Annotation of rpl/lapack/lapack/zlansy.f, revision 1.20
1.11 bertrand 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.
1.8 bertrand 2: *
3: * =========== DOCUMENTATION ===========
4: *
1.16 bertrand 5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
1.8 bertrand 7: *
8: *> \htmlonly
1.16 bertrand 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">
1.8 bertrand 15: *> [TXT]</a>
1.16 bertrand 16: *> \endhtmlonly
1.8 bertrand 17: *
18: * Definition:
19: * ===========
20: *
21: * DOUBLE PRECISION FUNCTION ZLANSY( NORM, UPLO, N, A, LDA, WORK )
1.16 bertrand 22: *
1.8 bertrand 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: * ..
1.16 bertrand 31: *
1.8 bertrand 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: *
1.16 bertrand 114: *> \author Univ. of Tennessee
115: *> \author Univ. of California Berkeley
116: *> \author Univ. of Colorado Denver
117: *> \author NAG Ltd.
1.8 bertrand 118: *
119: *> \ingroup complex16SYauxiliary
120: *
121: * =====================================================================
1.1 bertrand 122: DOUBLE PRECISION FUNCTION ZLANSY( NORM, UPLO, N, A, LDA, WORK )
123: *
1.20 ! bertrand 124: * -- LAPACK auxiliary routine --
1.1 bertrand 125: * -- LAPACK is a software package provided by Univ. of Tennessee, --
126: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
127: *
128: * .. Scalar Arguments ..
129: CHARACTER NORM, UPLO
130: INTEGER LDA, N
131: * ..
132: * .. Array Arguments ..
133: DOUBLE PRECISION WORK( * )
134: COMPLEX*16 A( LDA, * )
135: * ..
136: *
137: * =====================================================================
138: *
139: * .. Parameters ..
140: DOUBLE PRECISION ONE, ZERO
141: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
142: * ..
143: * .. Local Scalars ..
144: INTEGER I, J
1.20 ! bertrand 145: DOUBLE PRECISION ABSA, SCALE, SUM, VALUE
1.1 bertrand 146: * ..
147: * .. External Functions ..
1.11 bertrand 148: LOGICAL LSAME, DISNAN
149: EXTERNAL LSAME, DISNAN
1.1 bertrand 150: * ..
151: * .. External Subroutines ..
1.20 ! bertrand 152: EXTERNAL ZLASSQ
1.1 bertrand 153: * ..
154: * .. Intrinsic Functions ..
1.11 bertrand 155: INTRINSIC ABS, SQRT
1.1 bertrand 156: * ..
157: * .. Executable Statements ..
158: *
159: IF( N.EQ.0 ) THEN
160: VALUE = ZERO
161: ELSE IF( LSAME( NORM, 'M' ) ) THEN
162: *
163: * Find max(abs(A(i,j))).
164: *
165: VALUE = ZERO
166: IF( LSAME( UPLO, 'U' ) ) THEN
167: DO 20 J = 1, N
168: DO 10 I = 1, J
1.11 bertrand 169: SUM = ABS( A( I, J ) )
170: IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
1.1 bertrand 171: 10 CONTINUE
172: 20 CONTINUE
173: ELSE
174: DO 40 J = 1, N
175: DO 30 I = J, N
1.11 bertrand 176: SUM = ABS( A( I, J ) )
177: IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
1.1 bertrand 178: 30 CONTINUE
179: 40 CONTINUE
180: END IF
181: ELSE IF( ( LSAME( NORM, 'I' ) ) .OR. ( LSAME( NORM, 'O' ) ) .OR.
182: $ ( NORM.EQ.'1' ) ) THEN
183: *
184: * Find normI(A) ( = norm1(A), since A is symmetric).
185: *
186: VALUE = ZERO
187: IF( LSAME( UPLO, 'U' ) ) THEN
188: DO 60 J = 1, N
189: SUM = ZERO
190: DO 50 I = 1, J - 1
191: ABSA = ABS( A( I, J ) )
192: SUM = SUM + ABSA
193: WORK( I ) = WORK( I ) + ABSA
194: 50 CONTINUE
195: WORK( J ) = SUM + ABS( A( J, J ) )
196: 60 CONTINUE
197: DO 70 I = 1, N
1.11 bertrand 198: SUM = WORK( I )
199: IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
1.1 bertrand 200: 70 CONTINUE
201: ELSE
202: DO 80 I = 1, N
203: WORK( I ) = ZERO
204: 80 CONTINUE
205: DO 100 J = 1, N
206: SUM = WORK( J ) + ABS( A( J, J ) )
207: DO 90 I = J + 1, N
208: ABSA = ABS( A( I, J ) )
209: SUM = SUM + ABSA
210: WORK( I ) = WORK( I ) + ABSA
211: 90 CONTINUE
1.11 bertrand 212: IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
1.1 bertrand 213: 100 CONTINUE
214: END IF
215: ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
216: *
217: * Find normF(A).
218: *
1.20 ! bertrand 219: SCALE = ZERO
! 220: SUM = ONE
1.1 bertrand 221: IF( LSAME( UPLO, 'U' ) ) THEN
222: DO 110 J = 2, N
1.20 ! bertrand 223: CALL ZLASSQ( J-1, A( 1, J ), 1, SCALE, SUM )
1.1 bertrand 224: 110 CONTINUE
225: ELSE
226: DO 120 J = 1, N - 1
1.20 ! bertrand 227: CALL ZLASSQ( N-J, A( J+1, J ), 1, SCALE, SUM )
1.1 bertrand 228: 120 CONTINUE
229: END IF
1.20 ! bertrand 230: SUM = 2*SUM
! 231: CALL ZLASSQ( N, A, LDA+1, SCALE, SUM )
! 232: VALUE = SCALE*SQRT( SUM )
1.1 bertrand 233: END IF
234: *
235: ZLANSY = VALUE
236: RETURN
237: *
238: * End of ZLANSY
239: *
240: END
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