00001 SUBROUTINE SLAED7( ICOMPQ, N, QSIZ, TLVLS, CURLVL, CURPBM, D, Q, 00002 $ LDQ, INDXQ, RHO, CUTPNT, QSTORE, QPTR, PRMPTR, 00003 $ PERM, GIVPTR, GIVCOL, GIVNUM, WORK, 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, ICOMPQ, INFO, LDQ, N, 00013 $ QSIZ, TLVLS 00014 REAL RHO 00015 * .. 00016 * .. Array Arguments .. 00017 INTEGER GIVCOL( 2, * ), GIVPTR( * ), INDXQ( * ), 00018 $ IWORK( * ), PERM( * ), PRMPTR( * ), QPTR( * ) 00019 REAL D( * ), GIVNUM( 2, * ), Q( LDQ, * ), 00020 $ QSTORE( * ), WORK( * ) 00021 * .. 00022 * 00023 * Purpose 00024 * ======= 00025 * 00026 * SLAED7 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 symmetric matrix 00030 * that has been reduced to tridiagonal form. SLAED1 handles 00031 * the case in which all eigenvalues and eigenvectors of a symmetric 00032 * tridiagonal matrix are desired. 00033 * 00034 * T = Q(in) ( D(in) + RHO * Z*Z' ) Q'(in) = Q(out) * D(out) * Q'(out) 00035 * 00036 * where Z = Q'u, u is a vector of length N with ones in the 00037 * CUTPNT and CUTPNT + 1 th elements and zeros elsewhere. 00038 * 00039 * The eigenvectors of the original matrix are stored in Q, and the 00040 * eigenvalues are in D. The algorithm consists of three stages: 00041 * 00042 * The first stage consists of deflating the size of the problem 00043 * when there are multiple eigenvalues or if there is a zero in 00044 * the Z vector. For each such occurence the dimension of the 00045 * secular equation problem is reduced by one. This stage is 00046 * performed by the routine SLAED8. 00047 * 00048 * The second stage consists of calculating the updated 00049 * eigenvalues. This is done by finding the roots of the secular 00050 * equation via the routine SLAED4 (as called by SLAED9). 00051 * This routine also calculates the eigenvectors of the current 00052 * problem. 00053 * 00054 * The final stage consists of computing the updated eigenvectors 00055 * directly using the updated eigenvalues. The eigenvectors for 00056 * the current problem are multiplied with the eigenvectors from 00057 * the overall problem. 00058 * 00059 * Arguments 00060 * ========= 00061 * 00062 * ICOMPQ (input) INTEGER 00063 * = 0: Compute eigenvalues only. 00064 * = 1: Compute eigenvectors of original dense symmetric matrix 00065 * also. On entry, Q contains the orthogonal matrix used 00066 * to reduce the original matrix to tridiagonal form. 00067 * 00068 * N (input) INTEGER 00069 * The dimension of the symmetric tridiagonal matrix. N >= 0. 00070 * 00071 * QSIZ (input) INTEGER 00072 * The dimension of the orthogonal matrix used to reduce 00073 * the full matrix to tridiagonal form. QSIZ >= N if ICOMPQ = 1. 00074 * 00075 * TLVLS (input) INTEGER 00076 * The total number of merging levels in the overall divide and 00077 * conquer tree. 00078 * 00079 * CURLVL (input) INTEGER 00080 * The current level in the overall merge routine, 00081 * 0 <= CURLVL <= TLVLS. 00082 * 00083 * CURPBM (input) INTEGER 00084 * The current problem in the current level in the overall 00085 * merge routine (counting from upper left to lower right). 00086 * 00087 * D (input/output) REAL array, dimension (N) 00088 * On entry, the eigenvalues of the rank-1-perturbed matrix. 00089 * On exit, the eigenvalues of the repaired matrix. 00090 * 00091 * Q (input/output) REAL array, dimension (LDQ, N) 00092 * On entry, the eigenvectors of the rank-1-perturbed matrix. 00093 * On exit, the eigenvectors of the repaired tridiagonal matrix. 00094 * 00095 * LDQ (input) INTEGER 00096 * The leading dimension of the array Q. LDQ >= max(1,N). 00097 * 00098 * INDXQ (output) INTEGER array, dimension (N) 00099 * The permutation which will reintegrate the subproblem just 00100 * solved back into sorted order, i.e., D( INDXQ( I = 1, N ) ) 00101 * will be in ascending order. 00102 * 00103 * RHO (input) REAL 00104 * The subdiagonal element used to create the rank-1 00105 * modification. 00106 * 00107 * CUTPNT (input) INTEGER 00108 * Contains the location of the last eigenvalue in the leading 00109 * sub-matrix. min(1,N) <= CUTPNT <= N. 00110 * 00111 * QSTORE (input/output) REAL array, dimension (N**2+1) 00112 * Stores eigenvectors of submatrices encountered during 00113 * divide and conquer, packed together. QPTR points to 00114 * beginning of the submatrices. 00115 * 00116 * QPTR (input/output) INTEGER array, dimension (N+2) 00117 * List of indices pointing to beginning of submatrices stored 00118 * in QSTORE. The submatrices are numbered starting at the 00119 * bottom left of the divide and conquer tree, from left to 00120 * right and bottom to top. 00121 * 00122 * PRMPTR (input) INTEGER array, dimension (N lg N) 00123 * Contains a list of pointers which indicate where in PERM a 00124 * level's permutation is stored. PRMPTR(i+1) - PRMPTR(i) 00125 * indicates the size of the permutation and also the size of 00126 * the full, non-deflated problem. 00127 * 00128 * PERM (input) INTEGER array, dimension (N lg N) 00129 * Contains the permutations (from deflation and sorting) to be 00130 * applied to each eigenblock. 00131 * 00132 * GIVPTR (input) INTEGER array, dimension (N lg N) 00133 * Contains a list of pointers which indicate where in GIVCOL a 00134 * level's Givens rotations are stored. GIVPTR(i+1) - GIVPTR(i) 00135 * indicates the number of Givens rotations. 00136 * 00137 * GIVCOL (input) INTEGER array, dimension (2, N lg N) 00138 * Each pair of numbers indicates a pair of columns to take place 00139 * in a Givens rotation. 00140 * 00141 * GIVNUM (input) REAL array, dimension (2, N lg N) 00142 * Each number indicates the S value to be used in the 00143 * corresponding Givens rotation. 00144 * 00145 * WORK (workspace) REAL array, dimension (3*N+QSIZ*N) 00146 * 00147 * IWORK (workspace) INTEGER array, dimension (4*N) 00148 * 00149 * INFO (output) INTEGER 00150 * = 0: successful exit. 00151 * < 0: if INFO = -i, the i-th argument had an illegal value. 00152 * > 0: if INFO = 1, an eigenvalue did not converge 00153 * 00154 * Further Details 00155 * =============== 00156 * 00157 * Based on contributions by 00158 * Jeff Rutter, Computer Science Division, University of California 00159 * at Berkeley, USA 00160 * 00161 * ===================================================================== 00162 * 00163 * .. Parameters .. 00164 REAL ONE, ZERO 00165 PARAMETER ( ONE = 1.0E0, ZERO = 0.0E0 ) 00166 * .. 00167 * .. Local Scalars .. 00168 INTEGER COLTYP, CURR, I, IDLMDA, INDX, INDXC, INDXP, 00169 $ IQ2, IS, IW, IZ, K, LDQ2, N1, N2, PTR 00170 * .. 00171 * .. External Subroutines .. 00172 EXTERNAL SGEMM, SLAED8, SLAED9, SLAEDA, SLAMRG, XERBLA 00173 * .. 00174 * .. Intrinsic Functions .. 00175 INTRINSIC MAX, MIN 00176 * .. 00177 * .. Executable Statements .. 00178 * 00179 * Test the input parameters. 00180 * 00181 INFO = 0 00182 * 00183 IF( ICOMPQ.LT.0 .OR. ICOMPQ.GT.1 ) THEN 00184 INFO = -1 00185 ELSE IF( N.LT.0 ) THEN 00186 INFO = -2 00187 ELSE IF( ICOMPQ.EQ.1 .AND. QSIZ.LT.N ) THEN 00188 INFO = -4 00189 ELSE IF( LDQ.LT.MAX( 1, N ) ) THEN 00190 INFO = -9 00191 ELSE IF( MIN( 1, N ).GT.CUTPNT .OR. N.LT.CUTPNT ) THEN 00192 INFO = -12 00193 END IF 00194 IF( INFO.NE.0 ) THEN 00195 CALL XERBLA( 'SLAED7', -INFO ) 00196 RETURN 00197 END IF 00198 * 00199 * Quick return if possible 00200 * 00201 IF( N.EQ.0 ) 00202 $ RETURN 00203 * 00204 * The following values are for bookkeeping purposes only. They are 00205 * integer pointers which indicate the portion of the workspace 00206 * used by a particular array in SLAED8 and SLAED9. 00207 * 00208 IF( ICOMPQ.EQ.1 ) THEN 00209 LDQ2 = QSIZ 00210 ELSE 00211 LDQ2 = N 00212 END IF 00213 * 00214 IZ = 1 00215 IDLMDA = IZ + N 00216 IW = IDLMDA + N 00217 IQ2 = IW + N 00218 IS = IQ2 + N*LDQ2 00219 * 00220 INDX = 1 00221 INDXC = INDX + N 00222 COLTYP = INDXC + N 00223 INDXP = COLTYP + N 00224 * 00225 * Form the z-vector which consists of the last row of Q_1 and the 00226 * first row of Q_2. 00227 * 00228 PTR = 1 + 2**TLVLS 00229 DO 10 I = 1, CURLVL - 1 00230 PTR = PTR + 2**( TLVLS-I ) 00231 10 CONTINUE 00232 CURR = PTR + CURPBM 00233 CALL SLAEDA( N, TLVLS, CURLVL, CURPBM, PRMPTR, PERM, GIVPTR, 00234 $ GIVCOL, GIVNUM, QSTORE, QPTR, WORK( IZ ), 00235 $ WORK( IZ+N ), INFO ) 00236 * 00237 * When solving the final problem, we no longer need the stored data, 00238 * so we will overwrite the data from this level onto the previously 00239 * used storage space. 00240 * 00241 IF( CURLVL.EQ.TLVLS ) THEN 00242 QPTR( CURR ) = 1 00243 PRMPTR( CURR ) = 1 00244 GIVPTR( CURR ) = 1 00245 END IF 00246 * 00247 * Sort and Deflate eigenvalues. 00248 * 00249 CALL SLAED8( ICOMPQ, K, N, QSIZ, D, Q, LDQ, INDXQ, RHO, CUTPNT, 00250 $ WORK( IZ ), WORK( IDLMDA ), WORK( IQ2 ), LDQ2, 00251 $ WORK( IW ), PERM( PRMPTR( CURR ) ), GIVPTR( CURR+1 ), 00252 $ GIVCOL( 1, GIVPTR( CURR ) ), 00253 $ GIVNUM( 1, GIVPTR( CURR ) ), IWORK( INDXP ), 00254 $ IWORK( INDX ), INFO ) 00255 PRMPTR( CURR+1 ) = PRMPTR( CURR ) + N 00256 GIVPTR( CURR+1 ) = GIVPTR( CURR+1 ) + GIVPTR( CURR ) 00257 * 00258 * Solve Secular Equation. 00259 * 00260 IF( K.NE.0 ) THEN 00261 CALL SLAED9( K, 1, K, N, D, WORK( IS ), K, RHO, WORK( IDLMDA ), 00262 $ WORK( IW ), QSTORE( QPTR( CURR ) ), K, INFO ) 00263 IF( INFO.NE.0 ) 00264 $ GO TO 30 00265 IF( ICOMPQ.EQ.1 ) THEN 00266 CALL SGEMM( 'N', 'N', QSIZ, K, K, ONE, WORK( IQ2 ), LDQ2, 00267 $ QSTORE( QPTR( CURR ) ), K, ZERO, Q, LDQ ) 00268 END IF 00269 QPTR( CURR+1 ) = QPTR( CURR ) + K**2 00270 * 00271 * Prepare the INDXQ sorting permutation. 00272 * 00273 N1 = K 00274 N2 = N - K 00275 CALL SLAMRG( N1, N2, D, 1, -1, INDXQ ) 00276 ELSE 00277 QPTR( CURR+1 ) = QPTR( CURR ) 00278 DO 20 I = 1, N 00279 INDXQ( I ) = I 00280 20 CONTINUE 00281 END IF 00282 * 00283 30 CONTINUE 00284 RETURN 00285 * 00286 * End of SLAED7 00287 * 00288 END
1.7.2