbatim
59 *>
60 *> \param[in] DIAG
61 *> \verbatim
62 *> DIAG is CHARACTER*1
63 *> Specifies whether or not the matrix A is unit triangular.
64 *> = 'N': Non-unit triangular
65 *> = 'U': Unit triangular
66 *> \endverbatim
67 *>
68 *> \param[in] N
69 *> \verbatim
70 *> N is INTEGER
71 *> The order of the matrix A. N >= 0.
72 *> \endverbatim
73 *>
74 *> \param[in] NRHS
75 *> \verbatim
76 *> NRHS is INTEGER
77 *> The number of right hand sides, i.e., the number of columns
78 *> of the matrices X and B. NRHS >= 0.
79 *> \endverbatim
80 *>
81 *> \param[in] AP
82 *> \verbatim
83 *> AP is COMPLEX array, dimension (N*(N+1)/2)
84 *> The upper or lower triangular matrix A, packed columnwise in
85 *> a linear array. The j-th column of A is stored in the array
86 *> AP as follows:
87 *> if UPLO = 'U', AP((j-1)*j/2 + i) = A(i,j) for 1<=i<=j;
88 *> if UPLO = 'L',
89 *> AP((j-1)*(n-j) + j*(j+1)/2 + i-j) = A(i,j) for j<=i<=n.
90 *> \endverbatim
91 *>
92 *> \param[in] SCALE
93 *> \verbatim
94 *> SCALE is REAL
95 *> The scaling factor s used in solving the triangular system.
96 *> \endverbatim
97 *>
98 *> \param[in] CNORM
99 *> \verbatim
100 *> CNORM is REAL array, dimension (N)
101 *> The 1-norms of the columns of A, not counting the diagonal.
102 *> \endverbatim
103 *>
104 *> \param[in] TSCAL
105 *> \verbatim
106 *> TSCAL is REAL
107 *> The scaling factor used in computing the 1-norms in CNORM.
108 *> CNORM actually contains the column norms of TSCAL*A.
109 *> \endverbatim
110 *>
111 *> \param[in] X
112 *> \verbatim
113 *> X is COMPLEX array, dimension (LDX,NRHS)
114 *> The computed solution vectors for the system of linear
115 *> equations.
116 *> \endverbatim
117 *>
118 *> \param[in] LDX
119 *> \verbatim
120 *> LDX is INTEGER
121 *> The leading dimension of the array X. LDX >= max(1,N).
122 *> \endverbatim
123 *>
124 *> \param[in] B
125 *> \verbatim
126 *> B is COMPLEX array, dimension (LDB,NRHS)
127 *> The right hand side vectors for the system of linear
128 *> equations.
129 *> \endverbatim
130 *>
131 *> \param[in] LDB
132 *> \verbatim
133 *> LDB is INTEGER
134 *> The leading dimension of the array B. LDB >= max(1,N).
135 *> \endverbatim
136 *>
137 *> \param[out] WORK
138 *> \verbatim
139 *> WORK is COMPLEX array, dimension (N)
140 *> \endverbatim
141 *>
142 *> \param[out] RESID
143 *> \verbatim
144 *> RESID is REAL
145 *> The maximum over the number of right hand sides of
146 *> norm(op(A)*x - s*b) / ( norm(op(A)) * norm(x) * EPS ).
147 *> \endverbatim
148 *
149 * Authors:
150 * ========
151 *
152 *> \author Univ. of Tennessee
153 *> \author Univ. of California Berkeley
154 *> \author Univ. of Colorado Denver
155 *> \author NAG Ltd.
156 *
157 *> \ingroup complex_lin
158 *
159 * =====================================================================
160  SUBROUTINE ctpt03( UPLO, TRANS, DIAG, N, NRHS, AP, SCALE, CNORM,
161  $ TSCAL, X, LDX, B, LDB, WORK, RESID )
162 *
163 * -- LAPACK test routine --
164 * -- LAPACK is a software package provided by Univ. of Tennessee, --
165 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
166 *
167 * .. Scalar Arguments ..
168  CHARACTER DIAG, TRANS, UPLO
169  INTEGER LDB, LDX, N, NRHS
170  REAL RESID, SCALE, TSCAL
171 * ..
172 * .. Array Arguments ..
173  REAL CNORM( * )
174  COMPLEX AP( * ), B( LDB, * ), WORK( * ), X( LDX, * )
175 * ..
176 *
177 * =====================================================================
178 *
179 * .. Parameters ..
180  REAL ONE, ZERO
181  parameter( one = 1.0e+0, zero = 0.0e+0 )
182 * ..
183 * .. Local Scalars ..
184  INTEGER IX, J, JJ
185  REAL EPS, ERR, SMLNUM, TNORM, XNORM, XSCAL
186 * ..
187 * .. External Functions ..
188  LOGICAL LSAME
189  INTEGER ICAMAX
190  REAL SLAMCH
191  EXTERNAL lsame, icamax, slamch
192 * ..
193 * .. External Subroutines ..
194  EXTERNAL caxpy, ccopy, csscal, ctpmv
195 * ..
196 * .. Intrinsic Functions ..
197  INTRINSIC abs, cmplx, max, real
198 * ..
199 * .. Executable Statements ..
200 *
201 * Quick exit if N = 0.
202 *
203  IF( n.LE.0 .OR. nrhs.LE.0 ) THEN
204  resid = zero
205  RETURN
206  END IF
207  eps = slamch( 'Epsilon' )
208  smlnum = slamch( 'Safe minimum' )
209 *
210 * Compute the norm of the triangular matrix A using the column
211 * norms already computed by CLATPS.
212 *
213  tnorm = 0.
214  IF( lsame( diag, 'N' ) ) THEN
215  IF( lsame( uplo, 'U' ) ) THEN
216  jj = 1
217  DO 10 j = 1, n
218  tnorm = max( tnorm, tscal*abs( ap( jj ) )+cnorm( j ) )
219  jj = jj + j + 1
220  10 CONTINUE
221  ELSE
222  jj = 1
223  DO 20 j = 1, n
224  tnorm = max( tnorm, tscal*abs( ap( jj ) )+cnorm( j ) )
225  jj = jj + n - j + 1
226  20 CONTINUE
227  END IF
228  ELSE
229  DO 30 j = 1, n
230  tnorm = max( tnorm, tscal+cnorm( j ) )
231  30 CONTINUE
232  END IF
233 *
234 * Compute the maximum over the number of right hand sides of
235 * norm(op(A)*x - s*b) / ( norm(A) * norm(x) * EPS ).
236 *
237  resid = zero
238  DO 40 j = 1, nrhs
239  CALL ccopy( n, x( 1, j ), 1, work, 1 )
240  ix = icamax( n, work, 1 )
241  xnorm = max( one, abs( x( ix, j ) ) )
242  xscal = ( one / xnorm ) / real( n )
243  CALL csscal( n, xscal, work, 1 )
244  CALL ctpmv( uplo, trans, diag, n, ap, work, 1 )
245  CALL caxpy( n, cmplx( -scale*xscal ), b( 1, j ), 1, work, 1 )
246  ix = icamax( n, work, 1 )
247  err = tscal*abs( work( ix ) )
248  ix = icamax( n, x( 1, j ), 1 )
249  xnorm = abs( x( ix, j ) )
250  IF( err*smlnum.LE.xnorm ) THEN
251  IF( xnorm.GT.zero )
252  $ err = err / xnorm
253  ELSE
254  IF( err.GT.zero )
255  $ err = one / eps
256  END IF
257  IF( err*smlnum.LE.tnorm ) THEN
258  IF( tnorm.GT.zero )
259  $ err = err / tnorm
260  ELSE
261  IF( err.GT.zero )
262  $ err = one / eps
263  END IF
264  resid = max( resid, err )
265  40 CONTINUE
266 *
267  RETURN
268 *
269 * End of CTPT03
270 *
271  END
subroutine ccopy(N, CX, INCX, CY, INCY)
CCOPY
Definition: ccopy.f:81
subroutine csscal(N, SA, CX, INCX)
CSSCAL
Definition: csscal.f:78
subroutine caxpy(N, CA, CX, INCX, CY, INCY)
CAXPY
Definition: caxpy.f:88
subroutine ctpmv(UPLO, TRANS, DIAG, N, AP, X, INCX)
CTPMV
Definition: ctpmv.f:142
subroutine ctpt03(UPLO, TRANS, DIAG, N, NRHS, AP, SCALE, CNORM, TSCAL, X, LDX, B, LDB, WORK, RESID)
CTPT03
Definition: ctpt03.f:162