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
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlansy.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlansy.f">
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 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
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