Annotation of rpl/lapack/lapack/zlansy.f, revision 1.8
1.8 ! bertrand 1: *> \brief \b ZLANSY
! 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 November 2011
! 120: *
! 121: *> \ingroup complex16SYauxiliary
! 122: *
! 123: * =====================================================================
1.1 bertrand 124: DOUBLE PRECISION FUNCTION ZLANSY( NORM, UPLO, N, A, LDA, WORK )
125: *
1.8 ! bertrand 126: * -- LAPACK auxiliary routine (version 3.4.0) --
1.1 bertrand 127: * -- LAPACK is a software package provided by Univ. of Tennessee, --
128: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.8 ! bertrand 129: * November 2011
1.1 bertrand 130: *
131: * .. Scalar Arguments ..
132: CHARACTER NORM, UPLO
133: INTEGER LDA, N
134: * ..
135: * .. Array Arguments ..
136: DOUBLE PRECISION WORK( * )
137: COMPLEX*16 A( LDA, * )
138: * ..
139: *
140: * =====================================================================
141: *
142: * .. Parameters ..
143: DOUBLE PRECISION ONE, ZERO
144: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
145: * ..
146: * .. Local Scalars ..
147: INTEGER I, J
148: DOUBLE PRECISION ABSA, SCALE, SUM, VALUE
149: * ..
150: * .. External Functions ..
151: LOGICAL LSAME
152: EXTERNAL LSAME
153: * ..
154: * .. External Subroutines ..
155: EXTERNAL ZLASSQ
156: * ..
157: * .. Intrinsic Functions ..
158: INTRINSIC ABS, MAX, SQRT
159: * ..
160: * .. Executable Statements ..
161: *
162: IF( N.EQ.0 ) THEN
163: VALUE = ZERO
164: ELSE IF( LSAME( NORM, 'M' ) ) THEN
165: *
166: * Find max(abs(A(i,j))).
167: *
168: VALUE = ZERO
169: IF( LSAME( UPLO, 'U' ) ) THEN
170: DO 20 J = 1, N
171: DO 10 I = 1, J
172: VALUE = MAX( VALUE, ABS( A( I, J ) ) )
173: 10 CONTINUE
174: 20 CONTINUE
175: ELSE
176: DO 40 J = 1, N
177: DO 30 I = J, N
178: VALUE = MAX( VALUE, ABS( A( I, J ) ) )
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
199: VALUE = MAX( VALUE, WORK( I ) )
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
212: VALUE = MAX( VALUE, SUM )
213: 100 CONTINUE
214: END IF
215: ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN
216: *
217: * Find normF(A).
218: *
219: SCALE = ZERO
220: SUM = ONE
221: IF( LSAME( UPLO, 'U' ) ) THEN
222: DO 110 J = 2, N
223: CALL ZLASSQ( J-1, A( 1, J ), 1, SCALE, SUM )
224: 110 CONTINUE
225: ELSE
226: DO 120 J = 1, N - 1
227: CALL ZLASSQ( N-J, A( J+1, J ), 1, SCALE, SUM )
228: 120 CONTINUE
229: END IF
230: SUM = 2*SUM
231: CALL ZLASSQ( N, A, LDA+1, SCALE, SUM )
232: VALUE = SCALE*SQRT( SUM )
233: END IF
234: *
235: ZLANSY = VALUE
236: RETURN
237: *
238: * End of ZLANSY
239: *
240: END
CVSweb interface <joel.bertrand@systella.fr>
![[BACK]](/cvsweb/icons/back.gif){kind=icon}
Return to zlansy.f CVS log ![[TXT]](/cvsweb/icons/text.gif){kind=icon}
![[DIR]](/cvsweb/icons/dir.gif){kind=icon}
Up to [local] / rpl / lapack / lapack