示例#1
0
/* Subroutine */
int zsytf2_rook_(char *uplo, integer *n, doublecomplex *a, integer *lda, integer *ipiv, integer *info)
{
    /* System generated locals */
    integer a_dim1, a_offset, i__1, i__2, i__3, i__4;
    doublereal d__1, d__2;
    doublecomplex z__1, z__2, z__3, z__4, z__5, z__6;
    /* Builtin functions */
    double sqrt(doublereal), d_imag(doublecomplex *);
    void z_div(doublecomplex *, doublecomplex *, doublecomplex *);
    /* Local variables */
    integer i__, j, k, p;
    doublecomplex t, d11, d12, d21, d22;
    integer ii, kk, kp;
    doublecomplex wk, wkm1, wkp1;
    logical done;
    integer imax, jmax;
    extern /* Subroutine */
    int zsyr_(char *, integer *, doublecomplex *, doublecomplex *, integer *, doublecomplex *, integer *);
    doublereal alpha;
    extern logical lsame_(char *, char *);
    doublereal dtemp, sfmin;
    extern /* Subroutine */
    int zscal_(integer *, doublecomplex *, doublecomplex *, integer *);
    integer itemp, kstep;
    logical upper;
    extern /* Subroutine */
    int zswap_(integer *, doublecomplex *, integer *, doublecomplex *, integer *);
    extern doublereal dlamch_(char *);
    doublereal absakk;
    extern /* Subroutine */
    int xerbla_(char *, integer *);
    doublereal colmax;
    extern integer izamax_(integer *, doublecomplex *, integer *);
    doublereal rowmax;
    /* -- LAPACK computational routine (version 3.5.0) -- */
    /* -- LAPACK is a software package provided by Univ. of Tennessee, -- */
    /* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */
    /* November 2013 */
    /* .. Scalar Arguments .. */
    /* .. */
    /* .. Array Arguments .. */
    /* .. */
    /* ===================================================================== */
    /* .. Parameters .. */
    /* .. */
    /* .. Local Scalars .. */
    /* .. */
    /* .. External Functions .. */
    /* .. */
    /* .. External Subroutines .. */
    /* .. */
    /* .. Intrinsic Functions .. */
    /* .. */
    /* .. Statement Functions .. */
    /* .. */
    /* .. Statement Function definitions .. */
    /* .. */
    /* .. Executable Statements .. */
    /* Test the input parameters. */
    /* Parameter adjustments */
    a_dim1 = *lda;
    a_offset = 1 + a_dim1;
    a -= a_offset;
    --ipiv;
    /* Function Body */
    *info = 0;
    upper = lsame_(uplo, "U");
    if (! upper && ! lsame_(uplo, "L"))
    {
        *info = -1;
    }
    else if (*n < 0)
    {
        *info = -2;
    }
    else if (*lda < max(1,*n))
    {
        *info = -4;
    }
    if (*info != 0)
    {
        i__1 = -(*info);
        xerbla_("ZSYTF2_ROOK", &i__1);
        return 0;
    }
    /* Initialize ALPHA for use in choosing pivot block size. */
    alpha = (sqrt(17.) + 1.) / 8.;
    /* Compute machine safe minimum */
    sfmin = dlamch_("S");
    if (upper)
    {
        /* Factorize A as U*D*U**T using the upper triangle of A */
        /* K is the main loop index, decreasing from N to 1 in steps of */
        /* 1 or 2 */
        k = *n;
L10: /* If K < 1, exit from loop */
        if (k < 1)
        {
            goto L70;
        }
        kstep = 1;
        p = k;
        /* 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 * a_dim1;
        absakk = (d__1 = a[i__1].r, abs(d__1)) + (d__2 = d_imag(&a[k + k * a_dim1]), abs(d__2));
        /* IMAX is the row-index of the largest off-diagonal element in */
        /* column K, and COLMAX is its absolute value. */
        /* Determine both COLMAX and IMAX. */
        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_imag(&a[imax + k * a_dim1]), abs(d__2));
        }
        else
        {
            colmax = 0.;
        }
        if (max(absakk,colmax) == 0.)
        {
            /* Column K is zero or underflow: set INFO and continue */
            if (*info == 0)
            {
                *info = k;
            }
            kp = k;
        }
        else
        {
            /* Test for interchange */
            /* Equivalent to testing for (used to handle NaN and Inf) */
            /* ABSAKK.GE.ALPHA*COLMAX */
            if (! (absakk < alpha * colmax))
            {
                /* no interchange, */
                /* use 1-by-1 pivot block */
                kp = k;
            }
            else
            {
                done = FALSE_;
                /* Loop until pivot found */
L12: /* Begin pivot search loop body */
                /* JMAX is the column-index of the largest off-diagonal */
                /* element in row IMAX, and ROWMAX is its absolute value. */
                /* Determine both ROWMAX and JMAX. */
                if (imax != k)
                {
                    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_imag(& a[imax + jmax * a_dim1]), abs(d__2));
                }
                else
                {
                    rowmax = 0.;
                }
                if (imax > 1)
                {
                    i__1 = imax - 1;
                    itemp = izamax_(&i__1, &a[imax * a_dim1 + 1], &c__1);
                    i__1 = itemp + imax * a_dim1;
                    dtemp = (d__1 = a[i__1].r, abs(d__1)) + (d__2 = d_imag(&a[ itemp + imax * a_dim1]), abs(d__2));
                    if (dtemp > rowmax)
                    {
                        rowmax = dtemp;
                        jmax = itemp;
                    }
                }
                /* Equivalent to testing for (used to handle NaN and Inf) */
                /* CABS1( A( IMAX, IMAX ) ).GE.ALPHA*ROWMAX */
                i__1 = imax + imax * a_dim1;
                if (! ((d__1 = a[i__1].r, abs(d__1)) + (d__2 = d_imag(&a[imax + imax * a_dim1]), abs(d__2)) < alpha * rowmax))
                {
                    /* interchange rows and columns K and IMAX, */
                    /* use 1-by-1 pivot block */
                    kp = imax;
                    done = TRUE_;
                    /* Equivalent to testing for ROWMAX .EQ. COLMAX, */
                    /* used to handle NaN and Inf */
                }
                else if (p == jmax || rowmax <= colmax)
                {
                    /* interchange rows and columns K+1 and IMAX, */
                    /* use 2-by-2 pivot block */
                    kp = imax;
                    kstep = 2;
                    done = TRUE_;
                }
                else
                {
                    /* Pivot NOT found, set variables and repeat */
                    p = imax;
                    colmax = rowmax;
                    imax = jmax;
                }
                /* End pivot search loop body */
                if (! done)
                {
                    goto L12;
                }
            }
            /* Swap TWO rows and TWO columns */
            /* First swap */
            if (kstep == 2 && p != k)
            {
                /* Interchange rows and column K and P in the leading */
                /* submatrix A(1:k,1:k) if we have a 2-by-2 pivot */
                if (p > 1)
                {
                    i__1 = p - 1;
                    zswap_(&i__1, &a[k * a_dim1 + 1], &c__1, &a[p * a_dim1 + 1], &c__1);
                }
                if (p < k - 1)
                {
                    i__1 = k - p - 1;
                    zswap_(&i__1, &a[p + 1 + k * a_dim1], &c__1, &a[p + (p + 1) * a_dim1], lda);
                }
                i__1 = k + k * a_dim1;
                t.r = a[i__1].r;
                t.i = a[i__1].i; // , expr subst
                i__1 = k + k * a_dim1;
                i__2 = p + p * a_dim1;
                a[i__1].r = a[i__2].r;
                a[i__1].i = a[i__2].i; // , expr subst
                i__1 = p + p * a_dim1;
                a[i__1].r = t.r;
                a[i__1].i = t.i; // , expr subst
            }
            /* Second swap */
            kk = k - kstep + 1;
            if (kp != kk)
            {
                /* Interchange rows and columns KK and KP in the leading */
                /* submatrix A(1:k,1:k) */
                if (kp > 1)
                {
                    i__1 = kp - 1;
                    zswap_(&i__1, &a[kk * a_dim1 + 1], &c__1, &a[kp * a_dim1 + 1], &c__1);
                }
                if (kk > 1 && kp < kk - 1)
                {
                    i__1 = kk - kp - 1;
                    zswap_(&i__1, &a[kp + 1 + kk * a_dim1], &c__1, &a[kp + ( kp + 1) * a_dim1], lda);
                }
                i__1 = kk + kk * a_dim1;
                t.r = a[i__1].r;
                t.i = a[i__1].i; // , expr subst
                i__1 = kk + kk * a_dim1;
                i__2 = kp + kp * a_dim1;
                a[i__1].r = a[i__2].r;
                a[i__1].i = a[i__2].i; // , expr subst
                i__1 = kp + kp * a_dim1;
                a[i__1].r = t.r;
                a[i__1].i = t.i; // , expr subst
                if (kstep == 2)
                {
                    i__1 = k - 1 + k * a_dim1;
                    t.r = a[i__1].r;
                    t.i = a[i__1].i; // , expr subst
                    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; // , expr subst
                    i__1 = kp + k * a_dim1;
                    a[i__1].r = t.r;
                    a[i__1].i = t.i; // , expr subst
                }
            }
            /* Update the leading submatrix */
            if (kstep == 1)
            {
                /* 1-by-1 pivot block D(k): column k now holds */
                /* W(k) = U(k)*D(k) */
                /* where U(k) is the k-th column of U */
                if (k > 1)
                {
                    /* Perform a rank-1 update of A(1:k-1,1:k-1) and */
                    /* store U(k) in column k */
                    i__1 = k + k * a_dim1;
                    if ((d__1 = a[i__1].r, abs(d__1)) + (d__2 = d_imag(&a[k + k * a_dim1]), abs(d__2)) >= sfmin)
                    {
                        /* Perform a rank-1 update of A(1:k-1,1:k-1) as */
                        /* A := A - U(k)*D(k)*U(k)**T */
                        /* = A - W(k)*1/D(k)*W(k)**T */
                        z_div(&z__1, &c_b1, &a[k + k * a_dim1]);
                        d11.r = z__1.r;
                        d11.i = z__1.i; // , expr subst
                        i__1 = k - 1;
                        z__1.r = -d11.r;
                        z__1.i = -d11.i; // , expr subst
                        zsyr_(uplo, &i__1, &z__1, &a[k * a_dim1 + 1], &c__1, & a[a_offset], lda);
                        /* Store U(k) in column k */
                        i__1 = k - 1;
                        zscal_(&i__1, &d11, &a[k * a_dim1 + 1], &c__1);
                    }
                    else
                    {
                        /* Store L(k) in column K */
                        i__1 = k + k * a_dim1;
                        d11.r = a[i__1].r;
                        d11.i = a[i__1].i; // , expr subst
                        i__1 = k - 1;
                        for (ii = 1;
                                ii <= i__1;
                                ++ii)
                        {
                            i__2 = ii + k * a_dim1;
                            z_div(&z__1, &a[ii + k * a_dim1], &d11);
                            a[i__2].r = z__1.r;
                            a[i__2].i = z__1.i; // , expr subst
                            /* L16: */
                        }
                        /* Perform a rank-1 update of A(k+1:n,k+1:n) as */
                        /* A := A - U(k)*D(k)*U(k)**T */
                        /* = A - W(k)*(1/D(k))*W(k)**T */
                        /* = A - (W(k)/D(k))*(D(k))*(W(k)/D(K))**T */
                        i__1 = k - 1;
                        z__1.r = -d11.r;
                        z__1.i = -d11.i; // , expr subst
                        zsyr_(uplo, &i__1, &z__1, &a[k * a_dim1 + 1], &c__1, & a[a_offset], lda);
                    }
                }
            }
            else
            {
                /* 2-by-2 pivot block D(k): columns k and k-1 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 */
                /* Perform a rank-2 update of A(1:k-2,1:k-2) as */
                /* A := A - ( U(k-1) U(k) )*D(k)*( U(k-1) U(k) )**T */
                /* = A - ( ( A(k-1)A(k) )*inv(D(k)) ) * ( A(k-1)A(k) )**T */
                /* and store L(k) and L(k+1) in columns k and k+1 */
                if (k > 2)
                {
                    i__1 = k - 1 + k * a_dim1;
                    d12.r = a[i__1].r;
                    d12.i = a[i__1].i; // , expr subst
                    z_div(&z__1, &a[k - 1 + (k - 1) * a_dim1], &d12);
                    d22.r = z__1.r;
                    d22.i = z__1.i; // , expr subst
                    z_div(&z__1, &a[k + k * a_dim1], &d12);
                    d11.r = z__1.r;
                    d11.i = z__1.i; // , expr subst
                    z__3.r = d11.r * d22.r - d11.i * d22.i;
                    z__3.i = d11.r * d22.i + d11.i * d22.r; // , expr subst
                    z__2.r = z__3.r - 1.;
                    z__2.i = z__3.i - 0.; // , expr subst
                    z_div(&z__1, &c_b1, &z__2);
                    t.r = z__1.r;
                    t.i = z__1.i; // , expr subst
                    for (j = k - 2;
                            j >= 1;
                            --j)
                    {
                        i__1 = j + (k - 1) * a_dim1;
                        z__3.r = d11.r * a[i__1].r - d11.i * a[i__1].i;
                        z__3.i = d11.r * a[i__1].i + d11.i * a[i__1] .r; // , expr subst
                        i__2 = j + k * a_dim1;
                        z__2.r = z__3.r - a[i__2].r;
                        z__2.i = z__3.i - a[i__2] .i; // , expr subst
                        z__1.r = t.r * z__2.r - t.i * z__2.i;
                        z__1.i = t.r * z__2.i + t.i * z__2.r; // , expr subst
                        wkm1.r = z__1.r;
                        wkm1.i = z__1.i; // , expr subst
                        i__1 = j + k * a_dim1;
                        z__3.r = d22.r * a[i__1].r - d22.i * a[i__1].i;
                        z__3.i = d22.r * a[i__1].i + d22.i * a[i__1] .r; // , expr subst
                        i__2 = j + (k - 1) * a_dim1;
                        z__2.r = z__3.r - a[i__2].r;
                        z__2.i = z__3.i - a[i__2] .i; // , expr subst
                        z__1.r = t.r * z__2.r - t.i * z__2.i;
                        z__1.i = t.r * z__2.i + t.i * z__2.r; // , expr subst
                        wk.r = z__1.r;
                        wk.i = z__1.i; // , expr subst
                        for (i__ = j;
                                i__ >= 1;
                                --i__)
                        {
                            i__1 = i__ + j * a_dim1;
                            i__2 = i__ + j * a_dim1;
                            z_div(&z__4, &a[i__ + k * a_dim1], &d12);
                            z__3.r = z__4.r * wk.r - z__4.i * wk.i;
                            z__3.i = z__4.r * wk.i + z__4.i * wk.r; // , expr subst
                            z__2.r = a[i__2].r - z__3.r;
                            z__2.i = a[i__2].i - z__3.i; // , expr subst
                            z_div(&z__6, &a[i__ + (k - 1) * a_dim1], &d12);
                            z__5.r = z__6.r * wkm1.r - z__6.i * wkm1.i;
                            z__5.i = z__6.r * wkm1.i + z__6.i * wkm1.r; // , expr subst
                            z__1.r = z__2.r - z__5.r;
                            z__1.i = z__2.i - z__5.i; // , expr subst
                            a[i__1].r = z__1.r;
                            a[i__1].i = z__1.i; // , expr subst
                            /* L20: */
                        }
                        /* Store U(k) and U(k-1) in cols k and k-1 for row J */
                        i__1 = j + k * a_dim1;
                        z_div(&z__1, &wk, &d12);
                        a[i__1].r = z__1.r;
                        a[i__1].i = z__1.i; // , expr subst
                        i__1 = j + (k - 1) * a_dim1;
                        z_div(&z__1, &wkm1, &d12);
                        a[i__1].r = z__1.r;
                        a[i__1].i = z__1.i; // , expr subst
                        /* L30: */
                    }
                }
            }
        }
        /* Store details of the interchanges in IPIV */
        if (kstep == 1)
        {
            ipiv[k] = kp;
        }
        else
        {
            ipiv[k] = -p;
            ipiv[k - 1] = -kp;
        }
        /* Decrease K and return to the start of the main loop */
        k -= kstep;
        goto L10;
    }
    else
    {
        /* Factorize A as L*D*L**T using the lower triangle of A */
        /* K is the main loop index, increasing from 1 to N in steps of */
        /* 1 or 2 */
        k = 1;
L40: /* If K > N, exit from loop */
        if (k > *n)
        {
            goto L70;
        }
        kstep = 1;
        p = k;
        /* 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 * a_dim1;
        absakk = (d__1 = a[i__1].r, abs(d__1)) + (d__2 = d_imag(&a[k + k * a_dim1]), abs(d__2));
        /* IMAX is the row-index of the largest off-diagonal element in */
        /* column K, and COLMAX is its absolute value. */
        /* Determine both COLMAX and IMAX. */
        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_imag(&a[imax + k * a_dim1]), abs(d__2));
        }
        else
        {
            colmax = 0.;
        }
        if (max(absakk,colmax) == 0.)
        {
            /* Column K is zero or underflow: set INFO and continue */
            if (*info == 0)
            {
                *info = k;
            }
            kp = k;
        }
        else
        {
            /* Test for interchange */
            /* Equivalent to testing for (used to handle NaN and Inf) */
            /* ABSAKK.GE.ALPHA*COLMAX */
            if (! (absakk < alpha * colmax))
            {
                /* no interchange, use 1-by-1 pivot block */
                kp = k;
            }
            else
            {
                done = FALSE_;
                /* Loop until pivot found */
L42: /* Begin pivot search loop body */
                /* JMAX is the column-index of the largest off-diagonal */
                /* element in row IMAX, and ROWMAX is its absolute value. */
                /* Determine both ROWMAX and JMAX. */
                if (imax != k)
                {
                    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_imag(& a[imax + jmax * a_dim1]), abs(d__2));
                }
                else
                {
                    rowmax = 0.;
                }
                if (imax < *n)
                {
                    i__1 = *n - imax;
                    itemp = imax + izamax_(&i__1, &a[imax + 1 + imax * a_dim1] , &c__1);
                    i__1 = itemp + imax * a_dim1;
                    dtemp = (d__1 = a[i__1].r, abs(d__1)) + (d__2 = d_imag(&a[ itemp + imax * a_dim1]), abs(d__2));
                    if (dtemp > rowmax)
                    {
                        rowmax = dtemp;
                        jmax = itemp;
                    }
                }
                /* Equivalent to testing for (used to handle NaN and Inf) */
                /* CABS1( A( IMAX, IMAX ) ).GE.ALPHA*ROWMAX */
                i__1 = imax + imax * a_dim1;
                if (! ((d__1 = a[i__1].r, abs(d__1)) + (d__2 = d_imag(&a[imax + imax * a_dim1]), abs(d__2)) < alpha * rowmax))
                {
                    /* interchange rows and columns K and IMAX, */
                    /* use 1-by-1 pivot block */
                    kp = imax;
                    done = TRUE_;
                    /* Equivalent to testing for ROWMAX .EQ. COLMAX, */
                    /* used to handle NaN and Inf */
                }
                else if (p == jmax || rowmax <= colmax)
                {
                    /* interchange rows and columns K+1 and IMAX, */
                    /* use 2-by-2 pivot block */
                    kp = imax;
                    kstep = 2;
                    done = TRUE_;
                }
                else
                {
                    /* Pivot NOT found, set variables and repeat */
                    p = imax;
                    colmax = rowmax;
                    imax = jmax;
                }
                /* End pivot search loop body */
                if (! done)
                {
                    goto L42;
                }
            }
            /* Swap TWO rows and TWO columns */
            /* First swap */
            if (kstep == 2 && p != k)
            {
                /* Interchange rows and column K and P in the trailing */
                /* submatrix A(k:n,k:n) if we have a 2-by-2 pivot */
                if (p < *n)
                {
                    i__1 = *n - p;
                    zswap_(&i__1, &a[p + 1 + k * a_dim1], &c__1, &a[p + 1 + p * a_dim1], &c__1);
                }
                if (p > k + 1)
                {
                    i__1 = p - k - 1;
                    zswap_(&i__1, &a[k + 1 + k * a_dim1], &c__1, &a[p + (k + 1) * a_dim1], lda);
                }
                i__1 = k + k * a_dim1;
                t.r = a[i__1].r;
                t.i = a[i__1].i; // , expr subst
                i__1 = k + k * a_dim1;
                i__2 = p + p * a_dim1;
                a[i__1].r = a[i__2].r;
                a[i__1].i = a[i__2].i; // , expr subst
                i__1 = p + p * a_dim1;
                a[i__1].r = t.r;
                a[i__1].i = t.i; // , expr subst
            }
            /* Second swap */
            kk = k + kstep - 1;
            if (kp != kk)
            {
                /* Interchange rows and columns KK and KP in the trailing */
                /* submatrix A(k:n,k:n) */
                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);
                }
                if (kk < *n && kp > kk + 1)
                {
                    i__1 = kp - kk - 1;
                    zswap_(&i__1, &a[kk + 1 + kk * a_dim1], &c__1, &a[kp + ( kk + 1) * a_dim1], lda);
                }
                i__1 = kk + kk * a_dim1;
                t.r = a[i__1].r;
                t.i = a[i__1].i; // , expr subst
                i__1 = kk + kk * a_dim1;
                i__2 = kp + kp * a_dim1;
                a[i__1].r = a[i__2].r;
                a[i__1].i = a[i__2].i; // , expr subst
                i__1 = kp + kp * a_dim1;
                a[i__1].r = t.r;
                a[i__1].i = t.i; // , expr subst
                if (kstep == 2)
                {
                    i__1 = k + 1 + k * a_dim1;
                    t.r = a[i__1].r;
                    t.i = a[i__1].i; // , expr subst
                    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; // , expr subst
                    i__1 = kp + k * a_dim1;
                    a[i__1].r = t.r;
                    a[i__1].i = t.i; // , expr subst
                }
            }
            /* Update the trailing submatrix */
            if (kstep == 1)
            {
                /* 1-by-1 pivot block D(k): column k now holds */
                /* W(k) = L(k)*D(k) */
                /* where L(k) is the k-th column of L */
                if (k < *n)
                {
                    /* Perform a rank-1 update of A(k+1:n,k+1:n) and */
                    /* store L(k) in column k */
                    i__1 = k + k * a_dim1;
                    if ((d__1 = a[i__1].r, abs(d__1)) + (d__2 = d_imag(&a[k + k * a_dim1]), abs(d__2)) >= sfmin)
                    {
                        /* Perform a rank-1 update of A(k+1:n,k+1:n) as */
                        /* A := A - L(k)*D(k)*L(k)**T */
                        /* = A - W(k)*(1/D(k))*W(k)**T */
                        z_div(&z__1, &c_b1, &a[k + k * a_dim1]);
                        d11.r = z__1.r;
                        d11.i = z__1.i; // , expr subst
                        i__1 = *n - k;
                        z__1.r = -d11.r;
                        z__1.i = -d11.i; // , expr subst
                        zsyr_(uplo, &i__1, &z__1, &a[k + 1 + k * a_dim1], & c__1, &a[k + 1 + (k + 1) * a_dim1], lda);
                        /* Store L(k) in column k */
                        i__1 = *n - k;
                        zscal_(&i__1, &d11, &a[k + 1 + k * a_dim1], &c__1);
                    }
                    else
                    {
                        /* Store L(k) in column k */
                        i__1 = k + k * a_dim1;
                        d11.r = a[i__1].r;
                        d11.i = a[i__1].i; // , expr subst
                        i__1 = *n;
                        for (ii = k + 1;
                                ii <= i__1;
                                ++ii)
                        {
                            i__2 = ii + k * a_dim1;
                            z_div(&z__1, &a[ii + k * a_dim1], &d11);
                            a[i__2].r = z__1.r;
                            a[i__2].i = z__1.i; // , expr subst
                            /* L46: */
                        }
                        /* Perform a rank-1 update of A(k+1:n,k+1:n) as */
                        /* A := A - L(k)*D(k)*L(k)**T */
                        /* = A - W(k)*(1/D(k))*W(k)**T */
                        /* = A - (W(k)/D(k))*(D(k))*(W(k)/D(K))**T */
                        i__1 = *n - k;
                        z__1.r = -d11.r;
                        z__1.i = -d11.i; // , expr subst
                        zsyr_(uplo, &i__1, &z__1, &a[k + 1 + k * a_dim1], & c__1, &a[k + 1 + (k + 1) * a_dim1], lda);
                    }
                }
            }
            else
            {
                /* 2-by-2 pivot block D(k): columns k and k+1 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 */
                /* Perform a rank-2 update of A(k+2:n,k+2:n) as */
                /* A := A - ( L(k) L(k+1) ) * D(k) * ( L(k) L(k+1) )**T */
                /* = A - ( ( A(k)A(k+1) )*inv(D(k) ) * ( A(k)A(k+1) )**T */
                /* and store L(k) and L(k+1) in columns k and k+1 */
                if (k < *n - 1)
                {
                    i__1 = k + 1 + k * a_dim1;
                    d21.r = a[i__1].r;
                    d21.i = a[i__1].i; // , expr subst
                    z_div(&z__1, &a[k + 1 + (k + 1) * a_dim1], &d21);
                    d11.r = z__1.r;
                    d11.i = z__1.i; // , expr subst
                    z_div(&z__1, &a[k + k * a_dim1], &d21);
                    d22.r = z__1.r;
                    d22.i = z__1.i; // , expr subst
                    z__3.r = d11.r * d22.r - d11.i * d22.i;
                    z__3.i = d11.r * d22.i + d11.i * d22.r; // , expr subst
                    z__2.r = z__3.r - 1.;
                    z__2.i = z__3.i - 0.; // , expr subst
                    z_div(&z__1, &c_b1, &z__2);
                    t.r = z__1.r;
                    t.i = z__1.i; // , expr subst
                    i__1 = *n;
                    for (j = k + 2;
                            j <= i__1;
                            ++j)
                    {
                        /* Compute D21 * ( W(k)W(k+1) ) * inv(D(k)) for row J */
                        i__2 = j + k * a_dim1;
                        z__3.r = d11.r * a[i__2].r - d11.i * a[i__2].i;
                        z__3.i = d11.r * a[i__2].i + d11.i * a[i__2] .r; // , expr subst
                        i__3 = j + (k + 1) * a_dim1;
                        z__2.r = z__3.r - a[i__3].r;
                        z__2.i = z__3.i - a[i__3] .i; // , expr subst
                        z__1.r = t.r * z__2.r - t.i * z__2.i;
                        z__1.i = t.r * z__2.i + t.i * z__2.r; // , expr subst
                        wk.r = z__1.r;
                        wk.i = z__1.i; // , expr subst
                        i__2 = j + (k + 1) * a_dim1;
                        z__3.r = d22.r * a[i__2].r - d22.i * a[i__2].i;
                        z__3.i = d22.r * a[i__2].i + d22.i * a[i__2] .r; // , expr subst
                        i__3 = j + k * a_dim1;
                        z__2.r = z__3.r - a[i__3].r;
                        z__2.i = z__3.i - a[i__3] .i; // , expr subst
                        z__1.r = t.r * z__2.r - t.i * z__2.i;
                        z__1.i = t.r * z__2.i + t.i * z__2.r; // , expr subst
                        wkp1.r = z__1.r;
                        wkp1.i = z__1.i; // , expr subst
                        /* Perform a rank-2 update of A(k+2:n,k+2:n) */
                        i__2 = *n;
                        for (i__ = j;
                                i__ <= i__2;
                                ++i__)
                        {
                            i__3 = i__ + j * a_dim1;
                            i__4 = i__ + j * a_dim1;
                            z_div(&z__4, &a[i__ + k * a_dim1], &d21);
                            z__3.r = z__4.r * wk.r - z__4.i * wk.i;
                            z__3.i = z__4.r * wk.i + z__4.i * wk.r; // , expr subst
                            z__2.r = a[i__4].r - z__3.r;
                            z__2.i = a[i__4].i - z__3.i; // , expr subst
                            z_div(&z__6, &a[i__ + (k + 1) * a_dim1], &d21);
                            z__5.r = z__6.r * wkp1.r - z__6.i * wkp1.i;
                            z__5.i = z__6.r * wkp1.i + z__6.i * wkp1.r; // , expr subst
                            z__1.r = z__2.r - z__5.r;
                            z__1.i = z__2.i - z__5.i; // , expr subst
                            a[i__3].r = z__1.r;
                            a[i__3].i = z__1.i; // , expr subst
                            /* L50: */
                        }
                        /* Store L(k) and L(k+1) in cols k and k+1 for row J */
                        i__2 = j + k * a_dim1;
                        z_div(&z__1, &wk, &d21);
                        a[i__2].r = z__1.r;
                        a[i__2].i = z__1.i; // , expr subst
                        i__2 = j + (k + 1) * a_dim1;
                        z_div(&z__1, &wkp1, &d21);
                        a[i__2].r = z__1.r;
                        a[i__2].i = z__1.i; // , expr subst
                        /* L60: */
                    }
                }
            }
        }
        /* Store details of the interchanges in IPIV */
        if (kstep == 1)
        {
            ipiv[k] = kp;
        }
        else
        {
            ipiv[k] = -p;
            ipiv[k + 1] = -kp;
        }
        /* Increase K and return to the start of the main loop */
        k += kstep;
        goto L40;
    }
L70:
    return 0;
    /* End of ZSYTF2_ROOK */
}
示例#2
0
 int zsytf2_(char *uplo, int *n, doublecomplex *a, 
	int *lda, int *ipiv, int *info)
{
    /* System generated locals */
    int a_dim1, a_offset, i__1, i__2, i__3, i__4, i__5, i__6;
    double d__1, d__2, d__3, d__4;
    doublecomplex z__1, z__2, z__3, z__4;

    /* Builtin functions */
    double sqrt(double), d_imag(doublecomplex *);
    void z_div(doublecomplex *, doublecomplex *, doublecomplex *);

    /* Local variables */
    int i__, j, k;
    doublecomplex t, r1, d11, d12, d21, d22;
    int kk, kp;
    doublecomplex wk, wkm1, wkp1;
    int imax, jmax;
    extern  int zsyr_(char *, int *, doublecomplex *, 
	    doublecomplex *, int *, doublecomplex *, int *);
    double alpha;
    extern int lsame_(char *, char *);
    extern  int zscal_(int *, doublecomplex *, 
	    doublecomplex *, int *);
    int kstep;
    int upper;
    extern  int zswap_(int *, doublecomplex *, int *, 
	    doublecomplex *, int *);
    double absakk;
    extern int disnan_(double *);
    extern  int xerbla_(char *, int *);
    double colmax;
    extern int izamax_(int *, doublecomplex *, int *);
    double rowmax;


/*  -- LAPACK routine (version 3.2) -- */
/*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */
/*     November 2006 */

/*     .. Scalar Arguments .. */
/*     .. */
/*     .. Array Arguments .. */
/*     .. */

/*  Purpose */
/*  ======= */

/*  ZSYTF2 computes the factorization of a complex symmetric matrix A */
/*  using the Bunch-Kaufman diagonal pivoting method: */

/*     A = U*D*U'  or  A = L*D*L' */

/*  where U (or L) is a product of permutation and unit upper (lower) */
/*  triangular matrices, U' is the transpose of U, and D is symmetric and */
/*  block diagonal with 1-by-1 and 2-by-2 diagonal blocks. */

/*  This is the unblocked version of the algorithm, calling Level 2 BLAS. */

/*  Arguments */
/*  ========= */

/*  UPLO    (input) CHARACTER*1 */
/*          Specifies whether the upper or lower triangular part of the */
/*          symmetric matrix A is stored: */
/*          = 'U':  Upper triangular */
/*          = 'L':  Lower triangular */

/*  N       (input) INTEGER */
/*          The order of the matrix A.  N >= 0. */

/*  A       (input/output) COMPLEX*16 array, dimension (LDA,N) */
/*          On entry, the symmetric 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, the block diagonal matrix D and the multipliers used */
/*          to obtain the factor U or L (see below for further details). */

/*  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 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. */

/*  INFO    (output) INTEGER */
/*          = 0: successful exit */
/*          < 0: if INFO = -k, the k-th argument had an illegal value */
/*          > 0: if INFO = k, D(k,k) is exactly zero.  The factorization */
/*               has been completed, but the block diagonal matrix D is */
/*               exactly singular, and division by zero will occur if it */
/*               is used to solve a system of equations. */

/*  Further Details */
/*  =============== */

/*  09-29-06 - patch from */
/*    Bobby Cheng, MathWorks */

/*    Replace l.209 and l.377 */
/*         IF( MAX( ABSAKK, COLMAX ).EQ.ZERO ) THEN */
/*    by */
/*         IF( (MAX( ABSAKK, COLMAX ).EQ.ZERO) .OR. DISNAN(ABSAKK) ) THEN */

/*  1-96 - Based on modifications by J. Lewis, Boeing Computer Services */
/*         Company */

/*  If UPLO = 'U', then A = U*D*U', where */
/*     U = P(n)*U(n)* ... *P(k)U(k)* ..., */
/*  i.e., U is a product of terms P(k)*U(k), where k decreases from n to */
/*  1 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1 */
/*  and 2-by-2 diagonal blocks D(k).  P(k) is a permutation matrix as */
/*  defined by IPIV(k), and U(k) is a unit upper triangular matrix, such */
/*  that if the diagonal block D(k) is of order s (s = 1 or 2), then */

/*             (   I    v    0   )   k-s */
/*     U(k) =  (   0    I    0   )   s */
/*             (   0    0    I   )   n-k */
/*                k-s   s   n-k */

/*  If s = 1, D(k) overwrites A(k,k), and v overwrites A(1:k-1,k). */
/*  If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k), */
/*  and A(k,k), and v overwrites A(1:k-2,k-1:k). */

/*  If UPLO = 'L', then A = L*D*L', where */
/*     L = P(1)*L(1)* ... *P(k)*L(k)* ..., */
/*  i.e., L is a product of terms P(k)*L(k), where k increases from 1 to */
/*  n in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1 */
/*  and 2-by-2 diagonal blocks D(k).  P(k) is a permutation matrix as */
/*  defined by IPIV(k), and L(k) is a unit lower triangular matrix, such */
/*  that if the diagonal block D(k) is of order s (s = 1 or 2), then */

/*             (   I    0     0   )  k-1 */
/*     L(k) =  (   0    I     0   )  s */
/*             (   0    v     I   )  n-k-s+1 */
/*                k-1   s  n-k-s+1 */

/*  If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k). */
/*  If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k), */
/*  and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1). */

/*  ===================================================================== */

/*     .. Parameters .. */
/*     .. */
/*     .. Local Scalars .. */
/*     .. */
/*     .. External Functions .. */
/*     .. */
/*     .. External Subroutines .. */
/*     .. */
/*     .. Intrinsic Functions .. */
/*     .. */
/*     .. Statement Functions .. */
/*     .. */
/*     .. Statement Function definitions .. */
/*     .. */
/*     .. Executable Statements .. */

/*     Test the input parameters. */

    /* Parameter adjustments */
    a_dim1 = *lda;
    a_offset = 1 + a_dim1;
    a -= a_offset;
    --ipiv;

    /* Function Body */
    *info = 0;
    upper = lsame_(uplo, "U");
    if (! upper && ! lsame_(uplo, "L")) {
	*info = -1;
    } else if (*n < 0) {
	*info = -2;
    } else if (*lda < MAX(1,*n)) {
	*info = -4;
    }
    if (*info != 0) {
	i__1 = -(*info);
	xerbla_("ZSYTF2", &i__1);
	return 0;
    }

/*     Initialize ALPHA for use in choosing pivot block size. */

    alpha = (sqrt(17.) + 1.) / 8.;

    if (upper) {

/*        Factorize A as U*D*U' using the upper triangle of A */

/*        K is the main loop index, decreasing from N to 1 in steps of */
/*        1 or 2 */

	k = *n;
L10:

/*        If K < 1, exit from loop */

	if (k < 1) {
	    goto L70;
	}
	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 * a_dim1;
	absakk = (d__1 = a[i__1].r, ABS(d__1)) + (d__2 = d_imag(&a[k + k * 
		a_dim1]), ABS(d__2));

/*        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, &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_imag(&a[imax + 
		    k * a_dim1]), ABS(d__2));
	} else {
	    colmax = 0.;
	}

	if (MAX(absakk,colmax) == 0. || disnan_(&absakk)) {

/*           Column K is zero or contains a NaN: set INFO and continue */

	    if (*info == 0) {
		*info = k;
	    }
	    kp = k;
	} else {
	    if (absakk >= alpha * colmax) {

/*              no interchange, use 1-by-1 pivot block */

		kp = k;
	    } else {

/*              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, &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_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);
/* Computing MAX */
		    i__1 = jmax + imax * a_dim1;
		    d__3 = rowmax, d__4 = (d__1 = a[i__1].r, ABS(d__1)) + (
			    d__2 = d_imag(&a[jmax + imax * a_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 + imax * a_dim1;
		    if ((d__1 = a[i__1].r, ABS(d__1)) + (d__2 = d_imag(&a[
			    imax + imax * a_dim1]), ABS(d__2)) >= alpha * 
			    rowmax) {

/*                 interchange rows and columns K and IMAX, use 1-by-1 */
/*                 pivot block */

			kp = imax;
		    } else {

/*                 interchange rows and columns K-1 and IMAX, use 2-by-2 */
/*                 pivot block */

			kp = imax;
			kstep = 2;
		    }
		}
	    }

	    kk = k - kstep + 1;
	    if (kp != kk) {

/*              Interchange rows and columns KK and KP in the leading */
/*              submatrix A(1:k,1:k) */

		i__1 = kp - 1;
		zswap_(&i__1, &a[kk * a_dim1 + 1], &c__1, &a[kp * a_dim1 + 1], 
			 &c__1);
		i__1 = kk - kp - 1;
		zswap_(&i__1, &a[kp + 1 + kk * a_dim1], &c__1, &a[kp + (kp + 
			1) * a_dim1], lda);
		i__1 = kk + kk * a_dim1;
		t.r = a[i__1].r, t.i = a[i__1].i;
		i__1 = kk + kk * a_dim1;
		i__2 = kp + kp * a_dim1;
		a[i__1].r = a[i__2].r, a[i__1].i = a[i__2].i;
		i__1 = kp + kp * a_dim1;
		a[i__1].r = t.r, a[i__1].i = t.i;
		if (kstep == 2) {
		    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;
		}
	    }

/*           Update the leading submatrix */

	    if (kstep == 1) {

/*              1-by-1 pivot block D(k): column k now holds */

/*              W(k) = U(k)*D(k) */

/*              where U(k) is the k-th column of U */

/*              Perform a rank-1 update of A(1:k-1,1:k-1) as */

/*              A := A - U(k)*D(k)*U(k)' = A - W(k)*1/D(k)*W(k)' */

		z_div(&z__1, &c_b1, &a[k + k * a_dim1]);
		r1.r = z__1.r, r1.i = z__1.i;
		i__1 = k - 1;
		z__1.r = -r1.r, z__1.i = -r1.i;
		zsyr_(uplo, &i__1, &z__1, &a[k * a_dim1 + 1], &c__1, &a[
			a_offset], lda);

/*              Store U(k) in column k */

		i__1 = k - 1;
		zscal_(&i__1, &r1, &a[k * a_dim1 + 1], &c__1);
	    } else {

/*              2-by-2 pivot block D(k): columns k and k-1 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 */

/*              Perform a rank-2 update of A(1:k-2,1:k-2) as */

/*              A := A - ( U(k-1) U(k) )*D(k)*( U(k-1) U(k) )' */
/*                 = A - ( W(k-1) W(k) )*inv(D(k))*( W(k-1) W(k) )' */

		if (k > 2) {

		    i__1 = k - 1 + k * a_dim1;
		    d12.r = a[i__1].r, d12.i = a[i__1].i;
		    z_div(&z__1, &a[k - 1 + (k - 1) * a_dim1], &d12);
		    d22.r = z__1.r, d22.i = z__1.i;
		    z_div(&z__1, &a[k + k * a_dim1], &d12);
		    d11.r = z__1.r, d11.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_div(&z__1, &c_b1, &z__2);
		    t.r = z__1.r, t.i = z__1.i;
		    z_div(&z__1, &t, &d12);
		    d12.r = z__1.r, d12.i = z__1.i;

		    for (j = k - 2; j >= 1; --j) {
			i__1 = j + (k - 1) * a_dim1;
			z__3.r = d11.r * a[i__1].r - d11.i * a[i__1].i, 
				z__3.i = d11.r * a[i__1].i + d11.i * a[i__1]
				.r;
			i__2 = j + k * a_dim1;
			z__2.r = z__3.r - a[i__2].r, z__2.i = z__3.i - a[i__2]
				.i;
			z__1.r = d12.r * z__2.r - d12.i * z__2.i, z__1.i = 
				d12.r * z__2.i + d12.i * z__2.r;
			wkm1.r = z__1.r, wkm1.i = z__1.i;
			i__1 = j + k * a_dim1;
			z__3.r = d22.r * a[i__1].r - d22.i * a[i__1].i, 
				z__3.i = d22.r * a[i__1].i + d22.i * a[i__1]
				.r;
			i__2 = j + (k - 1) * a_dim1;
			z__2.r = z__3.r - a[i__2].r, z__2.i = z__3.i - a[i__2]
				.i;
			z__1.r = d12.r * z__2.r - d12.i * z__2.i, z__1.i = 
				d12.r * z__2.i + d12.i * z__2.r;
			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;
			    z__3.r = a[i__3].r * wk.r - a[i__3].i * wk.i, 
				    z__3.i = a[i__3].r * wk.i + a[i__3].i * 
				    wk.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;
			    z__4.r = a[i__4].r * wkm1.r - a[i__4].i * wkm1.i, 
				    z__4.i = a[i__4].r * wkm1.i + a[i__4].i * 
				    wkm1.r;
			    z__1.r = z__2.r - z__4.r, z__1.i = z__2.i - 
				    z__4.i;
			    a[i__1].r = z__1.r, a[i__1].i = z__1.i;
/* L20: */
			}
			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;
/* L30: */
		    }

		}

	    }
	}

/*        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;

    } else {

/*        Factorize A as L*D*L' using the lower triangle of A */

/*        K is the main loop index, increasing from 1 to N in steps of */
/*        1 or 2 */

	k = 1;
L40:

/*        If K > N, exit from loop */

	if (k > *n) {
	    goto L70;
	}
	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 * a_dim1;
	absakk = (d__1 = a[i__1].r, ABS(d__1)) + (d__2 = d_imag(&a[k + k * 
		a_dim1]), ABS(d__2));

/*        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, &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_imag(&a[imax + 
		    k * a_dim1]), ABS(d__2));
	} else {
	    colmax = 0.;
	}

	if (MAX(absakk,colmax) == 0. || disnan_(&absakk)) {

/*           Column K is zero or contains a NaN: set INFO and continue */

	    if (*info == 0) {
		*info = k;
	    }
	    kp = k;
	} else {
	    if (absakk >= alpha * colmax) {

/*              no interchange, use 1-by-1 pivot block */

		kp = k;
	    } else {

/*              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, &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_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);
/* Computing MAX */
		    i__1 = jmax + imax * a_dim1;
		    d__3 = rowmax, d__4 = (d__1 = a[i__1].r, ABS(d__1)) + (
			    d__2 = d_imag(&a[jmax + imax * a_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 + imax * a_dim1;
		    if ((d__1 = a[i__1].r, ABS(d__1)) + (d__2 = d_imag(&a[
			    imax + imax * a_dim1]), ABS(d__2)) >= alpha * 
			    rowmax) {

/*                 interchange rows and columns K and IMAX, use 1-by-1 */
/*                 pivot block */

			kp = imax;
		    } else {

/*                 interchange rows and columns K+1 and IMAX, use 2-by-2 */
/*                 pivot block */

			kp = imax;
			kstep = 2;
		    }
		}
	    }

	    kk = k + kstep - 1;
	    if (kp != kk) {

/*              Interchange rows and columns KK and KP in the trailing */
/*              submatrix A(k:n,k:n) */

		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 - kk - 1;
		zswap_(&i__1, &a[kk + 1 + kk * a_dim1], &c__1, &a[kp + (kk + 
			1) * a_dim1], lda);
		i__1 = kk + kk * a_dim1;
		t.r = a[i__1].r, t.i = a[i__1].i;
		i__1 = kk + kk * a_dim1;
		i__2 = kp + kp * a_dim1;
		a[i__1].r = a[i__2].r, a[i__1].i = a[i__2].i;
		i__1 = kp + kp * a_dim1;
		a[i__1].r = t.r, a[i__1].i = t.i;
		if (kstep == 2) {
		    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;
		}
	    }

/*           Update the trailing submatrix */

	    if (kstep == 1) {

/*              1-by-1 pivot block D(k): column k now holds */

/*              W(k) = L(k)*D(k) */

/*              where L(k) is the k-th column of L */

		if (k < *n) {

/*                 Perform a rank-1 update of A(k+1:n,k+1:n) as */

/*                 A := A - L(k)*D(k)*L(k)' = A - W(k)*(1/D(k))*W(k)' */

		    z_div(&z__1, &c_b1, &a[k + k * a_dim1]);
		    r1.r = z__1.r, r1.i = z__1.i;
		    i__1 = *n - k;
		    z__1.r = -r1.r, z__1.i = -r1.i;
		    zsyr_(uplo, &i__1, &z__1, &a[k + 1 + k * a_dim1], &c__1, &
			    a[k + 1 + (k + 1) * a_dim1], lda);

/*                 Store L(k) in column K */

		    i__1 = *n - k;
		    zscal_(&i__1, &r1, &a[k + 1 + k * a_dim1], &c__1);
		}
	    } else {

/*              2-by-2 pivot block D(k) */

		if (k < *n - 1) {

/*                 Perform a rank-2 update of A(k+2:n,k+2:n) as */

/*                 A := A - ( L(k) L(k+1) )*D(k)*( L(k) L(k+1) )' */
/*                    = A - ( W(k) W(k+1) )*inv(D(k))*( W(k) W(k+1) )' */

/*                 where L(k) and L(k+1) are the k-th and (k+1)-th */
/*                 columns of L */

		    i__1 = k + 1 + k * a_dim1;
		    d21.r = a[i__1].r, d21.i = a[i__1].i;
		    z_div(&z__1, &a[k + 1 + (k + 1) * a_dim1], &d21);
		    d11.r = z__1.r, d11.i = z__1.i;
		    z_div(&z__1, &a[k + k * a_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_div(&z__1, &c_b1, &z__2);
		    t.r = z__1.r, t.i = z__1.i;
		    z_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;
			z__3.r = d11.r * a[i__2].r - d11.i * a[i__2].i, 
				z__3.i = d11.r * a[i__2].i + d11.i * a[i__2]
				.r;
			i__3 = j + (k + 1) * a_dim1;
			z__2.r = z__3.r - a[i__3].r, z__2.i = z__3.i - a[i__3]
				.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;
			wk.r = z__1.r, wk.i = z__1.i;
			i__2 = j + (k + 1) * a_dim1;
			z__3.r = d22.r * a[i__2].r - d22.i * a[i__2].i, 
				z__3.i = d22.r * a[i__2].i + d22.i * a[i__2]
				.r;
			i__3 = j + k * a_dim1;
			z__2.r = z__3.r - a[i__3].r, z__2.i = z__3.i - a[i__3]
				.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;
			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;
			    z__3.r = a[i__5].r * wk.r - a[i__5].i * wk.i, 
				    z__3.i = a[i__5].r * wk.i + a[i__5].i * 
				    wk.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;
			    z__4.r = a[i__6].r * wkp1.r - a[i__6].i * wkp1.i, 
				    z__4.i = a[i__6].r * wkp1.i + a[i__6].i * 
				    wkp1.r;
			    z__1.r = z__2.r - z__4.r, z__1.i = z__2.i - 
				    z__4.i;
			    a[i__3].r = z__1.r, a[i__3].i = z__1.i;
/* L50: */
			}
			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;
/* L60: */
		    }
		}
	    }
	}

/*        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 L40;

    }

L70:
    return 0;

/*     End of ZSYTF2 */

} /* zsytf2_ */