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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief \b CLANHE 00002 * 00003 * =========== DOCUMENTATION =========== 00004 * 00005 * Online html documentation available at 00006 * http://www.netlib.org/lapack/explore-html/ 00007 * 00008 *> \htmlonly 00009 *> Download CLANHE + dependencies 00010 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/clanhe.f"> 00011 *> [TGZ]</a> 00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/clanhe.f"> 00013 *> [ZIP]</a> 00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/clanhe.f"> 00015 *> [TXT]</a> 00016 *> \endhtmlonly 00017 * 00018 * Definition: 00019 * =========== 00020 * 00021 * REAL FUNCTION CLANHE( 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 *> CLANHE 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 hermitian matrix A. 00041 *> \endverbatim 00042 *> 00043 *> \return CLANHE 00044 *> \verbatim 00045 *> 00046 *> CLANHE = ( 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 CLANHE 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 *> hermitian 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, CLANHE is 00083 *> set to zero. 00084 *> \endverbatim 00085 *> 00086 *> \param[in] A 00087 *> \verbatim 00088 *> A is COMPLEX array, dimension (LDA,N) 00089 *> The hermitian 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. Note that the imaginary parts of the diagonal 00096 *> elements need not be set and are assumed to be zero. 00097 *> \endverbatim 00098 *> 00099 *> \param[in] LDA 00100 *> \verbatim 00101 *> LDA is INTEGER 00102 *> The leading dimension of the array A. LDA >= max(N,1). 00103 *> \endverbatim 00104 *> 00105 *> \param[out] WORK 00106 *> \verbatim 00107 *> WORK is REAL array, dimension (MAX(1,LWORK)), 00108 *> where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise, 00109 *> WORK is not referenced. 00110 *> \endverbatim 00111 * 00112 * Authors: 00113 * ======== 00114 * 00115 *> \author Univ. of Tennessee 00116 *> \author Univ. of California Berkeley 00117 *> \author Univ. of Colorado Denver 00118 *> \author NAG Ltd. 00119 * 00120 *> \date November 2011 00121 * 00122 *> \ingroup complexHEauxiliary 00123 * 00124 * ===================================================================== 00125 REAL FUNCTION CLANHE( NORM, UPLO, N, A, LDA, WORK ) 00126 * 00127 * -- LAPACK auxiliary routine (version 3.4.0) -- 00128 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00129 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00130 * November 2011 00131 * 00132 * .. Scalar Arguments .. 00133 CHARACTER NORM, UPLO 00134 INTEGER LDA, N 00135 * .. 00136 * .. Array Arguments .. 00137 REAL WORK( * ) 00138 COMPLEX A( LDA, * ) 00139 * .. 00140 * 00141 * ===================================================================== 00142 * 00143 * .. Parameters .. 00144 REAL ONE, ZERO 00145 PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 ) 00146 * .. 00147 * .. Local Scalars .. 00148 INTEGER I, J 00149 REAL ABSA, SCALE, SUM, VALUE 00150 * .. 00151 * .. External Functions .. 00152 LOGICAL LSAME 00153 EXTERNAL LSAME 00154 * .. 00155 * .. External Subroutines .. 00156 EXTERNAL CLASSQ 00157 * .. 00158 * .. Intrinsic Functions .. 00159 INTRINSIC ABS, MAX, REAL, SQRT 00160 * .. 00161 * .. Executable Statements .. 00162 * 00163 IF( N.EQ.0 ) THEN 00164 VALUE = ZERO 00165 ELSE IF( LSAME( NORM, 'M' ) ) THEN 00166 * 00167 * Find max(abs(A(i,j))). 00168 * 00169 VALUE = ZERO 00170 IF( LSAME( UPLO, 'U' ) ) THEN 00171 DO 20 J = 1, N 00172 DO 10 I = 1, J - 1 00173 VALUE = MAX( VALUE, ABS( A( I, J ) ) ) 00174 10 CONTINUE 00175 VALUE = MAX( VALUE, ABS( REAL( A( J, J ) ) ) ) 00176 20 CONTINUE 00177 ELSE 00178 DO 40 J = 1, N 00179 VALUE = MAX( VALUE, ABS( REAL( A( J, J ) ) ) ) 00180 DO 30 I = J + 1, N 00181 VALUE = MAX( VALUE, ABS( A( I, J ) ) ) 00182 30 CONTINUE 00183 40 CONTINUE 00184 END IF 00185 ELSE IF( ( LSAME( NORM, 'I' ) ) .OR. ( LSAME( NORM, 'O' ) ) .OR. 00186 $ ( NORM.EQ.'1' ) ) THEN 00187 * 00188 * Find normI(A) ( = norm1(A), since A is hermitian). 00189 * 00190 VALUE = ZERO 00191 IF( LSAME( UPLO, 'U' ) ) THEN 00192 DO 60 J = 1, N 00193 SUM = ZERO 00194 DO 50 I = 1, J - 1 00195 ABSA = ABS( A( I, J ) ) 00196 SUM = SUM + ABSA 00197 WORK( I ) = WORK( I ) + ABSA 00198 50 CONTINUE 00199 WORK( J ) = SUM + ABS( REAL( A( J, J ) ) ) 00200 60 CONTINUE 00201 DO 70 I = 1, N 00202 VALUE = MAX( VALUE, WORK( I ) ) 00203 70 CONTINUE 00204 ELSE 00205 DO 80 I = 1, N 00206 WORK( I ) = ZERO 00207 80 CONTINUE 00208 DO 100 J = 1, N 00209 SUM = WORK( J ) + ABS( REAL( A( J, J ) ) ) 00210 DO 90 I = J + 1, N 00211 ABSA = ABS( A( I, J ) ) 00212 SUM = SUM + ABSA 00213 WORK( I ) = WORK( I ) + ABSA 00214 90 CONTINUE 00215 VALUE = MAX( VALUE, SUM ) 00216 100 CONTINUE 00217 END IF 00218 ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN 00219 * 00220 * Find normF(A). 00221 * 00222 SCALE = ZERO 00223 SUM = ONE 00224 IF( LSAME( UPLO, 'U' ) ) THEN 00225 DO 110 J = 2, N 00226 CALL CLASSQ( J-1, A( 1, J ), 1, SCALE, SUM ) 00227 110 CONTINUE 00228 ELSE 00229 DO 120 J = 1, N - 1 00230 CALL CLASSQ( N-J, A( J+1, J ), 1, SCALE, SUM ) 00231 120 CONTINUE 00232 END IF 00233 SUM = 2*SUM 00234 DO 130 I = 1, N 00235 IF( REAL( A( I, I ) ).NE.ZERO ) THEN 00236 ABSA = ABS( REAL( A( I, I ) ) ) 00237 IF( SCALE.LT.ABSA ) THEN 00238 SUM = ONE + SUM*( SCALE / ABSA )**2 00239 SCALE = ABSA 00240 ELSE 00241 SUM = SUM + ( ABSA / SCALE )**2 00242 END IF 00243 END IF 00244 130 CONTINUE 00245 VALUE = SCALE*SQRT( SUM ) 00246 END IF 00247 * 00248 CLANHE = VALUE 00249 RETURN 00250 * 00251 * End of CLANHE 00252 * 00253 END