LAPACK  3.9.0 LAPACK: Linear Algebra PACKage
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 *
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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 December 2016
120 *
121 *> \ingroup complex16SYauxiliary
122 *
123 * =====================================================================
124  DOUBLE PRECISION FUNCTION zlansy( NORM, UPLO, N, A, LDA, WORK )
125 *
126 * -- LAPACK auxiliary routine (version 3.7.0) --
127 * -- LAPACK is a software package provided by Univ. of Tennessee, --
128 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
129 * December 2016
130 *
131  IMPLICIT NONE
132 * .. Scalar Arguments ..
133  CHARACTER norm, uplo
134  INTEGER lda, n
135 * ..
136 * .. Array Arguments ..
137  DOUBLE PRECISION work( * )
138  COMPLEX*16 a( lda, * )
139 * ..
140 *
141 * =====================================================================
142 *
143 * .. Parameters ..
144  DOUBLE PRECISION one, zero
145  parameter( one = 1.0d+0, zero = 0.0d+0 )
146 * ..
147 * .. Local Scalars ..
148  INTEGER i, j
149  DOUBLE PRECISION absa, sum, value
150 * ..
151 * .. Local Arrays ..
152  DOUBLE PRECISION ssq( 2 ), colssq( 2 )
153 * ..
154 * .. External Functions ..
155  LOGICAL lsame, disnan
156  EXTERNAL lsame, disnan
157 * ..
158 * .. External Subroutines ..
159  EXTERNAL zlassq, dcombssq
160 * ..
161 * .. Intrinsic Functions ..
162  INTRINSIC abs, sqrt
163 * ..
164 * .. Executable Statements ..
165 *
166  IF( n.EQ.0 ) THEN
167  VALUE = zero
168  ELSE IF( lsame( norm, 'M' ) ) THEN
169 *
170 * Find max(abs(A(i,j))).
171 *
172  VALUE = zero
173  IF( lsame( uplo, 'U' ) ) THEN
174  DO 20 j = 1, n
175  DO 10 i = 1, j
176  sum = abs( a( i, j ) )
177  IF( VALUE .LT. sum .OR. disnan( sum ) ) VALUE = sum
178  10 CONTINUE
179  20 CONTINUE
180  ELSE
181  DO 40 j = 1, n
182  DO 30 i = j, n
183  sum = abs( a( i, j ) )
184  IF( VALUE .LT. sum .OR. disnan( sum ) ) VALUE = sum
185  30 CONTINUE
186  40 CONTINUE
187  END IF
188  ELSE IF( ( lsame( norm, 'I' ) ) .OR. ( lsame( norm, 'O' ) ) .OR.
189  \$ ( norm.EQ.'1' ) ) THEN
190 *
191 * Find normI(A) ( = norm1(A), since A is symmetric).
192 *
193  VALUE = zero
194  IF( lsame( uplo, 'U' ) ) THEN
195  DO 60 j = 1, n
196  sum = zero
197  DO 50 i = 1, j - 1
198  absa = abs( a( i, j ) )
199  sum = sum + absa
200  work( i ) = work( i ) + absa
201  50 CONTINUE
202  work( j ) = sum + abs( a( j, j ) )
203  60 CONTINUE
204  DO 70 i = 1, n
205  sum = work( i )
206  IF( VALUE .LT. sum .OR. disnan( sum ) ) VALUE = sum
207  70 CONTINUE
208  ELSE
209  DO 80 i = 1, n
210  work( i ) = zero
211  80 CONTINUE
212  DO 100 j = 1, n
213  sum = work( j ) + abs( a( j, j ) )
214  DO 90 i = j + 1, n
215  absa = abs( a( i, j ) )
216  sum = sum + absa
217  work( i ) = work( i ) + absa
218  90 CONTINUE
219  IF( VALUE .LT. sum .OR. disnan( sum ) ) VALUE = sum
220  100 CONTINUE
221  END IF
222  ELSE IF( ( lsame( norm, 'F' ) ) .OR. ( lsame( norm, 'E' ) ) ) THEN
223 *
224 * Find normF(A).
225 * SSQ(1) is scale
226 * SSQ(2) is sum-of-squares
227 * For better accuracy, sum each column separately.
228 *
229  ssq( 1 ) = zero
230  ssq( 2 ) = one
231 *
232 * Sum off-diagonals
233 *
234  IF( lsame( uplo, 'U' ) ) THEN
235  DO 110 j = 2, n
236  colssq( 1 ) = zero
237  colssq( 2 ) = one
238  CALL zlassq( j-1, a( 1, j ), 1, colssq(1), colssq(2) )
239  CALL dcombssq( ssq, colssq )
240  110 CONTINUE
241  ELSE
242  DO 120 j = 1, n - 1
243  colssq( 1 ) = zero
244  colssq( 2 ) = one
245  CALL zlassq( n-j, a( j+1, j ), 1, colssq(1), colssq(2) )
246  CALL dcombssq( ssq, colssq )
247  120 CONTINUE
248  END IF
249  ssq( 2 ) = 2*ssq( 2 )
250 *
251 * Sum diagonal
252 *
253  colssq( 1 ) = zero
254  colssq( 2 ) = one
255  CALL zlassq( n, a, lda+1, colssq( 1 ), colssq( 2 ) )
256  CALL dcombssq( ssq, colssq )
257  VALUE = ssq( 1 )*sqrt( ssq( 2 ) )
258  END IF
259 *
260  zlansy = VALUE
261  RETURN
262 *
263 * End of ZLANSY
264 *
265  END
zlansy
double precision function zlansy(NORM, UPLO, N, A, LDA, WORK)
ZLANSY returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition: zlansy.f:125
zlassq
subroutine zlassq(N, X, INCX, SCALE, SUMSQ)
ZLASSQ updates a sum of squares represented in scaled form.
Definition: zlassq.f:108
disnan
logical function disnan(DIN)
DISNAN tests input for NaN.
Definition: disnan.f:61
lsame
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
dcombssq
subroutine dcombssq(V1, V2)
DCOMBSSQ adds two scaled sum of squares quantities.
Definition: dcombssq.f:62