/* dlasyf.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 "clapack.h" /* Table of constant values */ static integer c__1 = 1; static doublereal c_b8 = -1.; static doublereal c_b9 = 1.; /* Subroutine */ int dlasyf_(char *uplo, integer *n, integer *nb, integer *kb, doublereal *a, integer *lda, integer *ipiv, doublereal *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; /* Builtin functions */ double sqrt(doublereal); /* Local variables */ integer j, k; doublereal t, r1, d11, d21, d22; integer jb, jj, kk, jp, kp, kw, kkw, imax, jmax; doublereal alpha; extern /* Subroutine */ int dscal_(integer *, doublereal *, doublereal *, integer *), dgemm_(char *, char *, integer *, integer *, integer * , doublereal *, doublereal *, integer *, doublereal *, integer *, doublereal *, doublereal *, integer *); extern logical lsame_(char *, char *); extern /* Subroutine */ int dgemv_(char *, integer *, integer *, doublereal *, doublereal *, integer *, doublereal *, integer *, doublereal *, doublereal *, integer *), dcopy_(integer *, doublereal *, integer *, doublereal *, integer *), dswap_(integer *, doublereal *, integer *, doublereal *, integer *); integer kstep; doublereal absakk; extern integer idamax_(integer *, doublereal *, integer *); doublereal colmax, rowmax; /* -- LAPACK routine (version 3.2) -- */ /* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ /* November 2006 */ /* .. Scalar Arguments .. */ /* .. */ /* .. Array Arguments .. */ /* .. */ /* Purpose */ /* ======= */ /* DLASYF computes a partial factorization of a real 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. */ /* DLASYF is an auxiliary routine called by DSYTRF. 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) DOUBLE PRECISION 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) DOUBLE PRECISION 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 .. */ /* .. */ /* .. 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 */ /* 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 */ dcopy_(&k, &a[k * a_dim1 + 1], &c__1, &w[kw * w_dim1 + 1], &c__1); if (k < *n) { i__1 = *n - k; dgemv_("No transpose", &k, &i__1, &c_b8, &a[(k + 1) * a_dim1 + 1], lda, &w[k + (kw + 1) * w_dim1], ldw, &c_b9, &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 */ absakk = (d__1 = w[k + kw * w_dim1], 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 = idamax_(&i__1, &w[kw * w_dim1 + 1], &c__1); colmax = (d__1 = w[imax + kw * w_dim1], abs(d__1)); } else { colmax = 0.; } if (max(absakk,colmax) == 0.) { /* 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 */ dcopy_(&imax, &a[imax * a_dim1 + 1], &c__1, &w[(kw - 1) * w_dim1 + 1], &c__1); i__1 = k - imax; dcopy_(&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; dgemv_("No transpose", &k, &i__1, &c_b8, &a[(k + 1) * a_dim1 + 1], lda, &w[imax + (kw + 1) * w_dim1], ldw, &c_b9, &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 + idamax_(&i__1, &w[imax + 1 + (kw - 1) * w_dim1], &c__1); rowmax = (d__1 = w[jmax + (kw - 1) * w_dim1], abs(d__1)); if (imax > 1) { i__1 = imax - 1; jmax = idamax_(&i__1, &w[(kw - 1) * w_dim1 + 1], &c__1); /* Computing MAX */ d__2 = rowmax, d__3 = (d__1 = w[jmax + (kw - 1) * w_dim1], abs(d__1)); rowmax = max(d__2,d__3); } if (absakk >= alpha * colmax * (colmax / rowmax)) { /* no interchange, use 1-by-1 pivot block */ kp = k; } else if ((d__1 = w[imax + (kw - 1) * w_dim1], 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 */ dcopy_(&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 */ a[kp + k * a_dim1] = a[kk + k * a_dim1]; i__1 = k - 1 - kp; dcopy_(&i__1, &a[kp + 1 + kk * a_dim1], &c__1, &a[kp + (kp + 1) * a_dim1], lda); dcopy_(&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; dswap_(&i__1, &a[kk + kk * a_dim1], lda, &a[kp + kk * a_dim1], lda); i__1 = *n - kk + 1; dswap_(&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 */ dcopy_(&k, &w[kw * w_dim1 + 1], &c__1, &a[k * a_dim1 + 1], & c__1); r1 = 1. / a[k + k * a_dim1]; i__1 = k - 1; dscal_(&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 */ d21 = w[k - 1 + kw * w_dim1]; d11 = w[k + kw * w_dim1] / d21; d22 = w[k - 1 + (kw - 1) * w_dim1] / d21; t = 1. / (d11 * d22 - 1.); d21 = t / d21; i__1 = k - 2; for (j = 1; j <= i__1; ++j) { a[j + (k - 1) * a_dim1] = d21 * (d11 * w[j + (kw - 1) * w_dim1] - w[j + kw * w_dim1]); a[j + k * a_dim1] = d21 * (d22 * w[j + kw * w_dim1] - w[j + (kw - 1) * w_dim1]); /* L20: */ } } /* Copy D(k) to A */ a[k - 1 + (k - 1) * a_dim1] = w[k - 1 + (kw - 1) * w_dim1]; a[k - 1 + k * a_dim1] = w[k - 1 + kw * w_dim1]; a[k + k * a_dim1] = w[k + kw * w_dim1]; } } /* 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; dgemv_("No transpose", &i__3, &i__4, &c_b8, &a[j + (k + 1) * a_dim1], lda, &w[jj + (kw + 1) * w_dim1], ldw, &c_b9, &a[j + jj * a_dim1], &c__1); /* L40: */ } /* Update the rectangular superdiagonal block */ i__2 = j - 1; i__3 = *n - k; dgemm_("No transpose", "Transpose", &i__2, &jb, &i__3, &c_b8, &a[( k + 1) * a_dim1 + 1], lda, &w[j + (kw + 1) * w_dim1], ldw, &c_b9, &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; dswap_(&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; dcopy_(&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; dgemv_("No transpose", &i__1, &i__2, &c_b8, &a[k + a_dim1], lda, &w[k + w_dim1], ldw, &c_b9, &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 */ absakk = (d__1 = w[k + k * w_dim1], 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 + idamax_(&i__1, &w[k + 1 + k * w_dim1], &c__1); colmax = (d__1 = w[imax + k * w_dim1], abs(d__1)); } else { colmax = 0.; } if (max(absakk,colmax) == 0.) { /* 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; dcopy_(&i__1, &a[imax + k * a_dim1], lda, &w[k + (k + 1) * w_dim1], &c__1); i__1 = *n - imax + 1; dcopy_(&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; dgemv_("No transpose", &i__1, &i__2, &c_b8, &a[k + a_dim1], lda, &w[imax + w_dim1], ldw, &c_b9, &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 + idamax_(&i__1, &w[k + (k + 1) * w_dim1], &c__1) ; rowmax = (d__1 = w[jmax + (k + 1) * w_dim1], abs(d__1)); if (imax < *n) { i__1 = *n - imax; jmax = imax + idamax_(&i__1, &w[imax + 1 + (k + 1) * w_dim1], &c__1); /* Computing MAX */ d__2 = rowmax, d__3 = (d__1 = w[jmax + (k + 1) * w_dim1], abs(d__1)); rowmax = max(d__2,d__3); } if (absakk >= alpha * colmax * (colmax / rowmax)) { /* no interchange, use 1-by-1 pivot block */ kp = k; } else if ((d__1 = w[imax + (k + 1) * w_dim1], 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; dcopy_(&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 */ a[kp + k * a_dim1] = a[kk + k * a_dim1]; i__1 = kp - k - 1; dcopy_(&i__1, &a[k + 1 + kk * a_dim1], &c__1, &a[kp + (k + 1) * a_dim1], lda); i__1 = *n - kp + 1; dcopy_(&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 */ dswap_(&kk, &a[kk + a_dim1], lda, &a[kp + a_dim1], lda); dswap_(&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; dcopy_(&i__1, &w[k + k * w_dim1], &c__1, &a[k + k * a_dim1], & c__1); if (k < *n) { r1 = 1. / a[k + k * a_dim1]; i__1 = *n - k; dscal_(&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 */ d21 = w[k + 1 + k * w_dim1]; d11 = w[k + 1 + (k + 1) * w_dim1] / d21; d22 = w[k + k * w_dim1] / d21; t = 1. / (d11 * d22 - 1.); d21 = t / d21; i__1 = *n; for (j = k + 2; j <= i__1; ++j) { a[j + k * a_dim1] = d21 * (d11 * w[j + k * w_dim1] - w[j + (k + 1) * w_dim1]); a[j + (k + 1) * a_dim1] = d21 * (d22 * w[j + (k + 1) * w_dim1] - w[j + k * w_dim1]); /* L80: */ } } /* Copy D(k) to A */ a[k + k * a_dim1] = w[k + k * w_dim1]; a[k + 1 + k * a_dim1] = w[k + 1 + k * w_dim1]; a[k + 1 + (k + 1) * a_dim1] = w[k + 1 + (k + 1) * w_dim1]; } } /* 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; dgemv_("No transpose", &i__4, &i__5, &c_b8, &a[jj + a_dim1], lda, &w[jj + w_dim1], ldw, &c_b9, &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; dgemm_("No transpose", "Transpose", &i__3, &jb, &i__4, &c_b8, &a[j + jb + a_dim1], lda, &w[j + w_dim1], ldw, &c_b9, &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) { dswap_(&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 DLASYF */ } /* dlasyf_ */