Annotation of rpl/lapack/lapack/dlaed7.f, revision 1.1
1.1 ! bertrand 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
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