LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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clanhe.f
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1*> \brief \b CLANHE 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 Hermitian 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/clanhe.f">
11*> [TGZ]</a>
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13*> [ZIP]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/clanhe.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18* Definition:
19* ===========
20*
21* REAL FUNCTION CLANHE( 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*> CLANHE 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 hermitian matrix A.
41*> \endverbatim
42*>
43*> \return CLANHE
44*> \verbatim
45*>
46*> CLANHE = ( 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 CLANHE 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*> hermitian 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, CLANHE is
83*> set to zero.
84*> \endverbatim
85*>
86*> \param[in] A
87*> \verbatim
88*> A is COMPLEX array, dimension (LDA,N)
89*> The hermitian 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. Note that the imaginary parts of the diagonal
96*> elements need not be set and are assumed to be zero.
97*> \endverbatim
98*>
99*> \param[in] LDA
100*> \verbatim
101*> LDA is INTEGER
102*> The leading dimension of the array A. LDA >= max(N,1).
103*> \endverbatim
104*>
105*> \param[out] WORK
106*> \verbatim
107*> WORK is REAL array, dimension (MAX(1,LWORK)),
108*> where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,
109*> WORK is not referenced.
110*> \endverbatim
111*
112* Authors:
113* ========
114*
115*> \author Univ. of Tennessee
116*> \author Univ. of California Berkeley
117*> \author Univ. of Colorado Denver
118*> \author NAG Ltd.
119*
120*> \ingroup lanhe
121*
122* =====================================================================
123 REAL function clanhe( norm, uplo, n, a, lda, work )
124*
125* -- LAPACK auxiliary routine --
126* -- LAPACK is a software package provided by Univ. of Tennessee, --
127* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
128*
129* .. Scalar Arguments ..
130 CHARACTER norm, uplo
131 INTEGER lda, n
132* ..
133* .. Array Arguments ..
134 REAL work( * )
135 COMPLEX a( lda, * )
136* ..
137*
138* =====================================================================
139*
140* .. Parameters ..
141 REAL one, zero
142 parameter( one = 1.0e+0, zero = 0.0e+0 )
143* ..
144* .. Local Scalars ..
145 INTEGER i, j
146 REAL absa, scale, sum, value
147* ..
148* .. External Functions ..
149 LOGICAL lsame, sisnan
150 EXTERNAL lsame, sisnan
151* ..
152* .. External Subroutines ..
153 EXTERNAL classq
154* ..
155* .. Intrinsic Functions ..
156 INTRINSIC abs, real, sqrt
157* ..
158* .. Executable Statements ..
159*
160 IF( n.EQ.0 ) THEN
161 VALUE = zero
162 ELSE IF( lsame( norm, 'M' ) ) THEN
163*
164* Find max(abs(A(i,j))).
165*
166 VALUE = zero
167 IF( lsame( uplo, 'U' ) ) THEN
168 DO 20 j = 1, n
169 DO 10 i = 1, j - 1
170 sum = abs( a( i, j ) )
171 IF( VALUE .LT. sum .OR. sisnan( sum ) ) VALUE = sum
172 10 CONTINUE
173 sum = abs( real( a( j, j ) ) )
174 IF( VALUE .LT. sum .OR. sisnan( sum ) ) VALUE = sum
175 20 CONTINUE
176 ELSE
177 DO 40 j = 1, n
178 sum = abs( real( a( j, j ) ) )
179 IF( VALUE .LT. sum .OR. sisnan( sum ) ) VALUE = sum
180 DO 30 i = j + 1, n
181 sum = abs( a( i, j ) )
182 IF( VALUE .LT. sum .OR. sisnan( sum ) ) VALUE = sum
183 30 CONTINUE
184 40 CONTINUE
185 END IF
186 ELSE IF( ( lsame( norm, 'I' ) ) .OR. ( lsame( norm, 'O' ) ) .OR.
187 \$ ( norm.EQ.'1' ) ) THEN
188*
189* Find normI(A) ( = norm1(A), since A is hermitian).
190*
191 VALUE = zero
192 IF( lsame( uplo, 'U' ) ) THEN
193 DO 60 j = 1, n
194 sum = zero
195 DO 50 i = 1, j - 1
196 absa = abs( a( i, j ) )
197 sum = sum + absa
198 work( i ) = work( i ) + absa
199 50 CONTINUE
200 work( j ) = sum + abs( real( a( j, j ) ) )
201 60 CONTINUE
202 DO 70 i = 1, n
203 sum = work( i )
204 IF( VALUE .LT. sum .OR. sisnan( sum ) ) VALUE = sum
205 70 CONTINUE
206 ELSE
207 DO 80 i = 1, n
208 work( i ) = zero
209 80 CONTINUE
210 DO 100 j = 1, n
211 sum = work( j ) + abs( real( a( j, j ) ) )
212 DO 90 i = j + 1, n
213 absa = abs( a( i, j ) )
214 sum = sum + absa
215 work( i ) = work( i ) + absa
216 90 CONTINUE
217 IF( VALUE .LT. sum .OR. sisnan( sum ) ) VALUE = sum
218 100 CONTINUE
219 END IF
220 ELSE IF( ( lsame( norm, 'F' ) ) .OR. ( lsame( norm, 'E' ) ) ) THEN
221*
222* Find normF(A).
223*
224 scale = zero
225 sum = one
226 IF( lsame( uplo, 'U' ) ) THEN
227 DO 110 j = 2, n
228 CALL classq( j-1, a( 1, j ), 1, scale, sum )
229 110 CONTINUE
230 ELSE
231 DO 120 j = 1, n - 1
232 CALL classq( n-j, a( j+1, j ), 1, scale, sum )
233 120 CONTINUE
234 END IF
235 sum = 2*sum
236 DO 130 i = 1, n
237 IF( real( a( i, i ) ).NE.zero ) THEN
238 absa = abs( real( a( i, i ) ) )
239 IF( scale.LT.absa ) THEN
240 sum = one + sum*( scale / absa )**2
241 scale = absa
242 ELSE
243 sum = sum + ( absa / scale )**2
244 END IF
245 END IF
246 130 CONTINUE
247 VALUE = scale*sqrt( sum )
248 END IF
249*
250 clanhe = VALUE
251 RETURN
252*
253* End of CLANHE
254*
255 END
logical function sisnan(sin)
SISNAN tests input for NaN.
Definition sisnan.f:59
real function clanhe(norm, uplo, n, a, lda, work)
CLANHE returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition clanhe.f:124
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