|
LAPACK 3.3.0
|
|
LAPACK 3.3.0
|
00001 SUBROUTINE ZHPEVD( JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, LWORK, 00002 $ RWORK, LRWORK, IWORK, LIWORK, INFO ) 00003 * 00004 * -- LAPACK driver routine (version 3.2) -- 00005 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00006 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00007 * November 2006 00008 * 00009 * .. Scalar Arguments .. 00010 CHARACTER JOBZ, UPLO 00011 INTEGER INFO, LDZ, LIWORK, LRWORK, LWORK, N 00012 * .. 00013 * .. Array Arguments .. 00014 INTEGER IWORK( * ) 00015 DOUBLE PRECISION RWORK( * ), W( * ) 00016 COMPLEX*16 AP( * ), WORK( * ), Z( LDZ, * ) 00017 * .. 00018 * 00019 * Purpose 00020 * ======= 00021 * 00022 * ZHPEVD computes all the eigenvalues and, optionally, eigenvectors of 00023 * a complex Hermitian matrix A in packed storage. If eigenvectors are 00024 * desired, it uses a divide and conquer algorithm. 00025 * 00026 * The divide and conquer algorithm makes very mild assumptions about 00027 * floating point arithmetic. It will work on machines with a guard 00028 * digit in add/subtract, or on those binary machines without guard 00029 * digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or 00030 * Cray-2. It could conceivably fail on hexadecimal or decimal machines 00031 * without guard digits, but we know of none. 00032 * 00033 * Arguments 00034 * ========= 00035 * 00036 * JOBZ (input) CHARACTER*1 00037 * = 'N': Compute eigenvalues only; 00038 * = 'V': Compute eigenvalues and eigenvectors. 00039 * 00040 * UPLO (input) CHARACTER*1 00041 * = 'U': Upper triangle of A is stored; 00042 * = 'L': Lower triangle of A is stored. 00043 * 00044 * N (input) INTEGER 00045 * The order of the matrix A. N >= 0. 00046 * 00047 * AP (input/output) COMPLEX*16 array, dimension (N*(N+1)/2) 00048 * On entry, the upper or lower triangle of the Hermitian matrix 00049 * A, packed columnwise in a linear array. The j-th column of A 00050 * is stored in the array AP as follows: 00051 * if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; 00052 * if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n. 00053 * 00054 * On exit, AP is overwritten by values generated during the 00055 * reduction to tridiagonal form. If UPLO = 'U', the diagonal 00056 * and first superdiagonal of the tridiagonal matrix T overwrite 00057 * the corresponding elements of A, and if UPLO = 'L', the 00058 * diagonal and first subdiagonal of T overwrite the 00059 * corresponding elements of A. 00060 * 00061 * W (output) DOUBLE PRECISION array, dimension (N) 00062 * If INFO = 0, the eigenvalues in ascending order. 00063 * 00064 * Z (output) COMPLEX*16 array, dimension (LDZ, N) 00065 * If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal 00066 * eigenvectors of the matrix A, with the i-th column of Z 00067 * holding the eigenvector associated with W(i). 00068 * If JOBZ = 'N', then Z is not referenced. 00069 * 00070 * LDZ (input) INTEGER 00071 * The leading dimension of the array Z. LDZ >= 1, and if 00072 * JOBZ = 'V', LDZ >= max(1,N). 00073 * 00074 * WORK (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK)) 00075 * On exit, if INFO = 0, WORK(1) returns the required LWORK. 00076 * 00077 * LWORK (input) INTEGER 00078 * The dimension of array WORK. 00079 * If N <= 1, LWORK must be at least 1. 00080 * If JOBZ = 'N' and N > 1, LWORK must be at least N. 00081 * If JOBZ = 'V' and N > 1, LWORK must be at least 2*N. 00082 * 00083 * If LWORK = -1, then a workspace query is assumed; the routine 00084 * only calculates the required sizes of the WORK, RWORK and 00085 * IWORK arrays, returns these values as the first entries of 00086 * the WORK, RWORK and IWORK arrays, and no error message 00087 * related to LWORK or LRWORK or LIWORK is issued by XERBLA. 00088 * 00089 * RWORK (workspace/output) DOUBLE PRECISION array, 00090 * dimension (LRWORK) 00091 * On exit, if INFO = 0, RWORK(1) returns the required LRWORK. 00092 * 00093 * LRWORK (input) INTEGER 00094 * The dimension of array RWORK. 00095 * If N <= 1, LRWORK must be at least 1. 00096 * If JOBZ = 'N' and N > 1, LRWORK must be at least N. 00097 * If JOBZ = 'V' and N > 1, LRWORK must be at least 00098 * 1 + 5*N + 2*N**2. 00099 * 00100 * If LRWORK = -1, then a workspace query is assumed; the 00101 * routine only calculates the required sizes of the WORK, RWORK 00102 * and IWORK arrays, returns these values as the first entries 00103 * of the WORK, RWORK and IWORK arrays, and no error message 00104 * related to LWORK or LRWORK or LIWORK is issued by XERBLA. 00105 * 00106 * IWORK (workspace/output) INTEGER array, dimension (MAX(1,LIWORK)) 00107 * On exit, if INFO = 0, IWORK(1) returns the required LIWORK. 00108 * 00109 * LIWORK (input) INTEGER 00110 * The dimension of array IWORK. 00111 * If JOBZ = 'N' or N <= 1, LIWORK must be at least 1. 00112 * If JOBZ = 'V' and N > 1, LIWORK must be at least 3 + 5*N. 00113 * 00114 * If LIWORK = -1, then a workspace query is assumed; the 00115 * routine only calculates the required sizes of the WORK, RWORK 00116 * and IWORK arrays, returns these values as the first entries 00117 * of the WORK, RWORK and IWORK arrays, and no error message 00118 * related to LWORK or LRWORK or LIWORK is issued by XERBLA. 00119 * 00120 * INFO (output) INTEGER 00121 * = 0: successful exit 00122 * < 0: if INFO = -i, the i-th argument had an illegal value. 00123 * > 0: if INFO = i, the algorithm failed to converge; i 00124 * off-diagonal elements of an intermediate tridiagonal 00125 * form did not converge to zero. 00126 * 00127 * ===================================================================== 00128 * 00129 * .. Parameters .. 00130 DOUBLE PRECISION ZERO, ONE 00131 PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) 00132 COMPLEX*16 CONE 00133 PARAMETER ( CONE = ( 1.0D+0, 0.0D+0 ) ) 00134 * .. 00135 * .. Local Scalars .. 00136 LOGICAL LQUERY, WANTZ 00137 INTEGER IINFO, IMAX, INDE, INDRWK, INDTAU, INDWRK, 00138 $ ISCALE, LIWMIN, LLRWK, LLWRK, LRWMIN, LWMIN 00139 DOUBLE PRECISION ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA, 00140 $ SMLNUM 00141 * .. 00142 * .. External Functions .. 00143 LOGICAL LSAME 00144 DOUBLE PRECISION DLAMCH, ZLANHP 00145 EXTERNAL LSAME, DLAMCH, ZLANHP 00146 * .. 00147 * .. External Subroutines .. 00148 EXTERNAL DSCAL, DSTERF, XERBLA, ZDSCAL, ZHPTRD, ZSTEDC, 00149 $ ZUPMTR 00150 * .. 00151 * .. Intrinsic Functions .. 00152 INTRINSIC SQRT 00153 * .. 00154 * .. Executable Statements .. 00155 * 00156 * Test the input parameters. 00157 * 00158 WANTZ = LSAME( JOBZ, 'V' ) 00159 LQUERY = ( LWORK.EQ.-1 .OR. LRWORK.EQ.-1 .OR. LIWORK.EQ.-1 ) 00160 * 00161 INFO = 0 00162 IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN 00163 INFO = -1 00164 ELSE IF( .NOT.( LSAME( UPLO, 'L' ) .OR. LSAME( UPLO, 'U' ) ) ) 00165 $ THEN 00166 INFO = -2 00167 ELSE IF( N.LT.0 ) THEN 00168 INFO = -3 00169 ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN 00170 INFO = -7 00171 END IF 00172 * 00173 IF( INFO.EQ.0 ) THEN 00174 IF( N.LE.1 ) THEN 00175 LWMIN = 1 00176 LIWMIN = 1 00177 LRWMIN = 1 00178 ELSE 00179 IF( WANTZ ) THEN 00180 LWMIN = 2*N 00181 LRWMIN = 1 + 5*N + 2*N**2 00182 LIWMIN = 3 + 5*N 00183 ELSE 00184 LWMIN = N 00185 LRWMIN = N 00186 LIWMIN = 1 00187 END IF 00188 END IF 00189 WORK( 1 ) = LWMIN 00190 RWORK( 1 ) = LRWMIN 00191 IWORK( 1 ) = LIWMIN 00192 * 00193 IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN 00194 INFO = -9 00195 ELSE IF( LRWORK.LT.LRWMIN .AND. .NOT.LQUERY ) THEN 00196 INFO = -11 00197 ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT.LQUERY ) THEN 00198 INFO = -13 00199 END IF 00200 END IF 00201 * 00202 IF( INFO.NE.0 ) THEN 00203 CALL XERBLA( 'ZHPEVD', -INFO ) 00204 RETURN 00205 ELSE IF( LQUERY ) THEN 00206 RETURN 00207 END IF 00208 * 00209 * Quick return if possible 00210 * 00211 IF( N.EQ.0 ) 00212 $ RETURN 00213 * 00214 IF( N.EQ.1 ) THEN 00215 W( 1 ) = AP( 1 ) 00216 IF( WANTZ ) 00217 $ Z( 1, 1 ) = CONE 00218 RETURN 00219 END IF 00220 * 00221 * Get machine constants. 00222 * 00223 SAFMIN = DLAMCH( 'Safe minimum' ) 00224 EPS = DLAMCH( 'Precision' ) 00225 SMLNUM = SAFMIN / EPS 00226 BIGNUM = ONE / SMLNUM 00227 RMIN = SQRT( SMLNUM ) 00228 RMAX = SQRT( BIGNUM ) 00229 * 00230 * Scale matrix to allowable range, if necessary. 00231 * 00232 ANRM = ZLANHP( 'M', UPLO, N, AP, RWORK ) 00233 ISCALE = 0 00234 IF( ANRM.GT.ZERO .AND. ANRM.LT.RMIN ) THEN 00235 ISCALE = 1 00236 SIGMA = RMIN / ANRM 00237 ELSE IF( ANRM.GT.RMAX ) THEN 00238 ISCALE = 1 00239 SIGMA = RMAX / ANRM 00240 END IF 00241 IF( ISCALE.EQ.1 ) THEN 00242 CALL ZDSCAL( ( N*( N+1 ) ) / 2, SIGMA, AP, 1 ) 00243 END IF 00244 * 00245 * Call ZHPTRD to reduce Hermitian packed matrix to tridiagonal form. 00246 * 00247 INDE = 1 00248 INDTAU = 1 00249 INDRWK = INDE + N 00250 INDWRK = INDTAU + N 00251 LLWRK = LWORK - INDWRK + 1 00252 LLRWK = LRWORK - INDRWK + 1 00253 CALL ZHPTRD( UPLO, N, AP, W, RWORK( INDE ), WORK( INDTAU ), 00254 $ IINFO ) 00255 * 00256 * For eigenvalues only, call DSTERF. For eigenvectors, first call 00257 * ZUPGTR to generate the orthogonal matrix, then call ZSTEDC. 00258 * 00259 IF( .NOT.WANTZ ) THEN 00260 CALL DSTERF( N, W, RWORK( INDE ), INFO ) 00261 ELSE 00262 CALL ZSTEDC( 'I', N, W, RWORK( INDE ), Z, LDZ, WORK( INDWRK ), 00263 $ LLWRK, RWORK( INDRWK ), LLRWK, IWORK, LIWORK, 00264 $ INFO ) 00265 CALL ZUPMTR( 'L', UPLO, 'N', N, N, AP, WORK( INDTAU ), Z, LDZ, 00266 $ WORK( INDWRK ), IINFO ) 00267 END IF 00268 * 00269 * If matrix was scaled, then rescale eigenvalues appropriately. 00270 * 00271 IF( ISCALE.EQ.1 ) THEN 00272 IF( INFO.EQ.0 ) THEN 00273 IMAX = N 00274 ELSE 00275 IMAX = INFO - 1 00276 END IF 00277 CALL DSCAL( IMAX, ONE / SIGMA, W, 1 ) 00278 END IF 00279 * 00280 WORK( 1 ) = LWMIN 00281 RWORK( 1 ) = LRWMIN 00282 IWORK( 1 ) = LIWMIN 00283 RETURN 00284 * 00285 * End of ZHPEVD 00286 * 00287 END
1.7.3 
