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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief \b ZLANHP 00002 * 00003 * =========== DOCUMENTATION =========== 00004 * 00005 * Online html documentation available at 00006 * http://www.netlib.org/lapack/explore-html/ 00007 * 00008 *> \htmlonly 00009 *> Download ZLANHP + dependencies 00010 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlanhp.f"> 00011 *> [TGZ]</a> 00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlanhp.f"> 00013 *> [ZIP]</a> 00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlanhp.f"> 00015 *> [TXT]</a> 00016 *> \endhtmlonly 00017 * 00018 * Definition: 00019 * =========== 00020 * 00021 * DOUBLE PRECISION FUNCTION ZLANHP( NORM, UPLO, N, AP, WORK ) 00022 * 00023 * .. Scalar Arguments .. 00024 * CHARACTER NORM, UPLO 00025 * INTEGER N 00026 * .. 00027 * .. Array Arguments .. 00028 * DOUBLE PRECISION WORK( * ) 00029 * COMPLEX*16 AP( * ) 00030 * .. 00031 * 00032 * 00033 *> \par Purpose: 00034 * ============= 00035 *> 00036 *> \verbatim 00037 *> 00038 *> ZLANHP 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, supplied in packed form. 00041 *> \endverbatim 00042 *> 00043 *> \return ZLANHP 00044 *> \verbatim 00045 *> 00046 *> ZLANHP = ( 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 ZLANHP 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 supplied. 00075 *> = 'U': Upper triangular part of A is supplied 00076 *> = 'L': Lower triangular part of A is supplied 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, ZLANHP is 00083 *> set to zero. 00084 *> \endverbatim 00085 *> 00086 *> \param[in] AP 00087 *> \verbatim 00088 *> AP is COMPLEX*16 array, dimension (N*(N+1)/2) 00089 *> The upper or lower triangle of the hermitian matrix A, packed 00090 *> columnwise in a linear array. The j-th column of A is stored 00091 *> in the array AP as follows: 00092 *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; 00093 *> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. 00094 *> Note that the imaginary parts of the diagonal elements need 00095 *> not be set and are assumed to be zero. 00096 *> \endverbatim 00097 *> 00098 *> \param[out] WORK 00099 *> \verbatim 00100 *> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)), 00101 *> where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise, 00102 *> WORK is not referenced. 00103 *> \endverbatim 00104 * 00105 * Authors: 00106 * ======== 00107 * 00108 *> \author Univ. of Tennessee 00109 *> \author Univ. of California Berkeley 00110 *> \author Univ. of Colorado Denver 00111 *> \author NAG Ltd. 00112 * 00113 *> \date November 2011 00114 * 00115 *> \ingroup complex16OTHERauxiliary 00116 * 00117 * ===================================================================== 00118 DOUBLE PRECISION FUNCTION ZLANHP( NORM, UPLO, N, AP, WORK ) 00119 * 00120 * -- LAPACK auxiliary routine (version 3.4.0) -- 00121 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00122 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00123 * November 2011 00124 * 00125 * .. Scalar Arguments .. 00126 CHARACTER NORM, UPLO 00127 INTEGER N 00128 * .. 00129 * .. Array Arguments .. 00130 DOUBLE PRECISION WORK( * ) 00131 COMPLEX*16 AP( * ) 00132 * .. 00133 * 00134 * ===================================================================== 00135 * 00136 * .. Parameters .. 00137 DOUBLE PRECISION ONE, ZERO 00138 PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) 00139 * .. 00140 * .. Local Scalars .. 00141 INTEGER I, J, K 00142 DOUBLE PRECISION ABSA, SCALE, SUM, VALUE 00143 * .. 00144 * .. External Functions .. 00145 LOGICAL LSAME 00146 EXTERNAL LSAME 00147 * .. 00148 * .. External Subroutines .. 00149 EXTERNAL ZLASSQ 00150 * .. 00151 * .. Intrinsic Functions .. 00152 INTRINSIC ABS, DBLE, MAX, SQRT 00153 * .. 00154 * .. Executable Statements .. 00155 * 00156 IF( N.EQ.0 ) THEN 00157 VALUE = ZERO 00158 ELSE IF( LSAME( NORM, 'M' ) ) THEN 00159 * 00160 * Find max(abs(A(i,j))). 00161 * 00162 VALUE = ZERO 00163 IF( LSAME( UPLO, 'U' ) ) THEN 00164 K = 0 00165 DO 20 J = 1, N 00166 DO 10 I = K + 1, K + J - 1 00167 VALUE = MAX( VALUE, ABS( AP( I ) ) ) 00168 10 CONTINUE 00169 K = K + J 00170 VALUE = MAX( VALUE, ABS( DBLE( AP( K ) ) ) ) 00171 20 CONTINUE 00172 ELSE 00173 K = 1 00174 DO 40 J = 1, N 00175 VALUE = MAX( VALUE, ABS( DBLE( AP( K ) ) ) ) 00176 DO 30 I = K + 1, K + N - J 00177 VALUE = MAX( VALUE, ABS( AP( I ) ) ) 00178 30 CONTINUE 00179 K = K + N - J + 1 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 hermitian). 00186 * 00187 VALUE = ZERO 00188 K = 1 00189 IF( LSAME( UPLO, 'U' ) ) THEN 00190 DO 60 J = 1, N 00191 SUM = ZERO 00192 DO 50 I = 1, J - 1 00193 ABSA = ABS( AP( K ) ) 00194 SUM = SUM + ABSA 00195 WORK( I ) = WORK( I ) + ABSA 00196 K = K + 1 00197 50 CONTINUE 00198 WORK( J ) = SUM + ABS( DBLE( AP( K ) ) ) 00199 K = K + 1 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( DBLE( AP( K ) ) ) 00210 K = K + 1 00211 DO 90 I = J + 1, N 00212 ABSA = ABS( AP( K ) ) 00213 SUM = SUM + ABSA 00214 WORK( I ) = WORK( I ) + ABSA 00215 K = K + 1 00216 90 CONTINUE 00217 VALUE = MAX( VALUE, SUM ) 00218 100 CONTINUE 00219 END IF 00220 ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN 00221 * 00222 * Find normF(A). 00223 * 00224 SCALE = ZERO 00225 SUM = ONE 00226 K = 2 00227 IF( LSAME( UPLO, 'U' ) ) THEN 00228 DO 110 J = 2, N 00229 CALL ZLASSQ( J-1, AP( K ), 1, SCALE, SUM ) 00230 K = K + J 00231 110 CONTINUE 00232 ELSE 00233 DO 120 J = 1, N - 1 00234 CALL ZLASSQ( N-J, AP( K ), 1, SCALE, SUM ) 00235 K = K + N - J + 1 00236 120 CONTINUE 00237 END IF 00238 SUM = 2*SUM 00239 K = 1 00240 DO 130 I = 1, N 00241 IF( DBLE( AP( K ) ).NE.ZERO ) THEN 00242 ABSA = ABS( DBLE( AP( K ) ) ) 00243 IF( SCALE.LT.ABSA ) THEN 00244 SUM = ONE + SUM*( SCALE / ABSA )**2 00245 SCALE = ABSA 00246 ELSE 00247 SUM = SUM + ( ABSA / SCALE )**2 00248 END IF 00249 END IF 00250 IF( LSAME( UPLO, 'U' ) ) THEN 00251 K = K + I + 1 00252 ELSE 00253 K = K + N - I + 1 00254 END IF 00255 130 CONTINUE 00256 VALUE = SCALE*SQRT( SUM ) 00257 END IF 00258 * 00259 ZLANHP = VALUE 00260 RETURN 00261 * 00262 * End of ZLANHP 00263 * 00264 END