Annotation of rpl/lapack/lapack/dlansy.f, revision 1.8
1.8 ! bertrand 1: *> \brief \b DLANSY
! 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: *
! 118: *> \date November 2011
! 119: *
! 120: *> \ingroup doubleSYauxiliary
! 121: *
! 122: * =====================================================================
1.1 bertrand 123: DOUBLE PRECISION FUNCTION DLANSY( NORM, UPLO, N, A, LDA, WORK )
124: *
1.8 ! bertrand 125: * -- LAPACK auxiliary routine (version 3.4.0) --
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..--
1.8 ! bertrand 128: * November 2011
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 ..
152: LOGICAL LSAME
153: EXTERNAL LSAME
154: * ..
155: * .. Intrinsic Functions ..
156: INTRINSIC ABS, MAX, SQRT
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
170: VALUE = MAX( VALUE, ABS( A( I, J ) ) )
171: 10 CONTINUE
172: 20 CONTINUE
173: ELSE
174: DO 40 J = 1, N
175: DO 30 I = J, N
176: VALUE = MAX( VALUE, ABS( A( I, J ) ) )
177: 30 CONTINUE
178: 40 CONTINUE
179: END IF
180: ELSE IF( ( LSAME( NORM, 'I' ) ) .OR. ( LSAME( NORM, 'O' ) ) .OR.
181: $ ( NORM.EQ.'1' ) ) THEN
182: *
183: * Find normI(A) ( = norm1(A), since A is symmetric).
184: *
185: VALUE = ZERO
186: IF( LSAME( UPLO, 'U' ) ) THEN
187: DO 60 J = 1, N
188: SUM = ZERO
189: DO 50 I = 1, J - 1
190: ABSA = ABS( A( I, J ) )
191: SUM = SUM + ABSA
192: WORK( I ) = WORK( I ) + ABSA
193: 50 CONTINUE
194: WORK( J ) = SUM + ABS( A( J, J ) )
195: 60 CONTINUE
196: DO 70 I = 1, N
197: VALUE = MAX( VALUE, WORK( I ) )
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
210: VALUE = MAX( VALUE, SUM )
211: 100 CONTINUE
212: END IF
213: ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
214: *
215: * Find normF(A).
216: *
217: SCALE = ZERO
218: SUM = ONE
219: IF( LSAME( UPLO, 'U' ) ) THEN
220: DO 110 J = 2, N
221: CALL DLASSQ( J-1, A( 1, J ), 1, SCALE, SUM )
222: 110 CONTINUE
223: ELSE
224: DO 120 J = 1, N - 1
225: CALL DLASSQ( N-J, A( J+1, J ), 1, SCALE, SUM )
226: 120 CONTINUE
227: END IF
228: SUM = 2*SUM
229: CALL DLASSQ( N, A, LDA+1, SCALE, SUM )
230: VALUE = SCALE*SQRT( SUM )
231: END IF
232: *
233: DLANSY = VALUE
234: RETURN
235: *
236: * End of DLANSY
237: *
238: END
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