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dlantp.f
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1 *> \brief \b DLANTP
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
7 *
8 *> \htmlonly
9 *> Download DLANTP + dependencies
10 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlantp.f">
11 *> [TGZ]</a>
12 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlantp.f">
13 *> [ZIP]</a>
14 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlantp.f">
15 *> [TXT]</a>
16 *> \endhtmlonly
17 *
18 * Definition:
19 * ===========
20 *
21 * DOUBLE PRECISION FUNCTION DLANTP( NORM, UPLO, DIAG, N, AP, WORK )
22 *
23 * .. Scalar Arguments ..
24 * CHARACTER DIAG, NORM, UPLO
25 * INTEGER N
26 * ..
27 * .. Array Arguments ..
28 * DOUBLE PRECISION AP( * ), WORK( * )
29 * ..
30 *
31 *
32 *> \par Purpose:
33 * =============
34 *>
35 *> \verbatim
36 *>
37 *> DLANTP returns the value of the one norm, or the Frobenius norm, or
38 *> the infinity norm, or the element of largest absolute value of a
39 *> triangular matrix A, supplied in packed form.
40 *> \endverbatim
41 *>
42 *> \return DLANTP
43 *> \verbatim
44 *>
45 *> DLANTP = ( max(abs(A(i,j))), NORM = 'M' or 'm'
46 *> (
47 *> ( norm1(A), NORM = '1', 'O' or 'o'
48 *> (
49 *> ( normI(A), NORM = 'I' or 'i'
50 *> (
51 *> ( normF(A), NORM = 'F', 'f', 'E' or 'e'
52 *>
53 *> where norm1 denotes the one norm of a matrix (maximum column sum),
54 *> normI denotes the infinity norm of a matrix (maximum row sum) and
55 *> normF denotes the Frobenius norm of a matrix (square root of sum of
56 *> squares). Note that max(abs(A(i,j))) is not a consistent matrix norm.
57 *> \endverbatim
58 *
59 * Arguments:
60 * ==========
61 *
62 *> \param[in] NORM
63 *> \verbatim
64 *> NORM is CHARACTER*1
65 *> Specifies the value to be returned in DLANTP as described
66 *> above.
67 *> \endverbatim
68 *>
69 *> \param[in] UPLO
70 *> \verbatim
71 *> UPLO is CHARACTER*1
72 *> Specifies whether the matrix A is upper or lower triangular.
73 *> = 'U': Upper triangular
74 *> = 'L': Lower triangular
75 *> \endverbatim
76 *>
77 *> \param[in] DIAG
78 *> \verbatim
79 *> DIAG is CHARACTER*1
80 *> Specifies whether or not the matrix A is unit triangular.
81 *> = 'N': Non-unit triangular
82 *> = 'U': Unit triangular
83 *> \endverbatim
84 *>
85 *> \param[in] N
86 *> \verbatim
87 *> N is INTEGER
88 *> The order of the matrix A. N >= 0. When N = 0, DLANTP is
89 *> set to zero.
90 *> \endverbatim
91 *>
92 *> \param[in] AP
93 *> \verbatim
94 *> AP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
95 *> The upper or lower triangular matrix A, packed columnwise in
96 *> a linear array. The j-th column of A is stored in the array
97 *> AP as follows:
98 *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
99 *> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
100 *> Note that when DIAG = 'U', the elements of the array AP
101 *> corresponding to the diagonal elements of the matrix A are
102 *> not referenced, but are assumed to be one.
103 *> \endverbatim
104 *>
105 *> \param[out] WORK
106 *> \verbatim
107 *> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
108 *> where LWORK >= N when NORM = 'I'; otherwise, WORK is not
109 *> referenced.
110 *> \endverbatim
111 *
112 * Authors:
113 * ========
114 *
115 *> \author Univ. of Tennessee
116 *> \author Univ. of California Berkeley
117 *> \author Univ. of Colorado Denver
118 *> \author NAG Ltd.
119 *
120 *> \date November 2011
121 *
122 *> \ingroup doubleOTHERauxiliary
123 *
124 * =====================================================================
125  DOUBLE PRECISION FUNCTION dlantp( NORM, UPLO, DIAG, N, AP, WORK )
126 *
127 * -- LAPACK auxiliary routine (version 3.4.0) --
128 * -- LAPACK is a software package provided by Univ. of Tennessee, --
129 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
130 * November 2011
131 *
132 * .. Scalar Arguments ..
133  CHARACTER diag, norm, uplo
134  INTEGER n
135 * ..
136 * .. Array Arguments ..
137  DOUBLE PRECISION ap( * ), work( * )
138 * ..
139 *
140 * =====================================================================
141 *
142 * .. Parameters ..
143  DOUBLE PRECISION one, zero
144  parameter( one = 1.0d+0, zero = 0.0d+0 )
145 * ..
146 * .. Local Scalars ..
147  LOGICAL udiag
148  INTEGER i, j, k
149  DOUBLE PRECISION scale, sum, value
150 * ..
151 * .. External Subroutines ..
152  EXTERNAL dlassq
153 * ..
154 * .. External Functions ..
155  LOGICAL lsame
156  EXTERNAL lsame
157 * ..
158 * .. Intrinsic Functions ..
159  INTRINSIC abs, max, sqrt
160 * ..
161 * .. Executable Statements ..
162 *
163  IF( n.EQ.0 ) THEN
164  value = zero
165  ELSE IF( lsame( norm, 'M' ) ) THEN
166 *
167 * Find max(abs(A(i,j))).
168 *
169  k = 1
170  IF( lsame( diag, 'U' ) ) THEN
171  value = one
172  IF( lsame( uplo, 'U' ) ) THEN
173  DO 20 j = 1, n
174  DO 10 i = k, k + j - 2
175  value = max( value, abs( ap( i ) ) )
176  10 CONTINUE
177  k = k + j
178  20 CONTINUE
179  ELSE
180  DO 40 j = 1, n
181  DO 30 i = k + 1, k + n - j
182  value = max( value, abs( ap( i ) ) )
183  30 CONTINUE
184  k = k + n - j + 1
185  40 CONTINUE
186  END IF
187  ELSE
188  value = zero
189  IF( lsame( uplo, 'U' ) ) THEN
190  DO 60 j = 1, n
191  DO 50 i = k, k + j - 1
192  value = max( value, abs( ap( i ) ) )
193  50 CONTINUE
194  k = k + j
195  60 CONTINUE
196  ELSE
197  DO 80 j = 1, n
198  DO 70 i = k, k + n - j
199  value = max( value, abs( ap( i ) ) )
200  70 CONTINUE
201  k = k + n - j + 1
202  80 CONTINUE
203  END IF
204  END IF
205  ELSE IF( ( lsame( norm, 'O' ) ) .OR. ( norm.EQ.'1' ) ) THEN
206 *
207 * Find norm1(A).
208 *
209  value = zero
210  k = 1
211  udiag = lsame( diag, 'U' )
212  IF( lsame( uplo, 'U' ) ) THEN
213  DO 110 j = 1, n
214  IF( udiag ) THEN
215  sum = one
216  DO 90 i = k, k + j - 2
217  sum = sum + abs( ap( i ) )
218  90 CONTINUE
219  ELSE
220  sum = zero
221  DO 100 i = k, k + j - 1
222  sum = sum + abs( ap( i ) )
223  100 CONTINUE
224  END IF
225  k = k + j
226  value = max( value, sum )
227  110 CONTINUE
228  ELSE
229  DO 140 j = 1, n
230  IF( udiag ) THEN
231  sum = one
232  DO 120 i = k + 1, k + n - j
233  sum = sum + abs( ap( i ) )
234  120 CONTINUE
235  ELSE
236  sum = zero
237  DO 130 i = k, k + n - j
238  sum = sum + abs( ap( i ) )
239  130 CONTINUE
240  END IF
241  k = k + n - j + 1
242  value = max( value, sum )
243  140 CONTINUE
244  END IF
245  ELSE IF( lsame( norm, 'I' ) ) THEN
246 *
247 * Find normI(A).
248 *
249  k = 1
250  IF( lsame( uplo, 'U' ) ) THEN
251  IF( lsame( diag, 'U' ) ) THEN
252  DO 150 i = 1, n
253  work( i ) = one
254  150 CONTINUE
255  DO 170 j = 1, n
256  DO 160 i = 1, j - 1
257  work( i ) = work( i ) + abs( ap( k ) )
258  k = k + 1
259  160 CONTINUE
260  k = k + 1
261  170 CONTINUE
262  ELSE
263  DO 180 i = 1, n
264  work( i ) = zero
265  180 CONTINUE
266  DO 200 j = 1, n
267  DO 190 i = 1, j
268  work( i ) = work( i ) + abs( ap( k ) )
269  k = k + 1
270  190 CONTINUE
271  200 CONTINUE
272  END IF
273  ELSE
274  IF( lsame( diag, 'U' ) ) THEN
275  DO 210 i = 1, n
276  work( i ) = one
277  210 CONTINUE
278  DO 230 j = 1, n
279  k = k + 1
280  DO 220 i = j + 1, n
281  work( i ) = work( i ) + abs( ap( k ) )
282  k = k + 1
283  220 CONTINUE
284  230 CONTINUE
285  ELSE
286  DO 240 i = 1, n
287  work( i ) = zero
288  240 CONTINUE
289  DO 260 j = 1, n
290  DO 250 i = j, n
291  work( i ) = work( i ) + abs( ap( k ) )
292  k = k + 1
293  250 CONTINUE
294  260 CONTINUE
295  END IF
296  END IF
297  value = zero
298  DO 270 i = 1, n
299  value = max( value, work( i ) )
300  270 CONTINUE
301  ELSE IF( ( lsame( norm, 'F' ) ) .OR. ( lsame( norm, 'E' ) ) ) THEN
302 *
303 * Find normF(A).
304 *
305  IF( lsame( uplo, 'U' ) ) THEN
306  IF( lsame( diag, 'U' ) ) THEN
307  scale = one
308  sum = n
309  k = 2
310  DO 280 j = 2, n
311  CALL dlassq( j-1, ap( k ), 1, scale, sum )
312  k = k + j
313  280 CONTINUE
314  ELSE
315  scale = zero
316  sum = one
317  k = 1
318  DO 290 j = 1, n
319  CALL dlassq( j, ap( k ), 1, scale, sum )
320  k = k + j
321  290 CONTINUE
322  END IF
323  ELSE
324  IF( lsame( diag, 'U' ) ) THEN
325  scale = one
326  sum = n
327  k = 2
328  DO 300 j = 1, n - 1
329  CALL dlassq( n-j, ap( k ), 1, scale, sum )
330  k = k + n - j + 1
331  300 CONTINUE
332  ELSE
333  scale = zero
334  sum = one
335  k = 1
336  DO 310 j = 1, n
337  CALL dlassq( n-j+1, ap( k ), 1, scale, sum )
338  k = k + n - j + 1
339  310 CONTINUE
340  END IF
341  END IF
342  value = scale*sqrt( sum )
343  END IF
344 *
345  dlantp = value
346  RETURN
347 *
348 * End of DLANTP
349 *
350  END