LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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clantb.f
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1*> \brief \b CLANTB returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a triangular band matrix.
2*
3* =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6* http://www.netlib.org/lapack/explore-html/
7*
8*> \htmlonly
10*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/clantb.f">
11*> [TGZ]</a>
12*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/clantb.f">
13*> [ZIP]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/clantb.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18* Definition:
19* ===========
20*
21* REAL FUNCTION CLANTB( NORM, UPLO, DIAG, N, K, AB,
22* LDAB, WORK )
23*
24* .. Scalar Arguments ..
25* CHARACTER DIAG, NORM, UPLO
26* INTEGER K, LDAB, N
27* ..
28* .. Array Arguments ..
29* REAL WORK( * )
30* COMPLEX AB( LDAB, * )
31* ..
32*
33*
34*> \par Purpose:
35* =============
36*>
37*> \verbatim
38*>
39*> CLANTB returns the value of the one norm, or the Frobenius norm, or
40*> the infinity norm, or the element of largest absolute value of an
41*> n by n triangular band matrix A, with ( k + 1 ) diagonals.
42*> \endverbatim
43*>
44*> \return CLANTB
45*> \verbatim
46*>
47*> CLANTB = ( max(abs(A(i,j))), NORM = 'M' or 'm'
48*> (
49*> ( norm1(A), NORM = '1', 'O' or 'o'
50*> (
51*> ( normI(A), NORM = 'I' or 'i'
52*> (
53*> ( normF(A), NORM = 'F', 'f', 'E' or 'e'
54*>
55*> where norm1 denotes the one norm of a matrix (maximum column sum),
56*> normI denotes the infinity norm of a matrix (maximum row sum) and
57*> normF denotes the Frobenius norm of a matrix (square root of sum of
58*> squares). Note that max(abs(A(i,j))) is not a consistent matrix norm.
59*> \endverbatim
60*
61* Arguments:
62* ==========
63*
64*> \param[in] NORM
65*> \verbatim
66*> NORM is CHARACTER*1
67*> Specifies the value to be returned in CLANTB as described
68*> above.
69*> \endverbatim
70*>
71*> \param[in] UPLO
72*> \verbatim
73*> UPLO is CHARACTER*1
74*> Specifies whether the matrix A is upper or lower triangular.
75*> = 'U': Upper triangular
76*> = 'L': Lower triangular
77*> \endverbatim
78*>
79*> \param[in] DIAG
80*> \verbatim
81*> DIAG is CHARACTER*1
82*> Specifies whether or not the matrix A is unit triangular.
83*> = 'N': Non-unit triangular
84*> = 'U': Unit triangular
85*> \endverbatim
86*>
87*> \param[in] N
88*> \verbatim
89*> N is INTEGER
90*> The order of the matrix A. N >= 0. When N = 0, CLANTB is
91*> set to zero.
92*> \endverbatim
93*>
94*> \param[in] K
95*> \verbatim
96*> K is INTEGER
97*> The number of super-diagonals of the matrix A if UPLO = 'U',
98*> or the number of sub-diagonals of the matrix A if UPLO = 'L'.
99*> K >= 0.
100*> \endverbatim
101*>
102*> \param[in] AB
103*> \verbatim
104*> AB is COMPLEX array, dimension (LDAB,N)
105*> The upper or lower triangular band matrix A, stored in the
106*> first k+1 rows of AB. The j-th column of A is stored
107*> in the j-th column of the array AB as follows:
108*> if UPLO = 'U', AB(k+1+i-j,j) = A(i,j) for max(1,j-k)<=i<=j;
109*> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+k).
110*> Note that when DIAG = 'U', the elements of the array AB
111*> corresponding to the diagonal elements of the matrix A are
112*> not referenced, but are assumed to be one.
113*> \endverbatim
114*>
115*> \param[in] LDAB
116*> \verbatim
117*> LDAB is INTEGER
118*> The leading dimension of the array AB. LDAB >= K+1.
119*> \endverbatim
120*>
121*> \param[out] WORK
122*> \verbatim
123*> WORK is REAL array, dimension (MAX(1,LWORK)),
124*> where LWORK >= N 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 lantb
137*
138* =====================================================================
139 REAL function clantb( norm, uplo, diag, n, k, ab,
140 \$ ldab, 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 k, ldab, n
149* ..
150* .. Array Arguments ..
151 REAL work( * )
152 COMPLEX ab( ldab, * )
153* ..
154*
155* =====================================================================
156*
157* .. Parameters ..
158 REAL one, zero
159 parameter( one = 1.0e+0, zero = 0.0e+0 )
160* ..
161* .. Local Scalars ..
162 LOGICAL udiag
163 INTEGER i, j, l
164 REAL scale, sum, value
165* ..
166* .. External Functions ..
167 LOGICAL lsame, sisnan
168 EXTERNAL lsame, sisnan
169* ..
170* .. External Subroutines ..
171 EXTERNAL classq
172* ..
173* .. Intrinsic Functions ..
174 INTRINSIC abs, max, min, sqrt
175* ..
176* .. Executable Statements ..
177*
178 IF( n.EQ.0 ) THEN
179 VALUE = zero
180 ELSE IF( lsame( norm, 'M' ) ) THEN
181*
182* Find max(abs(A(i,j))).
183*
184 IF( lsame( diag, 'U' ) ) THEN
185 VALUE = one
186 IF( lsame( uplo, 'U' ) ) THEN
187 DO 20 j = 1, n
188 DO 10 i = max( k+2-j, 1 ), k
189 sum = abs( ab( i, j ) )
190 IF( VALUE .LT. sum .OR. sisnan( sum ) ) VALUE = sum
191 10 CONTINUE
192 20 CONTINUE
193 ELSE
194 DO 40 j = 1, n
195 DO 30 i = 2, min( n+1-j, k+1 )
196 sum = abs( ab( i, j ) )
197 IF( VALUE .LT. sum .OR. sisnan( sum ) ) VALUE = sum
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 = max( k+2-j, 1 ), k + 1
206 sum = abs( ab( i, j ) )
207 IF( VALUE .LT. sum .OR. sisnan( sum ) ) VALUE = sum
208 50 CONTINUE
209 60 CONTINUE
210 ELSE
211 DO 80 j = 1, n
212 DO 70 i = 1, min( n+1-j, k+1 )
213 sum = abs( ab( i, j ) )
214 IF( VALUE .LT. sum .OR. sisnan( sum ) ) VALUE = sum
215 70 CONTINUE
216 80 CONTINUE
217 END IF
218 END IF
219 ELSE IF( ( lsame( norm, 'O' ) ) .OR. ( norm.EQ.'1' ) ) THEN
220*
221* Find norm1(A).
222*
223 VALUE = zero
224 udiag = lsame( diag, 'U' )
225 IF( lsame( uplo, 'U' ) ) THEN
226 DO 110 j = 1, n
227 IF( udiag ) THEN
228 sum = one
229 DO 90 i = max( k+2-j, 1 ), k
230 sum = sum + abs( ab( i, j ) )
231 90 CONTINUE
232 ELSE
233 sum = zero
234 DO 100 i = max( k+2-j, 1 ), k + 1
235 sum = sum + abs( ab( i, j ) )
236 100 CONTINUE
237 END IF
238 IF( VALUE .LT. sum .OR. sisnan( sum ) ) VALUE = sum
239 110 CONTINUE
240 ELSE
241 DO 140 j = 1, n
242 IF( udiag ) THEN
243 sum = one
244 DO 120 i = 2, min( n+1-j, k+1 )
245 sum = sum + abs( ab( i, j ) )
246 120 CONTINUE
247 ELSE
248 sum = zero
249 DO 130 i = 1, min( n+1-j, k+1 )
250 sum = sum + abs( ab( i, j ) )
251 130 CONTINUE
252 END IF
253 IF( VALUE .LT. sum .OR. sisnan( sum ) ) VALUE = sum
254 140 CONTINUE
255 END IF
256 ELSE IF( lsame( norm, 'I' ) ) THEN
257*
258* Find normI(A).
259*
260 VALUE = zero
261 IF( lsame( uplo, 'U' ) ) THEN
262 IF( lsame( diag, 'U' ) ) THEN
263 DO 150 i = 1, n
264 work( i ) = one
265 150 CONTINUE
266 DO 170 j = 1, n
267 l = k + 1 - j
268 DO 160 i = max( 1, j-k ), j - 1
269 work( i ) = work( i ) + abs( ab( l+i, j ) )
270 160 CONTINUE
271 170 CONTINUE
272 ELSE
273 DO 180 i = 1, n
274 work( i ) = zero
275 180 CONTINUE
276 DO 200 j = 1, n
277 l = k + 1 - j
278 DO 190 i = max( 1, j-k ), j
279 work( i ) = work( i ) + abs( ab( l+i, j ) )
280 190 CONTINUE
281 200 CONTINUE
282 END IF
283 ELSE
284 IF( lsame( diag, 'U' ) ) THEN
285 DO 210 i = 1, n
286 work( i ) = one
287 210 CONTINUE
288 DO 230 j = 1, n
289 l = 1 - j
290 DO 220 i = j + 1, min( n, j+k )
291 work( i ) = work( i ) + abs( ab( l+i, j ) )
292 220 CONTINUE
293 230 CONTINUE
294 ELSE
295 DO 240 i = 1, n
296 work( i ) = zero
297 240 CONTINUE
298 DO 260 j = 1, n
299 l = 1 - j
300 DO 250 i = j, min( n, j+k )
301 work( i ) = work( i ) + abs( ab( l+i, j ) )
302 250 CONTINUE
303 260 CONTINUE
304 END IF
305 END IF
306 DO 270 i = 1, n
307 sum = work( i )
308 IF( VALUE .LT. sum .OR. sisnan( sum ) ) VALUE = sum
309 270 CONTINUE
310 ELSE IF( ( lsame( norm, 'F' ) ) .OR. ( lsame( norm, 'E' ) ) ) THEN
311*
312* Find normF(A).
313*
314 IF( lsame( uplo, 'U' ) ) THEN
315 IF( lsame( diag, 'U' ) ) THEN
316 scale = one
317 sum = n
318 IF( k.GT.0 ) THEN
319 DO 280 j = 2, n
320 CALL classq( min( j-1, k ),
321 \$ ab( max( k+2-j, 1 ), j ), 1, scale,
322 \$ sum )
323 280 CONTINUE
324 END IF
325 ELSE
326 scale = zero
327 sum = one
328 DO 290 j = 1, n
329 CALL classq( min( j, k+1 ), ab( max( k+2-j, 1 ), j ),
330 \$ 1, scale, sum )
331 290 CONTINUE
332 END IF
333 ELSE
334 IF( lsame( diag, 'U' ) ) THEN
335 scale = one
336 sum = n
337 IF( k.GT.0 ) THEN
338 DO 300 j = 1, n - 1
339 CALL classq( min( n-j, k ), ab( 2, j ), 1, scale,
340 \$ sum )
341 300 CONTINUE
342 END IF
343 ELSE
344 scale = zero
345 sum = one
346 DO 310 j = 1, n
347 CALL classq( min( n-j+1, k+1 ), ab( 1, j ), 1, scale,
348 \$ sum )
349 310 CONTINUE
350 END IF
351 END IF
352 VALUE = scale*sqrt( sum )
353 END IF
354*
355 clantb = VALUE
356 RETURN
357*
358* End of CLANTB
359*
360 END
logical function sisnan(sin)
SISNAN tests input for NaN.
Definition sisnan.f:59
real function clantb(norm, uplo, diag, n, k, ab, ldab, work)
CLANTB returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition clantb.f:141
subroutine classq(n, x, incx, scale, sumsq)
CLASSQ updates a sum of squares represented in scaled form.
Definition classq.f90:124
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48