#include "blaswrap.h" /* slaeda.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" /* Table of constant values */ static integer c__2 = 2; static integer c__1 = 1; static real c_b24 = 1.f; static real c_b26 = 0.f; /* Subroutine */ int slaeda_(integer *n, integer *tlvls, integer *curlvl, integer *curpbm, integer *prmptr, integer *perm, integer *givptr, integer *givcol, real *givnum, real *q, integer *qptr, real *z__, real *ztemp, integer *info) { /* System generated locals */ integer i__1, i__2, i__3; /* Builtin functions */ integer pow_ii(integer *, integer *); double sqrt(doublereal); /* Local variables */ static integer i__, k, mid, ptr, curr; extern /* Subroutine */ int srot_(integer *, real *, integer *, real *, integer *, real *, real *); static integer bsiz1, bsiz2, psiz1, psiz2, zptr1; extern /* Subroutine */ int sgemv_(char *, integer *, integer *, real *, real *, integer *, real *, integer *, real *, real *, integer *), scopy_(integer *, real *, integer *, real *, integer *), xerbla_(char *, integer *); /* -- LAPACK routine (version 3.1) -- Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. November 2006 Purpose ======= SLAEDA computes the Z vector corresponding to the merge step in the CURLVLth step of the merge process with TLVLS steps for the CURPBMth problem. Arguments ========= N (input) INTEGER The dimension of the symmetric tridiagonal matrix. N >= 0. 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). 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 incidentally 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. Q (input) REAL array, dimension (N**2) Contains the square eigenblocks from previous levels, the starting positions for blocks are given by QPTR. QPTR (input) INTEGER array, dimension (N+2) Contains a list of pointers which indicate where in Q an eigenblock is stored. SQRT( QPTR(i+1) - QPTR(i) ) indicates the size of the block. Z (output) REAL array, dimension (N) On output this vector contains the updating vector (the last row of the first sub-eigenvector matrix and the first row of the second sub-eigenvector matrix). ZTEMP (workspace) REAL array, dimension (N) INFO (output) INTEGER = 0: successful exit. < 0: if INFO = -i, the i-th argument had an illegal value. Further Details =============== Based on contributions by Jeff Rutter, Computer Science Division, University of California at Berkeley, USA ===================================================================== Test the input parameters. Parameter adjustments */ --ztemp; --z__; --qptr; --q; givnum -= 3; givcol -= 3; --givptr; --perm; --prmptr; /* Function Body */ *info = 0; if (*n < 0) { *info = -1; } if (*info != 0) { i__1 = -(*info); xerbla_("SLAEDA", &i__1); return 0; } /* Quick return if possible */ if (*n == 0) { return 0; } /* Determine location of first number in second half. */ mid = *n / 2 + 1; /* Gather last/first rows of appropriate eigenblocks into center of Z */ ptr = 1; /* Determine location of lowest level subproblem in the full storage scheme */ i__1 = *curlvl - 1; curr = ptr + *curpbm * pow_ii(&c__2, curlvl) + pow_ii(&c__2, &i__1) - 1; /* Determine size of these matrices. We add HALF to the value of the SQRT in case the machine underestimates one of these square roots. */ bsiz1 = (integer) (sqrt((real) (qptr[curr + 1] - qptr[curr])) + .5f); bsiz2 = (integer) (sqrt((real) (qptr[curr + 2] - qptr[curr + 1])) + .5f); i__1 = mid - bsiz1 - 1; for (k = 1; k <= i__1; ++k) { z__[k] = 0.f; /* L10: */ } scopy_(&bsiz1, &q[qptr[curr] + bsiz1 - 1], &bsiz1, &z__[mid - bsiz1], & c__1); scopy_(&bsiz2, &q[qptr[curr + 1]], &bsiz2, &z__[mid], &c__1); i__1 = *n; for (k = mid + bsiz2; k <= i__1; ++k) { z__[k] = 0.f; /* L20: */ } /* Loop thru remaining levels 1 -> CURLVL applying the Givens rotations and permutation and then multiplying the center matrices against the current Z. */ ptr = pow_ii(&c__2, tlvls) + 1; i__1 = *curlvl - 1; for (k = 1; k <= i__1; ++k) { i__2 = *curlvl - k; i__3 = *curlvl - k - 1; curr = ptr + *curpbm * pow_ii(&c__2, &i__2) + pow_ii(&c__2, &i__3) - 1; psiz1 = prmptr[curr + 1] - prmptr[curr]; psiz2 = prmptr[curr + 2] - prmptr[curr + 1]; zptr1 = mid - psiz1; /* Apply Givens at CURR and CURR+1 */ i__2 = givptr[curr + 1] - 1; for (i__ = givptr[curr]; i__ <= i__2; ++i__) { srot_(&c__1, &z__[zptr1 + givcol[(i__ << 1) + 1] - 1], &c__1, & z__[zptr1 + givcol[(i__ << 1) + 2] - 1], &c__1, &givnum[( i__ << 1) + 1], &givnum[(i__ << 1) + 2]); /* L30: */ } i__2 = givptr[curr + 2] - 1; for (i__ = givptr[curr + 1]; i__ <= i__2; ++i__) { srot_(&c__1, &z__[mid - 1 + givcol[(i__ << 1) + 1]], &c__1, &z__[ mid - 1 + givcol[(i__ << 1) + 2]], &c__1, &givnum[(i__ << 1) + 1], &givnum[(i__ << 1) + 2]); /* L40: */ } psiz1 = prmptr[curr + 1] - prmptr[curr]; psiz2 = prmptr[curr + 2] - prmptr[curr + 1]; i__2 = psiz1 - 1; for (i__ = 0; i__ <= i__2; ++i__) { ztemp[i__ + 1] = z__[zptr1 + perm[prmptr[curr] + i__] - 1]; /* L50: */ } i__2 = psiz2 - 1; for (i__ = 0; i__ <= i__2; ++i__) { ztemp[psiz1 + i__ + 1] = z__[mid + perm[prmptr[curr + 1] + i__] - 1]; /* L60: */ } /* Multiply Blocks at CURR and CURR+1 Determine size of these matrices. We add HALF to the value of the SQRT in case the machine underestimates one of these square roots. */ bsiz1 = (integer) (sqrt((real) (qptr[curr + 1] - qptr[curr])) + .5f); bsiz2 = (integer) (sqrt((real) (qptr[curr + 2] - qptr[curr + 1])) + .5f); if (bsiz1 > 0) { sgemv_("T", &bsiz1, &bsiz1, &c_b24, &q[qptr[curr]], &bsiz1, & ztemp[1], &c__1, &c_b26, &z__[zptr1], &c__1); } i__2 = psiz1 - bsiz1; scopy_(&i__2, &ztemp[bsiz1 + 1], &c__1, &z__[zptr1 + bsiz1], &c__1); if (bsiz2 > 0) { sgemv_("T", &bsiz2, &bsiz2, &c_b24, &q[qptr[curr + 1]], &bsiz2, & ztemp[psiz1 + 1], &c__1, &c_b26, &z__[mid], &c__1); } i__2 = psiz2 - bsiz2; scopy_(&i__2, &ztemp[psiz1 + bsiz2 + 1], &c__1, &z__[mid + bsiz2], & c__1); i__2 = *tlvls - k; ptr += pow_ii(&c__2, &i__2); /* L70: */ } return 0; /* End of SLAEDA */ } /* slaeda_ */