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Mise à jour de lapack vers la version 3.3.0.
1: SUBROUTINE DLAED7( 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 3.2) -- 7: * -- LAPACK is a software package provided by Univ. of Tennessee, -- 8: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- 9: * November 2006 10: * 11: * .. Scalar Arguments .. 12: INTEGER CURLVL, CURPBM, CUTPNT, ICOMPQ, INFO, LDQ, N, 13: $ QSIZ, TLVLS 14: DOUBLE PRECISION RHO 15: * .. 16: * .. Array Arguments .. 17: INTEGER GIVCOL( 2, * ), GIVPTR( * ), INDXQ( * ), 18: $ IWORK( * ), PERM( * ), PRMPTR( * ), QPTR( * ) 19: DOUBLE PRECISION D( * ), GIVNUM( 2, * ), Q( LDQ, * ), 20: $ QSTORE( * ), WORK( * ) 21: * .. 22: * 23: * Purpose 24: * ======= 25: * 26: * DLAED7 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. DLAED1 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 DLAED8. 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 DLAED4 (as called by DLAED9). 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) DOUBLE PRECISION 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) DOUBLE PRECISION 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) DOUBLE PRECISION 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) DOUBLE PRECISION 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) DOUBLE PRECISION 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) DOUBLE PRECISION 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: DOUBLE PRECISION ONE, ZERO 165: PARAMETER ( ONE = 1.0D0, ZERO = 0.0D0 ) 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 DGEMM, DLAED8, DLAED9, DLAEDA, DLAMRG, 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( 'DLAED7', -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 DLAED8 and DLAED9. 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 DLAEDA( 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 DLAED8( 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 DLAED9( 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 DGEMM( '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 DLAMRG( 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 DLAED7 287: * 288: END