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LAPACK
3.4.1
LAPACK: Linear Algebra PACKage
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00001 *> \brief \b ZHBGST 00002 * 00003 * =========== DOCUMENTATION =========== 00004 * 00005 * Online html documentation available at 00006 * http://www.netlib.org/lapack/explore-html/ 00007 * 00008 *> \htmlonly 00009 *> Download ZHBGV + dependencies 00010 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zhbgv.f"> 00011 *> [TGZ]</a> 00012 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zhbgv.f"> 00013 *> [ZIP]</a> 00014 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zhbgv.f"> 00015 *> [TXT]</a> 00016 *> \endhtmlonly 00017 * 00018 * Definition: 00019 * =========== 00020 * 00021 * SUBROUTINE ZHBGV( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W, Z, 00022 * LDZ, WORK, RWORK, INFO ) 00023 * 00024 * .. Scalar Arguments .. 00025 * CHARACTER JOBZ, UPLO 00026 * INTEGER INFO, KA, KB, LDAB, LDBB, LDZ, N 00027 * .. 00028 * .. Array Arguments .. 00029 * DOUBLE PRECISION RWORK( * ), W( * ) 00030 * COMPLEX*16 AB( LDAB, * ), BB( LDBB, * ), WORK( * ), 00031 * $ Z( LDZ, * ) 00032 * .. 00033 * 00034 * 00035 *> \par Purpose: 00036 * ============= 00037 *> 00038 *> \verbatim 00039 *> 00040 *> ZHBGV computes all the eigenvalues, and optionally, the eigenvectors 00041 *> of a complex generalized Hermitian-definite banded eigenproblem, of 00042 *> the form A*x=(lambda)*B*x. Here A and B are assumed to be Hermitian 00043 *> and banded, and B is also positive definite. 00044 *> \endverbatim 00045 * 00046 * Arguments: 00047 * ========== 00048 * 00049 *> \param[in] JOBZ 00050 *> \verbatim 00051 *> JOBZ is CHARACTER*1 00052 *> = 'N': Compute eigenvalues only; 00053 *> = 'V': Compute eigenvalues and eigenvectors. 00054 *> \endverbatim 00055 *> 00056 *> \param[in] UPLO 00057 *> \verbatim 00058 *> UPLO is CHARACTER*1 00059 *> = 'U': Upper triangles of A and B are stored; 00060 *> = 'L': Lower triangles of A and B are stored. 00061 *> \endverbatim 00062 *> 00063 *> \param[in] N 00064 *> \verbatim 00065 *> N is INTEGER 00066 *> The order of the matrices A and B. N >= 0. 00067 *> \endverbatim 00068 *> 00069 *> \param[in] KA 00070 *> \verbatim 00071 *> KA is INTEGER 00072 *> The number of superdiagonals of the matrix A if UPLO = 'U', 00073 *> or the number of subdiagonals if UPLO = 'L'. KA >= 0. 00074 *> \endverbatim 00075 *> 00076 *> \param[in] KB 00077 *> \verbatim 00078 *> KB is INTEGER 00079 *> The number of superdiagonals of the matrix B if UPLO = 'U', 00080 *> or the number of subdiagonals if UPLO = 'L'. KB >= 0. 00081 *> \endverbatim 00082 *> 00083 *> \param[in,out] AB 00084 *> \verbatim 00085 *> AB is COMPLEX*16 array, dimension (LDAB, N) 00086 *> On entry, the upper or lower triangle of the Hermitian band 00087 *> matrix A, stored in the first ka+1 rows of the array. The 00088 *> j-th column of A is stored in the j-th column of the array AB 00089 *> as follows: 00090 *> if UPLO = 'U', AB(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j; 00091 *> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+ka). 00092 *> 00093 *> On exit, the contents of AB are destroyed. 00094 *> \endverbatim 00095 *> 00096 *> \param[in] LDAB 00097 *> \verbatim 00098 *> LDAB is INTEGER 00099 *> The leading dimension of the array AB. LDAB >= KA+1. 00100 *> \endverbatim 00101 *> 00102 *> \param[in,out] BB 00103 *> \verbatim 00104 *> BB is COMPLEX*16 array, dimension (LDBB, N) 00105 *> On entry, the upper or lower triangle of the Hermitian band 00106 *> matrix B, stored in the first kb+1 rows of the array. The 00107 *> j-th column of B is stored in the j-th column of the array BB 00108 *> as follows: 00109 *> if UPLO = 'U', BB(kb+1+i-j,j) = B(i,j) for max(1,j-kb)<=i<=j; 00110 *> if UPLO = 'L', BB(1+i-j,j) = B(i,j) for j<=i<=min(n,j+kb). 00111 *> 00112 *> On exit, the factor S from the split Cholesky factorization 00113 *> B = S**H*S, as returned by ZPBSTF. 00114 *> \endverbatim 00115 *> 00116 *> \param[in] LDBB 00117 *> \verbatim 00118 *> LDBB is INTEGER 00119 *> The leading dimension of the array BB. LDBB >= KB+1. 00120 *> \endverbatim 00121 *> 00122 *> \param[out] W 00123 *> \verbatim 00124 *> W is DOUBLE PRECISION array, dimension (N) 00125 *> If INFO = 0, the eigenvalues in ascending order. 00126 *> \endverbatim 00127 *> 00128 *> \param[out] Z 00129 *> \verbatim 00130 *> Z is COMPLEX*16 array, dimension (LDZ, N) 00131 *> If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of 00132 *> eigenvectors, with the i-th column of Z holding the 00133 *> eigenvector associated with W(i). The eigenvectors are 00134 *> normalized so that Z**H*B*Z = I. 00135 *> If JOBZ = 'N', then Z is not referenced. 00136 *> \endverbatim 00137 *> 00138 *> \param[in] LDZ 00139 *> \verbatim 00140 *> LDZ is INTEGER 00141 *> The leading dimension of the array Z. LDZ >= 1, and if 00142 *> JOBZ = 'V', LDZ >= N. 00143 *> \endverbatim 00144 *> 00145 *> \param[out] WORK 00146 *> \verbatim 00147 *> WORK is COMPLEX*16 array, dimension (N) 00148 *> \endverbatim 00149 *> 00150 *> \param[out] RWORK 00151 *> \verbatim 00152 *> RWORK is DOUBLE PRECISION array, dimension (3*N) 00153 *> \endverbatim 00154 *> 00155 *> \param[out] INFO 00156 *> \verbatim 00157 *> INFO is INTEGER 00158 *> = 0: successful exit 00159 *> < 0: if INFO = -i, the i-th argument had an illegal value 00160 *> > 0: if INFO = i, and i is: 00161 *> <= N: the algorithm failed to converge: 00162 *> i off-diagonal elements of an intermediate 00163 *> tridiagonal form did not converge to zero; 00164 *> > N: if INFO = N + i, for 1 <= i <= N, then ZPBSTF 00165 *> returned INFO = i: B is not positive definite. 00166 *> The factorization of B could not be completed and 00167 *> no eigenvalues or eigenvectors were computed. 00168 *> \endverbatim 00169 * 00170 * Authors: 00171 * ======== 00172 * 00173 *> \author Univ. of Tennessee 00174 *> \author Univ. of California Berkeley 00175 *> \author Univ. of Colorado Denver 00176 *> \author NAG Ltd. 00177 * 00178 *> \date November 2011 00179 * 00180 *> \ingroup complex16OTHEReigen 00181 * 00182 * ===================================================================== 00183 SUBROUTINE ZHBGV( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W, Z, 00184 $ LDZ, WORK, RWORK, INFO ) 00185 * 00186 * -- LAPACK driver routine (version 3.4.0) -- 00187 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00188 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00189 * November 2011 00190 * 00191 * .. Scalar Arguments .. 00192 CHARACTER JOBZ, UPLO 00193 INTEGER INFO, KA, KB, LDAB, LDBB, LDZ, N 00194 * .. 00195 * .. Array Arguments .. 00196 DOUBLE PRECISION RWORK( * ), W( * ) 00197 COMPLEX*16 AB( LDAB, * ), BB( LDBB, * ), WORK( * ), 00198 $ Z( LDZ, * ) 00199 * .. 00200 * 00201 * ===================================================================== 00202 * 00203 * .. Local Scalars .. 00204 LOGICAL UPPER, WANTZ 00205 CHARACTER VECT 00206 INTEGER IINFO, INDE, INDWRK 00207 * .. 00208 * .. External Functions .. 00209 LOGICAL LSAME 00210 EXTERNAL LSAME 00211 * .. 00212 * .. External Subroutines .. 00213 EXTERNAL DSTERF, XERBLA, ZHBGST, ZHBTRD, ZPBSTF, ZSTEQR 00214 * .. 00215 * .. Executable Statements .. 00216 * 00217 * Test the input parameters. 00218 * 00219 WANTZ = LSAME( JOBZ, 'V' ) 00220 UPPER = LSAME( UPLO, 'U' ) 00221 * 00222 INFO = 0 00223 IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN 00224 INFO = -1 00225 ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN 00226 INFO = -2 00227 ELSE IF( N.LT.0 ) THEN 00228 INFO = -3 00229 ELSE IF( KA.LT.0 ) THEN 00230 INFO = -4 00231 ELSE IF( KB.LT.0 .OR. KB.GT.KA ) THEN 00232 INFO = -5 00233 ELSE IF( LDAB.LT.KA+1 ) THEN 00234 INFO = -7 00235 ELSE IF( LDBB.LT.KB+1 ) THEN 00236 INFO = -9 00237 ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN 00238 INFO = -12 00239 END IF 00240 IF( INFO.NE.0 ) THEN 00241 CALL XERBLA( 'ZHBGV ', -INFO ) 00242 RETURN 00243 END IF 00244 * 00245 * Quick return if possible 00246 * 00247 IF( N.EQ.0 ) 00248 $ RETURN 00249 * 00250 * Form a split Cholesky factorization of B. 00251 * 00252 CALL ZPBSTF( UPLO, N, KB, BB, LDBB, INFO ) 00253 IF( INFO.NE.0 ) THEN 00254 INFO = N + INFO 00255 RETURN 00256 END IF 00257 * 00258 * Transform problem to standard eigenvalue problem. 00259 * 00260 INDE = 1 00261 INDWRK = INDE + N 00262 CALL ZHBGST( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, Z, LDZ, 00263 $ WORK, RWORK( INDWRK ), IINFO ) 00264 * 00265 * Reduce to tridiagonal form. 00266 * 00267 IF( WANTZ ) THEN 00268 VECT = 'U' 00269 ELSE 00270 VECT = 'N' 00271 END IF 00272 CALL ZHBTRD( VECT, UPLO, N, KA, AB, LDAB, W, RWORK( INDE ), Z, 00273 $ LDZ, WORK, IINFO ) 00274 * 00275 * For eigenvalues only, call DSTERF. For eigenvectors, call ZSTEQR. 00276 * 00277 IF( .NOT.WANTZ ) THEN 00278 CALL DSTERF( N, W, RWORK( INDE ), INFO ) 00279 ELSE 00280 CALL ZSTEQR( JOBZ, N, W, RWORK( INDE ), Z, LDZ, 00281 $ RWORK( INDWRK ), INFO ) 00282 END IF 00283 RETURN 00284 * 00285 * End of ZHBGV 00286 * 00287 END