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219 lines
6.4 KiB
219 lines
6.4 KiB
/* dlasq1.f -- translated by f2c (version 20061008). |
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You must link the resulting object file with libf2c: |
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on Microsoft Windows system, link with libf2c.lib; |
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on Linux or Unix systems, link with .../path/to/libf2c.a -lm |
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or, if you install libf2c.a in a standard place, with -lf2c -lm |
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-- in that order, at the end of the command line, as in |
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cc *.o -lf2c -lm |
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Source for libf2c is in /netlib/f2c/libf2c.zip, e.g., |
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http://www.netlib.org/f2c/libf2c.zip |
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*/ |
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#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__2 = 2; |
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static integer c__0 = 0; |
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/* Subroutine */ int dlasq1_(integer *n, doublereal *d__, doublereal *e, |
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doublereal *work, integer *info) |
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{ |
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/* System generated locals */ |
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integer i__1, i__2; |
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doublereal d__1, d__2, d__3; |
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/* Builtin functions */ |
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double sqrt(doublereal); |
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/* Local variables */ |
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integer i__; |
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doublereal eps; |
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extern /* Subroutine */ int dlas2_(doublereal *, doublereal *, doublereal |
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*, doublereal *, doublereal *); |
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doublereal scale; |
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integer iinfo; |
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doublereal sigmn; |
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extern /* Subroutine */ int dcopy_(integer *, doublereal *, integer *, |
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doublereal *, integer *); |
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doublereal sigmx; |
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extern /* Subroutine */ int dlasq2_(integer *, doublereal *, integer *); |
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extern doublereal dlamch_(char *); |
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extern /* Subroutine */ int dlascl_(char *, integer *, integer *, |
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doublereal *, doublereal *, integer *, integer *, doublereal *, |
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integer *, integer *); |
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doublereal safmin; |
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extern /* Subroutine */ int xerbla_(char *, integer *), dlasrt_( |
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char *, integer *, doublereal *, integer *); |
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/* -- LAPACK routine (version 3.2) -- */ |
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/* -- Contributed by Osni Marques of the Lawrence Berkeley National -- */ |
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/* -- Laboratory and Beresford Parlett of the Univ. of California at -- */ |
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/* -- Berkeley -- */ |
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/* -- November 2008 -- */ |
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/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */ |
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/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */ |
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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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/* DLASQ1 computes the singular values of a real N-by-N bidiagonal */ |
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/* matrix with diagonal D and off-diagonal E. The singular values */ |
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/* are computed to high relative accuracy, in the absence of */ |
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/* denormalization, underflow and overflow. The algorithm was first */ |
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/* presented in */ |
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/* "Accurate singular values and differential qd algorithms" by K. V. */ |
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/* Fernando and B. N. Parlett, Numer. Math., Vol-67, No. 2, pp. 191-230, */ |
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/* 1994, */ |
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/* and the present implementation is described in "An implementation of */ |
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/* the dqds Algorithm (Positive Case)", LAPACK Working Note. */ |
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/* Arguments */ |
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/* ========= */ |
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/* N (input) INTEGER */ |
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/* The number of rows and columns in the matrix. N >= 0. */ |
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/* D (input/output) DOUBLE PRECISION array, dimension (N) */ |
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/* On entry, D contains the diagonal elements of the */ |
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/* bidiagonal matrix whose SVD is desired. On normal exit, */ |
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/* D contains the singular values in decreasing order. */ |
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/* E (input/output) DOUBLE PRECISION array, dimension (N) */ |
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/* On entry, elements E(1:N-1) contain the off-diagonal elements */ |
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/* of the bidiagonal matrix whose SVD is desired. */ |
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/* On exit, E is overwritten. */ |
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/* WORK (workspace) DOUBLE PRECISION 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: the algorithm failed */ |
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/* = 1, a split was marked by a positive value in E */ |
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/* = 2, current block of Z not diagonalized after 30*N */ |
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/* iterations (in inner while loop) */ |
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/* = 3, termination criterion of outer while loop not met */ |
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/* (program created more than N unreduced blocks) */ |
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/* ===================================================================== */ |
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/* .. Parameters .. */ |
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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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/* .. External Functions .. */ |
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/* .. */ |
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/* .. Intrinsic Functions .. */ |
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/* .. */ |
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/* .. Executable Statements .. */ |
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/* Parameter adjustments */ |
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--work; |
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--e; |
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--d__; |
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/* Function Body */ |
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*info = 0; |
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if (*n < 0) { |
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*info = -2; |
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i__1 = -(*info); |
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xerbla_("DLASQ1", &i__1); |
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return 0; |
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} else if (*n == 0) { |
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return 0; |
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} else if (*n == 1) { |
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d__[1] = abs(d__[1]); |
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return 0; |
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} else if (*n == 2) { |
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dlas2_(&d__[1], &e[1], &d__[2], &sigmn, &sigmx); |
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d__[1] = sigmx; |
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d__[2] = sigmn; |
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return 0; |
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} |
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/* Estimate the largest singular value. */ |
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sigmx = 0.; |
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i__1 = *n - 1; |
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for (i__ = 1; i__ <= i__1; ++i__) { |
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d__[i__] = (d__1 = d__[i__], abs(d__1)); |
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/* Computing MAX */ |
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d__2 = sigmx, d__3 = (d__1 = e[i__], abs(d__1)); |
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sigmx = max(d__2,d__3); |
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/* L10: */ |
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} |
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d__[*n] = (d__1 = d__[*n], abs(d__1)); |
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/* Early return if SIGMX is zero (matrix is already diagonal). */ |
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if (sigmx == 0.) { |
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dlasrt_("D", n, &d__[1], &iinfo); |
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return 0; |
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} |
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i__1 = *n; |
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for (i__ = 1; i__ <= i__1; ++i__) { |
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/* Computing MAX */ |
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d__1 = sigmx, d__2 = d__[i__]; |
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sigmx = max(d__1,d__2); |
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/* L20: */ |
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} |
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/* Copy D and E into WORK (in the Z format) and scale (squaring the */ |
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/* input data makes scaling by a power of the radix pointless). */ |
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eps = dlamch_("Precision"); |
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safmin = dlamch_("Safe minimum"); |
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scale = sqrt(eps / safmin); |
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dcopy_(n, &d__[1], &c__1, &work[1], &c__2); |
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i__1 = *n - 1; |
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dcopy_(&i__1, &e[1], &c__1, &work[2], &c__2); |
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i__1 = (*n << 1) - 1; |
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i__2 = (*n << 1) - 1; |
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dlascl_("G", &c__0, &c__0, &sigmx, &scale, &i__1, &c__1, &work[1], &i__2, |
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&iinfo); |
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/* Compute the q's and e's. */ |
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i__1 = (*n << 1) - 1; |
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for (i__ = 1; i__ <= i__1; ++i__) { |
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/* Computing 2nd power */ |
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d__1 = work[i__]; |
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work[i__] = d__1 * d__1; |
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/* L30: */ |
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} |
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work[*n * 2] = 0.; |
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dlasq2_(n, &work[1], info); |
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if (*info == 0) { |
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i__1 = *n; |
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for (i__ = 1; i__ <= i__1; ++i__) { |
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d__[i__] = sqrt(work[i__]); |
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/* L40: */ |
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} |
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dlascl_("G", &c__0, &c__0, &scale, &sigmx, n, &c__1, &d__[1], n, & |
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iinfo); |
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} |
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return 0; |
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/* End of DLASQ1 */ |
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} /* dlasq1_ */
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