Annotation of rpl/lapack/lapack/dlansy.f, revision 1.14
1.11 bertrand 1: *> \brief \b DLANSY 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.
1.8 bertrand 2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
9: *> Download DLANSY + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlansy.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlansy.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlansy.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * DOUBLE PRECISION FUNCTION DLANSY( 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 A( LDA, * ), WORK( * )
29: * ..
30: *
31: *
32: *> \par Purpose:
33: * =============
34: *>
35: *> \verbatim
36: *>
37: *> DLANSY 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 DLANSY
43: *> \verbatim
44: *>
45: *> DLANSY = ( 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 DLANSY 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, DLANSY is
82: *> set to zero.
83: *> \endverbatim
84: *>
85: *> \param[in] A
86: *> \verbatim
87: *> A is DOUBLE PRECISION 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 DOUBLE PRECISION 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: *
1.14 ! bertrand 118: *> \date November 2015
1.8 bertrand 119: *
120: *> \ingroup doubleSYauxiliary
121: *
122: * =====================================================================
1.1 bertrand 123: DOUBLE PRECISION FUNCTION DLANSY( NORM, UPLO, N, A, LDA, WORK )
124: *
1.14 ! bertrand 125: * -- LAPACK auxiliary routine (version 3.6.0) --
1.1 bertrand 126: * -- LAPACK is a software package provided by Univ. of Tennessee, --
127: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.14 ! bertrand 128: * November 2015
1.1 bertrand 129: *
130: * .. Scalar Arguments ..
131: CHARACTER NORM, UPLO
132: INTEGER LDA, N
133: * ..
134: * .. Array Arguments ..
135: DOUBLE PRECISION A( LDA, * ), WORK( * )
136: * ..
137: *
138: * =====================================================================
139: *
140: * .. Parameters ..
141: DOUBLE PRECISION ONE, ZERO
142: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
143: * ..
144: * .. Local Scalars ..
145: INTEGER I, J
146: DOUBLE PRECISION ABSA, SCALE, SUM, VALUE
147: * ..
148: * .. External Subroutines ..
149: EXTERNAL DLASSQ
150: * ..
151: * .. External Functions ..
1.11 bertrand 152: LOGICAL LSAME, DISNAN
153: EXTERNAL LSAME, DISNAN
1.1 bertrand 154: * ..
155: * .. Intrinsic Functions ..
1.11 bertrand 156: INTRINSIC ABS, SQRT
1.1 bertrand 157: * ..
158: * .. Executable Statements ..
159: *
160: IF( N.EQ.0 ) THEN
161: VALUE = ZERO
162: ELSE IF( LSAME( NORM, 'M' ) ) THEN
163: *
164: * Find max(abs(A(i,j))).
165: *
166: VALUE = ZERO
167: IF( LSAME( UPLO, 'U' ) ) THEN
168: DO 20 J = 1, N
169: DO 10 I = 1, J
1.11 bertrand 170: SUM = ABS( A( I, J ) )
171: IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
1.1 bertrand 172: 10 CONTINUE
173: 20 CONTINUE
174: ELSE
175: DO 40 J = 1, N
176: DO 30 I = J, N
1.11 bertrand 177: SUM = ABS( A( I, J ) )
178: IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
1.1 bertrand 179: 30 CONTINUE
180: 40 CONTINUE
181: END IF
182: ELSE IF( ( LSAME( NORM, 'I' ) ) .OR. ( LSAME( NORM, 'O' ) ) .OR.
183: $ ( NORM.EQ.'1' ) ) THEN
184: *
185: * Find normI(A) ( = norm1(A), since A is symmetric).
186: *
187: VALUE = ZERO
188: IF( LSAME( UPLO, 'U' ) ) THEN
189: DO 60 J = 1, N
190: SUM = ZERO
191: DO 50 I = 1, J - 1
192: ABSA = ABS( A( I, J ) )
193: SUM = SUM + ABSA
194: WORK( I ) = WORK( I ) + ABSA
195: 50 CONTINUE
196: WORK( J ) = SUM + ABS( A( J, J ) )
197: 60 CONTINUE
198: DO 70 I = 1, N
1.11 bertrand 199: SUM = WORK( I )
200: IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
1.1 bertrand 201: 70 CONTINUE
202: ELSE
203: DO 80 I = 1, N
204: WORK( I ) = ZERO
205: 80 CONTINUE
206: DO 100 J = 1, N
207: SUM = WORK( J ) + ABS( A( J, J ) )
208: DO 90 I = J + 1, N
209: ABSA = ABS( A( I, J ) )
210: SUM = SUM + ABSA
211: WORK( I ) = WORK( I ) + ABSA
212: 90 CONTINUE
1.11 bertrand 213: IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
1.1 bertrand 214: 100 CONTINUE
215: END IF
216: ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
217: *
218: * Find normF(A).
219: *
220: SCALE = ZERO
221: SUM = ONE
222: IF( LSAME( UPLO, 'U' ) ) THEN
223: DO 110 J = 2, N
224: CALL DLASSQ( J-1, A( 1, J ), 1, SCALE, SUM )
225: 110 CONTINUE
226: ELSE
227: DO 120 J = 1, N - 1
228: CALL DLASSQ( N-J, A( J+1, J ), 1, SCALE, SUM )
229: 120 CONTINUE
230: END IF
231: SUM = 2*SUM
232: CALL DLASSQ( N, A, LDA+1, SCALE, SUM )
233: VALUE = SCALE*SQRT( SUM )
234: END IF
235: *
236: DLANSY = VALUE
237: RETURN
238: *
239: * End of DLANSY
240: *
241: END
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