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zlansy.f
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1 *> \brief \b ZLANSY 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
9 *> Download ZLANSY + dependencies
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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/zlansy.f">
15 *> [TXT]</a>
16 *> \endhtmlonly
17 *
18 * Definition:
19 * ===========
20 *
21 * DOUBLE PRECISION FUNCTION ZLANSY( NORM, UPLO, N, A, LDA, WORK )
22 *
23 * .. Scalar Arguments ..
24 * CHARACTER NORM, UPLO
25 * INTEGER LDA, N
26 * ..
27 * .. Array Arguments ..
28 * DOUBLE PRECISION WORK( * )
29 * COMPLEX*16 A( LDA, * )
30 * ..
31 *
32 *
33 *> \par Purpose:
34 * =============
35 *>
36 *> \verbatim
37 *>
38 *> ZLANSY 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 ZLANSY
44 *> \verbatim
45 *>
46 *> ZLANSY = ( 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 ZLANSY 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, ZLANSY is
83 *> set to zero.
84 *> \endverbatim
85 *>
86 *> \param[in] A
87 *> \verbatim
88 *> A is COMPLEX*16 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 DOUBLE PRECISION 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 *> \date September 2012
120 *
121 *> \ingroup complex16SYauxiliary
122 *
123 * =====================================================================
124  DOUBLE PRECISION FUNCTION zlansy( NORM, UPLO, N, A, LDA, WORK )
125 *
126 * -- LAPACK auxiliary routine (version 3.4.2) --
127 * -- LAPACK is a software package provided by Univ. of Tennessee, --
128 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
129 * September 2012
130 *
131 * .. Scalar Arguments ..
132  CHARACTER norm, uplo
133  INTEGER lda, n
134 * ..
135 * .. Array Arguments ..
136  DOUBLE PRECISION work( * )
137  COMPLEX*16 a( lda, * )
138 * ..
139 *
140 * =====================================================================
141 *
142 * .. Parameters ..
143  DOUBLE PRECISION one, zero
144  parameter( one = 1.0d+0, zero = 0.0d+0 )
145 * ..
146 * .. Local Scalars ..
147  INTEGER i, j
148  DOUBLE PRECISION absa, scale, sum, value
149 * ..
150 * .. External Functions ..
151  LOGICAL lsame, disnan
152  EXTERNAL lsame, disnan
153 * ..
154 * .. External Subroutines ..
155  EXTERNAL zlassq
156 * ..
157 * .. Intrinsic Functions ..
158  INTRINSIC abs, sqrt
159 * ..
160 * .. Executable Statements ..
161 *
162  IF( n.EQ.0 ) THEN
163  value = zero
164  ELSE IF( lsame( norm, 'M' ) ) THEN
165 *
166 * Find max(abs(A(i,j))).
167 *
168  value = zero
169  IF( lsame( uplo, 'U' ) ) THEN
170  DO 20 j = 1, n
171  DO 10 i = 1, j
172  sum = abs( a( i, j ) )
173  IF( value .LT. sum .OR. disnan( sum ) ) value = sum
174  10 CONTINUE
175  20 CONTINUE
176  ELSE
177  DO 40 j = 1, n
178  DO 30 i = j, n
179  sum = abs( a( i, j ) )
180  IF( value .LT. sum .OR. disnan( sum ) ) value = sum
181  30 CONTINUE
182  40 CONTINUE
183  END IF
184  ELSE IF( ( lsame( norm, 'I' ) ) .OR. ( lsame( norm, 'O' ) ) .OR.
185  $ ( norm.EQ.'1' ) ) THEN
186 *
187 * Find normI(A) ( = norm1(A), since A is symmetric).
188 *
189  value = zero
190  IF( lsame( uplo, 'U' ) ) THEN
191  DO 60 j = 1, n
192  sum = zero
193  DO 50 i = 1, j - 1
194  absa = abs( a( i, j ) )
195  sum = sum + absa
196  work( i ) = work( i ) + absa
197  50 CONTINUE
198  work( j ) = sum + abs( a( j, j ) )
199  60 CONTINUE
200  DO 70 i = 1, n
201  sum = work( i )
202  IF( value .LT. sum .OR. disnan( sum ) ) value = sum
203  70 CONTINUE
204  ELSE
205  DO 80 i = 1, n
206  work( i ) = zero
207  80 CONTINUE
208  DO 100 j = 1, n
209  sum = work( j ) + abs( a( j, j ) )
210  DO 90 i = j + 1, n
211  absa = abs( a( i, j ) )
212  sum = sum + absa
213  work( i ) = work( i ) + absa
214  90 CONTINUE
215  IF( value .LT. sum .OR. disnan( sum ) ) value = sum
216  100 CONTINUE
217  END IF
218  ELSE IF( ( lsame( norm, 'F' ) ) .OR. ( lsame( norm, 'E' ) ) ) THEN
219 *
220 * Find normF(A).
221 *
222  scale = zero
223  sum = one
224  IF( lsame( uplo, 'U' ) ) THEN
225  DO 110 j = 2, n
226  CALL zlassq( j-1, a( 1, j ), 1, scale, sum )
227  110 CONTINUE
228  ELSE
229  DO 120 j = 1, n - 1
230  CALL zlassq( n-j, a( j+1, j ), 1, scale, sum )
231  120 CONTINUE
232  END IF
233  sum = 2*sum
234  CALL zlassq( n, a, lda+1, scale, sum )
235  value = scale*sqrt( sum )
236  END IF
237 *
238  zlansy = value
239  RETURN
240 *
241 * End of ZLANSY
242 *
243  END