/* -- translated by f2c (version 20100827). 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 complex c_b1 = {1.f,0.f}; static blasint c__1 = 1; /** CSYTRF_ROOK_REC2 computes a partial factorization of a complex symmetric matrix using the bounded Bunch-K aufman ("rook") diagonal pivoting method. * * This routine is a minor modification of LAPACK's clasyf_rook. * It serves as an unblocked kernel in the recursive algorithms. * The blocked BLAS Level 3 updates were removed and moved to the * recursive algorithm. * */ /* Subroutine */ void RELAPACK_csytrf_rook_rec2(char *uplo, blasint *n, int *nb, blasint *kb, complex *a, blasint *lda, blasint *ipiv, complex *w, blasint *ldw, blasint *info, ftnlen uplo_len) { /* System generated locals */ blasint a_dim1, a_offset, w_dim1, w_offset, i__1, i__2, i__3, i__4; float r__1, r__2; complex q__1, q__2, q__3, q__4; /* Builtin functions */ double sqrt(double), r_imag(complex *); void c_div(complex *, complex *, complex *); /* Local variables */ static blasint j, k, p; static complex t, r1, d11, d12, d21, d22; static blasint ii, jj, kk, kp, kw, jp1, jp2, kkw; static logical done; static blasint imax, jmax; static float alpha; extern /* Subroutine */ blasint cscal_(int *, complex *, complex *, blasint *); extern logical lsame_(char *, char *, ftnlen, ftnlen); extern /* Subroutine */ blasint cgemv_(char *, blasint *, blasint *, complex * , complex *, blasint *, complex *, blasint *, complex *, complex * , blasint *, ftnlen); static float sfmin; extern /* Subroutine */ blasint ccopy_(int *, complex *, blasint *, complex *, blasint *); static blasint itemp; extern /* Subroutine */ blasint cswap_(int *, complex *, blasint *, complex *, blasint *); static blasint kstep; static float stemp, absakk; extern blasint icamax_(int *, complex *, blasint *); extern double slamch_(char *, ftnlen); static float colmax, rowmax; /* Parameter adjustments */ a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; --ipiv; w_dim1 = *ldw; w_offset = 1 + w_dim1; w -= w_offset; /* Function Body */ *info = 0; alpha = (sqrt(17.f) + 1.f) / 8.f; sfmin = slamch_("S", (ftnlen)1); if (lsame_(uplo, "U", (ftnlen)1, (ftnlen)1)) { k = *n; L10: kw = *nb + k - *n; if ((k <= *n - *nb + 1 && *nb < *n) || k < 1) { goto L30; } kstep = 1; p = k; ccopy_(&k, &a[k * a_dim1 + 1], &c__1, &w[kw * w_dim1 + 1], &c__1); if (k < *n) { i__1 = *n - k; q__1.r = -1.f, q__1.i = -0.f; cgemv_("No transpose", &k, &i__1, &q__1, &a[(k + 1) * a_dim1 + 1], lda, &w[k + (kw + 1) * w_dim1], ldw, &c_b1, &w[kw * w_dim1 + 1], &c__1, (ftnlen)12); } i__1 = k + kw * w_dim1; absakk = (r__1 = w[i__1].r, dabs(r__1)) + (r__2 = r_imag(&w[k + kw * w_dim1]), dabs(r__2)); if (k > 1) { i__1 = k - 1; imax = icamax_(&i__1, &w[kw * w_dim1 + 1], &c__1); i__1 = imax + kw * w_dim1; colmax = (r__1 = w[i__1].r, dabs(r__1)) + (r__2 = r_imag(&w[imax + kw * w_dim1]), dabs(r__2)); } else { colmax = 0.f; } if (dmax(absakk,colmax) == 0.f) { if (*info == 0) { *info = k; } kp = k; ccopy_(&k, &w[kw * w_dim1 + 1], &c__1, &a[k * a_dim1 + 1], &c__1); } else { if (! (absakk < alpha * colmax)) { kp = k; } else { done = FALSE_; L12: ccopy_(&imax, &a[imax * a_dim1 + 1], &c__1, &w[(kw - 1) * w_dim1 + 1], &c__1); i__1 = k - imax; ccopy_(&i__1, &a[imax + (imax + 1) * a_dim1], lda, &w[imax + 1 + (kw - 1) * w_dim1], &c__1); if (k < *n) { i__1 = *n - k; q__1.r = -1.f, q__1.i = -0.f; cgemv_("No transpose", &k, &i__1, &q__1, &a[(k + 1) * a_dim1 + 1], lda, &w[imax + (kw + 1) * w_dim1], ldw, &c_b1, &w[(kw - 1) * w_dim1 + 1], &c__1, ( ftnlen)12); } if (imax != k) { i__1 = k - imax; jmax = imax + icamax_(&i__1, &w[imax + 1 + (kw - 1) * w_dim1], &c__1); i__1 = jmax + (kw - 1) * w_dim1; rowmax = (r__1 = w[i__1].r, dabs(r__1)) + (r__2 = r_imag(& w[jmax + (kw - 1) * w_dim1]), dabs(r__2)); } else { rowmax = 0.f; } if (imax > 1) { i__1 = imax - 1; itemp = icamax_(&i__1, &w[(kw - 1) * w_dim1 + 1], &c__1); i__1 = itemp + (kw - 1) * w_dim1; stemp = (r__1 = w[i__1].r, dabs(r__1)) + (r__2 = r_imag(& w[itemp + (kw - 1) * w_dim1]), dabs(r__2)); if (stemp > rowmax) { rowmax = stemp; jmax = itemp; } } i__1 = imax + (kw - 1) * w_dim1; if (! ((r__1 = w[i__1].r, dabs(r__1)) + (r__2 = r_imag(&w[ imax + (kw - 1) * w_dim1]), dabs(r__2)) < alpha * rowmax)) { kp = imax; ccopy_(&k, &w[(kw - 1) * w_dim1 + 1], &c__1, &w[kw * w_dim1 + 1], &c__1); done = TRUE_; } else if (p == jmax || rowmax <= colmax) { kp = imax; kstep = 2; done = TRUE_; } else { p = imax; colmax = rowmax; imax = jmax; ccopy_(&k, &w[(kw - 1) * w_dim1 + 1], &c__1, &w[kw * w_dim1 + 1], &c__1); } if (! done) { goto L12; } } kk = k - kstep + 1; kkw = *nb + kk - *n; if (kstep == 2 && p != k) { i__1 = k - p; ccopy_(&i__1, &a[p + 1 + k * a_dim1], &c__1, &a[p + (p + 1) * a_dim1], lda); ccopy_(&p, &a[k * a_dim1 + 1], &c__1, &a[p * a_dim1 + 1], & c__1); i__1 = *n - k + 1; cswap_(&i__1, &a[k + k * a_dim1], lda, &a[p + k * a_dim1], lda); i__1 = *n - kk + 1; cswap_(&i__1, &w[k + kkw * w_dim1], ldw, &w[p + kkw * w_dim1], ldw); } if (kp != kk) { i__1 = kp + k * a_dim1; i__2 = kk + k * a_dim1; a[i__1].r = a[i__2].r, a[i__1].i = a[i__2].i; i__1 = k - 1 - kp; ccopy_(&i__1, &a[kp + 1 + kk * a_dim1], &c__1, &a[kp + (kp + 1) * a_dim1], lda); ccopy_(&kp, &a[kk * a_dim1 + 1], &c__1, &a[kp * a_dim1 + 1], & c__1); i__1 = *n - kk + 1; cswap_(&i__1, &a[kk + kk * a_dim1], lda, &a[kp + kk * a_dim1], lda); i__1 = *n - kk + 1; cswap_(&i__1, &w[kk + kkw * w_dim1], ldw, &w[kp + kkw * w_dim1], ldw); } if (kstep == 1) { ccopy_(&k, &w[kw * w_dim1 + 1], &c__1, &a[k * a_dim1 + 1], & c__1); if (k > 1) { i__1 = k + k * a_dim1; if ((r__1 = a[i__1].r, dabs(r__1)) + (r__2 = r_imag(&a[k + k * a_dim1]), dabs(r__2)) >= sfmin) { c_div(&q__1, &c_b1, &a[k + k * a_dim1]); r1.r = q__1.r, r1.i = q__1.i; i__1 = k - 1; cscal_(&i__1, &r1, &a[k * a_dim1 + 1], &c__1); } else /* if(complicated condition) */ { i__1 = k + k * a_dim1; if (a[i__1].r != 0.f || a[i__1].i != 0.f) { i__1 = k - 1; for (ii = 1; ii <= i__1; ++ii) { i__2 = ii + k * a_dim1; c_div(&q__1, &a[ii + k * a_dim1], &a[k + k * a_dim1]); a[i__2].r = q__1.r, a[i__2].i = q__1.i; /* L14: */ } } } } } else { if (k > 2) { i__1 = k - 1 + kw * w_dim1; d12.r = w[i__1].r, d12.i = w[i__1].i; c_div(&q__1, &w[k + kw * w_dim1], &d12); d11.r = q__1.r, d11.i = q__1.i; c_div(&q__1, &w[k - 1 + (kw - 1) * w_dim1], &d12); d22.r = q__1.r, d22.i = q__1.i; q__3.r = d11.r * d22.r - d11.i * d22.i, q__3.i = d11.r * d22.i + d11.i * d22.r; q__2.r = q__3.r - 1.f, q__2.i = q__3.i - 0.f; c_div(&q__1, &c_b1, &q__2); t.r = q__1.r, t.i = q__1.i; i__1 = k - 2; for (j = 1; j <= i__1; ++j) { i__2 = j + (k - 1) * a_dim1; i__3 = j + (kw - 1) * w_dim1; q__4.r = d11.r * w[i__3].r - d11.i * w[i__3].i, q__4.i = d11.r * w[i__3].i + d11.i * w[i__3] .r; i__4 = j + kw * w_dim1; q__3.r = q__4.r - w[i__4].r, q__3.i = q__4.i - w[i__4] .i; c_div(&q__2, &q__3, &d12); q__1.r = t.r * q__2.r - t.i * q__2.i, q__1.i = t.r * q__2.i + t.i * q__2.r; a[i__2].r = q__1.r, a[i__2].i = q__1.i; i__2 = j + k * a_dim1; i__3 = j + kw * w_dim1; q__4.r = d22.r * w[i__3].r - d22.i * w[i__3].i, q__4.i = d22.r * w[i__3].i + d22.i * w[i__3] .r; i__4 = j + (kw - 1) * w_dim1; q__3.r = q__4.r - w[i__4].r, q__3.i = q__4.i - w[i__4] .i; c_div(&q__2, &q__3, &d12); q__1.r = t.r * q__2.r - t.i * q__2.i, q__1.i = t.r * q__2.i + t.i * q__2.r; a[i__2].r = q__1.r, a[i__2].i = q__1.i; /* L20: */ } } i__1 = k - 1 + (k - 1) * a_dim1; i__2 = k - 1 + (kw - 1) * w_dim1; a[i__1].r = w[i__2].r, a[i__1].i = w[i__2].i; i__1 = k - 1 + k * a_dim1; i__2 = k - 1 + kw * w_dim1; a[i__1].r = w[i__2].r, a[i__1].i = w[i__2].i; i__1 = k + k * a_dim1; i__2 = k + kw * w_dim1; a[i__1].r = w[i__2].r, a[i__1].i = w[i__2].i; } } if (kstep == 1) { ipiv[k] = kp; } else { ipiv[k] = -p; ipiv[k - 1] = -kp; } k -= kstep; goto L10; L30: j = k + 1; L60: kstep = 1; jp1 = 1; jj = j; jp2 = ipiv[j]; if (jp2 < 0) { jp2 = -jp2; ++j; jp1 = -ipiv[j]; kstep = 2; } ++j; if (jp2 != jj && j <= *n) { i__1 = *n - j + 1; cswap_(&i__1, &a[jp2 + j * a_dim1], lda, &a[jj + j * a_dim1], lda) ; } jj = j - 1; if (jp1 != jj && kstep == 2) { i__1 = *n - j + 1; cswap_(&i__1, &a[jp1 + j * a_dim1], lda, &a[jj + j * a_dim1], lda) ; } if (j <= *n) { goto L60; } *kb = *n - k; } else { k = 1; L70: if ((k >= *nb && *nb < *n) || k > *n) { goto L90; } kstep = 1; p = k; i__1 = *n - k + 1; ccopy_(&i__1, &a[k + k * a_dim1], &c__1, &w[k + k * w_dim1], &c__1); if (k > 1) { i__1 = *n - k + 1; i__2 = k - 1; q__1.r = -1.f, q__1.i = -0.f; cgemv_("No transpose", &i__1, &i__2, &q__1, &a[k + a_dim1], lda, & w[k + w_dim1], ldw, &c_b1, &w[k + k * w_dim1], &c__1, ( ftnlen)12); } i__1 = k + k * w_dim1; absakk = (r__1 = w[i__1].r, dabs(r__1)) + (r__2 = r_imag(&w[k + k * w_dim1]), dabs(r__2)); if (k < *n) { i__1 = *n - k; imax = k + icamax_(&i__1, &w[k + 1 + k * w_dim1], &c__1); i__1 = imax + k * w_dim1; colmax = (r__1 = w[i__1].r, dabs(r__1)) + (r__2 = r_imag(&w[imax + k * w_dim1]), dabs(r__2)); } else { colmax = 0.f; } if (dmax(absakk,colmax) == 0.f) { if (*info == 0) { *info = k; } kp = k; i__1 = *n - k + 1; ccopy_(&i__1, &w[k + k * w_dim1], &c__1, &a[k + k * a_dim1], & c__1); } else { if (! (absakk < alpha * colmax)) { kp = k; } else { done = FALSE_; L72: i__1 = imax - k; ccopy_(&i__1, &a[imax + k * a_dim1], lda, &w[k + (k + 1) * w_dim1], &c__1); i__1 = *n - imax + 1; ccopy_(&i__1, &a[imax + imax * a_dim1], &c__1, &w[imax + (k + 1) * w_dim1], &c__1); if (k > 1) { i__1 = *n - k + 1; i__2 = k - 1; q__1.r = -1.f, q__1.i = -0.f; cgemv_("No transpose", &i__1, &i__2, &q__1, &a[k + a_dim1] , lda, &w[imax + w_dim1], ldw, &c_b1, &w[k + (k + 1) * w_dim1], &c__1, (ftnlen)12); } if (imax != k) { i__1 = imax - k; jmax = k - 1 + icamax_(&i__1, &w[k + (k + 1) * w_dim1], & c__1); i__1 = jmax + (k + 1) * w_dim1; rowmax = (r__1 = w[i__1].r, dabs(r__1)) + (r__2 = r_imag(& w[jmax + (k + 1) * w_dim1]), dabs(r__2)); } else { rowmax = 0.f; } if (imax < *n) { i__1 = *n - imax; itemp = imax + icamax_(&i__1, &w[imax + 1 + (k + 1) * w_dim1], &c__1); i__1 = itemp + (k + 1) * w_dim1; stemp = (r__1 = w[i__1].r, dabs(r__1)) + (r__2 = r_imag(& w[itemp + (k + 1) * w_dim1]), dabs(r__2)); if (stemp > rowmax) { rowmax = stemp; jmax = itemp; } } i__1 = imax + (k + 1) * w_dim1; if (! ((r__1 = w[i__1].r, dabs(r__1)) + (r__2 = r_imag(&w[ imax + (k + 1) * w_dim1]), dabs(r__2)) < alpha * rowmax)) { kp = imax; i__1 = *n - k + 1; ccopy_(&i__1, &w[k + (k + 1) * w_dim1], &c__1, &w[k + k * w_dim1], &c__1); done = TRUE_; } else if (p == jmax || rowmax <= colmax) { kp = imax; kstep = 2; done = TRUE_; } else { p = imax; colmax = rowmax; imax = jmax; i__1 = *n - k + 1; ccopy_(&i__1, &w[k + (k + 1) * w_dim1], &c__1, &w[k + k * w_dim1], &c__1); } if (! done) { goto L72; } } kk = k + kstep - 1; if (kstep == 2 && p != k) { i__1 = p - k; ccopy_(&i__1, &a[k + k * a_dim1], &c__1, &a[p + k * a_dim1], lda); i__1 = *n - p + 1; ccopy_(&i__1, &a[p + k * a_dim1], &c__1, &a[p + p * a_dim1], & c__1); cswap_(&k, &a[k + a_dim1], lda, &a[p + a_dim1], lda); cswap_(&kk, &w[k + w_dim1], ldw, &w[p + w_dim1], ldw); } if (kp != kk) { i__1 = kp + k * a_dim1; i__2 = kk + k * a_dim1; a[i__1].r = a[i__2].r, a[i__1].i = a[i__2].i; i__1 = kp - k - 1; ccopy_(&i__1, &a[k + 1 + kk * a_dim1], &c__1, &a[kp + (k + 1) * a_dim1], lda); i__1 = *n - kp + 1; ccopy_(&i__1, &a[kp + kk * a_dim1], &c__1, &a[kp + kp * a_dim1], &c__1); cswap_(&kk, &a[kk + a_dim1], lda, &a[kp + a_dim1], lda); cswap_(&kk, &w[kk + w_dim1], ldw, &w[kp + w_dim1], ldw); } if (kstep == 1) { i__1 = *n - k + 1; ccopy_(&i__1, &w[k + k * w_dim1], &c__1, &a[k + k * a_dim1], & c__1); if (k < *n) { i__1 = k + k * a_dim1; if ((r__1 = a[i__1].r, dabs(r__1)) + (r__2 = r_imag(&a[k + k * a_dim1]), dabs(r__2)) >= sfmin) { c_div(&q__1, &c_b1, &a[k + k * a_dim1]); r1.r = q__1.r, r1.i = q__1.i; i__1 = *n - k; cscal_(&i__1, &r1, &a[k + 1 + k * a_dim1], &c__1); } else /* if(complicated condition) */ { i__1 = k + k * a_dim1; if (a[i__1].r != 0.f || a[i__1].i != 0.f) { i__1 = *n; for (ii = k + 1; ii <= i__1; ++ii) { i__2 = ii + k * a_dim1; c_div(&q__1, &a[ii + k * a_dim1], &a[k + k * a_dim1]); a[i__2].r = q__1.r, a[i__2].i = q__1.i; /* L74: */ } } } } } else { if (k < *n - 1) { i__1 = k + 1 + k * w_dim1; d21.r = w[i__1].r, d21.i = w[i__1].i; c_div(&q__1, &w[k + 1 + (k + 1) * w_dim1], &d21); d11.r = q__1.r, d11.i = q__1.i; c_div(&q__1, &w[k + k * w_dim1], &d21); d22.r = q__1.r, d22.i = q__1.i; q__3.r = d11.r * d22.r - d11.i * d22.i, q__3.i = d11.r * d22.i + d11.i * d22.r; q__2.r = q__3.r - 1.f, q__2.i = q__3.i - 0.f; c_div(&q__1, &c_b1, &q__2); t.r = q__1.r, t.i = q__1.i; i__1 = *n; for (j = k + 2; j <= i__1; ++j) { i__2 = j + k * a_dim1; i__3 = j + k * w_dim1; q__4.r = d11.r * w[i__3].r - d11.i * w[i__3].i, q__4.i = d11.r * w[i__3].i + d11.i * w[i__3] .r; i__4 = j + (k + 1) * w_dim1; q__3.r = q__4.r - w[i__4].r, q__3.i = q__4.i - w[i__4] .i; c_div(&q__2, &q__3, &d21); q__1.r = t.r * q__2.r - t.i * q__2.i, q__1.i = t.r * q__2.i + t.i * q__2.r; a[i__2].r = q__1.r, a[i__2].i = q__1.i; i__2 = j + (k + 1) * a_dim1; i__3 = j + (k + 1) * w_dim1; q__4.r = d22.r * w[i__3].r - d22.i * w[i__3].i, q__4.i = d22.r * w[i__3].i + d22.i * w[i__3] .r; i__4 = j + k * w_dim1; q__3.r = q__4.r - w[i__4].r, q__3.i = q__4.i - w[i__4] .i; c_div(&q__2, &q__3, &d21); q__1.r = t.r * q__2.r - t.i * q__2.i, q__1.i = t.r * q__2.i + t.i * q__2.r; a[i__2].r = q__1.r, a[i__2].i = q__1.i; /* L80: */ } } i__1 = k + k * a_dim1; i__2 = k + k * w_dim1; a[i__1].r = w[i__2].r, a[i__1].i = w[i__2].i; i__1 = k + 1 + k * a_dim1; i__2 = k + 1 + k * w_dim1; a[i__1].r = w[i__2].r, a[i__1].i = w[i__2].i; i__1 = k + 1 + (k + 1) * a_dim1; i__2 = k + 1 + (k + 1) * w_dim1; a[i__1].r = w[i__2].r, a[i__1].i = w[i__2].i; } } if (kstep == 1) { ipiv[k] = kp; } else { ipiv[k] = -p; ipiv[k + 1] = -kp; } k += kstep; goto L70; L90: j = k - 1; L120: kstep = 1; jp1 = 1; jj = j; jp2 = ipiv[j]; if (jp2 < 0) { jp2 = -jp2; --j; jp1 = -ipiv[j]; kstep = 2; } --j; if (jp2 != jj && j >= 1) { cswap_(&j, &a[jp2 + a_dim1], lda, &a[jj + a_dim1], lda); } jj = j + 1; if (jp1 != jj && kstep == 2) { cswap_(&j, &a[jp1 + a_dim1], lda, &a[jj + a_dim1], lda); } if (j >= 1) { goto L120; } *kb = k - 1; } return; }