#include "blaswrap.h" #include "f2c.h" /* Subroutine */ int clasyf_(char *uplo, integer *n, integer *nb, integer *kb, complex *a, integer *lda, integer *ipiv, complex *w, integer *ldw, integer *info) { /* -- LAPACK routine (version 3.1) -- Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. November 2006 Purpose ======= CLASYF computes a partial factorization of a complex symmetric 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 transpose of U. CLASYF is an auxiliary routine called by CSYTRF. 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 symmetric 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 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, 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 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. ===================================================================== Parameter adjustments */ /* Table of constant values */ static complex c_b1 = {1.f,0.f}; static integer c__1 = 1; /* System generated locals */ integer a_dim1, a_offset, w_dim1, w_offset, i__1, i__2, i__3, i__4, i__5; real r__1, r__2, r__3, r__4; complex q__1, q__2, q__3; /* Builtin functions */ double sqrt(doublereal), r_imag(complex *); void c_div(complex *, complex *, complex *); /* Local variables */ static integer j, k; static complex t, r1, d11, d21, d22; static integer jb, jj, kk, jp, kp, kw, kkw, imax, jmax; static real alpha; extern /* Subroutine */ int cscal_(integer *, complex *, complex *, integer *), cgemm_(char *, char *, integer *, integer *, integer * , complex *, complex *, integer *, complex *, integer *, complex * , complex *, integer *); extern logical lsame_(char *, char *); extern /* Subroutine */ int cgemv_(char *, integer *, integer *, complex * , complex *, integer *, complex *, integer *, complex *, complex * , integer *), ccopy_(integer *, complex *, integer *, complex *, integer *), cswap_(integer *, complex *, integer *, complex *, integer *); static integer kstep; static real absakk; extern integer icamax_(integer *, complex *, integer *); static real colmax, rowmax; 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.f) + 1.f) / 8.f; 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 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 */ ccopy_(&k, &a[k * a_dim1 + 1], &c__1, &w[kw * w_dim1 + 1], &c__1); if (k < *n) { i__1 = *n - k; q__1.r = -1.f, q__1.i = -0.f; cgemv_("No transpose", &k, &i__1, &q__1, &a[(k + 1) * a_dim1 + 1], lda, &w[k + (kw + 1) * w_dim1], ldw, &c_b1, &w[kw * w_dim1 + 1], &c__1); } 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 = (r__1 = w[i__1].r, dabs(r__1)) + (r__2 = r_imag(&w[k + kw * w_dim1]), dabs(r__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 = icamax_(&i__1, &w[kw * w_dim1 + 1], &c__1); i__1 = imax + kw * w_dim1; colmax = (r__1 = w[i__1].r, dabs(r__1)) + (r__2 = r_imag(&w[imax + kw * w_dim1]), dabs(r__2)); } else { colmax = 0.f; } if (dmax(absakk,colmax) == 0.f) { /* Column K is zero: 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 { /* Copy column IMAX to column KW-1 of W and update it */ ccopy_(&imax, &a[imax * a_dim1 + 1], &c__1, &w[(kw - 1) * w_dim1 + 1], &c__1); i__1 = k - imax; ccopy_(&i__1, &a[imax + (imax + 1) * a_dim1], lda, &w[imax + 1 + (kw - 1) * w_dim1], &c__1); if (k < *n) { i__1 = *n - k; q__1.r = -1.f, q__1.i = -0.f; cgemv_("No transpose", &k, &i__1, &q__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); } /* 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 + icamax_(&i__1, &w[imax + 1 + (kw - 1) * w_dim1], &c__1); i__1 = jmax + (kw - 1) * w_dim1; rowmax = (r__1 = w[i__1].r, dabs(r__1)) + (r__2 = r_imag(&w[ jmax + (kw - 1) * w_dim1]), dabs(r__2)); if (imax > 1) { i__1 = imax - 1; jmax = icamax_(&i__1, &w[(kw - 1) * w_dim1 + 1], &c__1); /* Computing MAX */ i__1 = jmax + (kw - 1) * w_dim1; r__3 = rowmax, r__4 = (r__1 = w[i__1].r, dabs(r__1)) + ( r__2 = r_imag(&w[jmax + (kw - 1) * w_dim1]), dabs( r__2)); rowmax = dmax(r__3,r__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 ((r__1 = w[i__1].r, dabs(r__1)) + (r__2 = r_imag(&w[ imax + (kw - 1) * w_dim1]), dabs(r__2)) >= 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 */ ccopy_(&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 + k * a_dim1; i__2 = kk + k * a_dim1; a[i__1].r = a[i__2].r, a[i__1].i = a[i__2].i; i__1 = k - 1 - kp; ccopy_(&i__1, &a[kp + 1 + kk * a_dim1], &c__1, &a[kp + (kp + 1) * a_dim1], lda); ccopy_(&kp, &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 */ i__1 = *n - kk + 1; cswap_(&i__1, &a[kk + kk * a_dim1], lda, &a[kp + kk * a_dim1], lda); i__1 = *n - kk + 1; cswap_(&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 */ ccopy_(&k, &w[kw * w_dim1 + 1], &c__1, &a[k * a_dim1 + 1], & c__1); c_div(&q__1, &c_b1, &a[k + k * a_dim1]); r1.r = q__1.r, r1.i = q__1.i; i__1 = k - 1; cscal_(&i__1, &r1, &a[k * a_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; c_div(&q__1, &w[k + kw * w_dim1], &d21); d11.r = q__1.r, d11.i = q__1.i; c_div(&q__1, &w[k - 1 + (kw - 1) * w_dim1], &d21); d22.r = q__1.r, d22.i = q__1.i; q__3.r = d11.r * d22.r - d11.i * d22.i, q__3.i = d11.r * d22.i + d11.i * d22.r; q__2.r = q__3.r - 1.f, q__2.i = q__3.i - 0.f; c_div(&q__1, &c_b1, &q__2); t.r = q__1.r, t.i = q__1.i; c_div(&q__1, &t, &d21); d21.r = q__1.r, d21.i = q__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; q__3.r = d11.r * w[i__3].r - d11.i * w[i__3].i, q__3.i = d11.r * w[i__3].i + d11.i * w[i__3] .r; i__4 = j + kw * w_dim1; q__2.r = q__3.r - w[i__4].r, q__2.i = q__3.i - w[i__4] .i; q__1.r = d21.r * q__2.r - d21.i * q__2.i, q__1.i = d21.r * q__2.i + d21.i * q__2.r; a[i__2].r = q__1.r, a[i__2].i = q__1.i; i__2 = j + k * a_dim1; i__3 = j + kw * w_dim1; q__3.r = d22.r * w[i__3].r - d22.i * w[i__3].i, q__3.i = d22.r * w[i__3].i + d22.i * w[i__3] .r; i__4 = j + (kw - 1) * w_dim1; q__2.r = q__3.r - w[i__4].r, q__2.i = q__3.i - w[i__4] .i; q__1.r = d21.r * q__2.r - d21.i * q__2.i, q__1.i = d21.r * q__2.i + d21.i * q__2.r; a[i__2].r = q__1.r, a[i__2].i = q__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; } } /* 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 */ 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 - j + 1; i__4 = *n - k; q__1.r = -1.f, q__1.i = -0.f; cgemv_("No transpose", &i__3, &i__4, &q__1, &a[j + (k + 1) * a_dim1], lda, &w[jj + (kw + 1) * w_dim1], ldw, &c_b1, &a[j + jj * a_dim1], &c__1); /* L40: */ } /* Update the rectangular superdiagonal block */ i__2 = j - 1; i__3 = *n - k; q__1.r = -1.f, q__1.i = -0.f; cgemm_("No transpose", "Transpose", &i__2, &jb, &i__3, &q__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; cswap_(&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 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 = *n - k + 1; ccopy_(&i__1, &a[k + k * a_dim1], &c__1, &w[k + k * w_dim1], &c__1); i__1 = *n - k + 1; i__2 = k - 1; q__1.r = -1.f, q__1.i = -0.f; cgemv_("No transpose", &i__1, &i__2, &q__1, &a[k + a_dim1], lda, &w[k + w_dim1], ldw, &c_b1, &w[k + k * w_dim1], &c__1); 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 = (r__1 = w[i__1].r, dabs(r__1)) + (r__2 = r_imag(&w[k + k * w_dim1]), dabs(r__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 + icamax_(&i__1, &w[k + 1 + k * w_dim1], &c__1); i__1 = imax + k * w_dim1; colmax = (r__1 = w[i__1].r, dabs(r__1)) + (r__2 = r_imag(&w[imax + k * w_dim1]), dabs(r__2)); } else { colmax = 0.f; } if (dmax(absakk,colmax) == 0.f) { /* Column K is zero: 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 { /* Copy column IMAX to column K+1 of W and update it */ i__1 = imax - k; ccopy_(&i__1, &a[imax + k * a_dim1], lda, &w[k + (k + 1) * w_dim1], &c__1); i__1 = *n - imax + 1; ccopy_(&i__1, &a[imax + imax * a_dim1], &c__1, &w[imax + (k + 1) * w_dim1], &c__1); i__1 = *n - k + 1; i__2 = k - 1; q__1.r = -1.f, q__1.i = -0.f; cgemv_("No transpose", &i__1, &i__2, &q__1, &a[k + a_dim1], lda, &w[imax + w_dim1], ldw, &c_b1, &w[k + (k + 1) * w_dim1], &c__1); /* 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 + icamax_(&i__1, &w[k + (k + 1) * w_dim1], &c__1) ; i__1 = jmax + (k + 1) * w_dim1; rowmax = (r__1 = w[i__1].r, dabs(r__1)) + (r__2 = r_imag(&w[ jmax + (k + 1) * w_dim1]), dabs(r__2)); if (imax < *n) { i__1 = *n - imax; jmax = imax + icamax_(&i__1, &w[imax + 1 + (k + 1) * w_dim1], &c__1); /* Computing MAX */ i__1 = jmax + (k + 1) * w_dim1; r__3 = rowmax, r__4 = (r__1 = w[i__1].r, dabs(r__1)) + ( r__2 = r_imag(&w[jmax + (k + 1) * w_dim1]), dabs( r__2)); rowmax = dmax(r__3,r__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 ((r__1 = w[i__1].r, dabs(r__1)) + (r__2 = r_imag(&w[ imax + (k + 1) * w_dim1]), dabs(r__2)) >= 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; ccopy_(&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 + k * a_dim1; i__2 = kk + k * a_dim1; a[i__1].r = a[i__2].r, a[i__1].i = a[i__2].i; i__1 = kp - k - 1; ccopy_(&i__1, &a[k + 1 + kk * a_dim1], &c__1, &a[kp + (k + 1) * a_dim1], lda); i__1 = *n - kp + 1; ccopy_(&i__1, &a[kp + kk * a_dim1], &c__1, &a[kp + kp * a_dim1], &c__1); /* Interchange rows KK and KP in first KK columns of A and W */ cswap_(&kk, &a[kk + a_dim1], lda, &a[kp + a_dim1], lda); cswap_(&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; ccopy_(&i__1, &w[k + k * w_dim1], &c__1, &a[k + k * a_dim1], & c__1); if (k < *n) { c_div(&q__1, &c_b1, &a[k + k * a_dim1]); r1.r = q__1.r, r1.i = q__1.i; i__1 = *n - k; cscal_(&i__1, &r1, &a[k + 1 + k * a_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; c_div(&q__1, &w[k + 1 + (k + 1) * w_dim1], &d21); d11.r = q__1.r, d11.i = q__1.i; c_div(&q__1, &w[k + k * w_dim1], &d21); d22.r = q__1.r, d22.i = q__1.i; q__3.r = d11.r * d22.r - d11.i * d22.i, q__3.i = d11.r * d22.i + d11.i * d22.r; q__2.r = q__3.r - 1.f, q__2.i = q__3.i - 0.f; c_div(&q__1, &c_b1, &q__2); t.r = q__1.r, t.i = q__1.i; c_div(&q__1, &t, &d21); d21.r = q__1.r, d21.i = q__1.i; i__1 = *n; for (j = k + 2; j <= i__1; ++j) { i__2 = j + k * a_dim1; i__3 = j + k * w_dim1; q__3.r = d11.r * w[i__3].r - d11.i * w[i__3].i, q__3.i = d11.r * w[i__3].i + d11.i * w[i__3] .r; i__4 = j + (k + 1) * w_dim1; q__2.r = q__3.r - w[i__4].r, q__2.i = q__3.i - w[i__4] .i; q__1.r = d21.r * q__2.r - d21.i * q__2.i, q__1.i = d21.r * q__2.i + d21.i * q__2.r; a[i__2].r = q__1.r, a[i__2].i = q__1.i; i__2 = j + (k + 1) * a_dim1; i__3 = j + (k + 1) * w_dim1; q__3.r = d22.r * w[i__3].r - d22.i * w[i__3].i, q__3.i = d22.r * w[i__3].i + d22.i * w[i__3] .r; i__4 = j + k * w_dim1; q__2.r = q__3.r - w[i__4].r, q__2.i = q__3.i - w[i__4] .i; q__1.r = d21.r * q__2.r - d21.i * q__2.i, q__1.i = d21.r * q__2.i + d21.i * q__2.r; a[i__2].r = q__1.r, a[i__2].i = q__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; } } /* 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 */ 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 = j + jb - jj; i__5 = k - 1; q__1.r = -1.f, q__1.i = -0.f; cgemv_("No transpose", &i__4, &i__5, &q__1, &a[jj + a_dim1], lda, &w[jj + w_dim1], ldw, &c_b1, &a[jj + jj * a_dim1] , &c__1); /* L100: */ } /* Update the rectangular subdiagonal block */ if (j + jb <= *n) { i__3 = *n - j - jb + 1; i__4 = k - 1; q__1.r = -1.f, q__1.i = -0.f; cgemm_("No transpose", "Transpose", &i__3, &jb, &i__4, &q__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) { cswap_(&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 CLASYF */ } /* clasyf_ */