#ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" static doublecomplex c_b1 = {1., 0.}; static integer c__1 = 1; int zlahef_(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, i__5; doublereal d__1, d__2, d__3, d__4; doublecomplex z__1, z__2, z__3, z__4; double sqrt(doublereal), d_lmp_imag(doublecomplex *); void d_lmp_cnjg(doublecomplex *, doublecomplex *), z_lmp_div(doublecomplex *, doublecomplex *, doublecomplex *); integer j, k; doublereal t, r1; doublecomplex d11, d21, d22; integer jb, jj, kk, jp, kp, kw, kkw, imax, jmax; doublereal alpha; extern logical lsame_(char *, char *, ftnlen, ftnlen); extern int zgemm_(char *, char *, integer *, integer *, integer *, doublecomplex *, doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, doublecomplex *, integer *, ftnlen, ftnlen); 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; extern int zdscal_(integer *, doublereal *, doublecomplex *, integer *); doublereal colmax; extern int zlacgv_(integer *, doublecomplex *, integer *); extern integer izamax_(integer *, doublecomplex *, integer *); doublereal rowmax; 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; } kstep = 1; i__1 = k - 1; zcopy_(&i__1, &a[k * a_dim1 + 1], &c__1, &w[kw * w_dim1 + 1], &c__1); i__1 = k + kw * w_dim1; i__2 = k + k * a_dim1; d__1 = a[i__2].r; w[i__1].r = d__1, w[i__1].i = 0.; if (k < *n) { i__1 = *n - k; z__1.r = -1., z__1.i = -0.; zgemv_((char *)"No transpose", &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)12); i__1 = k + kw * w_dim1; i__2 = k + kw * w_dim1; d__1 = w[i__2].r; w[i__1].r = d__1, w[i__1].i = 0.; } i__1 = k + kw * w_dim1; absakk = (d__1 = w[i__1].r, abs(d__1)); 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; i__1 = k + k * a_dim1; i__2 = k + k * a_dim1; d__1 = a[i__2].r; a[i__1].r = d__1, a[i__1].i = 0.; } else { if (absakk >= alpha * colmax) { kp = k; } else { i__1 = imax - 1; zcopy_(&i__1, &a[imax * a_dim1 + 1], &c__1, &w[(kw - 1) * w_dim1 + 1], &c__1); i__1 = imax + (kw - 1) * w_dim1; i__2 = imax + imax * a_dim1; d__1 = a[i__2].r; w[i__1].r = d__1, w[i__1].i = 0.; i__1 = k - imax; zcopy_(&i__1, &a[imax + (imax + 1) * a_dim1], lda, &w[imax + 1 + (kw - 1) * w_dim1], &c__1); i__1 = k - imax; zlacgv_(&i__1, &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 *)"No transpose", &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)12); i__1 = imax + (kw - 1) * w_dim1; i__2 = imax + (kw - 1) * w_dim1; d__1 = w[i__2].r; w[i__1].r = d__1, w[i__1].i = 0.; } 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)) >= 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; d__1 = a[i__2].r; a[i__1].r = d__1, a[i__1].i = 0.; i__1 = kk - 1 - kp; zcopy_(&i__1, &a[kp + 1 + kk * a_dim1], &c__1, &a[kp + (kp + 1) * a_dim1], lda); i__1 = kk - 1 - kp; zlacgv_(&i__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); if (k > 1) { i__1 = k + k * a_dim1; r1 = 1. / a[i__1].r; i__1 = k - 1; zdscal_(&i__1, &r1, &a[k * a_dim1 + 1], &c__1); i__1 = k - 1; zlacgv_(&i__1, &w[kw * w_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; d_lmp_cnjg(&z__2, &d21); z_lmp_div(&z__1, &w[k + kw * w_dim1], &z__2); 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__1.r = d11.r * d22.r - d11.i * d22.i, z__1.i = d11.r * d22.i + d11.i * d22.r; t = 1. / (z__1.r - 1.); z__2.r = t, z__2.i = 0.; z_lmp_div(&z__1, &z__2, &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; d_lmp_cnjg(&z__2, &d21); i__3 = j + kw * w_dim1; z__4.r = d22.r * w[i__3].r - d22.i * w[i__3].i, z__4.i = d22.r * w[i__3].i + d22.i * w[i__3].r; i__4 = j + (kw - 1) * w_dim1; z__3.r = z__4.r - w[i__4].r, z__3.i = z__4.i - w[i__4].i; z__1.r = z__2.r * z__3.r - z__2.i * z__3.i, z__1.i = z__2.r * z__3.i + z__2.i * z__3.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; i__1 = k - 1; zlacgv_(&i__1, &w[kw * w_dim1 + 1], &c__1); i__1 = k - 2; zlacgv_(&i__1, &w[(kw - 1) * w_dim1 + 1], &c__1); } } if (kstep == 1) { ipiv[k] = kp; } else { ipiv[k] = -kp; ipiv[k - 1] = -kp; } k -= kstep; goto L10; L30: i__1 = -(*nb); for (j = (k - 1) / *nb * *nb + 1; i__1 < 0 ? j >= 1 : j <= 1; j += i__1) { i__2 = *nb, i__3 = k - j + 1; jb = min(i__2, i__3); i__2 = j + jb - 1; for (jj = j; jj <= i__2; ++jj) { i__3 = jj + jj * a_dim1; i__4 = jj + jj * a_dim1; d__1 = a[i__4].r; a[i__3].r = d__1, a[i__3].i = 0.; i__3 = jj - j + 1; i__4 = *n - k; z__1.r = -1., z__1.i = -0.; zgemv_((char *)"No transpose", &i__3, &i__4, &z__1, &a[j + (k + 1) * a_dim1], lda, &w[jj + (kw + 1) * w_dim1], ldw, &c_b1, &a[j + jj * a_dim1], &c__1, (ftnlen)12); i__3 = jj + jj * a_dim1; i__4 = jj + jj * a_dim1; d__1 = a[i__4].r; a[i__3].r = d__1, a[i__3].i = 0.; } i__2 = j - 1; i__3 = *n - k; z__1.r = -1., z__1.i = -0.; zgemm_((char *)"No transpose", (char *)"Transpose", &i__2, &jb, &i__3, &z__1, &a[(k + 1) * a_dim1 + 1], lda, &w[j + (kw + 1) * w_dim1], ldw, &c_b1, &a[j * a_dim1 + 1], lda, (ftnlen)12, (ftnlen)9); } 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; } kstep = 1; i__1 = k + k * w_dim1; i__2 = k + k * a_dim1; d__1 = a[i__2].r; w[i__1].r = d__1, w[i__1].i = 0.; if (k < *n) { i__1 = *n - k; zcopy_(&i__1, &a[k + 1 + k * a_dim1], &c__1, &w[k + 1 + k * w_dim1], &c__1); } i__1 = *n - k + 1; i__2 = k - 1; z__1.r = -1., z__1.i = -0.; zgemv_((char *)"No transpose", &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)12); i__1 = k + k * w_dim1; i__2 = k + k * w_dim1; d__1 = w[i__2].r; w[i__1].r = d__1, w[i__1].i = 0.; i__1 = k + k * w_dim1; absakk = (d__1 = w[i__1].r, abs(d__1)); 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; i__1 = k + k * a_dim1; i__2 = k + k * a_dim1; d__1 = a[i__2].r; a[i__1].r = d__1, a[i__1].i = 0.; } 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 = imax - k; zlacgv_(&i__1, &w[k + (k + 1) * w_dim1], &c__1); i__1 = imax + (k + 1) * w_dim1; i__2 = imax + imax * a_dim1; d__1 = a[i__2].r; w[i__1].r = d__1, w[i__1].i = 0.; if (imax < *n) { i__1 = *n - imax; zcopy_(&i__1, &a[imax + 1 + imax * a_dim1], &c__1, &w[imax + 1 + (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 *)"No transpose", &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)12); i__1 = imax + (k + 1) * w_dim1; i__2 = imax + (k + 1) * w_dim1; d__1 = w[i__2].r; w[i__1].r = d__1, w[i__1].i = 0.; 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)) >= 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; d__1 = a[i__2].r; a[i__1].r = d__1, a[i__1].i = 0.; i__1 = kp - kk - 1; zcopy_(&i__1, &a[kk + 1 + kk * a_dim1], &c__1, &a[kp + (kk + 1) * a_dim1], lda); i__1 = kp - kk - 1; zlacgv_(&i__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) { i__1 = k + k * a_dim1; r1 = 1. / a[i__1].r; i__1 = *n - k; zdscal_(&i__1, &r1, &a[k + 1 + k * a_dim1], &c__1); i__1 = *n - k; zlacgv_(&i__1, &w[k + 1 + k * w_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; d_lmp_cnjg(&z__2, &d21); z_lmp_div(&z__1, &w[k + k * w_dim1], &z__2); d22.r = z__1.r, d22.i = z__1.i; z__1.r = d11.r * d22.r - d11.i * d22.i, z__1.i = d11.r * d22.i + d11.i * d22.r; t = 1. / (z__1.r - 1.); z__2.r = t, z__2.i = 0.; z_lmp_div(&z__1, &z__2, &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; d_lmp_cnjg(&z__2, &d21); i__3 = j + k * w_dim1; z__4.r = d11.r * w[i__3].r - d11.i * w[i__3].i, z__4.i = d11.r * w[i__3].i + d11.i * w[i__3].r; i__4 = j + (k + 1) * w_dim1; z__3.r = z__4.r - w[i__4].r, z__3.i = z__4.i - w[i__4].i; z__1.r = z__2.r * z__3.r - z__2.i * z__3.i, z__1.i = z__2.r * z__3.i + z__2.i * z__3.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; i__1 = *n - k; zlacgv_(&i__1, &w[k + 1 + k * w_dim1], &c__1); i__1 = *n - k - 1; zlacgv_(&i__1, &w[k + 2 + (k + 1) * w_dim1], &c__1); } } if (kstep == 1) { ipiv[k] = kp; } else { ipiv[k] = -kp; ipiv[k + 1] = -kp; } k += kstep; goto L70; L90: i__1 = *n; i__2 = *nb; for (j = k; i__2 < 0 ? j >= i__1 : j <= i__1; j += i__2) { i__3 = *nb, i__4 = *n - j + 1; jb = min(i__3, i__4); i__3 = j + jb - 1; for (jj = j; jj <= i__3; ++jj) { i__4 = jj + jj * a_dim1; i__5 = jj + jj * a_dim1; d__1 = a[i__5].r; a[i__4].r = d__1, a[i__4].i = 0.; i__4 = j + jb - jj; i__5 = k - 1; z__1.r = -1., z__1.i = -0.; zgemv_((char *)"No transpose", &i__4, &i__5, &z__1, &a[jj + a_dim1], lda, &w[jj + w_dim1], ldw, &c_b1, &a[jj + jj * a_dim1], &c__1, (ftnlen)12); i__4 = jj + jj * a_dim1; i__5 = jj + jj * a_dim1; d__1 = a[i__5].r; a[i__4].r = d__1, a[i__4].i = 0.; } if (j + jb <= *n) { i__3 = *n - j - jb + 1; i__4 = k - 1; z__1.r = -1., z__1.i = -0.; zgemm_((char *)"No transpose", (char *)"Transpose", &i__3, &jb, &i__4, &z__1, &a[j + jb + a_dim1], lda, &w[j + w_dim1], ldw, &c_b1, &a[j + jb + j * a_dim1], lda, (ftnlen)12, (ftnlen)9); } } 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