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236 lines
7.4 KiB
236 lines
7.4 KiB
#include "clapack.h" |
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/* Table of constant values */ |
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static integer c__1 = 1; |
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static integer c_n1 = -1; |
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/* Subroutine */ int dlaed1_(integer *n, doublereal *d__, doublereal *q, |
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integer *ldq, integer *indxq, doublereal *rho, integer *cutpnt, |
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doublereal *work, integer *iwork, integer *info) |
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{ |
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/* System generated locals */ |
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integer q_dim1, q_offset, i__1, i__2; |
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/* Local variables */ |
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integer i__, k, n1, n2, is, iw, iz, iq2, zpp1, indx, indxc; |
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extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *, |
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doublereal *, integer *); |
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integer indxp; |
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extern /* Subroutine */ int dlaed2_(integer *, integer *, integer *, |
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doublereal *, doublereal *, integer *, integer *, doublereal *, |
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doublereal *, doublereal *, doublereal *, doublereal *, integer *, |
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integer *, integer *, integer *, integer *), dlaed3_(integer *, |
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integer *, integer *, doublereal *, doublereal *, integer *, |
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doublereal *, doublereal *, doublereal *, integer *, integer *, |
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doublereal *, doublereal *, integer *); |
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integer idlmda; |
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extern /* Subroutine */ int dlamrg_(integer *, integer *, doublereal *, |
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integer *, integer *, integer *), xerbla_(char *, integer *); |
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integer coltyp; |
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/* -- LAPACK routine (version 3.1) -- */ |
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/* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ |
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/* November 2006 */ |
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/* .. Scalar Arguments .. */ |
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/* .. */ |
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/* .. Array Arguments .. */ |
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/* .. */ |
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/* Purpose */ |
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/* ======= */ |
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/* DLAED1 computes the updated eigensystem of a diagonal */ |
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/* matrix after modification by a rank-one symmetric matrix. This */ |
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/* routine is used only for the eigenproblem which requires all */ |
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/* eigenvalues and eigenvectors of a tridiagonal matrix. DLAED7 handles */ |
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/* the case in which eigenvalues only or eigenvalues and eigenvectors */ |
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/* of a full symmetric matrix (which was reduced to tridiagonal form) */ |
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/* are desired. */ |
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/* T = Q(in) ( D(in) + RHO * Z*Z' ) Q'(in) = Q(out) * D(out) * Q'(out) */ |
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/* where Z = Q'u, u is a vector of length N with ones in the */ |
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/* CUTPNT and CUTPNT + 1 th elements and zeros elsewhere. */ |
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/* The eigenvectors of the original matrix are stored in Q, and the */ |
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/* eigenvalues are in D. The algorithm consists of three stages: */ |
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/* The first stage consists of deflating the size of the problem */ |
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/* when there are multiple eigenvalues or if there is a zero in */ |
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/* the Z vector. For each such occurence the dimension of the */ |
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/* secular equation problem is reduced by one. This stage is */ |
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/* performed by the routine DLAED2. */ |
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/* The second stage consists of calculating the updated */ |
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/* eigenvalues. This is done by finding the roots of the secular */ |
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/* equation via the routine DLAED4 (as called by DLAED3). */ |
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/* This routine also calculates the eigenvectors of the current */ |
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/* problem. */ |
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/* The final stage consists of computing the updated eigenvectors */ |
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/* directly using the updated eigenvalues. The eigenvectors for */ |
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/* the current problem are multiplied with the eigenvectors from */ |
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/* the overall problem. */ |
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/* Arguments */ |
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/* ========= */ |
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/* N (input) INTEGER */ |
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/* The dimension of the symmetric tridiagonal matrix. N >= 0. */ |
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/* D (input/output) DOUBLE PRECISION array, dimension (N) */ |
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/* On entry, the eigenvalues of the rank-1-perturbed matrix. */ |
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/* On exit, the eigenvalues of the repaired matrix. */ |
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/* Q (input/output) DOUBLE PRECISION array, dimension (LDQ,N) */ |
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/* On entry, the eigenvectors of the rank-1-perturbed matrix. */ |
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/* On exit, the eigenvectors of the repaired tridiagonal matrix. */ |
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/* LDQ (input) INTEGER */ |
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/* The leading dimension of the array Q. LDQ >= max(1,N). */ |
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/* INDXQ (input/output) INTEGER array, dimension (N) */ |
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/* On entry, the permutation which separately sorts the two */ |
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/* subproblems in D into ascending order. */ |
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/* On exit, the permutation which will reintegrate the */ |
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/* subproblems back into sorted order, */ |
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/* i.e. D( INDXQ( I = 1, N ) ) will be in ascending order. */ |
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/* RHO (input) DOUBLE PRECISION */ |
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/* The subdiagonal entry used to create the rank-1 modification. */ |
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/* CUTPNT (input) INTEGER */ |
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/* The location of the last eigenvalue in the leading sub-matrix. */ |
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/* min(1,N) <= CUTPNT <= N/2. */ |
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/* WORK (workspace) DOUBLE PRECISION array, dimension (4*N + N**2) */ |
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/* IWORK (workspace) INTEGER array, dimension (4*N) */ |
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/* INFO (output) INTEGER */ |
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/* = 0: successful exit. */ |
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/* < 0: if INFO = -i, the i-th argument had an illegal value. */ |
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/* > 0: if INFO = 1, an eigenvalue did not converge */ |
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/* Further Details */ |
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/* =============== */ |
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/* Based on contributions by */ |
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/* Jeff Rutter, Computer Science Division, University of California */ |
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/* at Berkeley, USA */ |
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/* Modified by Francoise Tisseur, University of Tennessee. */ |
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/* ===================================================================== */ |
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/* .. Local Scalars .. */ |
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/* .. */ |
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/* .. External Subroutines .. */ |
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/* .. */ |
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/* .. Intrinsic Functions .. */ |
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/* .. */ |
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/* .. Executable Statements .. */ |
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/* Test the input parameters. */ |
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/* Parameter adjustments */ |
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--d__; |
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q_dim1 = *ldq; |
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q_offset = 1 + q_dim1; |
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q -= q_offset; |
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--indxq; |
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--work; |
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--iwork; |
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/* Function Body */ |
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*info = 0; |
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if (*n < 0) { |
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*info = -1; |
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} else if (*ldq < max(1,*n)) { |
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*info = -4; |
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} else /* if(complicated condition) */ { |
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/* Computing MIN */ |
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i__1 = 1, i__2 = *n / 2; |
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if (min(i__1,i__2) > *cutpnt || *n / 2 < *cutpnt) { |
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*info = -7; |
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} |
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} |
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if (*info != 0) { |
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i__1 = -(*info); |
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xerbla_("DLAED1", &i__1); |
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return 0; |
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} |
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/* Quick return if possible */ |
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if (*n == 0) { |
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return 0; |
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} |
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/* The following values are integer pointers which indicate */ |
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/* the portion of the workspace */ |
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/* used by a particular array in DLAED2 and DLAED3. */ |
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iz = 1; |
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idlmda = iz + *n; |
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iw = idlmda + *n; |
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iq2 = iw + *n; |
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indx = 1; |
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indxc = indx + *n; |
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coltyp = indxc + *n; |
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indxp = coltyp + *n; |
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/* Form the z-vector which consists of the last row of Q_1 and the */ |
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/* first row of Q_2. */ |
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dcopy_(cutpnt, &q[*cutpnt + q_dim1], ldq, &work[iz], &c__1); |
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zpp1 = *cutpnt + 1; |
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i__1 = *n - *cutpnt; |
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dcopy_(&i__1, &q[zpp1 + zpp1 * q_dim1], ldq, &work[iz + *cutpnt], &c__1); |
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/* Deflate eigenvalues. */ |
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dlaed2_(&k, n, cutpnt, &d__[1], &q[q_offset], ldq, &indxq[1], rho, &work[ |
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iz], &work[idlmda], &work[iw], &work[iq2], &iwork[indx], &iwork[ |
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indxc], &iwork[indxp], &iwork[coltyp], info); |
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if (*info != 0) { |
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goto L20; |
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} |
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/* Solve Secular Equation. */ |
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if (k != 0) { |
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is = (iwork[coltyp] + iwork[coltyp + 1]) * *cutpnt + (iwork[coltyp + |
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1] + iwork[coltyp + 2]) * (*n - *cutpnt) + iq2; |
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dlaed3_(&k, n, cutpnt, &d__[1], &q[q_offset], ldq, rho, &work[idlmda], |
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&work[iq2], &iwork[indxc], &iwork[coltyp], &work[iw], &work[ |
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is], info); |
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if (*info != 0) { |
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goto L20; |
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} |
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/* Prepare the INDXQ sorting permutation. */ |
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n1 = k; |
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n2 = *n - k; |
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dlamrg_(&n1, &n2, &d__[1], &c__1, &c_n1, &indxq[1]); |
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} else { |
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i__1 = *n; |
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for (i__ = 1; i__ <= i__1; ++i__) { |
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indxq[i__] = i__; |
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/* L10: */ |
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} |
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} |
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L20: |
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return 0; |
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/* End of DLAED1 */ |
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} /* dlaed1_ */
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