1 SUBROUTINE SLAED7( ICOMPQ, N, QSIZ, TLVLS, CURLVL, CURPBM, D, Q, 2 $ LDQ, INDXQ, RHO, CUTPNT, QSTORE, QPTR, PRMPTR, 3 $ PERM, GIVPTR, GIVCOL, GIVNUM, WORK, IWORK, 4 $ INFO ) 5* 6* -- LAPACK routine (version 3.0) -- 7* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., 8* Courant Institute, Argonne National Lab, and Rice University 9* September 30, 1994 10* 11* .. Scalar Arguments .. 12 INTEGER CURLVL, CURPBM, CUTPNT, ICOMPQ, INFO, LDQ, N, 13 $ QSIZ, TLVLS 14 REAL RHO 15* .. 16* .. Array Arguments .. 17 INTEGER GIVCOL( 2, * ), GIVPTR( * ), INDXQ( * ), 18 $ IWORK( * ), PERM( * ), PRMPTR( * ), QPTR( * ) 19 REAL D( * ), GIVNUM( 2, * ), Q( LDQ, * ), 20 $ QSTORE( * ), WORK( * ) 21* .. 22* 23* Purpose 24* ======= 25* 26* SLAED7 computes the updated eigensystem of a diagonal 27* matrix after modification by a rank-one symmetric matrix. This 28* routine is used only for the eigenproblem which requires all 29* eigenvalues and optionally eigenvectors of a dense symmetric matrix 30* that has been reduced to tridiagonal form. SLAED1 handles 31* the case in which all eigenvalues and eigenvectors of a symmetric 32* tridiagonal matrix are desired. 33* 34* T = Q(in) ( D(in) + RHO * Z*Z' ) Q'(in) = Q(out) * D(out) * Q'(out) 35* 36* where Z = Q'u, u is a vector of length N with ones in the 37* CUTPNT and CUTPNT + 1 th elements and zeros elsewhere. 38* 39* The eigenvectors of the original matrix are stored in Q, and the 40* eigenvalues are in D. The algorithm consists of three stages: 41* 42* The first stage consists of deflating the size of the problem 43* when there are multiple eigenvalues or if there is a zero in 44* the Z vector. For each such occurence the dimension of the 45* secular equation problem is reduced by one. This stage is 46* performed by the routine SLAED8. 47* 48* The second stage consists of calculating the updated 49* eigenvalues. This is done by finding the roots of the secular 50* equation via the routine SLAED4 (as called by SLAED9). 51* This routine also calculates the eigenvectors of the current 52* problem. 53* 54* The final stage consists of computing the updated eigenvectors 55* directly using the updated eigenvalues. The eigenvectors for 56* the current problem are multiplied with the eigenvectors from 57* the overall problem. 58* 59* Arguments 60* ========= 61* 62* ICOMPQ (input) INTEGER 63* = 0: Compute eigenvalues only. 64* = 1: Compute eigenvectors of original dense symmetric matrix 65* also. On entry, Q contains the orthogonal matrix used 66* to reduce the original matrix to tridiagonal form. 67* 68* N (input) INTEGER 69* The dimension of the symmetric tridiagonal matrix. N >= 0. 70* 71* QSIZ (input) INTEGER 72* The dimension of the orthogonal matrix used to reduce 73* the full matrix to tridiagonal form. QSIZ >= N if ICOMPQ = 1. 74* 75* TLVLS (input) INTEGER 76* The total number of merging levels in the overall divide and 77* conquer tree. 78* 79* CURLVL (input) INTEGER 80* The current level in the overall merge routine, 81* 0 <= CURLVL <= TLVLS. 82* 83* CURPBM (input) INTEGER 84* The current problem in the current level in the overall 85* merge routine (counting from upper left to lower right). 86* 87* D (input/output) REAL array, dimension (N) 88* On entry, the eigenvalues of the rank-1-perturbed matrix. 89* On exit, the eigenvalues of the repaired matrix. 90* 91* Q (input/output) REAL array, dimension (LDQ, N) 92* On entry, the eigenvectors of the rank-1-perturbed matrix. 93* On exit, the eigenvectors of the repaired tridiagonal matrix. 94* 95* LDQ (input) INTEGER 96* The leading dimension of the array Q. LDQ >= max(1,N). 97* 98* INDXQ (output) INTEGER array, dimension (N) 99* The permutation which will reintegrate the subproblem just 100* solved back into sorted order, i.e., D( INDXQ( I = 1, N ) ) 101* will be in ascending order. 102* 103* RHO (input) REAL 104* The subdiagonal element used to create the rank-1 105* modification. 106* 107* CUTPNT (input) INTEGER 108* Contains the location of the last eigenvalue in the leading 109* sub-matrix. min(1,N) <= CUTPNT <= N. 110* 111* QSTORE (input/output) REAL array, dimension (N**2+1) 112* Stores eigenvectors of submatrices encountered during 113* divide and conquer, packed together. QPTR points to 114* beginning of the submatrices. 115* 116* QPTR (input/output) INTEGER array, dimension (N+2) 117* List of indices pointing to beginning of submatrices stored 118* in QSTORE. The submatrices are numbered starting at the 119* bottom left of the divide and conquer tree, from left to 120* right and bottom to top. 121* 122* PRMPTR (input) INTEGER array, dimension (N lg N) 123* Contains a list of pointers which indicate where in PERM a 124* level's permutation is stored. PRMPTR(i+1) - PRMPTR(i) 125* indicates the size of the permutation and also the size of 126* the full, non-deflated problem. 127* 128* PERM (input) INTEGER array, dimension (N lg N) 129* Contains the permutations (from deflation and sorting) to be 130* applied to each eigenblock. 131* 132* GIVPTR (input) INTEGER array, dimension (N lg N) 133* Contains a list of pointers which indicate where in GIVCOL a 134* level's Givens rotations are stored. GIVPTR(i+1) - GIVPTR(i) 135* indicates the number of Givens rotations. 136* 137* GIVCOL (input) INTEGER array, dimension (2, N lg N) 138* Each pair of numbers indicates a pair of columns to take place 139* in a Givens rotation. 140* 141* GIVNUM (input) REAL array, dimension (2, N lg N) 142* Each number indicates the S value to be used in the 143* corresponding Givens rotation. 144* 145* WORK (workspace) REAL array, dimension (3*N+QSIZ*N) 146* 147* IWORK (workspace) INTEGER array, dimension (4*N) 148* 149* INFO (output) INTEGER 150* = 0: successful exit. 151* < 0: if INFO = -i, the i-th argument had an illegal value. 152* > 0: if INFO = 1, an eigenvalue did not converge 153* 154* Further Details 155* =============== 156* 157* Based on contributions by 158* Jeff Rutter, Computer Science Division, University of California 159* at Berkeley, USA 160* 161* ===================================================================== 162* 163* .. Parameters .. 164 REAL ONE, ZERO 165 PARAMETER ( ONE = 1.0E0, ZERO = 0.0E0 ) 166* .. 167* .. Local Scalars .. 168 INTEGER COLTYP, CURR, I, IDLMDA, INDX, INDXC, INDXP, 169 $ IQ2, IS, IW, IZ, K, LDQ2, N1, N2, PTR 170* .. 171* .. External Subroutines .. 172 EXTERNAL SGEMM, SLAED8, SLAED9, SLAEDA, SLAMRG, XERBLA 173* .. 174* .. Intrinsic Functions .. 175 INTRINSIC MAX, MIN 176* .. 177* .. Executable Statements .. 178* 179* Test the input parameters. 180* 181 INFO = 0 182* 183 IF( ICOMPQ.LT.0 .OR. ICOMPQ.GT.1 ) THEN 184 INFO = -1 185 ELSE IF( N.LT.0 ) THEN 186 INFO = -2 187 ELSE IF( ICOMPQ.EQ.1 .AND. QSIZ.LT.N ) THEN 188 INFO = -4 189 ELSE IF( LDQ.LT.MAX( 1, N ) ) THEN 190 INFO = -9 191 ELSE IF( MIN( 1, N ).GT.CUTPNT .OR. N.LT.CUTPNT ) THEN 192 INFO = -12 193 END IF 194 IF( INFO.NE.0 ) THEN 195 CALL XERBLA( 'SLAED7', -INFO ) 196 RETURN 197 END IF 198* 199* Quick return if possible 200* 201 IF( N.EQ.0 ) 202 $ RETURN 203* 204* The following values are for bookkeeping purposes only. They are 205* integer pointers which indicate the portion of the workspace 206* used by a particular array in SLAED8 and SLAED9. 207* 208 IF( ICOMPQ.EQ.1 ) THEN 209 LDQ2 = QSIZ 210 ELSE 211 LDQ2 = N 212 END IF 213* 214 IZ = 1 215 IDLMDA = IZ + N 216 IW = IDLMDA + N 217 IQ2 = IW + N 218 IS = IQ2 + N*LDQ2 219* 220 INDX = 1 221 INDXC = INDX + N 222 COLTYP = INDXC + N 223 INDXP = COLTYP + N 224* 225* Form the z-vector which consists of the last row of Q_1 and the 226* first row of Q_2. 227* 228 PTR = 1 + 2**TLVLS 229 DO 10 I = 1, CURLVL - 1 230 PTR = PTR + 2**( TLVLS-I ) 231 10 CONTINUE 232 CURR = PTR + CURPBM 233 CALL SLAEDA( N, TLVLS, CURLVL, CURPBM, PRMPTR, PERM, GIVPTR, 234 $ GIVCOL, GIVNUM, QSTORE, QPTR, WORK( IZ ), 235 $ WORK( IZ+N ), INFO ) 236* 237* When solving the final problem, we no longer need the stored data, 238* so we will overwrite the data from this level onto the previously 239* used storage space. 240* 241 IF( CURLVL.EQ.TLVLS ) THEN 242 QPTR( CURR ) = 1 243 PRMPTR( CURR ) = 1 244 GIVPTR( CURR ) = 1 245 END IF 246* 247* Sort and Deflate eigenvalues. 248* 249 CALL SLAED8( ICOMPQ, K, N, QSIZ, D, Q, LDQ, INDXQ, RHO, CUTPNT, 250 $ WORK( IZ ), WORK( IDLMDA ), WORK( IQ2 ), LDQ2, 251 $ WORK( IW ), PERM( PRMPTR( CURR ) ), GIVPTR( CURR+1 ), 252 $ GIVCOL( 1, GIVPTR( CURR ) ), 253 $ GIVNUM( 1, GIVPTR( CURR ) ), IWORK( INDXP ), 254 $ IWORK( INDX ), INFO ) 255 PRMPTR( CURR+1 ) = PRMPTR( CURR ) + N 256 GIVPTR( CURR+1 ) = GIVPTR( CURR+1 ) + GIVPTR( CURR ) 257* 258* Solve Secular Equation. 259* 260 IF( K.NE.0 ) THEN 261 CALL SLAED9( K, 1, K, N, D, WORK( IS ), K, RHO, WORK( IDLMDA ), 262 $ WORK( IW ), QSTORE( QPTR( CURR ) ), K, INFO ) 263 IF( INFO.NE.0 ) 264 $ GO TO 30 265 IF( ICOMPQ.EQ.1 ) THEN 266 CALL SGEMM( 'N', 'N', QSIZ, K, K, ONE, WORK( IQ2 ), LDQ2, 267 $ QSTORE( QPTR( CURR ) ), K, ZERO, Q, LDQ ) 268 END IF 269 QPTR( CURR+1 ) = QPTR( CURR ) + K**2 270* 271* Prepare the INDXQ sorting permutation. 272* 273 N1 = K 274 N2 = N - K 275 CALL SLAMRG( N1, N2, D, 1, -1, INDXQ ) 276 ELSE 277 QPTR( CURR+1 ) = QPTR( CURR ) 278 DO 20 I = 1, N 279 INDXQ( I ) = I 280 20 CONTINUE 281 END IF 282* 283 30 CONTINUE 284 RETURN 285* 286* End of SLAED7 287* 288 END 289