Annotation of rpl/lapack/lapack/dlansy.f, revision 1.20
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: *
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 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">
1.8 bertrand 15: *> [TXT]</a>
1.16 bertrand 16: *> \endhtmlonly
1.8 bertrand 17: *
18: * Definition:
19: * ===========
20: *
21: * DOUBLE PRECISION FUNCTION DLANSY( 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 A( LDA, * ), WORK( * )
29: * ..
1.16 bertrand 30: *
1.8 bertrand 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: *
1.16 bertrand 113: *> \author Univ. of Tennessee
114: *> \author Univ. of California Berkeley
115: *> \author Univ. of Colorado Denver
116: *> \author NAG Ltd.
1.8 bertrand 117: *
118: *> \ingroup doubleSYauxiliary
119: *
120: * =====================================================================
1.1 bertrand 121: DOUBLE PRECISION FUNCTION DLANSY( NORM, UPLO, N, A, LDA, WORK )
122: *
1.20 ! bertrand 123: * -- LAPACK auxiliary routine --
1.1 bertrand 124: * -- LAPACK is a software package provided by Univ. of Tennessee, --
125: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
126: *
127: * .. Scalar Arguments ..
128: CHARACTER NORM, UPLO
129: INTEGER LDA, N
130: * ..
131: * .. Array Arguments ..
132: DOUBLE PRECISION A( LDA, * ), WORK( * )
133: * ..
134: *
135: * =====================================================================
136: *
137: * .. Parameters ..
138: DOUBLE PRECISION ONE, ZERO
139: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
140: * ..
141: * .. Local Scalars ..
142: INTEGER I, J
1.20 ! bertrand 143: DOUBLE PRECISION ABSA, SCALE, SUM, VALUE
1.1 bertrand 144: * ..
1.20 ! bertrand 145: * .. External Subroutines ..
! 146: EXTERNAL DLASSQ
1.1 bertrand 147: * ..
148: * .. External Functions ..
1.11 bertrand 149: LOGICAL LSAME, DISNAN
150: EXTERNAL LSAME, DISNAN
1.1 bertrand 151: * ..
152: * .. Intrinsic Functions ..
1.11 bertrand 153: INTRINSIC ABS, SQRT
1.1 bertrand 154: * ..
155: * .. Executable Statements ..
156: *
157: IF( N.EQ.0 ) THEN
158: VALUE = ZERO
159: ELSE IF( LSAME( NORM, 'M' ) ) THEN
160: *
161: * Find max(abs(A(i,j))).
162: *
163: VALUE = ZERO
164: IF( LSAME( UPLO, 'U' ) ) THEN
165: DO 20 J = 1, N
166: DO 10 I = 1, J
1.11 bertrand 167: SUM = ABS( A( I, J ) )
168: IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
1.1 bertrand 169: 10 CONTINUE
170: 20 CONTINUE
171: ELSE
172: DO 40 J = 1, N
173: DO 30 I = J, N
1.11 bertrand 174: SUM = ABS( A( I, J ) )
175: IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
1.1 bertrand 176: 30 CONTINUE
177: 40 CONTINUE
178: END IF
179: ELSE IF( ( LSAME( NORM, 'I' ) ) .OR. ( LSAME( NORM, 'O' ) ) .OR.
180: $ ( NORM.EQ.'1' ) ) THEN
181: *
182: * Find normI(A) ( = norm1(A), since A is symmetric).
183: *
184: VALUE = ZERO
185: IF( LSAME( UPLO, 'U' ) ) THEN
186: DO 60 J = 1, N
187: SUM = ZERO
188: DO 50 I = 1, J - 1
189: ABSA = ABS( A( I, J ) )
190: SUM = SUM + ABSA
191: WORK( I ) = WORK( I ) + ABSA
192: 50 CONTINUE
193: WORK( J ) = SUM + ABS( A( J, J ) )
194: 60 CONTINUE
195: DO 70 I = 1, N
1.11 bertrand 196: SUM = WORK( I )
197: IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
1.1 bertrand 198: 70 CONTINUE
199: ELSE
200: DO 80 I = 1, N
201: WORK( I ) = ZERO
202: 80 CONTINUE
203: DO 100 J = 1, N
204: SUM = WORK( J ) + ABS( A( J, J ) )
205: DO 90 I = J + 1, N
206: ABSA = ABS( A( I, J ) )
207: SUM = SUM + ABSA
208: WORK( I ) = WORK( I ) + ABSA
209: 90 CONTINUE
1.11 bertrand 210: IF( VALUE .LT. SUM .OR. DISNAN( SUM ) ) VALUE = SUM
1.1 bertrand 211: 100 CONTINUE
212: END IF
213: ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
214: *
215: * Find normF(A).
216: *
1.20 ! bertrand 217: SCALE = ZERO
! 218: SUM = ONE
1.1 bertrand 219: IF( LSAME( UPLO, 'U' ) ) THEN
220: DO 110 J = 2, N
1.20 ! bertrand 221: CALL DLASSQ( J-1, A( 1, J ), 1, SCALE, SUM )
1.1 bertrand 222: 110 CONTINUE
223: ELSE
224: DO 120 J = 1, N - 1
1.20 ! bertrand 225: CALL DLASSQ( N-J, A( J+1, J ), 1, SCALE, SUM )
1.1 bertrand 226: 120 CONTINUE
227: END IF
1.20 ! bertrand 228: SUM = 2*SUM
! 229: CALL DLASSQ( N, A, LDA+1, SCALE, SUM )
! 230: VALUE = SCALE*SQRT( SUM )
1.1 bertrand 231: END IF
232: *
233: DLANSY = VALUE
234: RETURN
235: *
236: * End of DLANSY
237: *
238: END
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