LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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slansy.f
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1*> \brief \b SLANSY returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real 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/slansy.f">
11*> [TGZ]</a>
12*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/slansy.f">
13*> [ZIP]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/slansy.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18* Definition:
19* ===========
20*
21* REAL FUNCTION SLANSY( NORM, UPLO, N, A, LDA, WORK )
22*
23* .. Scalar Arguments ..
24* CHARACTER NORM, UPLO
25* INTEGER LDA, N
26* ..
27* .. Array Arguments ..
28* REAL A( LDA, * ), WORK( * )
29* ..
30*
31*
32*> \par Purpose:
33* =============
34*>
35*> \verbatim
36*>
37*> SLANSY returns the value of the one norm, or the Frobenius norm, or
38*> the infinity norm, or the element of largest absolute value of a
39*> real symmetric matrix A.
40*> \endverbatim
41*>
42*> \return SLANSY
43*> \verbatim
44*>
45*> SLANSY = ( max(abs(A(i,j))), NORM = 'M' or 'm'
46*> (
47*> ( norm1(A), NORM = '1', 'O' or 'o'
48*> (
49*> ( normI(A), NORM = 'I' or 'i'
50*> (
51*> ( normF(A), NORM = 'F', 'f', 'E' or 'e'
52*>
53*> where norm1 denotes the one norm of a matrix (maximum column sum),
54*> normI denotes the infinity norm of a matrix (maximum row sum) and
55*> normF denotes the Frobenius norm of a matrix (square root of sum of
56*> squares). Note that max(abs(A(i,j))) is not a consistent matrix norm.
57*> \endverbatim
58*
59* Arguments:
60* ==========
61*
62*> \param[in] NORM
63*> \verbatim
64*> NORM is CHARACTER*1
65*> Specifies the value to be returned in SLANSY as described
66*> above.
67*> \endverbatim
68*>
69*> \param[in] UPLO
70*> \verbatim
71*> UPLO is CHARACTER*1
72*> Specifies whether the upper or lower triangular part of the
73*> symmetric matrix A is to be referenced.
74*> = 'U': Upper triangular part of A is referenced
75*> = 'L': Lower triangular part of A is referenced
76*> \endverbatim
77*>
78*> \param[in] N
79*> \verbatim
80*> N is INTEGER
81*> The order of the matrix A. N >= 0. When N = 0, SLANSY is
82*> set to zero.
83*> \endverbatim
84*>
85*> \param[in] A
86*> \verbatim
87*> A is REAL array, dimension (LDA,N)
88*> The symmetric matrix A. If UPLO = 'U', the leading n by n
89*> upper triangular part of A contains the upper triangular part
90*> of the matrix A, and the strictly lower triangular part of A
91*> is not referenced. If UPLO = 'L', the leading n by n lower
92*> triangular part of A contains the lower triangular part of
93*> the matrix A, and the strictly upper triangular part of A is
94*> not referenced.
95*> \endverbatim
96*>
97*> \param[in] LDA
98*> \verbatim
99*> LDA is INTEGER
100*> The leading dimension of the array A. LDA >= max(N,1).
101*> \endverbatim
102*>
103*> \param[out] WORK
104*> \verbatim
105*> WORK is REAL array, dimension (MAX(1,LWORK)),
106*> where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,
107*> WORK is not referenced.
108*> \endverbatim
109*
110* Authors:
111* ========
112*
113*> \author Univ. of Tennessee
114*> \author Univ. of California Berkeley
115*> \author Univ. of Colorado Denver
116*> \author NAG Ltd.
117*
118*> \ingroup realSYauxiliary
119*
120* =====================================================================
121 REAL function slansy( norm, uplo, n, a, lda, work )
122*
123* -- LAPACK auxiliary routine --
124* -- LAPACK is a software package provided by Univ. of Tennessee, --
125* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
126*
127* .. Scalar Arguments ..
128 CHARACTER norm, uplo
129 INTEGER lda, n
130* ..
131* .. Array Arguments ..
132 REAL a( lda, * ), work( * )
133* ..
134*
135* =====================================================================
136*
137* .. Parameters ..
138 REAL one, zero
139 parameter( one = 1.0e+0, zero = 0.0e+0 )
140* ..
141* .. Local Scalars ..
142 INTEGER i, j
143 REAL absa, scale, sum, value
144* ..
145* .. External Subroutines ..
146 EXTERNAL slassq
147* ..
148* .. External Functions ..
149 LOGICAL lsame, sisnan
150 EXTERNAL lsame, sisnan
151* ..
152* .. Intrinsic Functions ..
153 INTRINSIC abs, sqrt
154* ..
155* .. Executable Statements ..
156*
157 IF( n.EQ.0 ) THEN
158 VALUE = zero
159 ELSE IF( lsame( norm, 'M' ) ) THEN
160*
161* Find max(abs(A(i,j))).
162*
163 VALUE = zero
164 IF( lsame( uplo, 'U' ) ) THEN
165 DO 20 j = 1, n
166 DO 10 i = 1, j
167 sum = abs( a( i, j ) )
168 IF( VALUE .LT. sum .OR. sisnan( sum ) ) VALUE = sum
169 10 CONTINUE
170 20 CONTINUE
171 ELSE
172 DO 40 j = 1, n
173 DO 30 i = j, n
174 sum = abs( a( i, j ) )
175 IF( VALUE .LT. sum .OR. sisnan( sum ) ) VALUE = sum
176 30 CONTINUE
177 40 CONTINUE
178 END IF
179 ELSE IF( ( lsame( norm, 'I' ) ) .OR. ( lsame( norm, 'O' ) ) .OR.
180 \$ ( norm.EQ.'1' ) ) THEN
181*
182* Find normI(A) ( = norm1(A), since A is symmetric).
183*
184 VALUE = zero
185 IF( lsame( uplo, 'U' ) ) THEN
186 DO 60 j = 1, n
187 sum = zero
188 DO 50 i = 1, j - 1
189 absa = abs( a( i, j ) )
190 sum = sum + absa
191 work( i ) = work( i ) + absa
192 50 CONTINUE
193 work( j ) = sum + abs( a( j, j ) )
194 60 CONTINUE
195 DO 70 i = 1, n
196 sum = work( i )
197 IF( VALUE .LT. sum .OR. sisnan( sum ) ) VALUE = sum
198 70 CONTINUE
199 ELSE
200 DO 80 i = 1, n
201 work( i ) = zero
202 80 CONTINUE
203 DO 100 j = 1, n
204 sum = work( j ) + abs( a( j, j ) )
205 DO 90 i = j + 1, n
206 absa = abs( a( i, j ) )
207 sum = sum + absa
208 work( i ) = work( i ) + absa
209 90 CONTINUE
210 IF( VALUE .LT. sum .OR. sisnan( sum ) ) VALUE = sum
211 100 CONTINUE
212 END IF
213 ELSE IF( ( lsame( norm, 'F' ) ) .OR. ( lsame( norm, 'E' ) ) ) THEN
214*
215* Find normF(A).
216*
217 scale = zero
218 sum = one
219 IF( lsame( uplo, 'U' ) ) THEN
220 DO 110 j = 2, n
221 CALL slassq( j-1, a( 1, j ), 1, scale, sum )
222 110 CONTINUE
223 ELSE
224 DO 120 j = 1, n - 1
225 CALL slassq( n-j, a( j+1, j ), 1, scale, sum )
226 120 CONTINUE
227 END IF
228 sum = 2*sum
229 CALL slassq( n, a, lda+1, scale, sum )
230 VALUE = scale*sqrt( sum )
231 END IF
232*
233 slansy = VALUE
234 RETURN
235*
236* End of SLANSY
237*
238 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 slansy(NORM, UPLO, N, A, LDA, WORK)
SLANSY returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition: slansy.f:122