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slantr.f
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1 *> \brief \b SLANTR
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
7 *
8 *> \htmlonly
9 *> Download SLANTR + dependencies
10 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/slantr.f">
11 *> [TGZ]</a>
12 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/slantr.f">
13 *> [ZIP]</a>
14 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/slantr.f">
15 *> [TXT]</a>
16 *> \endhtmlonly
17 *
18 * Definition:
19 * ===========
20 *
21 * REAL FUNCTION SLANTR( 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 * REAL A( LDA, * ), WORK( * )
30 * ..
31 *
32 *
33 *> \par Purpose:
34 * =============
35 *>
36 *> \verbatim
37 *>
38 *> SLANTR 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 SLANTR
44 *> \verbatim
45 *>
46 *> SLANTR = ( 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 SLANTR 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, SLANTR 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, SLANTR is set to zero.
99 *> \endverbatim
100 *>
101 *> \param[in] A
102 *> \verbatim
103 *> A is REAL 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 REAL 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 November 2011
137 *
138 *> \ingroup realOTHERauxiliary
139 *
140 * =====================================================================
141  REAL FUNCTION slantr( NORM, UPLO, DIAG, M, N, A, LDA,
142  $ work )
143 *
144 * -- LAPACK auxiliary routine (version 3.4.0) --
145 * -- LAPACK is a software package provided by Univ. of Tennessee, --
146 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
147 * November 2011
148 *
149 * .. Scalar Arguments ..
150  CHARACTER diag, norm, uplo
151  INTEGER lda, m, n
152 * ..
153 * .. Array Arguments ..
154  REAL a( lda, * ), work( * )
155 * ..
156 *
157 * =====================================================================
158 *
159 * .. Parameters ..
160  REAL one, zero
161  parameter( one = 1.0e+0, zero = 0.0e+0 )
162 * ..
163 * .. Local Scalars ..
164  LOGICAL udiag
165  INTEGER i, j
166  REAL scale, sum, value
167 * ..
168 * .. External Subroutines ..
169  EXTERNAL slassq
170 * ..
171 * .. External Functions ..
172  LOGICAL lsame
173  EXTERNAL lsame
174 * ..
175 * .. Intrinsic Functions ..
176  INTRINSIC abs, max, 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  value = max( value, abs( a( i, j ) ) )
192  10 CONTINUE
193  20 CONTINUE
194  ELSE
195  DO 40 j = 1, n
196  DO 30 i = j + 1, m
197  value = max( value, abs( a( i, j ) ) )
198  30 CONTINUE
199  40 CONTINUE
200  END IF
201  ELSE
202  value = zero
203  IF( lsame( uplo, 'U' ) ) THEN
204  DO 60 j = 1, n
205  DO 50 i = 1, min( m, j )
206  value = max( value, abs( a( i, j ) ) )
207  50 CONTINUE
208  60 CONTINUE
209  ELSE
210  DO 80 j = 1, n
211  DO 70 i = j, m
212  value = max( value, abs( a( i, j ) ) )
213  70 CONTINUE
214  80 CONTINUE
215  END IF
216  END IF
217  ELSE IF( ( lsame( norm, 'O' ) ) .OR. ( norm.EQ.'1' ) ) THEN
218 *
219 * Find norm1(A).
220 *
221  value = zero
222  udiag = lsame( diag, 'U' )
223  IF( lsame( uplo, 'U' ) ) THEN
224  DO 110 j = 1, n
225  IF( ( udiag ) .AND. ( j.LE.m ) ) THEN
226  sum = one
227  DO 90 i = 1, j - 1
228  sum = sum + abs( a( i, j ) )
229  90 CONTINUE
230  ELSE
231  sum = zero
232  DO 100 i = 1, min( m, j )
233  sum = sum + abs( a( i, j ) )
234  100 CONTINUE
235  END IF
236  value = max( value, sum )
237  110 CONTINUE
238  ELSE
239  DO 140 j = 1, n
240  IF( udiag ) THEN
241  sum = one
242  DO 120 i = j + 1, m
243  sum = sum + abs( a( i, j ) )
244  120 CONTINUE
245  ELSE
246  sum = zero
247  DO 130 i = j, m
248  sum = sum + abs( a( i, j ) )
249  130 CONTINUE
250  END IF
251  value = max( value, sum )
252  140 CONTINUE
253  END IF
254  ELSE IF( lsame( norm, 'I' ) ) THEN
255 *
256 * Find normI(A).
257 *
258  IF( lsame( uplo, 'U' ) ) THEN
259  IF( lsame( diag, 'U' ) ) THEN
260  DO 150 i = 1, m
261  work( i ) = one
262  150 CONTINUE
263  DO 170 j = 1, n
264  DO 160 i = 1, min( m, j-1 )
265  work( i ) = work( i ) + abs( a( i, j ) )
266  160 CONTINUE
267  170 CONTINUE
268  ELSE
269  DO 180 i = 1, m
270  work( i ) = zero
271  180 CONTINUE
272  DO 200 j = 1, n
273  DO 190 i = 1, min( m, j )
274  work( i ) = work( i ) + abs( a( i, j ) )
275  190 CONTINUE
276  200 CONTINUE
277  END IF
278  ELSE
279  IF( lsame( diag, 'U' ) ) THEN
280  DO 210 i = 1, n
281  work( i ) = one
282  210 CONTINUE
283  DO 220 i = n + 1, m
284  work( i ) = zero
285  220 CONTINUE
286  DO 240 j = 1, n
287  DO 230 i = j + 1, m
288  work( i ) = work( i ) + abs( a( i, j ) )
289  230 CONTINUE
290  240 CONTINUE
291  ELSE
292  DO 250 i = 1, m
293  work( i ) = zero
294  250 CONTINUE
295  DO 270 j = 1, n
296  DO 260 i = j, m
297  work( i ) = work( i ) + abs( a( i, j ) )
298  260 CONTINUE
299  270 CONTINUE
300  END IF
301  END IF
302  value = zero
303  DO 280 i = 1, m
304  value = max( value, work( i ) )
305  280 CONTINUE
306  ELSE IF( ( lsame( norm, 'F' ) ) .OR. ( lsame( norm, 'E' ) ) ) THEN
307 *
308 * Find normF(A).
309 *
310  IF( lsame( uplo, 'U' ) ) THEN
311  IF( lsame( diag, 'U' ) ) THEN
312  scale = one
313  sum = min( m, n )
314  DO 290 j = 2, n
315  CALL slassq( min( m, j-1 ), a( 1, j ), 1, scale, sum )
316  290 CONTINUE
317  ELSE
318  scale = zero
319  sum = one
320  DO 300 j = 1, n
321  CALL slassq( min( m, j ), a( 1, j ), 1, scale, sum )
322  300 CONTINUE
323  END IF
324  ELSE
325  IF( lsame( diag, 'U' ) ) THEN
326  scale = one
327  sum = min( m, n )
328  DO 310 j = 1, n
329  CALL slassq( m-j, a( min( m, j+1 ), j ), 1, scale,
330  $ sum )
331  310 CONTINUE
332  ELSE
333  scale = zero
334  sum = one
335  DO 320 j = 1, n
336  CALL slassq( m-j+1, a( j, j ), 1, scale, sum )
337  320 CONTINUE
338  END IF
339  END IF
340  value = scale*sqrt( sum )
341  END IF
342 *
343  slantr = value
344  RETURN
345 *
346 * End of SLANTR
347 *
348  END