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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief \b CLANSY 00002 * 00003 * =========== DOCUMENTATION =========== 00004 * 00005 * Online html documentation available at 00006 * http://www.netlib.org/lapack/explore-html/ 00007 * 00008 *> \htmlonly 00009 *> Download CLANSY + dependencies 00010 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/clansy.f"> 00011 *> [TGZ]</a> 00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/clansy.f"> 00013 *> [ZIP]</a> 00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/clansy.f"> 00015 *> [TXT]</a> 00016 *> \endhtmlonly 00017 * 00018 * Definition: 00019 * =========== 00020 * 00021 * REAL FUNCTION CLANSY( NORM, UPLO, N, A, LDA, WORK ) 00022 * 00023 * .. Scalar Arguments .. 00024 * CHARACTER NORM, UPLO 00025 * INTEGER LDA, N 00026 * .. 00027 * .. Array Arguments .. 00028 * REAL WORK( * ) 00029 * COMPLEX A( LDA, * ) 00030 * .. 00031 * 00032 * 00033 *> \par Purpose: 00034 * ============= 00035 *> 00036 *> \verbatim 00037 *> 00038 *> CLANSY returns the value of the one norm, or the Frobenius norm, or 00039 *> the infinity norm, or the element of largest absolute value of a 00040 *> complex symmetric matrix A. 00041 *> \endverbatim 00042 *> 00043 *> \return CLANSY 00044 *> \verbatim 00045 *> 00046 *> CLANSY = ( max(abs(A(i,j))), NORM = 'M' or 'm' 00047 *> ( 00048 *> ( norm1(A), NORM = '1', 'O' or 'o' 00049 *> ( 00050 *> ( normI(A), NORM = 'I' or 'i' 00051 *> ( 00052 *> ( normF(A), NORM = 'F', 'f', 'E' or 'e' 00053 *> 00054 *> where norm1 denotes the one norm of a matrix (maximum column sum), 00055 *> normI denotes the infinity norm of a matrix (maximum row sum) and 00056 *> normF denotes the Frobenius norm of a matrix (square root of sum of 00057 *> squares). Note that max(abs(A(i,j))) is not a consistent matrix norm. 00058 *> \endverbatim 00059 * 00060 * Arguments: 00061 * ========== 00062 * 00063 *> \param[in] NORM 00064 *> \verbatim 00065 *> NORM is CHARACTER*1 00066 *> Specifies the value to be returned in CLANSY as described 00067 *> above. 00068 *> \endverbatim 00069 *> 00070 *> \param[in] UPLO 00071 *> \verbatim 00072 *> UPLO is CHARACTER*1 00073 *> Specifies whether the upper or lower triangular part of the 00074 *> symmetric matrix A is to be referenced. 00075 *> = 'U': Upper triangular part of A is referenced 00076 *> = 'L': Lower triangular part of A is referenced 00077 *> \endverbatim 00078 *> 00079 *> \param[in] N 00080 *> \verbatim 00081 *> N is INTEGER 00082 *> The order of the matrix A. N >= 0. When N = 0, CLANSY is 00083 *> set to zero. 00084 *> \endverbatim 00085 *> 00086 *> \param[in] A 00087 *> \verbatim 00088 *> A is COMPLEX array, dimension (LDA,N) 00089 *> The symmetric matrix A. If UPLO = 'U', the leading n by n 00090 *> upper triangular part of A contains the upper triangular part 00091 *> of the matrix A, and the strictly lower triangular part of A 00092 *> is not referenced. If UPLO = 'L', the leading n by n lower 00093 *> triangular part of A contains the lower triangular part of 00094 *> the matrix A, and the strictly upper triangular part of A is 00095 *> not referenced. 00096 *> \endverbatim 00097 *> 00098 *> \param[in] LDA 00099 *> \verbatim 00100 *> LDA is INTEGER 00101 *> The leading dimension of the array A. LDA >= max(N,1). 00102 *> \endverbatim 00103 *> 00104 *> \param[out] WORK 00105 *> \verbatim 00106 *> WORK is REAL array, dimension (MAX(1,LWORK)), 00107 *> where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise, 00108 *> WORK is not referenced. 00109 *> \endverbatim 00110 * 00111 * Authors: 00112 * ======== 00113 * 00114 *> \author Univ. of Tennessee 00115 *> \author Univ. of California Berkeley 00116 *> \author Univ. of Colorado Denver 00117 *> \author NAG Ltd. 00118 * 00119 *> \date November 2011 00120 * 00121 *> \ingroup complexSYauxiliary 00122 * 00123 * ===================================================================== 00124 REAL FUNCTION CLANSY( NORM, UPLO, N, A, LDA, WORK ) 00125 * 00126 * -- LAPACK auxiliary routine (version 3.4.0) -- 00127 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00128 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00129 * November 2011 00130 * 00131 * .. Scalar Arguments .. 00132 CHARACTER NORM, UPLO 00133 INTEGER LDA, N 00134 * .. 00135 * .. Array Arguments .. 00136 REAL WORK( * ) 00137 COMPLEX A( LDA, * ) 00138 * .. 00139 * 00140 * ===================================================================== 00141 * 00142 * .. Parameters .. 00143 REAL ONE, ZERO 00144 PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 ) 00145 * .. 00146 * .. Local Scalars .. 00147 INTEGER I, J 00148 REAL ABSA, SCALE, SUM, VALUE 00149 * .. 00150 * .. External Functions .. 00151 LOGICAL LSAME 00152 EXTERNAL LSAME 00153 * .. 00154 * .. External Subroutines .. 00155 EXTERNAL CLASSQ 00156 * .. 00157 * .. Intrinsic Functions .. 00158 INTRINSIC ABS, MAX, SQRT 00159 * .. 00160 * .. Executable Statements .. 00161 * 00162 IF( N.EQ.0 ) THEN 00163 VALUE = ZERO 00164 ELSE IF( LSAME( NORM, 'M' ) ) THEN 00165 * 00166 * Find max(abs(A(i,j))). 00167 * 00168 VALUE = ZERO 00169 IF( LSAME( UPLO, 'U' ) ) THEN 00170 DO 20 J = 1, N 00171 DO 10 I = 1, J 00172 VALUE = MAX( VALUE, ABS( A( I, J ) ) ) 00173 10 CONTINUE 00174 20 CONTINUE 00175 ELSE 00176 DO 40 J = 1, N 00177 DO 30 I = J, N 00178 VALUE = MAX( VALUE, ABS( A( I, J ) ) ) 00179 30 CONTINUE 00180 40 CONTINUE 00181 END IF 00182 ELSE IF( ( LSAME( NORM, 'I' ) ) .OR. ( LSAME( NORM, 'O' ) ) .OR. 00183 $ ( NORM.EQ.'1' ) ) THEN 00184 * 00185 * Find normI(A) ( = norm1(A), since A is symmetric). 00186 * 00187 VALUE = ZERO 00188 IF( LSAME( UPLO, 'U' ) ) THEN 00189 DO 60 J = 1, N 00190 SUM = ZERO 00191 DO 50 I = 1, J - 1 00192 ABSA = ABS( A( I, J ) ) 00193 SUM = SUM + ABSA 00194 WORK( I ) = WORK( I ) + ABSA 00195 50 CONTINUE 00196 WORK( J ) = SUM + ABS( A( J, J ) ) 00197 60 CONTINUE 00198 DO 70 I = 1, N 00199 VALUE = MAX( VALUE, WORK( I ) ) 00200 70 CONTINUE 00201 ELSE 00202 DO 80 I = 1, N 00203 WORK( I ) = ZERO 00204 80 CONTINUE 00205 DO 100 J = 1, N 00206 SUM = WORK( J ) + ABS( A( J, J ) ) 00207 DO 90 I = J + 1, N 00208 ABSA = ABS( A( I, J ) ) 00209 SUM = SUM + ABSA 00210 WORK( I ) = WORK( I ) + ABSA 00211 90 CONTINUE 00212 VALUE = MAX( VALUE, SUM ) 00213 100 CONTINUE 00214 END IF 00215 ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN 00216 * 00217 * Find normF(A). 00218 * 00219 SCALE = ZERO 00220 SUM = ONE 00221 IF( LSAME( UPLO, 'U' ) ) THEN 00222 DO 110 J = 2, N 00223 CALL CLASSQ( J-1, A( 1, J ), 1, SCALE, SUM ) 00224 110 CONTINUE 00225 ELSE 00226 DO 120 J = 1, N - 1 00227 CALL CLASSQ( N-J, A( J+1, J ), 1, SCALE, SUM ) 00228 120 CONTINUE 00229 END IF 00230 SUM = 2*SUM 00231 CALL CLASSQ( N, A, LDA+1, SCALE, SUM ) 00232 VALUE = SCALE*SQRT( SUM ) 00233 END IF 00234 * 00235 CLANSY = VALUE 00236 RETURN 00237 * 00238 * End of CLANSY 00239 * 00240 END