#include "f2c.h" #include "blaswrap.h" /* Table of constant values */ static doublecomplex c_b1 = {1.,0.}; static integer c__1 = 1; /* Subroutine */ int zlahef_(char *uplo, integer *n, integer *nb, integer *kb, doublecomplex *a, integer *lda, integer *ipiv, doublecomplex *w, integer *ldw, integer *info) { /* System generated locals */ 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; /* Builtin functions */ double sqrt(doublereal), d_imag(doublecomplex *); void d_cnjg(doublecomplex *, doublecomplex *), z_div(doublecomplex *, doublecomplex *, doublecomplex *); /* Local variables */ 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 *); extern /* Subroutine */ int zgemm_(char *, char *, integer *, integer *, integer *, doublecomplex *, doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, doublecomplex *, integer *); integer kstep; extern /* Subroutine */ int zgemv_(char *, integer *, integer *, doublecomplex *, doublecomplex *, integer *, doublecomplex *, integer *, doublecomplex *, doublecomplex *, integer *), zcopy_(integer *, doublecomplex *, integer *, doublecomplex *, integer *), zswap_(integer *, doublecomplex *, integer *, doublecomplex *, integer *); doublereal absakk; extern /* Subroutine */ int zdscal_(integer *, doublereal *, doublecomplex *, integer *); doublereal colmax; extern /* Subroutine */ int zlacgv_(integer *, doublecomplex *, integer *) ; extern integer izamax_(integer *, doublecomplex *, integer *); doublereal rowmax; /* -- LAPACK routine (version 3.1) -- */ /* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ /* November 2006 */ /* .. Scalar Arguments .. */ /* .. */ /* .. Array Arguments .. */ /* .. */ /* Purpose */ /* ======= */ /* ZLAHEF computes a partial factorization of a complex Hermitian */ /* matrix A using the Bunch-Kaufman diagonal pivoting method. The */ /* partial factorization has the form: */ /* A = ( I U12 ) ( A11 0 ) ( I 0 ) if UPLO = 'U', or: */ /* ( 0 U22 ) ( 0 D ) ( U12' U22' ) */ /* A = ( L11 0 ) ( D 0 ) ( L11' L21' ) if UPLO = 'L' */ /* ( L21 I ) ( 0 A22 ) ( 0 I ) */ /* where the order of D is at most NB. The actual order is returned in */ /* the argument KB, and is either NB or NB-1, or N if N <= NB. */ /* Note that U' denotes the conjugate transpose of U. */ /* ZLAHEF is an auxiliary routine called by ZHETRF. It uses blocked code */ /* (calling Level 3 BLAS) to update the submatrix A11 (if UPLO = 'U') or */ /* A22 (if UPLO = 'L'). */ /* Arguments */ /* ========= */ /* UPLO (input) CHARACTER*1 */ /* Specifies whether the upper or lower triangular part of the */ /* Hermitian matrix A is stored: */ /* = 'U': Upper triangular */ /* = 'L': Lower triangular */ /* N (input) INTEGER */ /* The order of the matrix A. N >= 0. */ /* NB (input) INTEGER */ /* The maximum number of columns of the matrix A that should be */ /* factored. NB should be at least 2 to allow for 2-by-2 pivot */ /* blocks. */ /* KB (output) INTEGER */ /* The number of columns of A that were actually factored. */ /* KB is either NB-1 or NB, or N if N <= NB. */ /* A (input/output) COMPLEX*16 array, dimension (LDA,N) */ /* On entry, the Hermitian matrix A. If UPLO = 'U', the leading */ /* n-by-n upper triangular part of A contains the upper */ /* triangular part of the matrix A, and the strictly lower */ /* triangular part of A is not referenced. If UPLO = 'L', the */ /* leading n-by-n lower triangular part of A contains the lower */ /* triangular part of the matrix A, and the strictly upper */ /* triangular part of A is not referenced. */ /* On exit, A contains details of the partial factorization. */ /* LDA (input) INTEGER */ /* The leading dimension of the array A. LDA >= max(1,N). */ /* IPIV (output) INTEGER array, dimension (N) */ /* Details of the interchanges and the block structure of D. */ /* If UPLO = 'U', only the last KB elements of IPIV are set; */ /* if UPLO = 'L', only the first KB elements are set. */ /* If IPIV(k) > 0, then rows and columns k and IPIV(k) were */ /* interchanged and D(k,k) is a 1-by-1 diagonal block. */ /* If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0, then rows and */ /* columns k-1 and -IPIV(k) were interchanged and D(k-1:k,k-1:k) */ /* is a 2-by-2 diagonal block. If UPLO = 'L' and IPIV(k) = */ /* IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k) were */ /* interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal block. */ /* W (workspace) COMPLEX*16 array, dimension (LDW,NB) */ /* LDW (input) INTEGER */ /* The leading dimension of the array W. LDW >= max(1,N). */ /* INFO (output) INTEGER */ /* = 0: successful exit */ /* > 0: if INFO = k, D(k,k) is exactly zero. The factorization */ /* has been completed, but the block diagonal matrix D is */ /* exactly singular. */ /* ===================================================================== */ /* .. Parameters .. */ /* .. */ /* .. Local Scalars .. */ /* .. */ /* .. External Functions .. */ /* .. */ /* .. External Subroutines .. */ /* .. */ /* .. Intrinsic Functions .. */ /* .. */ /* .. Statement Functions .. */ /* .. */ /* .. Statement Function definitions .. */ /* .. */ /* .. Executable Statements .. */ /* 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; /* Initialize ALPHA for use in choosing pivot block size. */ alpha = (sqrt(17.) + 1.) / 8.; if (lsame_(uplo, "U")) { /* Factorize the trailing columns of A using the upper triangle */ /* of A and working backwards, and compute the matrix W = U12*D */ /* for use in updating A11 (note that conjg(W) is actually stored) */ /* K is the main loop index, decreasing from N in steps of 1 or 2 */ /* KW is the column of W which corresponds to column K of A */ k = *n; L10: kw = *nb + k - *n; /* Exit from loop */ if (k <= *n - *nb + 1 && *nb < *n || k < 1) { goto L30; } /* Copy column K of A to column KW of W and update it */ 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_("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); 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.; } kstep = 1; /* Determine rows and columns to be interchanged and whether */ /* a 1-by-1 or 2-by-2 pivot block will be used */ i__1 = k + kw * w_dim1; absakk = (d__1 = w[i__1].r, abs(d__1)); /* IMAX is the row-index of the largest off-diagonal element in */ /* column K, and COLMAX is its absolute value */ 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_imag(&w[imax + kw * w_dim1]), abs(d__2)); } else { colmax = 0.; } if (max(absakk,colmax) == 0.) { /* Column K is zero: set INFO and continue */ 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) { /* no interchange, use 1-by-1 pivot block */ kp = k; } else { /* Copy column IMAX to column KW-1 of W and update it */ 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_("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); 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.; } /* JMAX is the column-index of the largest off-diagonal */ /* element in row IMAX, and ROWMAX is its absolute value */ 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_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); /* Computing MAX */ i__1 = jmax + (kw - 1) * w_dim1; d__3 = rowmax, d__4 = (d__1 = w[i__1].r, abs(d__1)) + ( d__2 = d_imag(&w[jmax + (kw - 1) * w_dim1]), abs( d__2)); rowmax = max(d__3,d__4); } if (absakk >= alpha * colmax * (colmax / rowmax)) { /* no interchange, use 1-by-1 pivot block */ kp = k; } else /* if(complicated condition) */ { i__1 = imax + (kw - 1) * w_dim1; if ((d__1 = w[i__1].r, abs(d__1)) >= alpha * rowmax) { /* interchange rows and columns K and IMAX, use 1-by-1 */ /* pivot block */ kp = imax; /* copy column KW-1 of W to column KW */ zcopy_(&k, &w[(kw - 1) * w_dim1 + 1], &c__1, &w[kw * w_dim1 + 1], &c__1); } else { /* interchange rows and columns K-1 and IMAX, use 2-by-2 */ /* pivot block */ kp = imax; kstep = 2; } } } kk = k - kstep + 1; kkw = *nb + kk - *n; /* Updated column KP is already stored in column KKW of W */ if (kp != kk) { /* Copy non-updated column KK to column KP */ 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); i__1 = kp - 1; zcopy_(&i__1, &a[kk * a_dim1 + 1], &c__1, &a[kp * a_dim1 + 1], &c__1); /* Interchange rows KK and KP in last KK columns of A and W */ if (kk < *n) { i__1 = *n - kk; zswap_(&i__1, &a[kk + (kk + 1) * a_dim1], lda, &a[kp + ( kk + 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) { /* 1-by-1 pivot block D(k): column KW of W now holds */ /* W(k) = U(k)*D(k) */ /* where U(k) is the k-th column of U */ /* Store U(k) in column k of A */ zcopy_(&k, &w[kw * w_dim1 + 1], &c__1, &a[k * a_dim1 + 1], & c__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); /* Conjugate W(k) */ i__1 = k - 1; zlacgv_(&i__1, &w[kw * w_dim1 + 1], &c__1); } else { /* 2-by-2 pivot block D(k): columns KW and KW-1 of W now */ /* hold */ /* ( W(k-1) W(k) ) = ( U(k-1) U(k) )*D(k) */ /* where U(k) and U(k-1) are the k-th and (k-1)-th columns */ /* of U */ if (k > 2) { /* Store U(k) and U(k-1) in columns k and k-1 of A */ i__1 = k - 1 + kw * w_dim1; d21.r = w[i__1].r, d21.i = w[i__1].i; d_cnjg(&z__2, &d21); z_div(&z__1, &w[k + kw * w_dim1], &z__2); d11.r = z__1.r, d11.i = z__1.i; z_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_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_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; /* L20: */ } } /* Copy D(k) to A */ 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; /* Conjugate W(k) and W(k-1) */ 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); } } /* Store details of the interchanges in IPIV */ if (kstep == 1) { ipiv[k] = kp; } else { ipiv[k] = -kp; ipiv[k - 1] = -kp; } /* Decrease K and return to the start of the main loop */ k -= kstep; goto L10; L30: /* Update the upper triangle of A11 (= A(1:k,1:k)) as */ /* A11 := A11 - U12*D*U12' = A11 - U12*W' */ /* computing blocks of NB columns at a time (note that conjg(W) is */ /* actually stored) */ i__1 = -(*nb); for (j = (k - 1) / *nb * *nb + 1; i__1 < 0 ? j >= 1 : j <= 1; j += i__1) { /* Computing MIN */ i__2 = *nb, i__3 = k - j + 1; jb = min(i__2,i__3); /* Update the upper triangle of the diagonal block */ 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_("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); 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.; /* L40: */ } /* Update the rectangular superdiagonal block */ i__2 = j - 1; i__3 = *n - k; z__1.r = -1., z__1.i = -0.; zgemm_("No transpose", "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); /* L50: */ } /* Put U12 in standard form by partially undoing the interchanges */ /* in columns k+1:n */ 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; } /* Set KB to the number of columns factorized */ *kb = *n - k; } else { /* Factorize the leading columns of A using the lower triangle */ /* of A and working forwards, and compute the matrix W = L21*D */ /* for use in updating A22 (note that conjg(W) is actually stored) */ /* K is the main loop index, increasing from 1 in steps of 1 or 2 */ k = 1; L70: /* Exit from loop */ if (k >= *nb && *nb < *n || k > *n) { goto L90; } /* Copy column K of A to column K of W and update it */ 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_("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); 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.; kstep = 1; /* Determine rows and columns to be interchanged and whether */ /* a 1-by-1 or 2-by-2 pivot block will be used */ i__1 = k + k * w_dim1; absakk = (d__1 = w[i__1].r, abs(d__1)); /* IMAX is the row-index of the largest off-diagonal element in */ /* column K, and COLMAX is its absolute value */ 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_imag(&w[imax + k * w_dim1]), abs(d__2)); } else { colmax = 0.; } if (max(absakk,colmax) == 0.) { /* Column K is zero: set INFO and continue */ 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) { /* no interchange, use 1-by-1 pivot block */ kp = k; } else { /* Copy column IMAX to column K+1 of W and update it */ 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_("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); 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.; /* JMAX is the column-index of the largest off-diagonal */ /* element in row IMAX, and ROWMAX is its absolute value */ 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_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); /* Computing MAX */ i__1 = jmax + (k + 1) * w_dim1; d__3 = rowmax, d__4 = (d__1 = w[i__1].r, abs(d__1)) + ( d__2 = d_imag(&w[jmax + (k + 1) * w_dim1]), abs( d__2)); rowmax = max(d__3,d__4); } if (absakk >= alpha * colmax * (colmax / rowmax)) { /* no interchange, use 1-by-1 pivot block */ kp = k; } else /* if(complicated condition) */ { i__1 = imax + (k + 1) * w_dim1; if ((d__1 = w[i__1].r, abs(d__1)) >= alpha * rowmax) { /* interchange rows and columns K and IMAX, use 1-by-1 */ /* pivot block */ kp = imax; /* copy column K+1 of W to column K */ i__1 = *n - k + 1; zcopy_(&i__1, &w[k + (k + 1) * w_dim1], &c__1, &w[k + k * w_dim1], &c__1); } else { /* interchange rows and columns K+1 and IMAX, use 2-by-2 */ /* pivot block */ kp = imax; kstep = 2; } } } kk = k + kstep - 1; /* Updated column KP is already stored in column KK of W */ if (kp != kk) { /* Copy non-updated column KK to column KP */ 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); } /* Interchange rows KK and KP in first KK columns of A and W */ i__1 = kk - 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) { /* 1-by-1 pivot block D(k): column k of W now holds */ /* W(k) = L(k)*D(k) */ /* where L(k) is the k-th column of L */ /* Store L(k) in column k of A */ 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); /* Conjugate W(k) */ i__1 = *n - k; zlacgv_(&i__1, &w[k + 1 + k * w_dim1], &c__1); } } else { /* 2-by-2 pivot block D(k): columns k and k+1 of W now hold */ /* ( W(k) W(k+1) ) = ( L(k) L(k+1) )*D(k) */ /* where L(k) and L(k+1) are the k-th and (k+1)-th columns */ /* of L */ if (k < *n - 1) { /* Store L(k) and L(k+1) in columns k and k+1 of A */ i__1 = k + 1 + k * w_dim1; d21.r = w[i__1].r, d21.i = w[i__1].i; z_div(&z__1, &w[k + 1 + (k + 1) * w_dim1], &d21); d11.r = z__1.r, d11.i = z__1.i; d_cnjg(&z__2, &d21); z_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_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_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; /* L80: */ } } /* Copy D(k) to A */ 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; /* Conjugate W(k) and W(k+1) */ 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); } } /* Store details of the interchanges in IPIV */ if (kstep == 1) { ipiv[k] = kp; } else { ipiv[k] = -kp; ipiv[k + 1] = -kp; } /* Increase K and return to the start of the main loop */ k += kstep; goto L70; L90: /* Update the lower triangle of A22 (= A(k:n,k:n)) as */ /* A22 := A22 - L21*D*L21' = A22 - L21*W' */ /* computing blocks of NB columns at a time (note that conjg(W) is */ /* actually stored) */ i__1 = *n; i__2 = *nb; for (j = k; i__2 < 0 ? j >= i__1 : j <= i__1; j += i__2) { /* Computing MIN */ i__3 = *nb, i__4 = *n - j + 1; jb = min(i__3,i__4); /* Update the lower triangle of the diagonal block */ 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_("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); 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.; /* L100: */ } /* Update the rectangular subdiagonal block */ if (j + jb <= *n) { i__3 = *n - j - jb + 1; i__4 = k - 1; z__1.r = -1., z__1.i = -0.; zgemm_("No transpose", "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); } /* L110: */ } /* Put L21 in standard form by partially undoing the interchanges */ /* in columns 1:k-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; } /* Set KB to the number of columns factorized */ *kb = k - 1; } return 0; /* End of ZLAHEF */ } /* zlahef_ */