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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief \b ZLANHB 00002 * 00003 * =========== DOCUMENTATION =========== 00004 * 00005 * Online html documentation available at 00006 * http://www.netlib.org/lapack/explore-html/ 00007 * 00008 *> \htmlonly 00009 *> Download ZLANHB + dependencies 00010 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlanhb.f"> 00011 *> [TGZ]</a> 00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlanhb.f"> 00013 *> [ZIP]</a> 00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlanhb.f"> 00015 *> [TXT]</a> 00016 *> \endhtmlonly 00017 * 00018 * Definition: 00019 * =========== 00020 * 00021 * DOUBLE PRECISION FUNCTION ZLANHB( NORM, UPLO, N, K, AB, LDAB, 00022 * WORK ) 00023 * 00024 * .. Scalar Arguments .. 00025 * CHARACTER NORM, UPLO 00026 * INTEGER K, LDAB, N 00027 * .. 00028 * .. Array Arguments .. 00029 * DOUBLE PRECISION WORK( * ) 00030 * COMPLEX*16 AB( LDAB, * ) 00031 * .. 00032 * 00033 * 00034 *> \par Purpose: 00035 * ============= 00036 *> 00037 *> \verbatim 00038 *> 00039 *> ZLANHB returns the value of the one norm, or the Frobenius norm, or 00040 *> the infinity norm, or the element of largest absolute value of an 00041 *> n by n hermitian band matrix A, with k super-diagonals. 00042 *> \endverbatim 00043 *> 00044 *> \return ZLANHB 00045 *> \verbatim 00046 *> 00047 *> ZLANHB = ( max(abs(A(i,j))), NORM = 'M' or 'm' 00048 *> ( 00049 *> ( norm1(A), NORM = '1', 'O' or 'o' 00050 *> ( 00051 *> ( normI(A), NORM = 'I' or 'i' 00052 *> ( 00053 *> ( normF(A), NORM = 'F', 'f', 'E' or 'e' 00054 *> 00055 *> where norm1 denotes the one norm of a matrix (maximum column sum), 00056 *> normI denotes the infinity norm of a matrix (maximum row sum) and 00057 *> normF denotes the Frobenius norm of a matrix (square root of sum of 00058 *> squares). Note that max(abs(A(i,j))) is not a consistent matrix norm. 00059 *> \endverbatim 00060 * 00061 * Arguments: 00062 * ========== 00063 * 00064 *> \param[in] NORM 00065 *> \verbatim 00066 *> NORM is CHARACTER*1 00067 *> Specifies the value to be returned in ZLANHB as described 00068 *> above. 00069 *> \endverbatim 00070 *> 00071 *> \param[in] UPLO 00072 *> \verbatim 00073 *> UPLO is CHARACTER*1 00074 *> Specifies whether the upper or lower triangular part of the 00075 *> band matrix A is supplied. 00076 *> = 'U': Upper triangular 00077 *> = 'L': Lower triangular 00078 *> \endverbatim 00079 *> 00080 *> \param[in] N 00081 *> \verbatim 00082 *> N is INTEGER 00083 *> The order of the matrix A. N >= 0. When N = 0, ZLANHB is 00084 *> set to zero. 00085 *> \endverbatim 00086 *> 00087 *> \param[in] K 00088 *> \verbatim 00089 *> K is INTEGER 00090 *> The number of super-diagonals or sub-diagonals of the 00091 *> band matrix A. K >= 0. 00092 *> \endverbatim 00093 *> 00094 *> \param[in] AB 00095 *> \verbatim 00096 *> AB is COMPLEX*16 array, dimension (LDAB,N) 00097 *> The upper or lower triangle of the hermitian band matrix A, 00098 *> stored in the first K+1 rows of AB. The j-th column of A is 00099 *> stored in the j-th column of the array AB as follows: 00100 *> if UPLO = 'U', AB(k+1+i-j,j) = A(i,j) for max(1,j-k)<=i<=j; 00101 *> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+k). 00102 *> Note that the imaginary parts of the diagonal elements need 00103 *> not be set and are assumed to be zero. 00104 *> \endverbatim 00105 *> 00106 *> \param[in] LDAB 00107 *> \verbatim 00108 *> LDAB is INTEGER 00109 *> The leading dimension of the array AB. LDAB >= K+1. 00110 *> \endverbatim 00111 *> 00112 *> \param[out] WORK 00113 *> \verbatim 00114 *> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)), 00115 *> where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise, 00116 *> WORK is not referenced. 00117 *> \endverbatim 00118 * 00119 * Authors: 00120 * ======== 00121 * 00122 *> \author Univ. of Tennessee 00123 *> \author Univ. of California Berkeley 00124 *> \author Univ. of Colorado Denver 00125 *> \author NAG Ltd. 00126 * 00127 *> \date November 2011 00128 * 00129 *> \ingroup complex16OTHERauxiliary 00130 * 00131 * ===================================================================== 00132 DOUBLE PRECISION FUNCTION ZLANHB( NORM, UPLO, N, K, AB, LDAB, 00133 $ WORK ) 00134 * 00135 * -- LAPACK auxiliary routine (version 3.4.0) -- 00136 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00137 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00138 * November 2011 00139 * 00140 * .. Scalar Arguments .. 00141 CHARACTER NORM, UPLO 00142 INTEGER K, LDAB, N 00143 * .. 00144 * .. Array Arguments .. 00145 DOUBLE PRECISION WORK( * ) 00146 COMPLEX*16 AB( LDAB, * ) 00147 * .. 00148 * 00149 * ===================================================================== 00150 * 00151 * .. Parameters .. 00152 DOUBLE PRECISION ONE, ZERO 00153 PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) 00154 * .. 00155 * .. Local Scalars .. 00156 INTEGER I, J, L 00157 DOUBLE PRECISION ABSA, SCALE, SUM, VALUE 00158 * .. 00159 * .. External Functions .. 00160 LOGICAL LSAME 00161 EXTERNAL LSAME 00162 * .. 00163 * .. External Subroutines .. 00164 EXTERNAL ZLASSQ 00165 * .. 00166 * .. Intrinsic Functions .. 00167 INTRINSIC ABS, DBLE, MAX, MIN, SQRT 00168 * .. 00169 * .. Executable Statements .. 00170 * 00171 IF( N.EQ.0 ) THEN 00172 VALUE = ZERO 00173 ELSE IF( LSAME( NORM, 'M' ) ) THEN 00174 * 00175 * Find max(abs(A(i,j))). 00176 * 00177 VALUE = ZERO 00178 IF( LSAME( UPLO, 'U' ) ) THEN 00179 DO 20 J = 1, N 00180 DO 10 I = MAX( K+2-J, 1 ), K 00181 VALUE = MAX( VALUE, ABS( AB( I, J ) ) ) 00182 10 CONTINUE 00183 VALUE = MAX( VALUE, ABS( DBLE( AB( K+1, J ) ) ) ) 00184 20 CONTINUE 00185 ELSE 00186 DO 40 J = 1, N 00187 VALUE = MAX( VALUE, ABS( DBLE( AB( 1, J ) ) ) ) 00188 DO 30 I = 2, MIN( N+1-J, K+1 ) 00189 VALUE = MAX( VALUE, ABS( AB( I, J ) ) ) 00190 30 CONTINUE 00191 40 CONTINUE 00192 END IF 00193 ELSE IF( ( LSAME( NORM, 'I' ) ) .OR. ( LSAME( NORM, 'O' ) ) .OR. 00194 $ ( NORM.EQ.'1' ) ) THEN 00195 * 00196 * Find normI(A) ( = norm1(A), since A is hermitian). 00197 * 00198 VALUE = ZERO 00199 IF( LSAME( UPLO, 'U' ) ) THEN 00200 DO 60 J = 1, N 00201 SUM = ZERO 00202 L = K + 1 - J 00203 DO 50 I = MAX( 1, J-K ), J - 1 00204 ABSA = ABS( AB( L+I, J ) ) 00205 SUM = SUM + ABSA 00206 WORK( I ) = WORK( I ) + ABSA 00207 50 CONTINUE 00208 WORK( J ) = SUM + ABS( DBLE( AB( K+1, J ) ) ) 00209 60 CONTINUE 00210 DO 70 I = 1, N 00211 VALUE = MAX( VALUE, WORK( I ) ) 00212 70 CONTINUE 00213 ELSE 00214 DO 80 I = 1, N 00215 WORK( I ) = ZERO 00216 80 CONTINUE 00217 DO 100 J = 1, N 00218 SUM = WORK( J ) + ABS( DBLE( AB( 1, J ) ) ) 00219 L = 1 - J 00220 DO 90 I = J + 1, MIN( N, J+K ) 00221 ABSA = ABS( AB( L+I, J ) ) 00222 SUM = SUM + ABSA 00223 WORK( I ) = WORK( I ) + ABSA 00224 90 CONTINUE 00225 VALUE = MAX( VALUE, SUM ) 00226 100 CONTINUE 00227 END IF 00228 ELSE IF( ( LSAME( NORM, 'F' ) ) .OR. ( LSAME( NORM, 'E' ) ) ) THEN 00229 * 00230 * Find normF(A). 00231 * 00232 SCALE = ZERO 00233 SUM = ONE 00234 IF( K.GT.0 ) THEN 00235 IF( LSAME( UPLO, 'U' ) ) THEN 00236 DO 110 J = 2, N 00237 CALL ZLASSQ( MIN( J-1, K ), AB( MAX( K+2-J, 1 ), J ), 00238 $ 1, SCALE, SUM ) 00239 110 CONTINUE 00240 L = K + 1 00241 ELSE 00242 DO 120 J = 1, N - 1 00243 CALL ZLASSQ( MIN( N-J, K ), AB( 2, J ), 1, SCALE, 00244 $ SUM ) 00245 120 CONTINUE 00246 L = 1 00247 END IF 00248 SUM = 2*SUM 00249 ELSE 00250 L = 1 00251 END IF 00252 DO 130 J = 1, N 00253 IF( DBLE( AB( L, J ) ).NE.ZERO ) THEN 00254 ABSA = ABS( DBLE( AB( L, J ) ) ) 00255 IF( SCALE.LT.ABSA ) THEN 00256 SUM = ONE + SUM*( SCALE / ABSA )**2 00257 SCALE = ABSA 00258 ELSE 00259 SUM = SUM + ( ABSA / SCALE )**2 00260 END IF 00261 END IF 00262 130 CONTINUE 00263 VALUE = SCALE*SQRT( SUM ) 00264 END IF 00265 * 00266 ZLANHB = VALUE 00267 RETURN 00268 * 00269 * End of ZLANHB 00270 * 00271 END