#include "clapack.h" /* Table of constant values */ static integer c__9 = 9; static integer c__0 = 0; static integer c__2 = 2; static doublereal c_b23 = 1.; static doublereal c_b24 = 0.; static integer c__1 = 1; /* Subroutine */ int dlaed0_(integer *icompq, integer *qsiz, integer *n, doublereal *d__, doublereal *e, doublereal *q, integer *ldq, doublereal *qstore, integer *ldqs, doublereal *work, integer *iwork, integer *info) { /* System generated locals */ integer q_dim1, q_offset, qstore_dim1, qstore_offset, i__1, i__2; doublereal d__1; /* Builtin functions */ double log(doublereal); integer pow_ii(integer *, integer *); /* Local variables */ integer i__, j, k, iq, lgn, msd2, smm1, spm1, spm2; doublereal temp; integer curr; extern /* Subroutine */ int dgemm_(char *, char *, integer *, integer *, integer *, doublereal *, doublereal *, integer *, doublereal *, integer *, doublereal *, doublereal *, integer *); integer iperm; extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *, doublereal *, integer *); integer indxq, iwrem; extern /* Subroutine */ int dlaed1_(integer *, doublereal *, doublereal *, integer *, integer *, doublereal *, integer *, doublereal *, integer *, integer *); integer iqptr; extern /* Subroutine */ int dlaed7_(integer *, integer *, integer *, integer *, integer *, integer *, doublereal *, doublereal *, integer *, integer *, doublereal *, integer *, doublereal *, integer *, integer *, integer *, integer *, integer *, doublereal *, doublereal *, integer *, integer *); integer tlvls; extern /* Subroutine */ int dlacpy_(char *, integer *, integer *, doublereal *, integer *, doublereal *, integer *); integer igivcl; extern /* Subroutine */ int xerbla_(char *, integer *); extern integer ilaenv_(integer *, char *, char *, integer *, integer *, integer *, integer *); integer igivnm, submat, curprb, subpbs, igivpt; extern /* Subroutine */ int dsteqr_(char *, integer *, doublereal *, doublereal *, doublereal *, integer *, doublereal *, integer *); integer curlvl, matsiz, iprmpt, smlsiz; /* -- LAPACK routine (version 3.1) -- */ /* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ /* November 2006 */ /* .. Scalar Arguments .. */ /* .. */ /* .. Array Arguments .. */ /* .. */ /* Purpose */ /* ======= */ /* DLAED0 computes all eigenvalues and corresponding eigenvectors of a */ /* symmetric tridiagonal matrix using the divide and conquer method. */ /* Arguments */ /* ========= */ /* ICOMPQ (input) INTEGER */ /* = 0: Compute eigenvalues only. */ /* = 1: Compute eigenvectors of original dense symmetric matrix */ /* also. On entry, Q contains the orthogonal matrix used */ /* to reduce the original matrix to tridiagonal form. */ /* = 2: Compute eigenvalues and eigenvectors of tridiagonal */ /* matrix. */ /* QSIZ (input) INTEGER */ /* The dimension of the orthogonal matrix used to reduce */ /* the full matrix to tridiagonal form. QSIZ >= N if ICOMPQ = 1. */ /* N (input) INTEGER */ /* The dimension of the symmetric tridiagonal matrix. N >= 0. */ /* D (input/output) DOUBLE PRECISION array, dimension (N) */ /* On entry, the main diagonal of the tridiagonal matrix. */ /* On exit, its eigenvalues. */ /* E (input) DOUBLE PRECISION array, dimension (N-1) */ /* The off-diagonal elements of the tridiagonal matrix. */ /* On exit, E has been destroyed. */ /* Q (input/output) DOUBLE PRECISION array, dimension (LDQ, N) */ /* On entry, Q must contain an N-by-N orthogonal matrix. */ /* If ICOMPQ = 0 Q is not referenced. */ /* If ICOMPQ = 1 On entry, Q is a subset of the columns of the */ /* orthogonal matrix used to reduce the full */ /* matrix to tridiagonal form corresponding to */ /* the subset of the full matrix which is being */ /* decomposed at this time. */ /* If ICOMPQ = 2 On entry, Q will be the identity matrix. */ /* On exit, Q contains the eigenvectors of the */ /* tridiagonal matrix. */ /* LDQ (input) INTEGER */ /* The leading dimension of the array Q. If eigenvectors are */ /* desired, then LDQ >= max(1,N). In any case, LDQ >= 1. */ /* QSTORE (workspace) DOUBLE PRECISION array, dimension (LDQS, N) */ /* Referenced only when ICOMPQ = 1. Used to store parts of */ /* the eigenvector matrix when the updating matrix multiplies */ /* take place. */ /* LDQS (input) INTEGER */ /* The leading dimension of the array QSTORE. If ICOMPQ = 1, */ /* then LDQS >= max(1,N). In any case, LDQS >= 1. */ /* WORK (workspace) DOUBLE PRECISION array, */ /* If ICOMPQ = 0 or 1, the dimension of WORK must be at least */ /* 1 + 3*N + 2*N*lg N + 2*N**2 */ /* ( lg( N ) = smallest integer k */ /* such that 2^k >= N ) */ /* If ICOMPQ = 2, the dimension of WORK must be at least */ /* 4*N + N**2. */ /* IWORK (workspace) INTEGER array, */ /* If ICOMPQ = 0 or 1, the dimension of IWORK must be at least */ /* 6 + 6*N + 5*N*lg N. */ /* ( lg( N ) = smallest integer k */ /* such that 2^k >= N ) */ /* If ICOMPQ = 2, the dimension of IWORK must be at least */ /* 3 + 5*N. */ /* INFO (output) INTEGER */ /* = 0: successful exit. */ /* < 0: if INFO = -i, the i-th argument had an illegal value. */ /* > 0: The algorithm failed to compute an eigenvalue while */ /* working on the submatrix lying in rows and columns */ /* INFO/(N+1) through mod(INFO,N+1). */ /* Further Details */ /* =============== */ /* Based on contributions by */ /* Jeff Rutter, Computer Science Division, University of California */ /* at Berkeley, USA */ /* ===================================================================== */ /* .. Parameters .. */ /* .. */ /* .. Local Scalars .. */ /* .. */ /* .. External Subroutines .. */ /* .. */ /* .. External Functions .. */ /* .. */ /* .. Intrinsic Functions .. */ /* .. */ /* .. Executable Statements .. */ /* Test the input parameters. */ /* Parameter adjustments */ --d__; --e; q_dim1 = *ldq; q_offset = 1 + q_dim1; q -= q_offset; qstore_dim1 = *ldqs; qstore_offset = 1 + qstore_dim1; qstore -= qstore_offset; --work; --iwork; /* Function Body */ *info = 0; if (*icompq < 0 || *icompq > 2) { *info = -1; } else if (*icompq == 1 && *qsiz < max(0,*n)) { *info = -2; } else if (*n < 0) { *info = -3; } else if (*ldq < max(1,*n)) { *info = -7; } else if (*ldqs < max(1,*n)) { *info = -9; } if (*info != 0) { i__1 = -(*info); xerbla_("DLAED0", &i__1); return 0; } /* Quick return if possible */ if (*n == 0) { return 0; } smlsiz = ilaenv_(&c__9, "DLAED0", " ", &c__0, &c__0, &c__0, &c__0); /* Determine the size and placement of the submatrices, and save in */ /* the leading elements of IWORK. */ iwork[1] = *n; subpbs = 1; tlvls = 0; L10: if (iwork[subpbs] > smlsiz) { for (j = subpbs; j >= 1; --j) { iwork[j * 2] = (iwork[j] + 1) / 2; iwork[(j << 1) - 1] = iwork[j] / 2; /* L20: */ } ++tlvls; subpbs <<= 1; goto L10; } i__1 = subpbs; for (j = 2; j <= i__1; ++j) { iwork[j] += iwork[j - 1]; /* L30: */ } /* Divide the matrix into SUBPBS submatrices of size at most SMLSIZ+1 */ /* using rank-1 modifications (cuts). */ spm1 = subpbs - 1; i__1 = spm1; for (i__ = 1; i__ <= i__1; ++i__) { submat = iwork[i__] + 1; smm1 = submat - 1; d__[smm1] -= (d__1 = e[smm1], abs(d__1)); d__[submat] -= (d__1 = e[smm1], abs(d__1)); /* L40: */ } indxq = (*n << 2) + 3; if (*icompq != 2) { /* Set up workspaces for eigenvalues only/accumulate new vectors */ /* routine */ temp = log((doublereal) (*n)) / log(2.); lgn = (integer) temp; if (pow_ii(&c__2, &lgn) < *n) { ++lgn; } if (pow_ii(&c__2, &lgn) < *n) { ++lgn; } iprmpt = indxq + *n + 1; iperm = iprmpt + *n * lgn; iqptr = iperm + *n * lgn; igivpt = iqptr + *n + 2; igivcl = igivpt + *n * lgn; igivnm = 1; iq = igivnm + (*n << 1) * lgn; /* Computing 2nd power */ i__1 = *n; iwrem = iq + i__1 * i__1 + 1; /* Initialize pointers */ i__1 = subpbs; for (i__ = 0; i__ <= i__1; ++i__) { iwork[iprmpt + i__] = 1; iwork[igivpt + i__] = 1; /* L50: */ } iwork[iqptr] = 1; } /* Solve each submatrix eigenproblem at the bottom of the divide and */ /* conquer tree. */ curr = 0; i__1 = spm1; for (i__ = 0; i__ <= i__1; ++i__) { if (i__ == 0) { submat = 1; matsiz = iwork[1]; } else { submat = iwork[i__] + 1; matsiz = iwork[i__ + 1] - iwork[i__]; } if (*icompq == 2) { dsteqr_("I", &matsiz, &d__[submat], &e[submat], &q[submat + submat * q_dim1], ldq, &work[1], info); if (*info != 0) { goto L130; } } else { dsteqr_("I", &matsiz, &d__[submat], &e[submat], &work[iq - 1 + iwork[iqptr + curr]], &matsiz, &work[1], info); if (*info != 0) { goto L130; } if (*icompq == 1) { dgemm_("N", "N", qsiz, &matsiz, &matsiz, &c_b23, &q[submat * q_dim1 + 1], ldq, &work[iq - 1 + iwork[iqptr + curr]], &matsiz, &c_b24, &qstore[submat * qstore_dim1 + 1], ldqs); } /* Computing 2nd power */ i__2 = matsiz; iwork[iqptr + curr + 1] = iwork[iqptr + curr] + i__2 * i__2; ++curr; } k = 1; i__2 = iwork[i__ + 1]; for (j = submat; j <= i__2; ++j) { iwork[indxq + j] = k; ++k; /* L60: */ } /* L70: */ } /* Successively merge eigensystems of adjacent submatrices */ /* into eigensystem for the corresponding larger matrix. */ /* while ( SUBPBS > 1 ) */ curlvl = 1; L80: if (subpbs > 1) { spm2 = subpbs - 2; i__1 = spm2; for (i__ = 0; i__ <= i__1; i__ += 2) { if (i__ == 0) { submat = 1; matsiz = iwork[2]; msd2 = iwork[1]; curprb = 0; } else { submat = iwork[i__] + 1; matsiz = iwork[i__ + 2] - iwork[i__]; msd2 = matsiz / 2; ++curprb; } /* Merge lower order eigensystems (of size MSD2 and MATSIZ - MSD2) */ /* into an eigensystem of size MATSIZ. */ /* DLAED1 is used only for the full eigensystem of a tridiagonal */ /* matrix. */ /* DLAED7 handles the cases in which eigenvalues only or eigenvalues */ /* and eigenvectors of a full symmetric matrix (which was reduced to */ /* tridiagonal form) are desired. */ if (*icompq == 2) { dlaed1_(&matsiz, &d__[submat], &q[submat + submat * q_dim1], ldq, &iwork[indxq + submat], &e[submat + msd2 - 1], & msd2, &work[1], &iwork[subpbs + 1], info); } else { dlaed7_(icompq, &matsiz, qsiz, &tlvls, &curlvl, &curprb, &d__[ submat], &qstore[submat * qstore_dim1 + 1], ldqs, & iwork[indxq + submat], &e[submat + msd2 - 1], &msd2, & work[iq], &iwork[iqptr], &iwork[iprmpt], &iwork[iperm] , &iwork[igivpt], &iwork[igivcl], &work[igivnm], & work[iwrem], &iwork[subpbs + 1], info); } if (*info != 0) { goto L130; } iwork[i__ / 2 + 1] = iwork[i__ + 2]; /* L90: */ } subpbs /= 2; ++curlvl; goto L80; } /* end while */ /* Re-merge the eigenvalues/vectors which were deflated at the final */ /* merge step. */ if (*icompq == 1) { i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { j = iwork[indxq + i__]; work[i__] = d__[j]; dcopy_(qsiz, &qstore[j * qstore_dim1 + 1], &c__1, &q[i__ * q_dim1 + 1], &c__1); /* L100: */ } dcopy_(n, &work[1], &c__1, &d__[1], &c__1); } else if (*icompq == 2) { i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { j = iwork[indxq + i__]; work[i__] = d__[j]; dcopy_(n, &q[j * q_dim1 + 1], &c__1, &work[*n * i__ + 1], &c__1); /* L110: */ } dcopy_(n, &work[1], &c__1, &d__[1], &c__1); dlacpy_("A", n, n, &work[*n + 1], n, &q[q_offset], ldq); } else { i__1 = *n; for (i__ = 1; i__ <= i__1; ++i__) { j = iwork[indxq + i__]; work[i__] = d__[j]; /* L120: */ } dcopy_(n, &work[1], &c__1, &d__[1], &c__1); } goto L140; L130: *info = submat * (*n + 1) + submat + matsiz - 1; L140: return 0; /* End of DLAED0 */ } /* dlaed0_ */