Annotation of rpl/lapack/lapack/zlaed7.f, revision 1.1
1.1 ! bertrand 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
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