LAPACK  3.8.0
LAPACK: Linear Algebra PACKage
dlantr.f
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1 *> \brief \b DLANTR returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a trapezoidal or triangular matrix.
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
7 *
8 *> \htmlonly
9 *> Download DLANTR + dependencies
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11 *> [TGZ]</a>
12 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlantr.f">
13 *> [ZIP]</a>
14 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlantr.f">
15 *> [TXT]</a>
16 *> \endhtmlonly
17 *
18 * Definition:
19 * ===========
20 *
21 * DOUBLE PRECISION FUNCTION DLANTR( NORM, UPLO, DIAG, M, N, A, LDA,
22 * WORK )
23 *
24 * .. Scalar Arguments ..
25 * CHARACTER DIAG, NORM, UPLO
26 * INTEGER LDA, M, N
27 * ..
28 * .. Array Arguments ..
29 * DOUBLE PRECISION A( LDA, * ), WORK( * )
30 * ..
31 *
32 *
33 *> \par Purpose:
34 * =============
35 *>
36 *> \verbatim
37 *>
38 *> DLANTR returns the value of the one norm, or the Frobenius norm, or
39 *> the infinity norm, or the element of largest absolute value of a
40 *> trapezoidal or triangular matrix A.
41 *> \endverbatim
42 *>
43 *> \return DLANTR
44 *> \verbatim
45 *>
46 *> DLANTR = ( max(abs(A(i,j))), NORM = 'M' or 'm'
47 *> (
48 *> ( norm1(A), NORM = '1', 'O' or 'o'
49 *> (
50 *> ( normI(A), NORM = 'I' or 'i'
51 *> (
52 *> ( normF(A), NORM = 'F', 'f', 'E' or 'e'
53 *>
54 *> where norm1 denotes the one norm of a matrix (maximum column sum),
55 *> normI denotes the infinity norm of a matrix (maximum row sum) and
56 *> normF denotes the Frobenius norm of a matrix (square root of sum of
57 *> squares). Note that max(abs(A(i,j))) is not a consistent matrix norm.
58 *> \endverbatim
59 *
60 * Arguments:
61 * ==========
62 *
63 *> \param[in] NORM
64 *> \verbatim
65 *> NORM is CHARACTER*1
66 *> Specifies the value to be returned in DLANTR as described
67 *> above.
68 *> \endverbatim
69 *>
70 *> \param[in] UPLO
71 *> \verbatim
72 *> UPLO is CHARACTER*1
73 *> Specifies whether the matrix A is upper or lower trapezoidal.
74 *> = 'U': Upper trapezoidal
75 *> = 'L': Lower trapezoidal
76 *> Note that A is triangular instead of trapezoidal if M = N.
77 *> \endverbatim
78 *>
79 *> \param[in] DIAG
80 *> \verbatim
81 *> DIAG is CHARACTER*1
82 *> Specifies whether or not the matrix A has unit diagonal.
83 *> = 'N': Non-unit diagonal
84 *> = 'U': Unit diagonal
85 *> \endverbatim
86 *>
87 *> \param[in] M
88 *> \verbatim
89 *> M is INTEGER
90 *> The number of rows of the matrix A. M >= 0, and if
91 *> UPLO = 'U', M <= N. When M = 0, DLANTR is set to zero.
92 *> \endverbatim
93 *>
94 *> \param[in] N
95 *> \verbatim
96 *> N is INTEGER
97 *> The number of columns of the matrix A. N >= 0, and if
98 *> UPLO = 'L', N <= M. When N = 0, DLANTR is set to zero.
99 *> \endverbatim
100 *>
101 *> \param[in] A
102 *> \verbatim
103 *> A is DOUBLE PRECISION array, dimension (LDA,N)
104 *> The trapezoidal matrix A (A is triangular if M = N).
105 *> If UPLO = 'U', the leading m by n upper trapezoidal part of
106 *> the array A contains the upper trapezoidal matrix, and the
107 *> strictly lower triangular part of A is not referenced.
108 *> If UPLO = 'L', the leading m by n lower trapezoidal part of
109 *> the array A contains the lower trapezoidal matrix, and the
110 *> strictly upper triangular part of A is not referenced. Note
111 *> that when DIAG = 'U', the diagonal elements of A are not
112 *> referenced and are assumed to be one.
113 *> \endverbatim
114 *>
115 *> \param[in] LDA
116 *> \verbatim
117 *> LDA is INTEGER
118 *> The leading dimension of the array A. LDA >= max(M,1).
119 *> \endverbatim
120 *>
121 *> \param[out] WORK
122 *> \verbatim
123 *> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
124 *> where LWORK >= M when NORM = 'I'; otherwise, WORK is not
125 *> referenced.
126 *> \endverbatim
127 *
128 * Authors:
129 * ========
130 *
131 *> \author Univ. of Tennessee
132 *> \author Univ. of California Berkeley
133 *> \author Univ. of Colorado Denver
134 *> \author NAG Ltd.
135 *
136 *> \date December 2016
137 *
138 *> \ingroup doubleOTHERauxiliary
139 *
140 * =====================================================================
141  DOUBLE PRECISION FUNCTION dlantr( NORM, UPLO, DIAG, M, N, A, LDA,
142  $ WORK )
143 *
144 * -- LAPACK auxiliary routine (version 3.7.0) --
145 * -- LAPACK is a software package provided by Univ. of Tennessee, --
146 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
147 * December 2016
148 *
149 * .. Scalar Arguments ..
150  CHARACTER DIAG, NORM, UPLO
151  INTEGER LDA, M, N
152 * ..
153 * .. Array Arguments ..
154  DOUBLE PRECISION A( lda, * ), WORK( * )
155 * ..
156 *
157 * =====================================================================
158 *
159 * .. Parameters ..
160  DOUBLE PRECISION ONE, ZERO
161  parameter( one = 1.0d+0, zero = 0.0d+0 )
162 * ..
163 * .. Local Scalars ..
164  LOGICAL UDIAG
165  INTEGER I, J
166  DOUBLE PRECISION SCALE, SUM, VALUE
167 * ..
168 * .. External Subroutines ..
169  EXTERNAL dlassq
170 * ..
171 * .. External Functions ..
172  LOGICAL LSAME, DISNAN
173  EXTERNAL lsame, disnan
174 * ..
175 * .. Intrinsic Functions ..
176  INTRINSIC abs, min, sqrt
177 * ..
178 * .. Executable Statements ..
179 *
180  IF( min( m, n ).EQ.0 ) THEN
181  VALUE = zero
182  ELSE IF( lsame( norm, 'M' ) ) THEN
183 *
184 * Find max(abs(A(i,j))).
185 *
186  IF( lsame( diag, 'U' ) ) THEN
187  VALUE = one
188  IF( lsame( uplo, 'U' ) ) THEN
189  DO 20 j = 1, n
190  DO 10 i = 1, min( m, j-1 )
191  sum = abs( a( i, j ) )
192  IF( VALUE .LT. sum .OR. disnan( sum ) ) VALUE = sum
193  10 CONTINUE
194  20 CONTINUE
195  ELSE
196  DO 40 j = 1, n
197  DO 30 i = j + 1, m
198  sum = abs( a( i, j ) )
199  IF( VALUE .LT. sum .OR. disnan( sum ) ) VALUE = sum
200  30 CONTINUE
201  40 CONTINUE
202  END IF
203  ELSE
204  VALUE = zero
205  IF( lsame( uplo, 'U' ) ) THEN
206  DO 60 j = 1, n
207  DO 50 i = 1, min( m, j )
208  sum = abs( a( i, j ) )
209  IF( VALUE .LT. sum .OR. disnan( sum ) ) VALUE = sum
210  50 CONTINUE
211  60 CONTINUE
212  ELSE
213  DO 80 j = 1, n
214  DO 70 i = j, m
215  sum = abs( a( i, j ) )
216  IF( VALUE .LT. sum .OR. disnan( sum ) ) VALUE = sum
217  70 CONTINUE
218  80 CONTINUE
219  END IF
220  END IF
221  ELSE IF( ( lsame( norm, 'O' ) ) .OR. ( norm.EQ.'1' ) ) THEN
222 *
223 * Find norm1(A).
224 *
225  VALUE = zero
226  udiag = lsame( diag, 'U' )
227  IF( lsame( uplo, 'U' ) ) THEN
228  DO 110 j = 1, n
229  IF( ( udiag ) .AND. ( j.LE.m ) ) THEN
230  sum = one
231  DO 90 i = 1, j - 1
232  sum = sum + abs( a( i, j ) )
233  90 CONTINUE
234  ELSE
235  sum = zero
236  DO 100 i = 1, min( m, j )
237  sum = sum + abs( a( i, j ) )
238  100 CONTINUE
239  END IF
240  IF( VALUE .LT. sum .OR. disnan( sum ) ) VALUE = sum
241  110 CONTINUE
242  ELSE
243  DO 140 j = 1, n
244  IF( udiag ) THEN
245  sum = one
246  DO 120 i = j + 1, m
247  sum = sum + abs( a( i, j ) )
248  120 CONTINUE
249  ELSE
250  sum = zero
251  DO 130 i = j, m
252  sum = sum + abs( a( i, j ) )
253  130 CONTINUE
254  END IF
255  IF( VALUE .LT. sum .OR. disnan( sum ) ) VALUE = sum
256  140 CONTINUE
257  END IF
258  ELSE IF( lsame( norm, 'I' ) ) THEN
259 *
260 * Find normI(A).
261 *
262  IF( lsame( uplo, 'U' ) ) THEN
263  IF( lsame( diag, 'U' ) ) THEN
264  DO 150 i = 1, m
265  work( i ) = one
266  150 CONTINUE
267  DO 170 j = 1, n
268  DO 160 i = 1, min( m, j-1 )
269  work( i ) = work( i ) + abs( a( i, j ) )
270  160 CONTINUE
271  170 CONTINUE
272  ELSE
273  DO 180 i = 1, m
274  work( i ) = zero
275  180 CONTINUE
276  DO 200 j = 1, n
277  DO 190 i = 1, min( m, j )
278  work( i ) = work( i ) + abs( a( i, j ) )
279  190 CONTINUE
280  200 CONTINUE
281  END IF
282  ELSE
283  IF( lsame( diag, 'U' ) ) THEN
284  DO 210 i = 1, n
285  work( i ) = one
286  210 CONTINUE
287  DO 220 i = n + 1, m
288  work( i ) = zero
289  220 CONTINUE
290  DO 240 j = 1, n
291  DO 230 i = j + 1, m
292  work( i ) = work( i ) + abs( a( i, j ) )
293  230 CONTINUE
294  240 CONTINUE
295  ELSE
296  DO 250 i = 1, m
297  work( i ) = zero
298  250 CONTINUE
299  DO 270 j = 1, n
300  DO 260 i = j, m
301  work( i ) = work( i ) + abs( a( i, j ) )
302  260 CONTINUE
303  270 CONTINUE
304  END IF
305  END IF
306  VALUE = zero
307  DO 280 i = 1, m
308  sum = work( i )
309  IF( VALUE .LT. sum .OR. disnan( sum ) ) VALUE = sum
310  280 CONTINUE
311  ELSE IF( ( lsame( norm, 'F' ) ) .OR. ( lsame( norm, 'E' ) ) ) THEN
312 *
313 * Find normF(A).
314 *
315  IF( lsame( uplo, 'U' ) ) THEN
316  IF( lsame( diag, 'U' ) ) THEN
317  scale = one
318  sum = min( m, n )
319  DO 290 j = 2, n
320  CALL dlassq( min( m, j-1 ), a( 1, j ), 1, scale, sum )
321  290 CONTINUE
322  ELSE
323  scale = zero
324  sum = one
325  DO 300 j = 1, n
326  CALL dlassq( min( m, j ), a( 1, j ), 1, scale, sum )
327  300 CONTINUE
328  END IF
329  ELSE
330  IF( lsame( diag, 'U' ) ) THEN
331  scale = one
332  sum = min( m, n )
333  DO 310 j = 1, n
334  CALL dlassq( m-j, a( min( m, j+1 ), j ), 1, scale,
335  $ sum )
336  310 CONTINUE
337  ELSE
338  scale = zero
339  sum = one
340  DO 320 j = 1, n
341  CALL dlassq( m-j+1, a( j, j ), 1, scale, sum )
342  320 CONTINUE
343  END IF
344  END IF
345  VALUE = scale*sqrt( sum )
346  END IF
347 *
348  dlantr = VALUE
349  RETURN
350 *
351 * End of DLANTR
352 *
353  END
subroutine dlassq(N, X, INCX, SCALE, SUMSQ)
DLASSQ updates a sum of squares represented in scaled form.
Definition: dlassq.f:105
double precision function dlantr(NORM, UPLO, DIAG, M, N, A, LDA, WORK)
DLANTR returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a trapezoidal or triangular matrix.
Definition: dlantr.f:143