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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief \b ZLANSP 00002 * 00003 * =========== DOCUMENTATION =========== 00004 * 00005 * Online html documentation available at 00006 * http://www.netlib.org/lapack/explore-html/ 00007 * 00008 *> \htmlonly 00009 *> Download ZLANSP + dependencies 00010 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlansp.f"> 00011 *> [TGZ]</a> 00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlansp.f"> 00013 *> [ZIP]</a> 00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlansp.f"> 00015 *> [TXT]</a> 00016 *> \endhtmlonly 00017 * 00018 * Definition: 00019 * =========== 00020 * 00021 * DOUBLE PRECISION FUNCTION ZLANSP( 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 *> ZLANSP 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, supplied in packed form. 00041 *> \endverbatim 00042 *> 00043 *> \return ZLANSP 00044 *> \verbatim 00045 *> 00046 *> ZLANSP = ( 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 ZLANSP 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 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, ZLANSP 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 symmetric 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 *> \endverbatim 00095 *> 00096 *> \param[out] WORK 00097 *> \verbatim 00098 *> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)), 00099 *> where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise, 00100 *> WORK is not referenced. 00101 *> \endverbatim 00102 * 00103 * Authors: 00104 * ======== 00105 * 00106 *> \author Univ. of Tennessee 00107 *> \author Univ. of California Berkeley 00108 *> \author Univ. of Colorado Denver 00109 *> \author NAG Ltd. 00110 * 00111 *> \date November 2011 00112 * 00113 *> \ingroup complex16OTHERauxiliary 00114 * 00115 * ===================================================================== 00116 DOUBLE PRECISION FUNCTION ZLANSP( NORM, UPLO, N, AP, WORK ) 00117 * 00118 * -- LAPACK auxiliary routine (version 3.4.0) -- 00119 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00120 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00121 * November 2011 00122 * 00123 * .. Scalar Arguments .. 00124 CHARACTER NORM, UPLO 00125 INTEGER N 00126 * .. 00127 * .. Array Arguments .. 00128 DOUBLE PRECISION WORK( * ) 00129 COMPLEX*16 AP( * ) 00130 * .. 00131 * 00132 * ===================================================================== 00133 * 00134 * .. Parameters .. 00135 DOUBLE PRECISION ONE, ZERO 00136 PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) 00137 * .. 00138 * .. Local Scalars .. 00139 INTEGER I, J, K 00140 DOUBLE PRECISION ABSA, SCALE, SUM, VALUE 00141 * .. 00142 * .. External Functions .. 00143 LOGICAL LSAME 00144 EXTERNAL LSAME 00145 * .. 00146 * .. External Subroutines .. 00147 EXTERNAL ZLASSQ 00148 * .. 00149 * .. Intrinsic Functions .. 00150 INTRINSIC ABS, DBLE, DIMAG, MAX, SQRT 00151 * .. 00152 * .. Executable Statements .. 00153 * 00154 IF( N.EQ.0 ) THEN 00155 VALUE = ZERO 00156 ELSE IF( LSAME( NORM, 'M' ) ) THEN 00157 * 00158 * Find max(abs(A(i,j))). 00159 * 00160 VALUE = ZERO 00161 IF( LSAME( UPLO, 'U' ) ) THEN 00162 K = 1 00163 DO 20 J = 1, N 00164 DO 10 I = K, K + J - 1 00165 VALUE = MAX( VALUE, ABS( AP( I ) ) ) 00166 10 CONTINUE 00167 K = K + J 00168 20 CONTINUE 00169 ELSE 00170 K = 1 00171 DO 40 J = 1, N 00172 DO 30 I = K, K + N - J 00173 VALUE = MAX( VALUE, ABS( AP( I ) ) ) 00174 30 CONTINUE 00175 K = K + N - J + 1 00176 40 CONTINUE 00177 END IF 00178 ELSE IF( ( LSAME( NORM, 'I' ) ) .OR. ( LSAME( NORM, 'O' ) ) .OR. 00179 $ ( NORM.EQ.'1' ) ) THEN 00180 * 00181 * Find normI(A) ( = norm1(A), since A is symmetric). 00182 * 00183 VALUE = ZERO 00184 K = 1 00185 IF( LSAME( UPLO, 'U' ) ) THEN 00186 DO 60 J = 1, N 00187 SUM = ZERO 00188 DO 50 I = 1, J - 1 00189 ABSA = ABS( AP( K ) ) 00190 SUM = SUM + ABSA 00191 WORK( I ) = WORK( I ) + ABSA 00192 K = K + 1 00193 50 CONTINUE 00194 WORK( J ) = SUM + ABS( AP( K ) ) 00195 K = K + 1 00196 60 CONTINUE 00197 DO 70 I = 1, N 00198 VALUE = MAX( VALUE, WORK( I ) ) 00199 70 CONTINUE 00200 ELSE 00201 DO 80 I = 1, N 00202 WORK( I ) = ZERO 00203 80 CONTINUE 00204 DO 100 J = 1, N 00205 SUM = WORK( J ) + ABS( AP( K ) ) 00206 K = K + 1 00207 DO 90 I = J + 1, N 00208 ABSA = ABS( AP( K ) ) 00209 SUM = SUM + ABSA 00210 WORK( I ) = WORK( I ) + ABSA 00211 K = K + 1 00212 90 CONTINUE 00213 VALUE = MAX( VALUE, SUM ) 00214 100 CONTINUE 00215 END IF 00216 ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN 00217 * 00218 * Find normF(A). 00219 * 00220 SCALE = ZERO 00221 SUM = ONE 00222 K = 2 00223 IF( LSAME( UPLO, 'U' ) ) THEN 00224 DO 110 J = 2, N 00225 CALL ZLASSQ( J-1, AP( K ), 1, SCALE, SUM ) 00226 K = K + J 00227 110 CONTINUE 00228 ELSE 00229 DO 120 J = 1, N - 1 00230 CALL ZLASSQ( N-J, AP( K ), 1, SCALE, SUM ) 00231 K = K + N - J + 1 00232 120 CONTINUE 00233 END IF 00234 SUM = 2*SUM 00235 K = 1 00236 DO 130 I = 1, N 00237 IF( DBLE( AP( K ) ).NE.ZERO ) THEN 00238 ABSA = ABS( DBLE( AP( K ) ) ) 00239 IF( SCALE.LT.ABSA ) THEN 00240 SUM = ONE + SUM*( SCALE / ABSA )**2 00241 SCALE = ABSA 00242 ELSE 00243 SUM = SUM + ( ABSA / SCALE )**2 00244 END IF 00245 END IF 00246 IF( DIMAG( AP( K ) ).NE.ZERO ) THEN 00247 ABSA = ABS( DIMAG( AP( K ) ) ) 00248 IF( SCALE.LT.ABSA ) THEN 00249 SUM = ONE + SUM*( SCALE / ABSA )**2 00250 SCALE = ABSA 00251 ELSE 00252 SUM = SUM + ( ABSA / SCALE )**2 00253 END IF 00254 END IF 00255 IF( LSAME( UPLO, 'U' ) ) THEN 00256 K = K + I + 1 00257 ELSE 00258 K = K + N - I + 1 00259 END IF 00260 130 CONTINUE 00261 VALUE = SCALE*SQRT( SUM ) 00262 END IF 00263 * 00264 ZLANSP = VALUE 00265 RETURN 00266 * 00267 * End of ZLANSP 00268 * 00269 END