00001 SUBROUTINE ZLAED7( N, CUTPNT, QSIZ, TLVLS, CURLVL, CURPBM, D, Q, 00002 $ LDQ, RHO, INDXQ, QSTORE, QPTR, PRMPTR, PERM, 00003 $ GIVPTR, GIVCOL, GIVNUM, WORK, RWORK, IWORK, 00004 $ INFO ) 00005 * 00006 * -- LAPACK routine (version 3.2) -- 00007 * -- LAPACK is a software package provided by Univ. of Tennessee, -- 00008 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 00009 * November 2006 00010 * 00011 * .. Scalar Arguments .. 00012 INTEGER CURLVL, CURPBM, CUTPNT, INFO, LDQ, N, QSIZ, 00013 $ TLVLS 00014 DOUBLE PRECISION RHO 00015 * .. 00016 * .. Array Arguments .. 00017 INTEGER GIVCOL( 2, * ), GIVPTR( * ), INDXQ( * ), 00018 $ IWORK( * ), PERM( * ), PRMPTR( * ), QPTR( * ) 00019 DOUBLE PRECISION D( * ), GIVNUM( 2, * ), QSTORE( * ), RWORK( * ) 00020 COMPLEX*16 Q( LDQ, * ), WORK( * ) 00021 * .. 00022 * 00023 * Purpose 00024 * ======= 00025 * 00026 * ZLAED7 computes the updated eigensystem of a diagonal 00027 * matrix after modification by a rank-one symmetric matrix. This 00028 * routine is used only for the eigenproblem which requires all 00029 * eigenvalues and optionally eigenvectors of a dense or banded 00030 * Hermitian matrix that has been reduced to tridiagonal form. 00031 * 00032 * T = Q(in) ( D(in) + RHO * Z*Z' ) Q'(in) = Q(out) * D(out) * Q'(out) 00033 * 00034 * where Z = Q'u, u is a vector of length N with ones in the 00035 * CUTPNT and CUTPNT + 1 th elements and zeros elsewhere. 00036 * 00037 * The eigenvectors of the original matrix are stored in Q, and the 00038 * eigenvalues are in D. The algorithm consists of three stages: 00039 * 00040 * The first stage consists of deflating the size of the problem 00041 * when there are multiple eigenvalues or if there is a zero in 00042 * the Z vector. For each such occurence the dimension of the 00043 * secular equation problem is reduced by one. This stage is 00044 * performed by the routine DLAED2. 00045 * 00046 * The second stage consists of calculating the updated 00047 * eigenvalues. This is done by finding the roots of the secular 00048 * equation via the routine DLAED4 (as called by SLAED3). 00049 * This routine also calculates the eigenvectors of the current 00050 * problem. 00051 * 00052 * The final stage consists of computing the updated eigenvectors 00053 * directly using the updated eigenvalues. The eigenvectors for 00054 * the current problem are multiplied with the eigenvectors from 00055 * the overall problem. 00056 * 00057 * Arguments 00058 * ========= 00059 * 00060 * N (input) INTEGER 00061 * The dimension of the symmetric tridiagonal matrix. N >= 0. 00062 * 00063 * CUTPNT (input) INTEGER 00064 * Contains the location of the last eigenvalue in the leading 00065 * sub-matrix. min(1,N) <= CUTPNT <= N. 00066 * 00067 * QSIZ (input) INTEGER 00068 * The dimension of the unitary matrix used to reduce 00069 * the full matrix to tridiagonal form. QSIZ >= N. 00070 * 00071 * TLVLS (input) INTEGER 00072 * The total number of merging levels in the overall divide and 00073 * conquer tree. 00074 * 00075 * CURLVL (input) INTEGER 00076 * The current level in the overall merge routine, 00077 * 0 <= curlvl <= tlvls. 00078 * 00079 * CURPBM (input) INTEGER 00080 * The current problem in the current level in the overall 00081 * merge routine (counting from upper left to lower right). 00082 * 00083 * D (input/output) DOUBLE PRECISION array, dimension (N) 00084 * On entry, the eigenvalues of the rank-1-perturbed matrix. 00085 * On exit, the eigenvalues of the repaired matrix. 00086 * 00087 * Q (input/output) COMPLEX*16 array, dimension (LDQ,N) 00088 * On entry, the eigenvectors of the rank-1-perturbed matrix. 00089 * On exit, the eigenvectors of the repaired tridiagonal matrix. 00090 * 00091 * LDQ (input) INTEGER 00092 * The leading dimension of the array Q. LDQ >= max(1,N). 00093 * 00094 * RHO (input) DOUBLE PRECISION 00095 * Contains the subdiagonal element used to create the rank-1 00096 * modification. 00097 * 00098 * INDXQ (output) INTEGER array, dimension (N) 00099 * This contains the permutation which will reintegrate the 00100 * subproblem just solved back into sorted order, 00101 * ie. D( INDXQ( I = 1, N ) ) will be in ascending order. 00102 * 00103 * IWORK (workspace) INTEGER array, dimension (4*N) 00104 * 00105 * RWORK (workspace) DOUBLE PRECISION array, 00106 * dimension (3*N+2*QSIZ*N) 00107 * 00108 * WORK (workspace) COMPLEX*16 array, dimension (QSIZ*N) 00109 * 00110 * QSTORE (input/output) DOUBLE PRECISION array, dimension (N**2+1) 00111 * Stores eigenvectors of submatrices encountered during 00112 * divide and conquer, packed together. QPTR points to 00113 * beginning of the submatrices. 00114 * 00115 * QPTR (input/output) INTEGER array, dimension (N+2) 00116 * List of indices pointing to beginning of submatrices stored 00117 * in QSTORE. The submatrices are numbered starting at the 00118 * bottom left of the divide and conquer tree, from left to 00119 * right and bottom to top. 00120 * 00121 * PRMPTR (input) INTEGER array, dimension (N lg N) 00122 * Contains a list of pointers which indicate where in PERM a 00123 * level's permutation is stored. PRMPTR(i+1) - PRMPTR(i) 00124 * indicates the size of the permutation and also the size of 00125 * the full, non-deflated problem. 00126 * 00127 * PERM (input) INTEGER array, dimension (N lg N) 00128 * Contains the permutations (from deflation and sorting) to be 00129 * applied to each eigenblock. 00130 * 00131 * GIVPTR (input) INTEGER array, dimension (N lg N) 00132 * Contains a list of pointers which indicate where in GIVCOL a 00133 * level's Givens rotations are stored. GIVPTR(i+1) - GIVPTR(i) 00134 * indicates the number of Givens rotations. 00135 * 00136 * GIVCOL (input) INTEGER array, dimension (2, N lg N) 00137 * Each pair of numbers indicates a pair of columns to take place 00138 * in a Givens rotation. 00139 * 00140 * GIVNUM (input) DOUBLE PRECISION array, dimension (2, N lg N) 00141 * Each number indicates the S value to be used in the 00142 * corresponding Givens rotation. 00143 * 00144 * INFO (output) INTEGER 00145 * = 0: successful exit. 00146 * < 0: if INFO = -i, the i-th argument had an illegal value. 00147 * > 0: if INFO = 1, an eigenvalue did not converge 00148 * 00149 * ===================================================================== 00150 * 00151 * .. Local Scalars .. 00152 INTEGER COLTYP, CURR, I, IDLMDA, INDX, 00153 $ INDXC, INDXP, IQ, IW, IZ, K, N1, N2, PTR 00154 * .. 00155 * .. External Subroutines .. 00156 EXTERNAL DLAED9, DLAEDA, DLAMRG, XERBLA, ZLACRM, ZLAED8 00157 * .. 00158 * .. Intrinsic Functions .. 00159 INTRINSIC MAX, MIN 00160 * .. 00161 * .. Executable Statements .. 00162 * 00163 * Test the input parameters. 00164 * 00165 INFO = 0 00166 * 00167 * IF( ICOMPQ.LT.0 .OR. ICOMPQ.GT.1 ) THEN 00168 * INFO = -1 00169 * ELSE IF( N.LT.0 ) THEN 00170 IF( N.LT.0 ) THEN 00171 INFO = -1 00172 ELSE IF( MIN( 1, N ).GT.CUTPNT .OR. N.LT.CUTPNT ) THEN 00173 INFO = -2 00174 ELSE IF( QSIZ.LT.N ) THEN 00175 INFO = -3 00176 ELSE IF( LDQ.LT.MAX( 1, N ) ) THEN 00177 INFO = -9 00178 END IF 00179 IF( INFO.NE.0 ) THEN 00180 CALL XERBLA( 'ZLAED7', -INFO ) 00181 RETURN 00182 END IF 00183 * 00184 * Quick return if possible 00185 * 00186 IF( N.EQ.0 ) 00187 $ RETURN 00188 * 00189 * The following values are for bookkeeping purposes only. They are 00190 * integer pointers which indicate the portion of the workspace 00191 * used by a particular array in DLAED2 and SLAED3. 00192 * 00193 IZ = 1 00194 IDLMDA = IZ + N 00195 IW = IDLMDA + N 00196 IQ = IW + N 00197 * 00198 INDX = 1 00199 INDXC = INDX + N 00200 COLTYP = INDXC + N 00201 INDXP = COLTYP + N 00202 * 00203 * Form the z-vector which consists of the last row of Q_1 and the 00204 * first row of Q_2. 00205 * 00206 PTR = 1 + 2**TLVLS 00207 DO 10 I = 1, CURLVL - 1 00208 PTR = PTR + 2**( TLVLS-I ) 00209 10 CONTINUE 00210 CURR = PTR + CURPBM 00211 CALL DLAEDA( N, TLVLS, CURLVL, CURPBM, PRMPTR, PERM, GIVPTR, 00212 $ GIVCOL, GIVNUM, QSTORE, QPTR, RWORK( IZ ), 00213 $ RWORK( IZ+N ), INFO ) 00214 * 00215 * When solving the final problem, we no longer need the stored data, 00216 * so we will overwrite the data from this level onto the previously 00217 * used storage space. 00218 * 00219 IF( CURLVL.EQ.TLVLS ) THEN 00220 QPTR( CURR ) = 1 00221 PRMPTR( CURR ) = 1 00222 GIVPTR( CURR ) = 1 00223 END IF 00224 * 00225 * Sort and Deflate eigenvalues. 00226 * 00227 CALL ZLAED8( K, N, QSIZ, Q, LDQ, D, RHO, CUTPNT, RWORK( IZ ), 00228 $ RWORK( IDLMDA ), WORK, QSIZ, RWORK( IW ), 00229 $ IWORK( INDXP ), IWORK( INDX ), INDXQ, 00230 $ PERM( PRMPTR( CURR ) ), GIVPTR( CURR+1 ), 00231 $ GIVCOL( 1, GIVPTR( CURR ) ), 00232 $ GIVNUM( 1, GIVPTR( CURR ) ), INFO ) 00233 PRMPTR( CURR+1 ) = PRMPTR( CURR ) + N 00234 GIVPTR( CURR+1 ) = GIVPTR( CURR+1 ) + GIVPTR( CURR ) 00235 * 00236 * Solve Secular Equation. 00237 * 00238 IF( K.NE.0 ) THEN 00239 CALL DLAED9( K, 1, K, N, D, RWORK( IQ ), K, RHO, 00240 $ RWORK( IDLMDA ), RWORK( IW ), 00241 $ QSTORE( QPTR( CURR ) ), K, INFO ) 00242 CALL ZLACRM( QSIZ, K, WORK, QSIZ, QSTORE( QPTR( CURR ) ), K, Q, 00243 $ LDQ, RWORK( IQ ) ) 00244 QPTR( CURR+1 ) = QPTR( CURR ) + K**2 00245 IF( INFO.NE.0 ) THEN 00246 RETURN 00247 END IF 00248 * 00249 * Prepare the INDXQ sorting premutation. 00250 * 00251 N1 = K 00252 N2 = N - K 00253 CALL DLAMRG( N1, N2, D, 1, -1, INDXQ ) 00254 ELSE 00255 QPTR( CURR+1 ) = QPTR( CURR ) 00256 DO 20 I = 1, N 00257 INDXQ( I ) = I 00258 20 CONTINUE 00259 END IF 00260 * 00261 RETURN 00262 * 00263 * End of ZLAED7 00264 * 00265 END
1.7.2