Annotation of rpl/lapack/lapack/dlaed1.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE DLAED1( N, D, Q, LDQ, INDXQ, RHO, CUTPNT, WORK, IWORK,
! 2: $ INFO )
! 3: *
! 4: * -- LAPACK routine (version 3.2) --
! 5: * -- LAPACK is a software package provided by Univ. of Tennessee, --
! 6: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! 7: * November 2006
! 8: *
! 9: * .. Scalar Arguments ..
! 10: INTEGER CUTPNT, INFO, LDQ, N
! 11: DOUBLE PRECISION RHO
! 12: * ..
! 13: * .. Array Arguments ..
! 14: INTEGER INDXQ( * ), IWORK( * )
! 15: DOUBLE PRECISION D( * ), Q( LDQ, * ), WORK( * )
! 16: * ..
! 17: *
! 18: * Purpose
! 19: * =======
! 20: *
! 21: * DLAED1 computes the updated eigensystem of a diagonal
! 22: * matrix after modification by a rank-one symmetric matrix. This
! 23: * routine is used only for the eigenproblem which requires all
! 24: * eigenvalues and eigenvectors of a tridiagonal matrix. DLAED7 handles
! 25: * the case in which eigenvalues only or eigenvalues and eigenvectors
! 26: * of a full symmetric matrix (which was reduced to tridiagonal form)
! 27: * are desired.
! 28: *
! 29: * T = Q(in) ( D(in) + RHO * Z*Z' ) Q'(in) = Q(out) * D(out) * Q'(out)
! 30: *
! 31: * where Z = Q'u, u is a vector of length N with ones in the
! 32: * CUTPNT and CUTPNT + 1 th elements and zeros elsewhere.
! 33: *
! 34: * The eigenvectors of the original matrix are stored in Q, and the
! 35: * eigenvalues are in D. The algorithm consists of three stages:
! 36: *
! 37: * The first stage consists of deflating the size of the problem
! 38: * when there are multiple eigenvalues or if there is a zero in
! 39: * the Z vector. For each such occurence the dimension of the
! 40: * secular equation problem is reduced by one. This stage is
! 41: * performed by the routine DLAED2.
! 42: *
! 43: * The second stage consists of calculating the updated
! 44: * eigenvalues. This is done by finding the roots of the secular
! 45: * equation via the routine DLAED4 (as called by DLAED3).
! 46: * This routine also calculates the eigenvectors of the current
! 47: * problem.
! 48: *
! 49: * The final stage consists of computing the updated eigenvectors
! 50: * directly using the updated eigenvalues. The eigenvectors for
! 51: * the current problem are multiplied with the eigenvectors from
! 52: * the overall problem.
! 53: *
! 54: * Arguments
! 55: * =========
! 56: *
! 57: * N (input) INTEGER
! 58: * The dimension of the symmetric tridiagonal matrix. N >= 0.
! 59: *
! 60: * D (input/output) DOUBLE PRECISION array, dimension (N)
! 61: * On entry, the eigenvalues of the rank-1-perturbed matrix.
! 62: * On exit, the eigenvalues of the repaired matrix.
! 63: *
! 64: * Q (input/output) DOUBLE PRECISION array, dimension (LDQ,N)
! 65: * On entry, the eigenvectors of the rank-1-perturbed matrix.
! 66: * On exit, the eigenvectors of the repaired tridiagonal matrix.
! 67: *
! 68: * LDQ (input) INTEGER
! 69: * The leading dimension of the array Q. LDQ >= max(1,N).
! 70: *
! 71: * INDXQ (input/output) INTEGER array, dimension (N)
! 72: * On entry, the permutation which separately sorts the two
! 73: * subproblems in D into ascending order.
! 74: * On exit, the permutation which will reintegrate the
! 75: * subproblems back into sorted order,
! 76: * i.e. D( INDXQ( I = 1, N ) ) will be in ascending order.
! 77: *
! 78: * RHO (input) DOUBLE PRECISION
! 79: * The subdiagonal entry used to create the rank-1 modification.
! 80: *
! 81: * CUTPNT (input) INTEGER
! 82: * The location of the last eigenvalue in the leading sub-matrix.
! 83: * min(1,N) <= CUTPNT <= N/2.
! 84: *
! 85: * WORK (workspace) DOUBLE PRECISION array, dimension (4*N + N**2)
! 86: *
! 87: * IWORK (workspace) INTEGER array, dimension (4*N)
! 88: *
! 89: * INFO (output) INTEGER
! 90: * = 0: successful exit.
! 91: * < 0: if INFO = -i, the i-th argument had an illegal value.
! 92: * > 0: if INFO = 1, an eigenvalue did not converge
! 93: *
! 94: * Further Details
! 95: * ===============
! 96: *
! 97: * Based on contributions by
! 98: * Jeff Rutter, Computer Science Division, University of California
! 99: * at Berkeley, USA
! 100: * Modified by Francoise Tisseur, University of Tennessee.
! 101: *
! 102: * =====================================================================
! 103: *
! 104: * .. Local Scalars ..
! 105: INTEGER COLTYP, I, IDLMDA, INDX, INDXC, INDXP, IQ2, IS,
! 106: $ IW, IZ, K, N1, N2, ZPP1
! 107: * ..
! 108: * .. External Subroutines ..
! 109: EXTERNAL DCOPY, DLAED2, DLAED3, DLAMRG, XERBLA
! 110: * ..
! 111: * .. Intrinsic Functions ..
! 112: INTRINSIC MAX, MIN
! 113: * ..
! 114: * .. Executable Statements ..
! 115: *
! 116: * Test the input parameters.
! 117: *
! 118: INFO = 0
! 119: *
! 120: IF( N.LT.0 ) THEN
! 121: INFO = -1
! 122: ELSE IF( LDQ.LT.MAX( 1, N ) ) THEN
! 123: INFO = -4
! 124: ELSE IF( MIN( 1, N / 2 ).GT.CUTPNT .OR. ( N / 2 ).LT.CUTPNT ) THEN
! 125: INFO = -7
! 126: END IF
! 127: IF( INFO.NE.0 ) THEN
! 128: CALL XERBLA( 'DLAED1', -INFO )
! 129: RETURN
! 130: END IF
! 131: *
! 132: * Quick return if possible
! 133: *
! 134: IF( N.EQ.0 )
! 135: $ RETURN
! 136: *
! 137: * The following values are integer pointers which indicate
! 138: * the portion of the workspace
! 139: * used by a particular array in DLAED2 and DLAED3.
! 140: *
! 141: IZ = 1
! 142: IDLMDA = IZ + N
! 143: IW = IDLMDA + N
! 144: IQ2 = IW + N
! 145: *
! 146: INDX = 1
! 147: INDXC = INDX + N
! 148: COLTYP = INDXC + N
! 149: INDXP = COLTYP + N
! 150: *
! 151: *
! 152: * Form the z-vector which consists of the last row of Q_1 and the
! 153: * first row of Q_2.
! 154: *
! 155: CALL DCOPY( CUTPNT, Q( CUTPNT, 1 ), LDQ, WORK( IZ ), 1 )
! 156: ZPP1 = CUTPNT + 1
! 157: CALL DCOPY( N-CUTPNT, Q( ZPP1, ZPP1 ), LDQ, WORK( IZ+CUTPNT ), 1 )
! 158: *
! 159: * Deflate eigenvalues.
! 160: *
! 161: CALL DLAED2( K, N, CUTPNT, D, Q, LDQ, INDXQ, RHO, WORK( IZ ),
! 162: $ WORK( IDLMDA ), WORK( IW ), WORK( IQ2 ),
! 163: $ IWORK( INDX ), IWORK( INDXC ), IWORK( INDXP ),
! 164: $ IWORK( COLTYP ), INFO )
! 165: *
! 166: IF( INFO.NE.0 )
! 167: $ GO TO 20
! 168: *
! 169: * Solve Secular Equation.
! 170: *
! 171: IF( K.NE.0 ) THEN
! 172: IS = ( IWORK( COLTYP )+IWORK( COLTYP+1 ) )*CUTPNT +
! 173: $ ( IWORK( COLTYP+1 )+IWORK( COLTYP+2 ) )*( N-CUTPNT ) + IQ2
! 174: CALL DLAED3( K, N, CUTPNT, D, Q, LDQ, RHO, WORK( IDLMDA ),
! 175: $ WORK( IQ2 ), IWORK( INDXC ), IWORK( COLTYP ),
! 176: $ WORK( IW ), WORK( IS ), INFO )
! 177: IF( INFO.NE.0 )
! 178: $ GO TO 20
! 179: *
! 180: * Prepare the INDXQ sorting permutation.
! 181: *
! 182: N1 = K
! 183: N2 = N - K
! 184: CALL DLAMRG( N1, N2, D, 1, -1, INDXQ )
! 185: ELSE
! 186: DO 10 I = 1, N
! 187: INDXQ( I ) = I
! 188: 10 CONTINUE
! 189: END IF
! 190: *
! 191: 20 CONTINUE
! 192: RETURN
! 193: *
! 194: * End of DLAED1
! 195: *
! 196: END
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