/* claed7.f -- translated by f2c (version 20061008). You must link the resulting object file with libf2c: on Microsoft Windows system, link with libf2c.lib; on Linux or Unix systems, link with .../path/to/libf2c.a -lm or, if you install libf2c.a in a standard place, with -lf2c -lm -- in that order, at the end of the command line, as in cc *.o -lf2c -lm Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., http://www.netlib.org/f2c/libf2c.zip */ #include "f2c.h" #include "blaswrap.h" /* Table of constant values */ static integer c__2 = 2; static integer c__1 = 1; static integer c_n1 = -1; /* Subroutine */ int claed7_(integer *n, integer *cutpnt, integer *qsiz, integer *tlvls, integer *curlvl, integer *curpbm, real *d__, complex * q, integer *ldq, real *rho, integer *indxq, real *qstore, integer * qptr, integer *prmptr, integer *perm, integer *givptr, integer * givcol, real *givnum, complex *work, real *rwork, integer *iwork, integer *info) { /* System generated locals */ integer q_dim1, q_offset, i__1, i__2; /* Builtin functions */ integer pow_ii(integer *, integer *); /* Local variables */ integer i__, k, n1, n2, iq, iw, iz, ptr, indx, curr, indxc, indxp; extern /* Subroutine */ int claed8_(integer *, integer *, integer *, complex *, integer *, real *, real *, integer *, real *, real *, complex *, integer *, real *, integer *, integer *, integer *, integer *, integer *, integer *, real *, integer *), slaed9_( integer *, integer *, integer *, integer *, real *, real *, integer *, real *, real *, real *, real *, integer *, integer *), slaeda_(integer *, integer *, integer *, integer *, integer *, integer *, integer *, integer *, real *, real *, integer *, real * , real *, integer *); integer idlmda; extern /* Subroutine */ int clacrm_(integer *, integer *, complex *, integer *, real *, integer *, complex *, integer *, real *), xerbla_(char *, integer *), slamrg_(integer *, integer *, real *, integer *, integer *, integer *); integer coltyp; /* -- LAPACK routine (version 3.2) -- */ /* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ /* November 2006 */ /* .. Scalar Arguments .. */ /* .. */ /* .. Array Arguments .. */ /* .. */ /* Purpose */ /* ======= */ /* CLAED7 computes the updated eigensystem of a diagonal */ /* matrix after modification by a rank-one symmetric matrix. This */ /* routine is used only for the eigenproblem which requires all */ /* eigenvalues and optionally eigenvectors of a dense or banded */ /* Hermitian matrix that has been reduced to tridiagonal form. */ /* T = Q(in) ( D(in) + RHO * Z*Z' ) Q'(in) = Q(out) * D(out) * Q'(out) */ /* where Z = Q'u, u is a vector of length N with ones in the */ /* CUTPNT and CUTPNT + 1 th elements and zeros elsewhere. */ /* The eigenvectors of the original matrix are stored in Q, and the */ /* eigenvalues are in D. The algorithm consists of three stages: */ /* The first stage consists of deflating the size of the problem */ /* when there are multiple eigenvalues or if there is a zero in */ /* the Z vector. For each such occurence the dimension of the */ /* secular equation problem is reduced by one. This stage is */ /* performed by the routine SLAED2. */ /* The second stage consists of calculating the updated */ /* eigenvalues. This is done by finding the roots of the secular */ /* equation via the routine SLAED4 (as called by SLAED3). */ /* This routine also calculates the eigenvectors of the current */ /* problem. */ /* The final stage consists of computing the updated eigenvectors */ /* directly using the updated eigenvalues. The eigenvectors for */ /* the current problem are multiplied with the eigenvectors from */ /* the overall problem. */ /* Arguments */ /* ========= */ /* N (input) INTEGER */ /* The dimension of the symmetric tridiagonal matrix. N >= 0. */ /* CUTPNT (input) INTEGER */ /* Contains the location of the last eigenvalue in the leading */ /* sub-matrix. min(1,N) <= CUTPNT <= N. */ /* QSIZ (input) INTEGER */ /* The dimension of the unitary matrix used to reduce */ /* the full matrix to tridiagonal form. QSIZ >= N. */ /* TLVLS (input) INTEGER */ /* The total number of merging levels in the overall divide and */ /* conquer tree. */ /* CURLVL (input) INTEGER */ /* The current level in the overall merge routine, */ /* 0 <= curlvl <= tlvls. */ /* CURPBM (input) INTEGER */ /* The current problem in the current level in the overall */ /* merge routine (counting from upper left to lower right). */ /* D (input/output) REAL array, dimension (N) */ /* On entry, the eigenvalues of the rank-1-perturbed matrix. */ /* On exit, the eigenvalues of the repaired matrix. */ /* Q (input/output) COMPLEX array, dimension (LDQ,N) */ /* On entry, the eigenvectors of the rank-1-perturbed matrix. */ /* On exit, the eigenvectors of the repaired tridiagonal matrix. */ /* LDQ (input) INTEGER */ /* The leading dimension of the array Q. LDQ >= max(1,N). */ /* RHO (input) REAL */ /* Contains the subdiagonal element used to create the rank-1 */ /* modification. */ /* INDXQ (output) INTEGER array, dimension (N) */ /* This contains the permutation which will reintegrate the */ /* subproblem just solved back into sorted order, */ /* ie. D( INDXQ( I = 1, N ) ) will be in ascending order. */ /* IWORK (workspace) INTEGER array, dimension (4*N) */ /* RWORK (workspace) REAL array, */ /* dimension (3*N+2*QSIZ*N) */ /* WORK (workspace) COMPLEX array, dimension (QSIZ*N) */ /* QSTORE (input/output) REAL array, dimension (N**2+1) */ /* Stores eigenvectors of submatrices encountered during */ /* divide and conquer, packed together. QPTR points to */ /* beginning of the submatrices. */ /* QPTR (input/output) INTEGER array, dimension (N+2) */ /* List of indices pointing to beginning of submatrices stored */ /* in QSTORE. The submatrices are numbered starting at the */ /* bottom left of the divide and conquer tree, from left to */ /* right and bottom to top. */ /* PRMPTR (input) INTEGER array, dimension (N lg N) */ /* Contains a list of pointers which indicate where in PERM a */ /* level's permutation is stored. PRMPTR(i+1) - PRMPTR(i) */ /* indicates the size of the permutation and also the size of */ /* the full, non-deflated problem. */ /* PERM (input) INTEGER array, dimension (N lg N) */ /* Contains the permutations (from deflation and sorting) to be */ /* applied to each eigenblock. */ /* GIVPTR (input) INTEGER array, dimension (N lg N) */ /* Contains a list of pointers which indicate where in GIVCOL a */ /* level's Givens rotations are stored. GIVPTR(i+1) - GIVPTR(i) */ /* indicates the number of Givens rotations. */ /* GIVCOL (input) INTEGER array, dimension (2, N lg N) */ /* Each pair of numbers indicates a pair of columns to take place */ /* in a Givens rotation. */ /* GIVNUM (input) REAL array, dimension (2, N lg N) */ /* Each number indicates the S value to be used in the */ /* corresponding Givens rotation. */ /* INFO (output) INTEGER */ /* = 0: successful exit. */ /* < 0: if INFO = -i, the i-th argument had an illegal value. */ /* > 0: if INFO = 1, an eigenvalue did not converge */ /* ===================================================================== */ /* .. Local Scalars .. */ /* .. */ /* .. External Subroutines .. */ /* .. */ /* .. Intrinsic Functions .. */ /* .. */ /* .. Executable Statements .. */ /* Test the input parameters. */ /* Parameter adjustments */ --d__; q_dim1 = *ldq; q_offset = 1 + q_dim1; q -= q_offset; --indxq; --qstore; --qptr; --prmptr; --perm; --givptr; givcol -= 3; givnum -= 3; --work; --rwork; --iwork; /* Function Body */ *info = 0; /* IF( ICOMPQ.LT.0 .OR. ICOMPQ.GT.1 ) THEN */ /* INFO = -1 */ /* ELSE IF( N.LT.0 ) THEN */ if (*n < 0) { *info = -1; } else if (min(1,*n) > *cutpnt || *n < *cutpnt) { *info = -2; } else if (*qsiz < *n) { *info = -3; } else if (*ldq < max(1,*n)) { *info = -9; } if (*info != 0) { i__1 = -(*info); xerbla_("CLAED7", &i__1); return 0; } /* Quick return if possible */ if (*n == 0) { return 0; } /* The following values are for bookkeeping purposes only. They are */ /* integer pointers which indicate the portion of the workspace */ /* used by a particular array in SLAED2 and SLAED3. */ iz = 1; idlmda = iz + *n; iw = idlmda + *n; iq = iw + *n; indx = 1; indxc = indx + *n; coltyp = indxc + *n; indxp = coltyp + *n; /* Form the z-vector which consists of the last row of Q_1 and the */ /* first row of Q_2. */ ptr = pow_ii(&c__2, tlvls) + 1; i__1 = *curlvl - 1; for (i__ = 1; i__ <= i__1; ++i__) { i__2 = *tlvls - i__; ptr += pow_ii(&c__2, &i__2); /* L10: */ } curr = ptr + *curpbm; slaeda_(n, tlvls, curlvl, curpbm, &prmptr[1], &perm[1], &givptr[1], & givcol[3], &givnum[3], &qstore[1], &qptr[1], &rwork[iz], &rwork[ iz + *n], info); /* When solving the final problem, we no longer need the stored data, */ /* so we will overwrite the data from this level onto the previously */ /* used storage space. */ if (*curlvl == *tlvls) { qptr[curr] = 1; prmptr[curr] = 1; givptr[curr] = 1; } /* Sort and Deflate eigenvalues. */ claed8_(&k, n, qsiz, &q[q_offset], ldq, &d__[1], rho, cutpnt, &rwork[iz], &rwork[idlmda], &work[1], qsiz, &rwork[iw], &iwork[indxp], &iwork[ indx], &indxq[1], &perm[prmptr[curr]], &givptr[curr + 1], &givcol[ (givptr[curr] << 1) + 1], &givnum[(givptr[curr] << 1) + 1], info); prmptr[curr + 1] = prmptr[curr] + *n; givptr[curr + 1] += givptr[curr]; /* Solve Secular Equation. */ if (k != 0) { slaed9_(&k, &c__1, &k, n, &d__[1], &rwork[iq], &k, rho, &rwork[idlmda] , &rwork[iw], &qstore[qptr[curr]], &k, info); clacrm_(qsiz, &k, &work[1], qsiz, &qstore[qptr[curr]], &k, &q[ q_offset], ldq, &rwork[iq]); /* Computing 2nd power */ i__1 = k; qptr[curr + 1] = qptr[curr] + i__1 * i__1; if (*info != 0) { return 0; } /* Prepare the INDXQ sorting premutation. */ n1 = k; n2 = *n - k; slamrg_(&n1, &n2, &d__[1], &c__1, &c_n1, &indxq[1]); } else { qptr[curr + 1] = qptr[curr]; i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { indxq[i__] = i__; /* L20: */ } } return 0; /* End of CLAED7 */ } /* claed7_ */