LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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clansy.f
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1*> \brief \b CLANSY returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex symmetric 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/clansy.f">
11*> [TGZ]</a>
12*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/clansy.f">
13*> [ZIP]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/clansy.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18* Definition:
19* ===========
20*
21* REAL FUNCTION CLANSY( NORM, UPLO, N, A, LDA, WORK )
22*
23* .. Scalar Arguments ..
24* CHARACTER NORM, UPLO
25* INTEGER LDA, N
26* ..
27* .. Array Arguments ..
28* REAL WORK( * )
29* COMPLEX A( LDA, * )
30* ..
31*
32*
33*> \par Purpose:
34* =============
35*>
36*> \verbatim
37*>
38*> CLANSY 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*> complex symmetric matrix A.
41*> \endverbatim
42*>
43*> \return CLANSY
44*> \verbatim
45*>
46*> CLANSY = ( 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 CLANSY as described
67*> above.
68*> \endverbatim
69*>
70*> \param[in] UPLO
71*> \verbatim
72*> UPLO is CHARACTER*1
73*> Specifies whether the upper or lower triangular part of the
74*> symmetric matrix A is to be referenced.
75*> = 'U': Upper triangular part of A is referenced
76*> = 'L': Lower triangular part of A is referenced
77*> \endverbatim
78*>
79*> \param[in] N
80*> \verbatim
81*> N is INTEGER
82*> The order of the matrix A. N >= 0. When N = 0, CLANSY is
83*> set to zero.
84*> \endverbatim
85*>
86*> \param[in] A
87*> \verbatim
88*> A is COMPLEX array, dimension (LDA,N)
89*> The symmetric matrix A. If UPLO = 'U', the leading n by n
90*> upper triangular part of A contains the upper triangular part
91*> of the matrix A, and the strictly lower triangular part of A
92*> is not referenced. If UPLO = 'L', the leading n by n lower
93*> triangular part of A contains the lower triangular part of
94*> the matrix A, and the strictly upper triangular part of A is
95*> not referenced.
96*> \endverbatim
97*>
98*> \param[in] LDA
99*> \verbatim
100*> LDA is INTEGER
101*> The leading dimension of the array A. LDA >= max(N,1).
102*> \endverbatim
103*>
104*> \param[out] WORK
105*> \verbatim
106*> WORK is REAL array, dimension (MAX(1,LWORK)),
107*> where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,
108*> WORK is not referenced.
109*> \endverbatim
110*
111* Authors:
112* ========
113*
114*> \author Univ. of Tennessee
115*> \author Univ. of California Berkeley
116*> \author Univ. of Colorado Denver
117*> \author NAG Ltd.
118*
119*> \ingroup complexSYauxiliary
120*
121* =====================================================================
122 REAL function clansy( norm, uplo, n, a, lda, work )
123*
124* -- LAPACK auxiliary routine --
125* -- LAPACK is a software package provided by Univ. of Tennessee, --
126* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
127*
128* .. Scalar Arguments ..
129 CHARACTER norm, uplo
130 INTEGER lda, n
131* ..
132* .. Array Arguments ..
133 REAL work( * )
134 COMPLEX a( lda, * )
135* ..
136*
137* =====================================================================
138*
139* .. Parameters ..
140 REAL one, zero
141 parameter( one = 1.0e+0, zero = 0.0e+0 )
142* ..
143* .. Local Scalars ..
144 INTEGER i, j
145 REAL absa, scale, sum, value
146* ..
147* .. External Functions ..
148 LOGICAL lsame, sisnan
149 EXTERNAL lsame, sisnan
150* ..
151* .. External Subroutines ..
152 EXTERNAL classq
153* ..
154* .. Intrinsic Functions ..
155 INTRINSIC abs, sqrt
156* ..
157* .. Executable Statements ..
158*
159 IF( n.EQ.0 ) THEN
160 VALUE = zero
161 ELSE IF( lsame( norm, 'M' ) ) THEN
162*
163* Find max(abs(A(i,j))).
164*
165 VALUE = zero
166 IF( lsame( uplo, 'U' ) ) THEN
167 DO 20 j = 1, n
168 DO 10 i = 1, j
169 sum = abs( a( i, j ) )
170 IF( VALUE .LT. sum .OR. sisnan( sum ) ) VALUE = sum
171 10 CONTINUE
172 20 CONTINUE
173 ELSE
174 DO 40 j = 1, n
175 DO 30 i = j, n
176 sum = abs( a( i, j ) )
177 IF( VALUE .LT. sum .OR. sisnan( sum ) ) VALUE = sum
178 30 CONTINUE
179 40 CONTINUE
180 END IF
181 ELSE IF( ( lsame( norm, 'I' ) ) .OR. ( lsame( norm, 'O' ) ) .OR.
182 \$ ( norm.EQ.'1' ) ) THEN
183*
184* Find normI(A) ( = norm1(A), since A is symmetric).
185*
186 VALUE = zero
187 IF( lsame( uplo, 'U' ) ) THEN
188 DO 60 j = 1, n
189 sum = zero
190 DO 50 i = 1, j - 1
191 absa = abs( a( i, j ) )
192 sum = sum + absa
193 work( i ) = work( i ) + absa
194 50 CONTINUE
195 work( j ) = sum + abs( a( j, j ) )
196 60 CONTINUE
197 DO 70 i = 1, n
198 sum = work( i )
199 IF( VALUE .LT. sum .OR. sisnan( sum ) ) VALUE = sum
200 70 CONTINUE
201 ELSE
202 DO 80 i = 1, n
203 work( i ) = zero
204 80 CONTINUE
205 DO 100 j = 1, n
206 sum = work( j ) + abs( a( j, j ) )
207 DO 90 i = j + 1, n
208 absa = abs( a( i, j ) )
209 sum = sum + absa
210 work( i ) = work( i ) + absa
211 90 CONTINUE
212 IF( VALUE .LT. sum .OR. sisnan( sum ) ) VALUE = sum
213 100 CONTINUE
214 END IF
215 ELSE IF( ( lsame( norm, 'F' ) ) .OR. ( lsame( norm, 'E' ) ) ) THEN
216*
217* Find normF(A).
218*
219 scale = zero
220 sum = one
221 IF( lsame( uplo, 'U' ) ) THEN
222 DO 110 j = 2, n
223 CALL classq( j-1, a( 1, j ), 1, scale, sum )
224 110 CONTINUE
225 ELSE
226 DO 120 j = 1, n - 1
227 CALL classq( n-j, a( j+1, j ), 1, scale, sum )
228 120 CONTINUE
229 END IF
230 sum = 2*sum
231 CALL classq( n, a, lda+1, scale, sum )
232 VALUE = scale*sqrt( sum )
233 END IF
234*
235 clansy = VALUE
236 RETURN
237*
238* End of CLANSY
239*
240 END
subroutine classq(n, x, incx, scl, sumsq)
CLASSQ updates a sum of squares represented in scaled form.
Definition: classq.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 clansy(NORM, UPLO, N, A, LDA, WORK)
CLANSY returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition: clansy.f:123