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LAPACK 3.3.1
Linear Algebra PACKage
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LAPACK 3.3.1
Linear Algebra PACKage
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00001 SUBROUTINE ZHBGVD( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W, 00002 $ Z, LDZ, WORK, LWORK, RWORK, LRWORK, IWORK, 00003 $ LIWORK, INFO ) 00004 * 00005 * -- LAPACK driver routine (version 3.3.1) -- 00006 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00007 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00008 * -- April 2011 -- 00009 * @precisions normal z -> c 00010 * 00011 * .. Scalar Arguments .. 00012 CHARACTER JOBZ, UPLO 00013 INTEGER INFO, KA, KB, LDAB, LDBB, LDZ, LIWORK, LRWORK, 00014 $ LWORK, N 00015 * .. 00016 * .. Array Arguments .. 00017 INTEGER IWORK( * ) 00018 DOUBLE PRECISION RWORK( * ), W( * ) 00019 COMPLEX*16 AB( LDAB, * ), BB( LDBB, * ), WORK( * ), 00020 $ Z( LDZ, * ) 00021 * .. 00022 * 00023 * Purpose 00024 * ======= 00025 * 00026 * ZHBGVD computes all the eigenvalues, and optionally, the eigenvectors 00027 * of a complex generalized Hermitian-definite banded eigenproblem, of 00028 * the form A*x=(lambda)*B*x. Here A and B are assumed to be Hermitian 00029 * and banded, and B is also positive definite. If eigenvectors are 00030 * desired, it uses a divide and conquer algorithm. 00031 * 00032 * The divide and conquer algorithm makes very mild assumptions about 00033 * floating point arithmetic. It will work on machines with a guard 00034 * digit in add/subtract, or on those binary machines without guard 00035 * digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or 00036 * Cray-2. It could conceivably fail on hexadecimal or decimal machines 00037 * without guard digits, but we know of none. 00038 * 00039 * Arguments 00040 * ========= 00041 * 00042 * JOBZ (input) CHARACTER*1 00043 * = 'N': Compute eigenvalues only; 00044 * = 'V': Compute eigenvalues and eigenvectors. 00045 * 00046 * UPLO (input) CHARACTER*1 00047 * = 'U': Upper triangles of A and B are stored; 00048 * = 'L': Lower triangles of A and B are stored. 00049 * 00050 * N (input) INTEGER 00051 * The order of the matrices A and B. N >= 0. 00052 * 00053 * KA (input) INTEGER 00054 * The number of superdiagonals of the matrix A if UPLO = 'U', 00055 * or the number of subdiagonals if UPLO = 'L'. KA >= 0. 00056 * 00057 * KB (input) INTEGER 00058 * The number of superdiagonals of the matrix B if UPLO = 'U', 00059 * or the number of subdiagonals if UPLO = 'L'. KB >= 0. 00060 * 00061 * AB (input/output) COMPLEX*16 array, dimension (LDAB, N) 00062 * On entry, the upper or lower triangle of the Hermitian band 00063 * matrix A, stored in the first ka+1 rows of the array. The 00064 * j-th column of A is stored in the j-th column of the array AB 00065 * as follows: 00066 * if UPLO = 'U', AB(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j; 00067 * if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+ka). 00068 * 00069 * On exit, the contents of AB are destroyed. 00070 * 00071 * LDAB (input) INTEGER 00072 * The leading dimension of the array AB. LDAB >= KA+1. 00073 * 00074 * BB (input/output) COMPLEX*16 array, dimension (LDBB, N) 00075 * On entry, the upper or lower triangle of the Hermitian band 00076 * matrix B, stored in the first kb+1 rows of the array. The 00077 * j-th column of B is stored in the j-th column of the array BB 00078 * as follows: 00079 * if UPLO = 'U', BB(kb+1+i-j,j) = B(i,j) for max(1,j-kb)<=i<=j; 00080 * if UPLO = 'L', BB(1+i-j,j) = B(i,j) for j<=i<=min(n,j+kb). 00081 * 00082 * On exit, the factor S from the split Cholesky factorization 00083 * B = S**H*S, as returned by ZPBSTF. 00084 * 00085 * LDBB (input) INTEGER 00086 * The leading dimension of the array BB. LDBB >= KB+1. 00087 * 00088 * W (output) DOUBLE PRECISION array, dimension (N) 00089 * If INFO = 0, the eigenvalues in ascending order. 00090 * 00091 * Z (output) COMPLEX*16 array, dimension (LDZ, N) 00092 * If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of 00093 * eigenvectors, with the i-th column of Z holding the 00094 * eigenvector associated with W(i). The eigenvectors are 00095 * normalized so that Z**H*B*Z = I. 00096 * If JOBZ = 'N', then Z is not referenced. 00097 * 00098 * LDZ (input) INTEGER 00099 * The leading dimension of the array Z. LDZ >= 1, and if 00100 * JOBZ = 'V', LDZ >= N. 00101 * 00102 * WORK (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK)) 00103 * On exit, if INFO=0, WORK(1) returns the optimal LWORK. 00104 * 00105 * LWORK (input) INTEGER 00106 * The dimension of the array WORK. 00107 * If N <= 1, LWORK >= 1. 00108 * If JOBZ = 'N' and N > 1, LWORK >= N. 00109 * If JOBZ = 'V' and N > 1, LWORK >= 2*N**2. 00110 * 00111 * If LWORK = -1, then a workspace query is assumed; the routine 00112 * only calculates the optimal sizes of the WORK, RWORK and 00113 * IWORK arrays, returns these values as the first entries of 00114 * the WORK, RWORK and IWORK arrays, and no error message 00115 * related to LWORK or LRWORK or LIWORK is issued by XERBLA. 00116 * 00117 * RWORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LRWORK)) 00118 * On exit, if INFO=0, RWORK(1) returns the optimal LRWORK. 00119 * 00120 * LRWORK (input) INTEGER 00121 * The dimension of array RWORK. 00122 * If N <= 1, LRWORK >= 1. 00123 * If JOBZ = 'N' and N > 1, LRWORK >= N. 00124 * If JOBZ = 'V' and N > 1, LRWORK >= 1 + 5*N + 2*N**2. 00125 * 00126 * If LRWORK = -1, then a workspace query is assumed; the 00127 * routine only calculates the optimal sizes of the WORK, RWORK 00128 * and IWORK arrays, returns these values as the first entries 00129 * of the WORK, RWORK and IWORK arrays, and no error message 00130 * related to LWORK or LRWORK or LIWORK is issued by XERBLA. 00131 * 00132 * IWORK (workspace/output) INTEGER array, dimension (MAX(1,LIWORK)) 00133 * On exit, if INFO=0, IWORK(1) returns the optimal LIWORK. 00134 * 00135 * LIWORK (input) INTEGER 00136 * The dimension of array IWORK. 00137 * If JOBZ = 'N' or N <= 1, LIWORK >= 1. 00138 * If JOBZ = 'V' and N > 1, LIWORK >= 3 + 5*N. 00139 * 00140 * If LIWORK = -1, then a workspace query is assumed; the 00141 * routine only calculates the optimal sizes of the WORK, RWORK 00142 * and IWORK arrays, returns these values as the first entries 00143 * of the WORK, RWORK and IWORK arrays, and no error message 00144 * related to LWORK or LRWORK or LIWORK is issued by XERBLA. 00145 * 00146 * INFO (output) INTEGER 00147 * = 0: successful exit 00148 * < 0: if INFO = -i, the i-th argument had an illegal value 00149 * > 0: if INFO = i, and i is: 00150 * <= N: the algorithm failed to converge: 00151 * i off-diagonal elements of an intermediate 00152 * tridiagonal form did not converge to zero; 00153 * > N: if INFO = N + i, for 1 <= i <= N, then ZPBSTF 00154 * returned INFO = i: B is not positive definite. 00155 * The factorization of B could not be completed and 00156 * no eigenvalues or eigenvectors were computed. 00157 * 00158 * Further Details 00159 * =============== 00160 * 00161 * Based on contributions by 00162 * Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA 00163 * 00164 * ===================================================================== 00165 * 00166 * .. Parameters .. 00167 COMPLEX*16 CONE, CZERO 00168 PARAMETER ( CONE = ( 1.0D+0, 0.0D+0 ), 00169 $ CZERO = ( 0.0D+0, 0.0D+0 ) ) 00170 * .. 00171 * .. Local Scalars .. 00172 LOGICAL LQUERY, UPPER, WANTZ 00173 CHARACTER VECT 00174 INTEGER IINFO, INDE, INDWK2, INDWRK, LIWMIN, LLRWK, 00175 $ LLWK2, LRWMIN, LWMIN 00176 * .. 00177 * .. External Functions .. 00178 LOGICAL LSAME 00179 EXTERNAL LSAME 00180 * .. 00181 * .. External Subroutines .. 00182 EXTERNAL DSTERF, XERBLA, ZGEMM, ZHBGST, ZHBTRD, ZLACPY, 00183 $ ZPBSTF, ZSTEDC 00184 * .. 00185 * .. Executable Statements .. 00186 * 00187 * Test the input parameters. 00188 * 00189 WANTZ = LSAME( JOBZ, 'V' ) 00190 UPPER = LSAME( UPLO, 'U' ) 00191 LQUERY = ( LWORK.EQ.-1 .OR. LRWORK.EQ.-1 .OR. LIWORK.EQ.-1 ) 00192 * 00193 INFO = 0 00194 IF( N.LE.1 ) THEN 00195 LWMIN = 1+N 00196 LRWMIN = 1+N 00197 LIWMIN = 1 00198 ELSE IF( WANTZ ) THEN 00199 LWMIN = 2*N**2 00200 LRWMIN = 1 + 5*N + 2*N**2 00201 LIWMIN = 3 + 5*N 00202 ELSE 00203 LWMIN = N 00204 LRWMIN = N 00205 LIWMIN = 1 00206 END IF 00207 IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN 00208 INFO = -1 00209 ELSE IF( .NOT.( UPPER .OR. LSAME( UPLO, 'L' ) ) ) THEN 00210 INFO = -2 00211 ELSE IF( N.LT.0 ) THEN 00212 INFO = -3 00213 ELSE IF( KA.LT.0 ) THEN 00214 INFO = -4 00215 ELSE IF( KB.LT.0 .OR. KB.GT.KA ) THEN 00216 INFO = -5 00217 ELSE IF( LDAB.LT.KA+1 ) THEN 00218 INFO = -7 00219 ELSE IF( LDBB.LT.KB+1 ) THEN 00220 INFO = -9 00221 ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN 00222 INFO = -12 00223 END IF 00224 * 00225 IF( INFO.EQ.0 ) THEN 00226 WORK( 1 ) = LWMIN 00227 RWORK( 1 ) = LRWMIN 00228 IWORK( 1 ) = LIWMIN 00229 * 00230 IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN 00231 INFO = -14 00232 ELSE IF( LRWORK.LT.LRWMIN .AND. .NOT.LQUERY ) THEN 00233 INFO = -16 00234 ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT.LQUERY ) THEN 00235 INFO = -18 00236 END IF 00237 END IF 00238 * 00239 IF( INFO.NE.0 ) THEN 00240 CALL XERBLA( 'ZHBGVD', -INFO ) 00241 RETURN 00242 ELSE IF( LQUERY ) THEN 00243 RETURN 00244 END IF 00245 * 00246 * Quick return if possible 00247 * 00248 IF( N.EQ.0 ) 00249 $ RETURN 00250 * 00251 * Form a split Cholesky factorization of B. 00252 * 00253 CALL ZPBSTF( UPLO, N, KB, BB, LDBB, INFO ) 00254 IF( INFO.NE.0 ) THEN 00255 INFO = N + INFO 00256 RETURN 00257 END IF 00258 * 00259 * Transform problem to standard eigenvalue problem. 00260 * 00261 INDE = 1 00262 INDWRK = INDE + N 00263 INDWK2 = 1 + N*N 00264 LLWK2 = LWORK - INDWK2 + 2 00265 LLRWK = LRWORK - INDWRK + 2 00266 CALL ZHBGST( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, Z, LDZ, 00267 $ WORK, RWORK( INDWRK ), IINFO ) 00268 * 00269 * Reduce Hermitian band matrix to tridiagonal form. 00270 * 00271 IF( WANTZ ) THEN 00272 VECT = 'U' 00273 ELSE 00274 VECT = 'N' 00275 END IF 00276 CALL ZHBTRD( VECT, UPLO, N, KA, AB, LDAB, W, RWORK( INDE ), Z, 00277 $ LDZ, WORK, IINFO ) 00278 * 00279 * For eigenvalues only, call DSTERF. For eigenvectors, call ZSTEDC. 00280 * 00281 IF( .NOT.WANTZ ) THEN 00282 CALL DSTERF( N, W, RWORK( INDE ), INFO ) 00283 ELSE 00284 CALL ZSTEDC( 'I', N, W, RWORK( INDE ), WORK, N, WORK( INDWK2 ), 00285 $ LLWK2, RWORK( INDWRK ), LLRWK, IWORK, LIWORK, 00286 $ INFO ) 00287 CALL ZGEMM( 'N', 'N', N, N, N, CONE, Z, LDZ, WORK, N, CZERO, 00288 $ WORK( INDWK2 ), N ) 00289 CALL ZLACPY( 'A', N, N, WORK( INDWK2 ), N, Z, LDZ ) 00290 END IF 00291 * 00292 WORK( 1 ) = LWMIN 00293 RWORK( 1 ) = LRWMIN 00294 IWORK( 1 ) = LIWMIN 00295 RETURN 00296 * 00297 * End of ZHBGVD 00298 * 00299 END
1.7.3 
