LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
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slantr.f
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1*> \brief \b SLANTR 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 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*> \ingroup realOTHERauxiliary
137*
138* =====================================================================
139 REAL function slantr( norm, uplo, diag, m, n, a, lda,
140 $ work )
141*
142* -- LAPACK auxiliary routine --
143* -- LAPACK is a software package provided by Univ. of Tennessee, --
144* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
145*
146* .. Scalar Arguments ..
147 CHARACTER diag, norm, uplo
148 INTEGER lda, m, n
149* ..
150* .. Array Arguments ..
151 REAL a( lda, * ), work( * )
152* ..
153*
154* =====================================================================
155*
156* .. Parameters ..
157 REAL one, zero
158 parameter( one = 1.0e+0, zero = 0.0e+0 )
159* ..
160* .. Local Scalars ..
161 LOGICAL udiag
162 INTEGER i, j
163 REAL scale, sum, value
164* ..
165* .. External Subroutines ..
166 EXTERNAL slassq
167* ..
168* .. External Functions ..
169 LOGICAL lsame, sisnan
170 EXTERNAL lsame, sisnan
171* ..
172* .. Intrinsic Functions ..
173 INTRINSIC abs, min, sqrt
174* ..
175* .. Executable Statements ..
176*
177 IF( min( m, n ).EQ.0 ) THEN
178 VALUE = zero
179 ELSE IF( lsame( norm, 'M' ) ) THEN
180*
181* Find max(abs(A(i,j))).
182*
183 IF( lsame( diag, 'U' ) ) THEN
184 VALUE = one
185 IF( lsame( uplo, 'U' ) ) THEN
186 DO 20 j = 1, n
187 DO 10 i = 1, min( m, j-1 )
188 sum = abs( a( i, j ) )
189 IF( VALUE .LT. sum .OR. sisnan( sum ) ) VALUE = sum
190 10 CONTINUE
191 20 CONTINUE
192 ELSE
193 DO 40 j = 1, n
194 DO 30 i = j + 1, m
195 sum = abs( a( i, j ) )
196 IF( VALUE .LT. sum .OR. sisnan( sum ) ) VALUE = sum
197 30 CONTINUE
198 40 CONTINUE
199 END IF
200 ELSE
201 VALUE = zero
202 IF( lsame( uplo, 'U' ) ) THEN
203 DO 60 j = 1, n
204 DO 50 i = 1, min( m, j )
205 sum = abs( a( i, j ) )
206 IF( VALUE .LT. sum .OR. sisnan( sum ) ) VALUE = sum
207 50 CONTINUE
208 60 CONTINUE
209 ELSE
210 DO 80 j = 1, n
211 DO 70 i = j, m
212 sum = abs( a( i, j ) )
213 IF( VALUE .LT. sum .OR. sisnan( sum ) ) VALUE = sum
214 70 CONTINUE
215 80 CONTINUE
216 END IF
217 END IF
218 ELSE IF( ( lsame( norm, 'O' ) ) .OR. ( norm.EQ.'1' ) ) THEN
219*
220* Find norm1(A).
221*
222 VALUE = zero
223 udiag = lsame( diag, 'U' )
224 IF( lsame( uplo, 'U' ) ) THEN
225 DO 110 j = 1, n
226 IF( ( udiag ) .AND. ( j.LE.m ) ) THEN
227 sum = one
228 DO 90 i = 1, j - 1
229 sum = sum + abs( a( i, j ) )
230 90 CONTINUE
231 ELSE
232 sum = zero
233 DO 100 i = 1, min( m, j )
234 sum = sum + abs( a( i, j ) )
235 100 CONTINUE
236 END IF
237 IF( VALUE .LT. sum .OR. sisnan( sum ) ) VALUE = sum
238 110 CONTINUE
239 ELSE
240 DO 140 j = 1, n
241 IF( udiag ) THEN
242 sum = one
243 DO 120 i = j + 1, m
244 sum = sum + abs( a( i, j ) )
245 120 CONTINUE
246 ELSE
247 sum = zero
248 DO 130 i = j, m
249 sum = sum + abs( a( i, j ) )
250 130 CONTINUE
251 END IF
252 IF( VALUE .LT. sum .OR. sisnan( sum ) ) VALUE = sum
253 140 CONTINUE
254 END IF
255 ELSE IF( lsame( norm, 'I' ) ) THEN
256*
257* Find normI(A).
258*
259 IF( lsame( uplo, 'U' ) ) THEN
260 IF( lsame( diag, 'U' ) ) THEN
261 DO 150 i = 1, m
262 work( i ) = one
263 150 CONTINUE
264 DO 170 j = 1, n
265 DO 160 i = 1, min( m, j-1 )
266 work( i ) = work( i ) + abs( a( i, j ) )
267 160 CONTINUE
268 170 CONTINUE
269 ELSE
270 DO 180 i = 1, m
271 work( i ) = zero
272 180 CONTINUE
273 DO 200 j = 1, n
274 DO 190 i = 1, min( m, j )
275 work( i ) = work( i ) + abs( a( i, j ) )
276 190 CONTINUE
277 200 CONTINUE
278 END IF
279 ELSE
280 IF( lsame( diag, 'U' ) ) THEN
281 DO 210 i = 1, min( m, n )
282 work( i ) = one
283 210 CONTINUE
284 DO 220 i = n + 1, m
285 work( i ) = zero
286 220 CONTINUE
287 DO 240 j = 1, n
288 DO 230 i = j + 1, m
289 work( i ) = work( i ) + abs( a( i, j ) )
290 230 CONTINUE
291 240 CONTINUE
292 ELSE
293 DO 250 i = 1, m
294 work( i ) = zero
295 250 CONTINUE
296 DO 270 j = 1, n
297 DO 260 i = j, m
298 work( i ) = work( i ) + abs( a( i, j ) )
299 260 CONTINUE
300 270 CONTINUE
301 END IF
302 END IF
303 VALUE = zero
304 DO 280 i = 1, m
305 sum = work( i )
306 IF( VALUE .LT. sum .OR. sisnan( sum ) ) VALUE = sum
307 280 CONTINUE
308 ELSE IF( ( lsame( norm, 'F' ) ) .OR. ( lsame( norm, 'E' ) ) ) THEN
309*
310* Find normF(A).
311*
312 IF( lsame( uplo, 'U' ) ) THEN
313 IF( lsame( diag, 'U' ) ) THEN
314 scale = one
315 sum = min( m, n )
316 DO 290 j = 2, n
317 CALL slassq( min( m, j-1 ), a( 1, j ), 1, scale, sum )
318 290 CONTINUE
319 ELSE
320 scale = zero
321 sum = one
322 DO 300 j = 1, n
323 CALL slassq( min( m, j ), a( 1, j ), 1, scale, sum )
324 300 CONTINUE
325 END IF
326 ELSE
327 IF( lsame( diag, 'U' ) ) THEN
328 scale = one
329 sum = min( m, n )
330 DO 310 j = 1, n
331 CALL slassq( m-j, a( min( m, j+1 ), j ), 1, scale,
332 $ sum )
333 310 CONTINUE
334 ELSE
335 scale = zero
336 sum = one
337 DO 320 j = 1, n
338 CALL slassq( m-j+1, a( j, j ), 1, scale, sum )
339 320 CONTINUE
340 END IF
341 END IF
342 VALUE = scale*sqrt( sum )
343 END IF
344*
345 slantr = VALUE
346 RETURN
347*
348* End of SLANTR
349*
350 END
subroutine slassq(n, x, incx, scl, sumsq)
SLASSQ updates a sum of squares represented in scaled form.
Definition: slassq.f90:137
logical function sisnan(SIN)
SISNAN tests input for NaN.
Definition: sisnan.f:59
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
real function slantr(NORM, UPLO, DIAG, M, N, A, LDA, WORK)
SLANTR returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition: slantr.f:141