LAPACK  3.8.0
LAPACK: Linear Algebra PACKage
ztpt03.f
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1 *> \brief \b ZTPT03
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 ZTPT03( 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 * DOUBLE PRECISION RESID, SCALE, TSCAL
18 * ..
19 * .. Array Arguments ..
20 * DOUBLE PRECISION CNORM( * )
21 * COMPLEX*16 AP( * ), B( LDB, * ), WORK( * ), X( LDX, * )
22 * ..
23 *
24 *
25 *> \par Purpose:
26 * =============
27 *>
28 *> \verbatim
29 *>
30 *> ZTPT03 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*16 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 DOUBLE PRECISION
95 *> The scaling factor s used in solving the triangular system.
96 *> \endverbatim
97 *>
98 *> \param[in] CNORM
99 *> \verbatim
100 *> CNORM is DOUBLE PRECISION 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 DOUBLE PRECISION
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*16 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*16 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*16 array, dimension (N)
140 *> \endverbatim
141 *>
142 *> \param[out] RESID
143 *> \verbatim
144 *> RESID is DOUBLE PRECISION
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 *> \date December 2016
158 *
159 *> \ingroup complex16_lin
160 *
161 * =====================================================================
162  SUBROUTINE ztpt03( UPLO, TRANS, DIAG, N, NRHS, AP, SCALE, CNORM,
163  $ TSCAL, X, LDX, B, LDB, WORK, RESID )
164 *
165 * -- LAPACK test routine (version 3.7.0) --
166 * -- LAPACK is a software package provided by Univ. of Tennessee, --
167 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
168 * December 2016
169 *
170 * .. Scalar Arguments ..
171  CHARACTER DIAG, TRANS, UPLO
172  INTEGER LDB, LDX, N, NRHS
173  DOUBLE PRECISION RESID, SCALE, TSCAL
174 * ..
175 * .. Array Arguments ..
176  DOUBLE PRECISION CNORM( * )
177  COMPLEX*16 AP( * ), B( ldb, * ), WORK( * ), X( ldx, * )
178 * ..
179 *
180 * =====================================================================
181 *
182 * .. Parameters ..
183  DOUBLE PRECISION ONE, ZERO
184  parameter( one = 1.0d+0, zero = 0.0d+0 )
185 * ..
186 * .. Local Scalars ..
187  INTEGER IX, J, JJ
188  DOUBLE PRECISION EPS, ERR, SMLNUM, TNORM, XNORM, XSCAL
189 * ..
190 * .. External Functions ..
191  LOGICAL LSAME
192  INTEGER IZAMAX
193  DOUBLE PRECISION DLAMCH
194  EXTERNAL lsame, izamax, dlamch
195 * ..
196 * .. External Subroutines ..
197  EXTERNAL zaxpy, zcopy, zdscal, ztpmv
198 * ..
199 * .. Intrinsic Functions ..
200  INTRINSIC abs, dble, dcmplx, max
201 * ..
202 * .. Executable Statements ..
203 *
204 * Quick exit if N = 0.
205 *
206  IF( n.LE.0 .OR. nrhs.LE.0 ) THEN
207  resid = zero
208  RETURN
209  END IF
210  eps = dlamch( 'Epsilon' )
211  smlnum = dlamch( 'Safe minimum' )
212 *
213 * Compute the norm of the triangular matrix A using the column
214 * norms already computed by ZLATPS.
215 *
216  tnorm = 0.d0
217  IF( lsame( diag, 'N' ) ) THEN
218  IF( lsame( uplo, 'U' ) ) THEN
219  jj = 1
220  DO 10 j = 1, n
221  tnorm = max( tnorm, tscal*abs( ap( jj ) )+cnorm( j ) )
222  jj = jj + j
223  10 CONTINUE
224  ELSE
225  jj = 1
226  DO 20 j = 1, n
227  tnorm = max( tnorm, tscal*abs( ap( jj ) )+cnorm( j ) )
228  jj = jj + n - j + 1
229  20 CONTINUE
230  END IF
231  ELSE
232  DO 30 j = 1, n
233  tnorm = max( tnorm, tscal+cnorm( j ) )
234  30 CONTINUE
235  END IF
236 *
237 * Compute the maximum over the number of right hand sides of
238 * norm(op(A)*x - s*b) / ( norm(A) * norm(x) * EPS ).
239 *
240  resid = zero
241  DO 40 j = 1, nrhs
242  CALL zcopy( n, x( 1, j ), 1, work, 1 )
243  ix = izamax( n, work, 1 )
244  xnorm = max( one, abs( x( ix, j ) ) )
245  xscal = ( one / xnorm ) / dble( n )
246  CALL zdscal( n, xscal, work, 1 )
247  CALL ztpmv( uplo, trans, diag, n, ap, work, 1 )
248  CALL zaxpy( n, dcmplx( -scale*xscal ), b( 1, j ), 1, work, 1 )
249  ix = izamax( n, work, 1 )
250  err = tscal*abs( work( ix ) )
251  ix = izamax( n, x( 1, j ), 1 )
252  xnorm = abs( x( ix, j ) )
253  IF( err*smlnum.LE.xnorm ) THEN
254  IF( xnorm.GT.zero )
255  $ err = err / xnorm
256  ELSE
257  IF( err.GT.zero )
258  $ err = one / eps
259  END IF
260  IF( err*smlnum.LE.tnorm ) THEN
261  IF( tnorm.GT.zero )
262  $ err = err / tnorm
263  ELSE
264  IF( err.GT.zero )
265  $ err = one / eps
266  END IF
267  resid = max( resid, err )
268  40 CONTINUE
269 *
270  RETURN
271 *
272 * End of ZTPT03
273 *
274  END
subroutine zcopy(N, ZX, INCX, ZY, INCY)
ZCOPY
Definition: zcopy.f:83
subroutine ztpmv(UPLO, TRANS, DIAG, N, AP, X, INCX)
ZTPMV
Definition: ztpmv.f:144
subroutine zdscal(N, DA, ZX, INCX)
ZDSCAL
Definition: zdscal.f:80
subroutine ztpt03(UPLO, TRANS, DIAG, N, NRHS, AP, SCALE, CNORM, TSCAL, X, LDX, B, LDB, WORK, RESID)
ZTPT03
Definition: ztpt03.f:164
subroutine zaxpy(N, ZA, ZX, INCX, ZY, INCY)
ZAXPY
Definition: zaxpy.f:90