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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief \b DLANSP 00002 * 00003 * =========== DOCUMENTATION =========== 00004 * 00005 * Online html documentation available at 00006 * http://www.netlib.org/lapack/explore-html/ 00007 * 00008 *> \htmlonly 00009 *> Download DLANSP + dependencies 00010 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlansp.f"> 00011 *> [TGZ]</a> 00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlansp.f"> 00013 *> [ZIP]</a> 00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlansp.f"> 00015 *> [TXT]</a> 00016 *> \endhtmlonly 00017 * 00018 * Definition: 00019 * =========== 00020 * 00021 * DOUBLE PRECISION FUNCTION DLANSP( NORM, UPLO, N, AP, WORK ) 00022 * 00023 * .. Scalar Arguments .. 00024 * CHARACTER NORM, UPLO 00025 * INTEGER N 00026 * .. 00027 * .. Array Arguments .. 00028 * DOUBLE PRECISION AP( * ), WORK( * ) 00029 * .. 00030 * 00031 * 00032 *> \par Purpose: 00033 * ============= 00034 *> 00035 *> \verbatim 00036 *> 00037 *> DLANSP returns the value of the one norm, or the Frobenius norm, or 00038 *> the infinity norm, or the element of largest absolute value of a 00039 *> real symmetric matrix A, supplied in packed form. 00040 *> \endverbatim 00041 *> 00042 *> \return DLANSP 00043 *> \verbatim 00044 *> 00045 *> DLANSP = ( max(abs(A(i,j))), NORM = 'M' or 'm' 00046 *> ( 00047 *> ( norm1(A), NORM = '1', 'O' or 'o' 00048 *> ( 00049 *> ( normI(A), NORM = 'I' or 'i' 00050 *> ( 00051 *> ( normF(A), NORM = 'F', 'f', 'E' or 'e' 00052 *> 00053 *> where norm1 denotes the one norm of a matrix (maximum column sum), 00054 *> normI denotes the infinity norm of a matrix (maximum row sum) and 00055 *> normF denotes the Frobenius norm of a matrix (square root of sum of 00056 *> squares). Note that max(abs(A(i,j))) is not a consistent matrix norm. 00057 *> \endverbatim 00058 * 00059 * Arguments: 00060 * ========== 00061 * 00062 *> \param[in] NORM 00063 *> \verbatim 00064 *> NORM is CHARACTER*1 00065 *> Specifies the value to be returned in DLANSP as described 00066 *> above. 00067 *> \endverbatim 00068 *> 00069 *> \param[in] UPLO 00070 *> \verbatim 00071 *> UPLO is CHARACTER*1 00072 *> Specifies whether the upper or lower triangular part of the 00073 *> symmetric matrix A is supplied. 00074 *> = 'U': Upper triangular part of A is supplied 00075 *> = 'L': Lower triangular part of A is supplied 00076 *> \endverbatim 00077 *> 00078 *> \param[in] N 00079 *> \verbatim 00080 *> N is INTEGER 00081 *> The order of the matrix A. N >= 0. When N = 0, DLANSP is 00082 *> set to zero. 00083 *> \endverbatim 00084 *> 00085 *> \param[in] AP 00086 *> \verbatim 00087 *> AP is DOUBLE PRECISION array, dimension (N*(N+1)/2) 00088 *> The upper or lower triangle of the symmetric matrix A, packed 00089 *> columnwise in a linear array. The j-th column of A is stored 00090 *> in the array AP as follows: 00091 *> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; 00092 *> if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. 00093 *> \endverbatim 00094 *> 00095 *> \param[out] WORK 00096 *> \verbatim 00097 *> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)), 00098 *> where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise, 00099 *> WORK is not referenced. 00100 *> \endverbatim 00101 * 00102 * Authors: 00103 * ======== 00104 * 00105 *> \author Univ. of Tennessee 00106 *> \author Univ. of California Berkeley 00107 *> \author Univ. of Colorado Denver 00108 *> \author NAG Ltd. 00109 * 00110 *> \date November 2011 00111 * 00112 *> \ingroup doubleOTHERauxiliary 00113 * 00114 * ===================================================================== 00115 DOUBLE PRECISION FUNCTION DLANSP( NORM, UPLO, N, AP, WORK ) 00116 * 00117 * -- LAPACK auxiliary routine (version 3.4.0) -- 00118 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00119 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00120 * November 2011 00121 * 00122 * .. Scalar Arguments .. 00123 CHARACTER NORM, UPLO 00124 INTEGER N 00125 * .. 00126 * .. Array Arguments .. 00127 DOUBLE PRECISION AP( * ), WORK( * ) 00128 * .. 00129 * 00130 * ===================================================================== 00131 * 00132 * .. Parameters .. 00133 DOUBLE PRECISION ONE, ZERO 00134 PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) 00135 * .. 00136 * .. Local Scalars .. 00137 INTEGER I, J, K 00138 DOUBLE PRECISION ABSA, SCALE, SUM, VALUE 00139 * .. 00140 * .. External Subroutines .. 00141 EXTERNAL DLASSQ 00142 * .. 00143 * .. External Functions .. 00144 LOGICAL LSAME 00145 EXTERNAL LSAME 00146 * .. 00147 * .. Intrinsic Functions .. 00148 INTRINSIC ABS, MAX, SQRT 00149 * .. 00150 * .. Executable Statements .. 00151 * 00152 IF( N.EQ.0 ) THEN 00153 VALUE = ZERO 00154 ELSE IF( LSAME( NORM, 'M' ) ) THEN 00155 * 00156 * Find max(abs(A(i,j))). 00157 * 00158 VALUE = ZERO 00159 IF( LSAME( UPLO, 'U' ) ) THEN 00160 K = 1 00161 DO 20 J = 1, N 00162 DO 10 I = K, K + J - 1 00163 VALUE = MAX( VALUE, ABS( AP( I ) ) ) 00164 10 CONTINUE 00165 K = K + J 00166 20 CONTINUE 00167 ELSE 00168 K = 1 00169 DO 40 J = 1, N 00170 DO 30 I = K, K + N - J 00171 VALUE = MAX( VALUE, ABS( AP( I ) ) ) 00172 30 CONTINUE 00173 K = K + N - J + 1 00174 40 CONTINUE 00175 END IF 00176 ELSE IF( ( LSAME( NORM, 'I' ) ) .OR. ( LSAME( NORM, 'O' ) ) .OR. 00177 $ ( NORM.EQ.'1' ) ) THEN 00178 * 00179 * Find normI(A) ( = norm1(A), since A is symmetric). 00180 * 00181 VALUE = ZERO 00182 K = 1 00183 IF( LSAME( UPLO, 'U' ) ) THEN 00184 DO 60 J = 1, N 00185 SUM = ZERO 00186 DO 50 I = 1, J - 1 00187 ABSA = ABS( AP( K ) ) 00188 SUM = SUM + ABSA 00189 WORK( I ) = WORK( I ) + ABSA 00190 K = K + 1 00191 50 CONTINUE 00192 WORK( J ) = SUM + ABS( AP( K ) ) 00193 K = K + 1 00194 60 CONTINUE 00195 DO 70 I = 1, N 00196 VALUE = MAX( VALUE, WORK( I ) ) 00197 70 CONTINUE 00198 ELSE 00199 DO 80 I = 1, N 00200 WORK( I ) = ZERO 00201 80 CONTINUE 00202 DO 100 J = 1, N 00203 SUM = WORK( J ) + ABS( AP( K ) ) 00204 K = K + 1 00205 DO 90 I = J + 1, N 00206 ABSA = ABS( AP( K ) ) 00207 SUM = SUM + ABSA 00208 WORK( I ) = WORK( I ) + ABSA 00209 K = K + 1 00210 90 CONTINUE 00211 VALUE = MAX( VALUE, SUM ) 00212 100 CONTINUE 00213 END IF 00214 ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN 00215 * 00216 * Find normF(A). 00217 * 00218 SCALE = ZERO 00219 SUM = ONE 00220 K = 2 00221 IF( LSAME( UPLO, 'U' ) ) THEN 00222 DO 110 J = 2, N 00223 CALL DLASSQ( J-1, AP( K ), 1, SCALE, SUM ) 00224 K = K + J 00225 110 CONTINUE 00226 ELSE 00227 DO 120 J = 1, N - 1 00228 CALL DLASSQ( N-J, AP( K ), 1, SCALE, SUM ) 00229 K = K + N - J + 1 00230 120 CONTINUE 00231 END IF 00232 SUM = 2*SUM 00233 K = 1 00234 DO 130 I = 1, N 00235 IF( AP( K ).NE.ZERO ) THEN 00236 ABSA = ABS( AP( K ) ) 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 IF( LSAME( UPLO, 'U' ) ) THEN 00245 K = K + I + 1 00246 ELSE 00247 K = K + N - I + 1 00248 END IF 00249 130 CONTINUE 00250 VALUE = SCALE*SQRT( SUM ) 00251 END IF 00252 * 00253 DLANSP = VALUE 00254 RETURN 00255 * 00256 * End of DLANSP 00257 * 00258 END