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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief \b ZLANHT 00002 * 00003 * =========== DOCUMENTATION =========== 00004 * 00005 * Online html documentation available at 00006 * http://www.netlib.org/lapack/explore-html/ 00007 * 00008 *> \htmlonly 00009 *> Download ZLANHT + dependencies 00010 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlanht.f"> 00011 *> [TGZ]</a> 00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlanht.f"> 00013 *> [ZIP]</a> 00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlanht.f"> 00015 *> [TXT]</a> 00016 *> \endhtmlonly 00017 * 00018 * Definition: 00019 * =========== 00020 * 00021 * DOUBLE PRECISION FUNCTION ZLANHT( NORM, N, D, E ) 00022 * 00023 * .. Scalar Arguments .. 00024 * CHARACTER NORM 00025 * INTEGER N 00026 * .. 00027 * .. Array Arguments .. 00028 * DOUBLE PRECISION D( * ) 00029 * COMPLEX*16 E( * ) 00030 * .. 00031 * 00032 * 00033 *> \par Purpose: 00034 * ============= 00035 *> 00036 *> \verbatim 00037 *> 00038 *> ZLANHT 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 tridiagonal matrix A. 00041 *> \endverbatim 00042 *> 00043 *> \return ZLANHT 00044 *> \verbatim 00045 *> 00046 *> ZLANHT = ( 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 ZLANHT as described 00067 *> above. 00068 *> \endverbatim 00069 *> 00070 *> \param[in] N 00071 *> \verbatim 00072 *> N is INTEGER 00073 *> The order of the matrix A. N >= 0. When N = 0, ZLANHT is 00074 *> set to zero. 00075 *> \endverbatim 00076 *> 00077 *> \param[in] D 00078 *> \verbatim 00079 *> D is DOUBLE PRECISION array, dimension (N) 00080 *> The diagonal elements of A. 00081 *> \endverbatim 00082 *> 00083 *> \param[in] E 00084 *> \verbatim 00085 *> E is COMPLEX*16 array, dimension (N-1) 00086 *> The (n-1) sub-diagonal or super-diagonal elements of A. 00087 *> \endverbatim 00088 * 00089 * Authors: 00090 * ======== 00091 * 00092 *> \author Univ. of Tennessee 00093 *> \author Univ. of California Berkeley 00094 *> \author Univ. of Colorado Denver 00095 *> \author NAG Ltd. 00096 * 00097 *> \date November 2011 00098 * 00099 *> \ingroup complex16OTHERauxiliary 00100 * 00101 * ===================================================================== 00102 DOUBLE PRECISION FUNCTION ZLANHT( NORM, N, D, E ) 00103 * 00104 * -- LAPACK auxiliary routine (version 3.4.0) -- 00105 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00106 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00107 * November 2011 00108 * 00109 * .. Scalar Arguments .. 00110 CHARACTER NORM 00111 INTEGER N 00112 * .. 00113 * .. Array Arguments .. 00114 DOUBLE PRECISION D( * ) 00115 COMPLEX*16 E( * ) 00116 * .. 00117 * 00118 * ===================================================================== 00119 * 00120 * .. Parameters .. 00121 DOUBLE PRECISION ONE, ZERO 00122 PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) 00123 * .. 00124 * .. Local Scalars .. 00125 INTEGER I 00126 DOUBLE PRECISION ANORM, SCALE, SUM 00127 * .. 00128 * .. External Functions .. 00129 LOGICAL LSAME 00130 EXTERNAL LSAME 00131 * .. 00132 * .. External Subroutines .. 00133 EXTERNAL DLASSQ, ZLASSQ 00134 * .. 00135 * .. Intrinsic Functions .. 00136 INTRINSIC ABS, MAX, SQRT 00137 * .. 00138 * .. Executable Statements .. 00139 * 00140 IF( N.LE.0 ) THEN 00141 ANORM = ZERO 00142 ELSE IF( LSAME( NORM, 'M' ) ) THEN 00143 * 00144 * Find max(abs(A(i,j))). 00145 * 00146 ANORM = ABS( D( N ) ) 00147 DO 10 I = 1, N - 1 00148 ANORM = MAX( ANORM, ABS( D( I ) ) ) 00149 ANORM = MAX( ANORM, ABS( E( I ) ) ) 00150 10 CONTINUE 00151 ELSE IF( LSAME( NORM, 'O' ) .OR. NORM.EQ.'1' .OR. 00152 $ LSAME( NORM, 'I' ) ) THEN 00153 * 00154 * Find norm1(A). 00155 * 00156 IF( N.EQ.1 ) THEN 00157 ANORM = ABS( D( 1 ) ) 00158 ELSE 00159 ANORM = MAX( ABS( D( 1 ) )+ABS( E( 1 ) ), 00160 $ ABS( E( N-1 ) )+ABS( D( N ) ) ) 00161 DO 20 I = 2, N - 1 00162 ANORM = MAX( ANORM, ABS( D( I ) )+ABS( E( I ) )+ 00163 $ ABS( E( I-1 ) ) ) 00164 20 CONTINUE 00165 END IF 00166 ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN 00167 * 00168 * Find normF(A). 00169 * 00170 SCALE = ZERO 00171 SUM = ONE 00172 IF( N.GT.1 ) THEN 00173 CALL ZLASSQ( N-1, E, 1, SCALE, SUM ) 00174 SUM = 2*SUM 00175 END IF 00176 CALL DLASSQ( N, D, 1, SCALE, SUM ) 00177 ANORM = SCALE*SQRT( SUM ) 00178 END IF 00179 * 00180 ZLANHT = ANORM 00181 RETURN 00182 * 00183 * End of ZLANHT 00184 * 00185 END