LAPACK  3.10.1
LAPACK: Linear Algebra PACKage
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
9 *> Download SLANSY + dependencies
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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