X-Git-Url: http://vcs.maemo.org/git/?a=blobdiff_plain;f=3rdparty%2Flapack%2Fdlasyf.c;fp=3rdparty%2Flapack%2Fdlasyf.c;h=bcaf32d8a50fe36b945319e1f2603747b9433ea6;hb=e4c14cdbdf2fe805e79cd96ded236f57e7b89060;hp=0000000000000000000000000000000000000000;hpb=454138ff8a20f6edb9b65a910101403d8b520643;p=opencv diff --git a/3rdparty/lapack/dlasyf.c b/3rdparty/lapack/dlasyf.c new file mode 100644 index 0000000..bcaf32d --- /dev/null +++ b/3rdparty/lapack/dlasyf.c @@ -0,0 +1,690 @@ +#include "clapack.h" + +/* Subroutine */ int dlasyf_(char *uplo, integer *n, integer *nb, integer *kb, + doublereal *a, integer *lda, integer *ipiv, doublereal *w, integer * + ldw, integer *info) +{ +/* -- LAPACK routine (version 3.1) -- + Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. + November 2006 + + + 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. + + ===================================================================== + + + Parameter adjustments */ + /* Table of constant values */ + static integer c__1 = 1; + static doublereal c_b8 = -1.; + static doublereal c_b9 = 1.; + + /* 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 */ + static integer j, k; + static doublereal t, r1, d11, d21, d22; + static integer jb, jj, kk, jp, kp, kw, kkw, imax, jmax; + static 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 *); + static integer kstep; + static doublereal absakk; + extern integer idamax_(integer *, doublereal *, integer *); + static doublereal 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.) + 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_ */