LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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slansp.f
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1*> \brief \b SLANSP returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a symmetric matrix supplied in packed form.
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/slansp.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/slansp.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18* Definition:
19* ===========
20*
21* REAL FUNCTION SLANSP( NORM, UPLO, N, AP, WORK )
22*
23* .. Scalar Arguments ..
24* CHARACTER NORM, UPLO
25* INTEGER N
26* ..
27* .. Array Arguments ..
28* REAL AP( * ), WORK( * )
29* ..
30*
31*
32*> \par Purpose:
33* =============
34*>
35*> \verbatim
36*>
37*> SLANSP 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, supplied in packed form.
40*> \endverbatim
41*>
42*> \return SLANSP
43*> \verbatim
44*>
45*> SLANSP = ( 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 SLANSP 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 supplied.
74*> = 'U': Upper triangular part of A is supplied
75*> = 'L': Lower triangular part of A is supplied
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, SLANSP is
82*> set to zero.
83*> \endverbatim
84*>
85*> \param[in] AP
86*> \verbatim
87*> AP is REAL array, dimension (N*(N+1)/2)
88*> The upper or lower triangle of the symmetric matrix A, packed
89*> columnwise in a linear array. The j-th column of A is stored
90*> in the array AP as follows:
91*> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
92*> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
93*> \endverbatim
94*>
95*> \param[out] WORK
96*> \verbatim
97*> WORK is REAL array, dimension (MAX(1,LWORK)),
98*> where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,
99*> WORK is not referenced.
100*> \endverbatim
101*
102* Authors:
103* ========
104*
105*> \author Univ. of Tennessee
106*> \author Univ. of California Berkeley
107*> \author Univ. of Colorado Denver
108*> \author NAG Ltd.
109*
110*> \ingroup lanhp
111*
112* =====================================================================
113 REAL function slansp( norm, uplo, n, ap, work )
114*
115* -- LAPACK auxiliary routine --
116* -- LAPACK is a software package provided by Univ. of Tennessee, --
117* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
118*
119* .. Scalar Arguments ..
120 CHARACTER norm, uplo
121 INTEGER n
122* ..
123* .. Array Arguments ..
124 REAL ap( * ), work( * )
125* ..
126*
127* =====================================================================
128*
129* .. Parameters ..
130 REAL one, zero
131 parameter( one = 1.0e+0, zero = 0.0e+0 )
132* ..
133* .. Local Scalars ..
134 INTEGER i, j, k
135 REAL absa, scale, sum, value
136* ..
137* .. External Subroutines ..
138 EXTERNAL slassq
139* ..
140* .. External Functions ..
141 LOGICAL lsame, sisnan
142 EXTERNAL lsame, sisnan
143* ..
144* .. Intrinsic Functions ..
145 INTRINSIC abs, sqrt
146* ..
147* .. Executable Statements ..
148*
149 IF( n.EQ.0 ) THEN
150 VALUE = zero
151 ELSE IF( lsame( norm, 'M' ) ) THEN
152*
153* Find max(abs(A(i,j))).
154*
155 VALUE = zero
156 IF( lsame( uplo, 'U' ) ) THEN
157 k = 1
158 DO 20 j = 1, n
159 DO 10 i = k, k + j - 1
160 sum = abs( ap( i ) )
161 IF( VALUE .LT. sum .OR. sisnan( sum ) ) VALUE = sum
162 10 CONTINUE
163 k = k + j
164 20 CONTINUE
165 ELSE
166 k = 1
167 DO 40 j = 1, n
168 DO 30 i = k, k + n - j
169 sum = abs( ap( i ) )
170 IF( VALUE .LT. sum .OR. sisnan( sum ) ) VALUE = sum
171 30 CONTINUE
172 k = k + n - j + 1
173 40 CONTINUE
174 END IF
175 ELSE IF( ( lsame( norm, 'I' ) ) .OR. ( lsame( norm, 'O' ) ) .OR.
176 \$ ( norm.EQ.'1' ) ) THEN
177*
178* Find normI(A) ( = norm1(A), since A is symmetric).
179*
180 VALUE = zero
181 k = 1
182 IF( lsame( uplo, 'U' ) ) THEN
183 DO 60 j = 1, n
184 sum = zero
185 DO 50 i = 1, j - 1
186 absa = abs( ap( k ) )
187 sum = sum + absa
188 work( i ) = work( i ) + absa
189 k = k + 1
190 50 CONTINUE
191 work( j ) = sum + abs( ap( k ) )
192 k = k + 1
193 60 CONTINUE
194 DO 70 i = 1, n
195 sum = work( i )
196 IF( VALUE .LT. sum .OR. sisnan( sum ) ) VALUE = sum
197 70 CONTINUE
198 ELSE
199 DO 80 i = 1, n
200 work( i ) = zero
201 80 CONTINUE
202 DO 100 j = 1, n
203 sum = work( j ) + abs( ap( k ) )
204 k = k + 1
205 DO 90 i = j + 1, n
206 absa = abs( ap( k ) )
207 sum = sum + absa
208 work( i ) = work( i ) + absa
209 k = k + 1
210 90 CONTINUE
211 IF( VALUE .LT. sum .OR. sisnan( sum ) ) VALUE = sum
212 100 CONTINUE
213 END IF
214 ELSE IF( ( lsame( norm, 'F' ) ) .OR. ( lsame( norm, 'E' ) ) ) THEN
215*
216* Find normF(A).
217*
218 scale = zero
219 sum = one
220 k = 2
221 IF( lsame( uplo, 'U' ) ) THEN
222 DO 110 j = 2, n
223 CALL slassq( j-1, ap( k ), 1, scale, sum )
224 k = k + j
225 110 CONTINUE
226 ELSE
227 DO 120 j = 1, n - 1
228 CALL slassq( n-j, ap( k ), 1, scale, sum )
229 k = k + n - j + 1
230 120 CONTINUE
231 END IF
232 sum = 2*sum
233 k = 1
234 DO 130 i = 1, n
235 IF( ap( k ).NE.zero ) THEN
236 absa = abs( ap( k ) )
237 IF( scale.LT.absa ) THEN
238 sum = one + sum*( scale / absa )**2
239 scale = absa
240 ELSE
241 sum = sum + ( absa / scale )**2
242 END IF
243 END IF
244 IF( lsame( uplo, 'U' ) ) THEN
245 k = k + i + 1
246 ELSE
247 k = k + n - i + 1
248 END IF
249 130 CONTINUE
250 VALUE = scale*sqrt( sum )
251 END IF
252*
253 slansp = VALUE
254 RETURN
255*
256* End of SLANSP
257*
258 END
logical function sisnan(sin)
SISNAN tests input for NaN.
Definition sisnan.f:59
real function slansp(norm, uplo, n, ap, work)
SLANSP returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition slansp.f:114
subroutine slassq(n, x, incx, scale, sumsq)
SLASSQ updates a sum of squares represented in scaled form.
Definition slassq.f90:124
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48