#ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" static doublecomplex c_b1 = {1., 0.}; static integer c__1 = 1; int zlasyf_(char *uplo, integer *n, integer *nb, integer *kb, doublecomplex *a, integer *lda, integer *ipiv, doublecomplex *w, integer *ldw, integer *info, ftnlen uplo_len) { integer a_dim1, a_offset, w_dim1, w_offset, i__1, i__2, i__3, i__4; doublereal d__1, d__2, d__3, d__4; doublecomplex z__1, z__2, z__3; double sqrt(doublereal), d_lmp_imag(doublecomplex *); void z_lmp_div(doublecomplex *, doublecomplex *, doublecomplex *); integer j, k; doublecomplex t, r1, d11, d21, d22; integer jj, kk, jp, kp, kw, kkw, imax, jmax; doublereal alpha; extern logical lsame_(char *, char *, ftnlen, ftnlen); extern int zscal_(integer *, doublecomplex *, doublecomplex *, integer *); integer kstep; extern int zgemv_(char *, integer *, integer *, doublecomplex *, doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, doublecomplex *, integer *, ftnlen), zcopy_(integer *, doublecomplex *, integer *, doublecomplex *, integer *), zswap_(integer *, doublecomplex *, integer *, doublecomplex *, integer *); doublereal absakk, colmax; extern integer izamax_(integer *, doublecomplex *, integer *); doublereal rowmax; extern int zgemmtr_(char *, char *, char *, integer *, integer *, doublecomplex *, doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, doublecomplex *, integer *, ftnlen, ftnlen, ftnlen); a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; --ipiv; w_dim1 = *ldw; w_offset = 1 + w_dim1; w -= w_offset; *info = 0; alpha = (sqrt(17.) + 1.) / 8.; if (lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1)) { k = *n; L10: kw = *nb + k - *n; if (k <= *n - *nb + 1 && *nb < *n || k < 1) { goto L30; } zcopy_(&k, &a[k * a_dim1 + 1], &c__1, &w[kw * w_dim1 + 1], &c__1); if (k < *n) { i__1 = *n - k; z__1.r = -1., z__1.i = -0.; zgemv_((char *)"N", &k, &i__1, &z__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)1); } kstep = 1; i__1 = k + kw * w_dim1; absakk = (d__1 = w[i__1].r, abs(d__1)) + (d__2 = d_lmp_imag(&w[k + kw * w_dim1]), abs(d__2)); if (k > 1) { i__1 = k - 1; imax = izamax_(&i__1, &w[kw * w_dim1 + 1], &c__1); i__1 = imax + kw * w_dim1; colmax = (d__1 = w[i__1].r, abs(d__1)) + (d__2 = d_lmp_imag(&w[imax + kw * w_dim1]), abs(d__2)); } else { colmax = 0.; } if (max(absakk, colmax) == 0.) { if (*info == 0) { *info = k; } kp = k; } else { if (absakk >= alpha * colmax) { kp = k; } else { zcopy_(&imax, &a[imax * a_dim1 + 1], &c__1, &w[(kw - 1) * w_dim1 + 1], &c__1); i__1 = k - imax; zcopy_(&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; z__1.r = -1., z__1.i = -0.; zgemv_((char *)"N", &k, &i__1, &z__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)1); } i__1 = k - imax; jmax = imax + izamax_(&i__1, &w[imax + 1 + (kw - 1) * w_dim1], &c__1); i__1 = jmax + (kw - 1) * w_dim1; rowmax = (d__1 = w[i__1].r, abs(d__1)) + (d__2 = d_lmp_imag(&w[jmax + (kw - 1) * w_dim1]), abs(d__2)); if (imax > 1) { i__1 = imax - 1; jmax = izamax_(&i__1, &w[(kw - 1) * w_dim1 + 1], &c__1); i__1 = jmax + (kw - 1) * w_dim1; d__3 = rowmax, d__4 = (d__1 = w[i__1].r, abs(d__1)) + (d__2 = d_lmp_imag(&w[jmax + (kw - 1) * w_dim1]), abs(d__2)); rowmax = max(d__3, d__4); } if (absakk >= alpha * colmax * (colmax / rowmax)) { kp = k; } else { i__1 = imax + (kw - 1) * w_dim1; if ((d__1 = w[i__1].r, abs(d__1)) + (d__2 = d_lmp_imag(&w[imax + (kw - 1) * w_dim1]), abs(d__2)) >= alpha * rowmax) { kp = imax; zcopy_(&k, &w[(kw - 1) * w_dim1 + 1], &c__1, &w[kw * w_dim1 + 1], &c__1); } else { kp = imax; kstep = 2; } } } kk = k - kstep + 1; kkw = *nb + kk - *n; if (kp != kk) { i__1 = kp + kp * a_dim1; i__2 = kk + kk * a_dim1; a[i__1].r = a[i__2].r, a[i__1].i = a[i__2].i; i__1 = kk - 1 - kp; zcopy_(&i__1, &a[kp + 1 + kk * a_dim1], &c__1, &a[kp + (kp + 1) * a_dim1], lda); if (kp > 1) { i__1 = kp - 1; zcopy_(&i__1, &a[kk * a_dim1 + 1], &c__1, &a[kp * a_dim1 + 1], &c__1); } if (k < *n) { i__1 = *n - k; zswap_(&i__1, &a[kk + (k + 1) * a_dim1], lda, &a[kp + (k + 1) * a_dim1], lda); } i__1 = *n - kk + 1; zswap_(&i__1, &w[kk + kkw * w_dim1], ldw, &w[kp + kkw * w_dim1], ldw); } if (kstep == 1) { zcopy_(&k, &w[kw * w_dim1 + 1], &c__1, &a[k * a_dim1 + 1], &c__1); z_lmp_div(&z__1, &c_b1, &a[k + k * a_dim1]); r1.r = z__1.r, r1.i = z__1.i; i__1 = k - 1; zscal_(&i__1, &r1, &a[k * a_dim1 + 1], &c__1); } else { if (k > 2) { i__1 = k - 1 + kw * w_dim1; d21.r = w[i__1].r, d21.i = w[i__1].i; z_lmp_div(&z__1, &w[k + kw * w_dim1], &d21); d11.r = z__1.r, d11.i = z__1.i; z_lmp_div(&z__1, &w[k - 1 + (kw - 1) * w_dim1], &d21); d22.r = z__1.r, d22.i = z__1.i; z__3.r = d11.r * d22.r - d11.i * d22.i, z__3.i = d11.r * d22.i + d11.i * d22.r; z__2.r = z__3.r - 1., z__2.i = z__3.i - 0.; z_lmp_div(&z__1, &c_b1, &z__2); t.r = z__1.r, t.i = z__1.i; z_lmp_div(&z__1, &t, &d21); d21.r = z__1.r, d21.i = z__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; z__3.r = d11.r * w[i__3].r - d11.i * w[i__3].i, z__3.i = d11.r * w[i__3].i + d11.i * w[i__3].r; i__4 = j + kw * w_dim1; z__2.r = z__3.r - w[i__4].r, z__2.i = z__3.i - w[i__4].i; z__1.r = d21.r * z__2.r - d21.i * z__2.i, z__1.i = d21.r * z__2.i + d21.i * z__2.r; a[i__2].r = z__1.r, a[i__2].i = z__1.i; i__2 = j + k * a_dim1; i__3 = j + kw * w_dim1; z__3.r = d22.r * w[i__3].r - d22.i * w[i__3].i, z__3.i = d22.r * w[i__3].i + d22.i * w[i__3].r; i__4 = j + (kw - 1) * w_dim1; z__2.r = z__3.r - w[i__4].r, z__2.i = z__3.i - w[i__4].i; z__1.r = d21.r * z__2.r - d21.i * z__2.i, z__1.i = d21.r * z__2.i + d21.i * z__2.r; a[i__2].r = z__1.r, a[i__2].i = z__1.i; } } 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] = -kp; ipiv[k - 1] = -kp; } k -= kstep; goto L10; L30: i__1 = *n - k; z__1.r = -1., z__1.i = -0.; zgemmtr_((char *)"U", (char *)"N", (char *)"T", &k, &i__1, &z__1, &a[(k + 1) * a_dim1 + 1], lda, &w[(kw + 1) * w_dim1 + 1], ldw, &c_b1, &a[a_dim1 + 1], lda, (ftnlen)1, (ftnlen)1, (ftnlen)1); j = k + 1; L60: jj = j; jp = ipiv[j]; if (jp < 0) { jp = -jp; ++j; } ++j; if (jp != jj && j <= *n) { i__1 = *n - j + 1; zswap_(&i__1, &a[jp + 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; } i__1 = *n - k + 1; zcopy_(&i__1, &a[k + k * a_dim1], &c__1, &w[k + k * w_dim1], &c__1); i__1 = *n - k + 1; i__2 = k - 1; z__1.r = -1., z__1.i = -0.; zgemv_((char *)"N", &i__1, &i__2, &z__1, &a[k + a_dim1], lda, &w[k + w_dim1], ldw, &c_b1, &w[k + k * w_dim1], &c__1, (ftnlen)1); kstep = 1; i__1 = k + k * w_dim1; absakk = (d__1 = w[i__1].r, abs(d__1)) + (d__2 = d_lmp_imag(&w[k + k * w_dim1]), abs(d__2)); if (k < *n) { i__1 = *n - k; imax = k + izamax_(&i__1, &w[k + 1 + k * w_dim1], &c__1); i__1 = imax + k * w_dim1; colmax = (d__1 = w[i__1].r, abs(d__1)) + (d__2 = d_lmp_imag(&w[imax + k * w_dim1]), abs(d__2)); } else { colmax = 0.; } if (max(absakk, colmax) == 0.) { if (*info == 0) { *info = k; } kp = k; } else { if (absakk >= alpha * colmax) { kp = k; } else { i__1 = imax - k; zcopy_(&i__1, &a[imax + k * a_dim1], lda, &w[k + (k + 1) * w_dim1], &c__1); i__1 = *n - imax + 1; zcopy_(&i__1, &a[imax + imax * a_dim1], &c__1, &w[imax + (k + 1) * w_dim1], &c__1); i__1 = *n - k + 1; i__2 = k - 1; z__1.r = -1., z__1.i = -0.; zgemv_((char *)"N", &i__1, &i__2, &z__1, &a[k + a_dim1], lda, &w[imax + w_dim1], ldw, &c_b1, &w[k + (k + 1) * w_dim1], &c__1, (ftnlen)1); i__1 = imax - k; jmax = k - 1 + izamax_(&i__1, &w[k + (k + 1) * w_dim1], &c__1); i__1 = jmax + (k + 1) * w_dim1; rowmax = (d__1 = w[i__1].r, abs(d__1)) + (d__2 = d_lmp_imag(&w[jmax + (k + 1) * w_dim1]), abs(d__2)); if (imax < *n) { i__1 = *n - imax; jmax = imax + izamax_(&i__1, &w[imax + 1 + (k + 1) * w_dim1], &c__1); i__1 = jmax + (k + 1) * w_dim1; d__3 = rowmax, d__4 = (d__1 = w[i__1].r, abs(d__1)) + (d__2 = d_lmp_imag(&w[jmax + (k + 1) * w_dim1]), abs(d__2)); rowmax = max(d__3, d__4); } if (absakk >= alpha * colmax * (colmax / rowmax)) { kp = k; } else { i__1 = imax + (k + 1) * w_dim1; if ((d__1 = w[i__1].r, abs(d__1)) + (d__2 = d_lmp_imag(&w[imax + (k + 1) * w_dim1]), abs(d__2)) >= alpha * rowmax) { kp = imax; i__1 = *n - k + 1; zcopy_(&i__1, &w[k + (k + 1) * w_dim1], &c__1, &w[k + k * w_dim1], &c__1); } else { kp = imax; kstep = 2; } } } kk = k + kstep - 1; if (kp != kk) { i__1 = kp + kp * a_dim1; i__2 = kk + kk * a_dim1; a[i__1].r = a[i__2].r, a[i__1].i = a[i__2].i; i__1 = kp - kk - 1; zcopy_(&i__1, &a[kk + 1 + kk * a_dim1], &c__1, &a[kp + (kk + 1) * a_dim1], lda); if (kp < *n) { i__1 = *n - kp; zcopy_(&i__1, &a[kp + 1 + kk * a_dim1], &c__1, &a[kp + 1 + kp * a_dim1], &c__1); } if (k > 1) { i__1 = k - 1; zswap_(&i__1, &a[kk + a_dim1], lda, &a[kp + a_dim1], lda); } zswap_(&kk, &w[kk + w_dim1], ldw, &w[kp + w_dim1], ldw); } if (kstep == 1) { i__1 = *n - k + 1; zcopy_(&i__1, &w[k + k * w_dim1], &c__1, &a[k + k * a_dim1], &c__1); if (k < *n) { z_lmp_div(&z__1, &c_b1, &a[k + k * a_dim1]); r1.r = z__1.r, r1.i = z__1.i; i__1 = *n - k; zscal_(&i__1, &r1, &a[k + 1 + k * a_dim1], &c__1); } } else { if (k < *n - 1) { i__1 = k + 1 + k * w_dim1; d21.r = w[i__1].r, d21.i = w[i__1].i; z_lmp_div(&z__1, &w[k + 1 + (k + 1) * w_dim1], &d21); d11.r = z__1.r, d11.i = z__1.i; z_lmp_div(&z__1, &w[k + k * w_dim1], &d21); d22.r = z__1.r, d22.i = z__1.i; z__3.r = d11.r * d22.r - d11.i * d22.i, z__3.i = d11.r * d22.i + d11.i * d22.r; z__2.r = z__3.r - 1., z__2.i = z__3.i - 0.; z_lmp_div(&z__1, &c_b1, &z__2); t.r = z__1.r, t.i = z__1.i; z_lmp_div(&z__1, &t, &d21); d21.r = z__1.r, d21.i = z__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; z__3.r = d11.r * w[i__3].r - d11.i * w[i__3].i, z__3.i = d11.r * w[i__3].i + d11.i * w[i__3].r; i__4 = j + (k + 1) * w_dim1; z__2.r = z__3.r - w[i__4].r, z__2.i = z__3.i - w[i__4].i; z__1.r = d21.r * z__2.r - d21.i * z__2.i, z__1.i = d21.r * z__2.i + d21.i * z__2.r; a[i__2].r = z__1.r, a[i__2].i = z__1.i; i__2 = j + (k + 1) * a_dim1; i__3 = j + (k + 1) * w_dim1; z__3.r = d22.r * w[i__3].r - d22.i * w[i__3].i, z__3.i = d22.r * w[i__3].i + d22.i * w[i__3].r; i__4 = j + k * w_dim1; z__2.r = z__3.r - w[i__4].r, z__2.i = z__3.i - w[i__4].i; z__1.r = d21.r * z__2.r - d21.i * z__2.i, z__1.i = d21.r * z__2.i + d21.i * z__2.r; a[i__2].r = z__1.r, a[i__2].i = z__1.i; } } 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] = -kp; ipiv[k + 1] = -kp; } k += kstep; goto L70; L90: i__1 = *n - k + 1; i__2 = k - 1; z__1.r = -1., z__1.i = -0.; zgemmtr_((char *)"L", (char *)"N", (char *)"T", &i__1, &i__2, &z__1, &a[k + a_dim1], lda, &w[k + w_dim1], ldw, &c_b1, &a[k + k * a_dim1], lda, (ftnlen)1, (ftnlen)1, (ftnlen)1); j = k - 1; L120: jj = j; jp = ipiv[j]; if (jp < 0) { jp = -jp; --j; } --j; if (jp != jj && j >= 1) { zswap_(&j, &a[jp + a_dim1], lda, &a[jj + a_dim1], lda); } if (j > 1) { goto L120; } *kb = k - 1; } return 0; } #ifdef __cplusplus } #endif