[] add metering mode to CLI

1 files changed, 938 insertions, 0 deletions

diff --git a/contrib/libs/clapack/zlahef.c b/contrib/libs/clapack/zlahef.c
new file mode 100644
index 0000000000..048db906be
--- /dev/null
+++ b/contrib/libs/clapack/zlahef.c
@@ -0,0 +1,938 @@
+/* zlahef.f -- translated by f2c (version 20061008).
+   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"
+#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 3.2) -- */
+/*     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_ */