#ifdef __cplusplus extern "C" { #endif #include "lmp_f2c.h" static integer c__1 = 1; int zhetf2_(char *uplo, integer *n, doublecomplex *a, integer *lda, integer *ipiv, integer *info, ftnlen uplo_len) { integer a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5, i__6; doublereal d__1, d__2, d__3, d__4; doublecomplex z__1, z__2, z__3, z__4, z__5, z__6; double sqrt(doublereal), d_lmp_imag(doublecomplex *); void d_lmp_cnjg(doublecomplex *, doublecomplex *); doublereal d__; integer i__, j, k; doublecomplex t; doublereal r1, d11; doublecomplex d12; doublereal d22; doublecomplex d21; integer kk, kp; doublecomplex wk; doublereal tt; doublecomplex wkm1, wkp1; integer imax, jmax; extern int zher_(char *, integer *, doublereal *, doublecomplex *, integer *, doublecomplex *, integer *, ftnlen); doublereal alpha; extern logical lsame_(char *, char *, ftnlen, ftnlen); integer kstep; logical upper; extern int zswap_(integer *, doublecomplex *, integer *, doublecomplex *, integer *); extern doublereal dlapy2_(doublereal *, doublereal *); doublereal absakk; extern logical disnan_(doublereal *); extern int xerbla_(char *, integer *, ftnlen), zdscal_(integer *, doublereal *, doublecomplex *, integer *); doublereal colmax; extern integer izamax_(integer *, doublecomplex *, integer *); doublereal rowmax; a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; --ipiv; *info = 0; upper = lsame_(uplo, (char *)"U", (ftnlen)1, (ftnlen)1); if (!upper && !lsame_(uplo, (char *)"L", (ftnlen)1, (ftnlen)1)) { *info = -1; } else if (*n < 0) { *info = -2; } else if (*lda < max(1, *n)) { *info = -4; } if (*info != 0) { i__1 = -(*info); xerbla_((char *)"ZHETF2", &i__1, (ftnlen)6); return 0; } alpha = (sqrt(17.) + 1.) / 8.; if (upper) { k = *n; L10: if (k < 1) { goto L90; } kstep = 1; i__1 = k + k * a_dim1; absakk = (d__1 = a[i__1].r, abs(d__1)); if (k > 1) { i__1 = k - 1; imax = izamax_(&i__1, &a[k * a_dim1 + 1], &c__1); i__1 = imax + k * a_dim1; colmax = (d__1 = a[i__1].r, abs(d__1)) + (d__2 = d_lmp_imag(&a[imax + k * a_dim1]), abs(d__2)); } else { colmax = 0.; } if (max(absakk, colmax) == 0. || disnan_(&absakk)) { 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 = k - imax; jmax = imax + izamax_(&i__1, &a[imax + (imax + 1) * a_dim1], lda); i__1 = imax + jmax * a_dim1; rowmax = (d__1 = a[i__1].r, abs(d__1)) + (d__2 = d_lmp_imag(&a[imax + jmax * a_dim1]), abs(d__2)); if (imax > 1) { i__1 = imax - 1; jmax = izamax_(&i__1, &a[imax * a_dim1 + 1], &c__1); i__1 = jmax + imax * a_dim1; d__3 = rowmax, d__4 = (d__1 = a[i__1].r, abs(d__1)) + (d__2 = d_lmp_imag(&a[jmax + imax * a_dim1]), abs(d__2)); rowmax = max(d__3, d__4); } if (absakk >= alpha * colmax * (colmax / rowmax)) { kp = k; } else { i__1 = imax + imax * a_dim1; if ((d__1 = a[i__1].r, abs(d__1)) >= alpha * rowmax) { kp = imax; } else { kp = imax; kstep = 2; } } } kk = k - kstep + 1; if (kp != kk) { i__1 = kp - 1; zswap_(&i__1, &a[kk * a_dim1 + 1], &c__1, &a[kp * a_dim1 + 1], &c__1); i__1 = kk - 1; for (j = kp + 1; j <= i__1; ++j) { d_lmp_cnjg(&z__1, &a[j + kk * a_dim1]); t.r = z__1.r, t.i = z__1.i; i__2 = j + kk * a_dim1; d_lmp_cnjg(&z__1, &a[kp + j * a_dim1]); a[i__2].r = z__1.r, a[i__2].i = z__1.i; i__2 = kp + j * a_dim1; a[i__2].r = t.r, a[i__2].i = t.i; } i__1 = kp + kk * a_dim1; d_lmp_cnjg(&z__1, &a[kp + kk * a_dim1]); a[i__1].r = z__1.r, a[i__1].i = z__1.i; i__1 = kk + kk * a_dim1; r1 = a[i__1].r; i__1 = kk + kk * a_dim1; i__2 = kp + kp * a_dim1; d__1 = a[i__2].r; a[i__1].r = d__1, a[i__1].i = 0.; i__1 = kp + kp * a_dim1; a[i__1].r = r1, a[i__1].i = 0.; if (kstep == 2) { 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.; i__1 = k - 1 + k * a_dim1; t.r = a[i__1].r, t.i = a[i__1].i; i__1 = k - 1 + k * a_dim1; i__2 = kp + k * a_dim1; a[i__1].r = a[i__2].r, a[i__1].i = a[i__2].i; i__1 = kp + k * a_dim1; a[i__1].r = t.r, a[i__1].i = t.i; } } else { 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.; if (kstep == 2) { i__1 = k - 1 + (k - 1) * a_dim1; i__2 = k - 1 + (k - 1) * a_dim1; d__1 = a[i__2].r; a[i__1].r = d__1, a[i__1].i = 0.; } } if (kstep == 1) { i__1 = k + k * a_dim1; r1 = 1. / a[i__1].r; i__1 = k - 1; d__1 = -r1; zher_(uplo, &i__1, &d__1, &a[k * a_dim1 + 1], &c__1, &a[a_offset], lda, (ftnlen)1); i__1 = k - 1; zdscal_(&i__1, &r1, &a[k * a_dim1 + 1], &c__1); } else { if (k > 2) { i__1 = k - 1 + k * a_dim1; d__1 = a[i__1].r; d__2 = d_lmp_imag(&a[k - 1 + k * a_dim1]); d__ = dlapy2_(&d__1, &d__2); i__1 = k - 1 + (k - 1) * a_dim1; d22 = a[i__1].r / d__; i__1 = k + k * a_dim1; d11 = a[i__1].r / d__; tt = 1. / (d11 * d22 - 1.); i__1 = k - 1 + k * a_dim1; z__1.r = a[i__1].r / d__, z__1.i = a[i__1].i / d__; d12.r = z__1.r, d12.i = z__1.i; d__ = tt / d__; for (j = k - 2; j >= 1; --j) { i__1 = j + (k - 1) * a_dim1; z__3.r = d11 * a[i__1].r, z__3.i = d11 * a[i__1].i; d_lmp_cnjg(&z__5, &d12); i__2 = j + k * a_dim1; z__4.r = z__5.r * a[i__2].r - z__5.i * a[i__2].i, z__4.i = z__5.r * a[i__2].i + z__5.i * a[i__2].r; z__2.r = z__3.r - z__4.r, z__2.i = z__3.i - z__4.i; z__1.r = d__ * z__2.r, z__1.i = d__ * z__2.i; wkm1.r = z__1.r, wkm1.i = z__1.i; i__1 = j + k * a_dim1; z__3.r = d22 * a[i__1].r, z__3.i = d22 * a[i__1].i; i__2 = j + (k - 1) * a_dim1; z__4.r = d12.r * a[i__2].r - d12.i * a[i__2].i, z__4.i = d12.r * a[i__2].i + d12.i * a[i__2].r; z__2.r = z__3.r - z__4.r, z__2.i = z__3.i - z__4.i; z__1.r = d__ * z__2.r, z__1.i = d__ * z__2.i; wk.r = z__1.r, wk.i = z__1.i; for (i__ = j; i__ >= 1; --i__) { i__1 = i__ + j * a_dim1; i__2 = i__ + j * a_dim1; i__3 = i__ + k * a_dim1; d_lmp_cnjg(&z__4, &wk); z__3.r = a[i__3].r * z__4.r - a[i__3].i * z__4.i, z__3.i = a[i__3].r * z__4.i + a[i__3].i * z__4.r; z__2.r = a[i__2].r - z__3.r, z__2.i = a[i__2].i - z__3.i; i__4 = i__ + (k - 1) * a_dim1; d_lmp_cnjg(&z__6, &wkm1); z__5.r = a[i__4].r * z__6.r - a[i__4].i * z__6.i, z__5.i = a[i__4].r * z__6.i + a[i__4].i * z__6.r; z__1.r = z__2.r - z__5.r, z__1.i = z__2.i - z__5.i; a[i__1].r = z__1.r, a[i__1].i = z__1.i; } i__1 = j + k * a_dim1; a[i__1].r = wk.r, a[i__1].i = wk.i; i__1 = j + (k - 1) * a_dim1; a[i__1].r = wkm1.r, a[i__1].i = wkm1.i; i__1 = j + j * a_dim1; i__2 = j + j * a_dim1; d__1 = a[i__2].r; z__1.r = d__1, z__1.i = 0.; a[i__1].r = z__1.r, a[i__1].i = z__1.i; } } } } if (kstep == 1) { ipiv[k] = kp; } else { ipiv[k] = -kp; ipiv[k - 1] = -kp; } k -= kstep; goto L10; } else { k = 1; L50: if (k > *n) { goto L90; } kstep = 1; i__1 = k + k * a_dim1; absakk = (d__1 = a[i__1].r, abs(d__1)); if (k < *n) { i__1 = *n - k; imax = k + izamax_(&i__1, &a[k + 1 + k * a_dim1], &c__1); i__1 = imax + k * a_dim1; colmax = (d__1 = a[i__1].r, abs(d__1)) + (d__2 = d_lmp_imag(&a[imax + k * a_dim1]), abs(d__2)); } else { colmax = 0.; } if (max(absakk, colmax) == 0. || disnan_(&absakk)) { 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; jmax = k - 1 + izamax_(&i__1, &a[imax + k * a_dim1], lda); i__1 = imax + jmax * a_dim1; rowmax = (d__1 = a[i__1].r, abs(d__1)) + (d__2 = d_lmp_imag(&a[imax + jmax * a_dim1]), abs(d__2)); if (imax < *n) { i__1 = *n - imax; jmax = imax + izamax_(&i__1, &a[imax + 1 + imax * a_dim1], &c__1); i__1 = jmax + imax * a_dim1; d__3 = rowmax, d__4 = (d__1 = a[i__1].r, abs(d__1)) + (d__2 = d_lmp_imag(&a[jmax + imax * a_dim1]), abs(d__2)); rowmax = max(d__3, d__4); } if (absakk >= alpha * colmax * (colmax / rowmax)) { kp = k; } else { i__1 = imax + imax * a_dim1; if ((d__1 = a[i__1].r, abs(d__1)) >= alpha * rowmax) { kp = imax; } else { kp = imax; kstep = 2; } } } kk = k + kstep - 1; if (kp != kk) { if (kp < *n) { i__1 = *n - kp; zswap_(&i__1, &a[kp + 1 + kk * a_dim1], &c__1, &a[kp + 1 + kp * a_dim1], &c__1); } i__1 = kp - 1; for (j = kk + 1; j <= i__1; ++j) { d_lmp_cnjg(&z__1, &a[j + kk * a_dim1]); t.r = z__1.r, t.i = z__1.i; i__2 = j + kk * a_dim1; d_lmp_cnjg(&z__1, &a[kp + j * a_dim1]); a[i__2].r = z__1.r, a[i__2].i = z__1.i; i__2 = kp + j * a_dim1; a[i__2].r = t.r, a[i__2].i = t.i; } i__1 = kp + kk * a_dim1; d_lmp_cnjg(&z__1, &a[kp + kk * a_dim1]); a[i__1].r = z__1.r, a[i__1].i = z__1.i; i__1 = kk + kk * a_dim1; r1 = a[i__1].r; i__1 = kk + kk * a_dim1; i__2 = kp + kp * a_dim1; d__1 = a[i__2].r; a[i__1].r = d__1, a[i__1].i = 0.; i__1 = kp + kp * a_dim1; a[i__1].r = r1, a[i__1].i = 0.; if (kstep == 2) { 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.; i__1 = k + 1 + k * a_dim1; t.r = a[i__1].r, t.i = a[i__1].i; i__1 = k + 1 + k * a_dim1; i__2 = kp + k * a_dim1; a[i__1].r = a[i__2].r, a[i__1].i = a[i__2].i; i__1 = kp + k * a_dim1; a[i__1].r = t.r, a[i__1].i = t.i; } } else { 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.; if (kstep == 2) { i__1 = k + 1 + (k + 1) * a_dim1; i__2 = k + 1 + (k + 1) * a_dim1; d__1 = a[i__2].r; a[i__1].r = d__1, a[i__1].i = 0.; } } if (kstep == 1) { if (k < *n) { i__1 = k + k * a_dim1; r1 = 1. / a[i__1].r; i__1 = *n - k; d__1 = -r1; zher_(uplo, &i__1, &d__1, &a[k + 1 + k * a_dim1], &c__1, &a[k + 1 + (k + 1) * a_dim1], lda, (ftnlen)1); i__1 = *n - k; zdscal_(&i__1, &r1, &a[k + 1 + k * a_dim1], &c__1); } } else { if (k < *n - 1) { i__1 = k + 1 + k * a_dim1; d__1 = a[i__1].r; d__2 = d_lmp_imag(&a[k + 1 + k * a_dim1]); d__ = dlapy2_(&d__1, &d__2); i__1 = k + 1 + (k + 1) * a_dim1; d11 = a[i__1].r / d__; i__1 = k + k * a_dim1; d22 = a[i__1].r / d__; tt = 1. / (d11 * d22 - 1.); i__1 = k + 1 + k * a_dim1; z__1.r = a[i__1].r / d__, z__1.i = a[i__1].i / d__; d21.r = z__1.r, d21.i = z__1.i; d__ = tt / d__; i__1 = *n; for (j = k + 2; j <= i__1; ++j) { i__2 = j + k * a_dim1; z__3.r = d11 * a[i__2].r, z__3.i = d11 * a[i__2].i; i__3 = j + (k + 1) * a_dim1; z__4.r = d21.r * a[i__3].r - d21.i * a[i__3].i, z__4.i = d21.r * a[i__3].i + d21.i * a[i__3].r; z__2.r = z__3.r - z__4.r, z__2.i = z__3.i - z__4.i; z__1.r = d__ * z__2.r, z__1.i = d__ * z__2.i; wk.r = z__1.r, wk.i = z__1.i; i__2 = j + (k + 1) * a_dim1; z__3.r = d22 * a[i__2].r, z__3.i = d22 * a[i__2].i; d_lmp_cnjg(&z__5, &d21); i__3 = j + k * a_dim1; z__4.r = z__5.r * a[i__3].r - z__5.i * a[i__3].i, z__4.i = z__5.r * a[i__3].i + z__5.i * a[i__3].r; z__2.r = z__3.r - z__4.r, z__2.i = z__3.i - z__4.i; z__1.r = d__ * z__2.r, z__1.i = d__ * z__2.i; wkp1.r = z__1.r, wkp1.i = z__1.i; i__2 = *n; for (i__ = j; i__ <= i__2; ++i__) { i__3 = i__ + j * a_dim1; i__4 = i__ + j * a_dim1; i__5 = i__ + k * a_dim1; d_lmp_cnjg(&z__4, &wk); z__3.r = a[i__5].r * z__4.r - a[i__5].i * z__4.i, z__3.i = a[i__5].r * z__4.i + a[i__5].i * z__4.r; z__2.r = a[i__4].r - z__3.r, z__2.i = a[i__4].i - z__3.i; i__6 = i__ + (k + 1) * a_dim1; d_lmp_cnjg(&z__6, &wkp1); z__5.r = a[i__6].r * z__6.r - a[i__6].i * z__6.i, z__5.i = a[i__6].r * z__6.i + a[i__6].i * z__6.r; z__1.r = z__2.r - z__5.r, z__1.i = z__2.i - z__5.i; a[i__3].r = z__1.r, a[i__3].i = z__1.i; } i__2 = j + k * a_dim1; a[i__2].r = wk.r, a[i__2].i = wk.i; i__2 = j + (k + 1) * a_dim1; a[i__2].r = wkp1.r, a[i__2].i = wkp1.i; i__2 = j + j * a_dim1; i__3 = j + j * a_dim1; d__1 = a[i__3].r; z__1.r = d__1, z__1.i = 0.; a[i__2].r = z__1.r, a[i__2].i = z__1.i; } } } } if (kstep == 1) { ipiv[k] = kp; } else { ipiv[k] = -kp; ipiv[k + 1] = -kp; } k += kstep; goto L50; } L90: return 0; } #ifdef __cplusplus } #endif