![]() ![]() | ![]() |
Mise à jour de lapack vers la version 3.3.0.
1: SUBROUTINE ZLAED7( N, CUTPNT, QSIZ, TLVLS, CURLVL, CURPBM, D, Q, 2: $ LDQ, RHO, INDXQ, QSTORE, QPTR, PRMPTR, PERM, 3: $ GIVPTR, GIVCOL, GIVNUM, WORK, RWORK, 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, INFO, LDQ, N, QSIZ, 13: $ 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, * ), QSTORE( * ), RWORK( * ) 20: COMPLEX*16 Q( LDQ, * ), WORK( * ) 21: * .. 22: * 23: * Purpose 24: * ======= 25: * 26: * ZLAED7 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 or banded 30: * Hermitian matrix that has been reduced to tridiagonal form. 31: * 32: * T = Q(in) ( D(in) + RHO * Z*Z' ) Q'(in) = Q(out) * D(out) * Q'(out) 33: * 34: * where Z = Q'u, u is a vector of length N with ones in the 35: * CUTPNT and CUTPNT + 1 th elements and zeros elsewhere. 36: * 37: * The eigenvectors of the original matrix are stored in Q, and the 38: * eigenvalues are in D. The algorithm consists of three stages: 39: * 40: * The first stage consists of deflating the size of the problem 41: * when there are multiple eigenvalues or if there is a zero in 42: * the Z vector. For each such occurence the dimension of the 43: * secular equation problem is reduced by one. This stage is 44: * performed by the routine DLAED2. 45: * 46: * The second stage consists of calculating the updated 47: * eigenvalues. This is done by finding the roots of the secular 48: * equation via the routine DLAED4 (as called by SLAED3). 49: * This routine also calculates the eigenvectors of the current 50: * problem. 51: * 52: * The final stage consists of computing the updated eigenvectors 53: * directly using the updated eigenvalues. The eigenvectors for 54: * the current problem are multiplied with the eigenvectors from 55: * the overall problem. 56: * 57: * Arguments 58: * ========= 59: * 60: * N (input) INTEGER 61: * The dimension of the symmetric tridiagonal matrix. N >= 0. 62: * 63: * CUTPNT (input) INTEGER 64: * Contains the location of the last eigenvalue in the leading 65: * sub-matrix. min(1,N) <= CUTPNT <= N. 66: * 67: * QSIZ (input) INTEGER 68: * The dimension of the unitary matrix used to reduce 69: * the full matrix to tridiagonal form. QSIZ >= N. 70: * 71: * TLVLS (input) INTEGER 72: * The total number of merging levels in the overall divide and 73: * conquer tree. 74: * 75: * CURLVL (input) INTEGER 76: * The current level in the overall merge routine, 77: * 0 <= curlvl <= tlvls. 78: * 79: * CURPBM (input) INTEGER 80: * The current problem in the current level in the overall 81: * merge routine (counting from upper left to lower right). 82: * 83: * D (input/output) DOUBLE PRECISION array, dimension (N) 84: * On entry, the eigenvalues of the rank-1-perturbed matrix. 85: * On exit, the eigenvalues of the repaired matrix. 86: * 87: * Q (input/output) COMPLEX*16 array, dimension (LDQ,N) 88: * On entry, the eigenvectors of the rank-1-perturbed matrix. 89: * On exit, the eigenvectors of the repaired tridiagonal matrix. 90: * 91: * LDQ (input) INTEGER 92: * The leading dimension of the array Q. LDQ >= max(1,N). 93: * 94: * RHO (input) DOUBLE PRECISION 95: * Contains the subdiagonal element used to create the rank-1 96: * modification. 97: * 98: * INDXQ (output) INTEGER array, dimension (N) 99: * This contains the permutation which will reintegrate the 100: * subproblem just solved back into sorted order, 101: * ie. D( INDXQ( I = 1, N ) ) will be in ascending order. 102: * 103: * IWORK (workspace) INTEGER array, dimension (4*N) 104: * 105: * RWORK (workspace) DOUBLE PRECISION array, 106: * dimension (3*N+2*QSIZ*N) 107: * 108: * WORK (workspace) COMPLEX*16 array, dimension (QSIZ*N) 109: * 110: * QSTORE (input/output) DOUBLE PRECISION array, dimension (N**2+1) 111: * Stores eigenvectors of submatrices encountered during 112: * divide and conquer, packed together. QPTR points to 113: * beginning of the submatrices. 114: * 115: * QPTR (input/output) INTEGER array, dimension (N+2) 116: * List of indices pointing to beginning of submatrices stored 117: * in QSTORE. The submatrices are numbered starting at the 118: * bottom left of the divide and conquer tree, from left to 119: * right and bottom to top. 120: * 121: * PRMPTR (input) INTEGER array, dimension (N lg N) 122: * Contains a list of pointers which indicate where in PERM a 123: * level's permutation is stored. PRMPTR(i+1) - PRMPTR(i) 124: * indicates the size of the permutation and also the size of 125: * the full, non-deflated problem. 126: * 127: * PERM (input) INTEGER array, dimension (N lg N) 128: * Contains the permutations (from deflation and sorting) to be 129: * applied to each eigenblock. 130: * 131: * GIVPTR (input) INTEGER array, dimension (N lg N) 132: * Contains a list of pointers which indicate where in GIVCOL a 133: * level's Givens rotations are stored. GIVPTR(i+1) - GIVPTR(i) 134: * indicates the number of Givens rotations. 135: * 136: * GIVCOL (input) INTEGER array, dimension (2, N lg N) 137: * Each pair of numbers indicates a pair of columns to take place 138: * in a Givens rotation. 139: * 140: * GIVNUM (input) DOUBLE PRECISION array, dimension (2, N lg N) 141: * Each number indicates the S value to be used in the 142: * corresponding Givens rotation. 143: * 144: * INFO (output) INTEGER 145: * = 0: successful exit. 146: * < 0: if INFO = -i, the i-th argument had an illegal value. 147: * > 0: if INFO = 1, an eigenvalue did not converge 148: * 149: * ===================================================================== 150: * 151: * .. Local Scalars .. 152: INTEGER COLTYP, CURR, I, IDLMDA, INDX, 153: $ INDXC, INDXP, IQ, IW, IZ, K, N1, N2, PTR 154: * .. 155: * .. External Subroutines .. 156: EXTERNAL DLAED9, DLAEDA, DLAMRG, XERBLA, ZLACRM, ZLAED8 157: * .. 158: * .. Intrinsic Functions .. 159: INTRINSIC MAX, MIN 160: * .. 161: * .. Executable Statements .. 162: * 163: * Test the input parameters. 164: * 165: INFO = 0 166: * 167: * IF( ICOMPQ.LT.0 .OR. ICOMPQ.GT.1 ) THEN 168: * INFO = -1 169: * ELSE IF( N.LT.0 ) THEN 170: IF( N.LT.0 ) THEN 171: INFO = -1 172: ELSE IF( MIN( 1, N ).GT.CUTPNT .OR. N.LT.CUTPNT ) THEN 173: INFO = -2 174: ELSE IF( QSIZ.LT.N ) THEN 175: INFO = -3 176: ELSE IF( LDQ.LT.MAX( 1, N ) ) THEN 177: INFO = -9 178: END IF 179: IF( INFO.NE.0 ) THEN 180: CALL XERBLA( 'ZLAED7', -INFO ) 181: RETURN 182: END IF 183: * 184: * Quick return if possible 185: * 186: IF( N.EQ.0 ) 187: $ RETURN 188: * 189: * The following values are for bookkeeping purposes only. They are 190: * integer pointers which indicate the portion of the workspace 191: * used by a particular array in DLAED2 and SLAED3. 192: * 193: IZ = 1 194: IDLMDA = IZ + N 195: IW = IDLMDA + N 196: IQ = IW + N 197: * 198: INDX = 1 199: INDXC = INDX + N 200: COLTYP = INDXC + N 201: INDXP = COLTYP + N 202: * 203: * Form the z-vector which consists of the last row of Q_1 and the 204: * first row of Q_2. 205: * 206: PTR = 1 + 2**TLVLS 207: DO 10 I = 1, CURLVL - 1 208: PTR = PTR + 2**( TLVLS-I ) 209: 10 CONTINUE 210: CURR = PTR + CURPBM 211: CALL DLAEDA( N, TLVLS, CURLVL, CURPBM, PRMPTR, PERM, GIVPTR, 212: $ GIVCOL, GIVNUM, QSTORE, QPTR, RWORK( IZ ), 213: $ RWORK( IZ+N ), INFO ) 214: * 215: * When solving the final problem, we no longer need the stored data, 216: * so we will overwrite the data from this level onto the previously 217: * used storage space. 218: * 219: IF( CURLVL.EQ.TLVLS ) THEN 220: QPTR( CURR ) = 1 221: PRMPTR( CURR ) = 1 222: GIVPTR( CURR ) = 1 223: END IF 224: * 225: * Sort and Deflate eigenvalues. 226: * 227: CALL ZLAED8( K, N, QSIZ, Q, LDQ, D, RHO, CUTPNT, RWORK( IZ ), 228: $ RWORK( IDLMDA ), WORK, QSIZ, RWORK( IW ), 229: $ IWORK( INDXP ), IWORK( INDX ), INDXQ, 230: $ PERM( PRMPTR( CURR ) ), GIVPTR( CURR+1 ), 231: $ GIVCOL( 1, GIVPTR( CURR ) ), 232: $ GIVNUM( 1, GIVPTR( CURR ) ), INFO ) 233: PRMPTR( CURR+1 ) = PRMPTR( CURR ) + N 234: GIVPTR( CURR+1 ) = GIVPTR( CURR+1 ) + GIVPTR( CURR ) 235: * 236: * Solve Secular Equation. 237: * 238: IF( K.NE.0 ) THEN 239: CALL DLAED9( K, 1, K, N, D, RWORK( IQ ), K, RHO, 240: $ RWORK( IDLMDA ), RWORK( IW ), 241: $ QSTORE( QPTR( CURR ) ), K, INFO ) 242: CALL ZLACRM( QSIZ, K, WORK, QSIZ, QSTORE( QPTR( CURR ) ), K, Q, 243: $ LDQ, RWORK( IQ ) ) 244: QPTR( CURR+1 ) = QPTR( CURR ) + K**2 245: IF( INFO.NE.0 ) THEN 246: RETURN 247: END IF 248: * 249: * Prepare the INDXQ sorting premutation. 250: * 251: N1 = K 252: N2 = N - K 253: CALL DLAMRG( N1, N2, D, 1, -1, INDXQ ) 254: ELSE 255: QPTR( CURR+1 ) = QPTR( CURR ) 256: DO 20 I = 1, N 257: INDXQ( I ) = I 258: 20 CONTINUE 259: END IF 260: * 261: RETURN 262: * 263: * End of ZLAED7 264: * 265: END