#include "blaswrap.h" #include "f2c.h" /* Subroutine */ int csytrf_(char *uplo, integer *n, complex *a, integer *lda, integer *ipiv, complex *work, integer *lwork, integer *info) { /* -- LAPACK routine (version 3.0) -- Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., Courant Institute, Argonne National Lab, and Rice University June 30, 1999 Purpose ======= CSYTRF computes the factorization of a complex symmetric matrix A using the Bunch-Kaufman diagonal pivoting method. The form of the factorization is A = U*D*U**T or A = L*D*L**T where U (or L) is a product of permutation and unit upper (lower) triangular matrices, and D is symmetric and block diagonal with with 1-by-1 and 2-by-2 diagonal blocks. This is the blocked version of the algorithm, calling Level 3 BLAS. Arguments ========= UPLO (input) CHARACTER*1 = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored. N (input) INTEGER The order of the matrix A. N >= 0. 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, 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. WORK (workspace/output) COMPLEX array, dimension (LWORK) On exit, if INFO = 0, WORK(1) returns the optimal LWORK. LWORK (input) INTEGER The length of WORK. LWORK >=1. For best performance LWORK >= N*NB, where NB is the block size returned by ILAENV. If LWORK = -1, then a workspace query is assumed; the routine only calculates the optimal size of the WORK array, returns this value as the first entry of the WORK array, and no error message related to LWORK is issued by XERBLA. INFO (output) INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: if INFO = i, D(i,i) 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 =============== 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). ===================================================================== Test the input parameters. Parameter adjustments */ /* Table of constant values */ static integer c__1 = 1; static integer c_n1 = -1; static integer c__2 = 2; /* System generated locals */ integer a_dim1, a_offset, i__1, i__2; /* Local variables */ static integer j, k; extern logical lsame_(char *, char *); static integer nbmin, iinfo; static logical upper; extern /* Subroutine */ int csytf2_(char *, integer *, complex *, integer *, integer *, integer *); static integer kb, nb; extern /* Subroutine */ int xerbla_(char *, integer *); extern integer ilaenv_(integer *, char *, char *, integer *, integer *, integer *, integer *, ftnlen, ftnlen); extern /* Subroutine */ int clasyf_(char *, integer *, integer *, integer *, complex *, integer *, integer *, complex *, integer *, integer *); static integer ldwork, lwkopt; static logical lquery; static integer iws; #define a_subscr(a_1,a_2) (a_2)*a_dim1 + a_1 #define a_ref(a_1,a_2) a[a_subscr(a_1,a_2)] a_dim1 = *lda; a_offset = 1 + a_dim1 * 1; a -= a_offset; --ipiv; --work; /* Function Body */ *info = 0; upper = lsame_(uplo, "U"); lquery = *lwork == -1; if (! upper && ! lsame_(uplo, "L")) { *info = -1; } else if (*n < 0) { *info = -2; } else if (*lda < max(1,*n)) { *info = -4; } else if (*lwork < 1 && ! lquery) { *info = -7; } if (*info == 0) { /* Determine the block size */ nb = ilaenv_(&c__1, "CSYTRF", uplo, n, &c_n1, &c_n1, &c_n1, (ftnlen)6, (ftnlen)1); lwkopt = *n * nb; work[1].r = (real) lwkopt, work[1].i = 0.f; } if (*info != 0) { i__1 = -(*info); xerbla_("CSYTRF", &i__1); return 0; } else if (lquery) { return 0; } nbmin = 2; ldwork = *n; if (nb > 1 && nb < *n) { iws = ldwork * nb; if (*lwork < iws) { /* Computing MAX */ i__1 = *lwork / ldwork; nb = max(i__1,1); /* Computing MAX */ i__1 = 2, i__2 = ilaenv_(&c__2, "CSYTRF", uplo, n, &c_n1, &c_n1, & c_n1, (ftnlen)6, (ftnlen)1); nbmin = max(i__1,i__2); } } else { iws = 1; } if (nb < nbmin) { nb = *n; } 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 KB, where KB is the number of columns factorized by CLASYF; KB is either NB or NB-1, or K for the last block */ k = *n; L10: /* If K < 1, exit from loop */ if (k < 1) { goto L40; } if (k > nb) { /* Factorize columns k-kb+1:k of A and use blocked code to update columns 1:k-kb */ clasyf_(uplo, &k, &nb, &kb, &a[a_offset], lda, &ipiv[1], &work[1], n, &iinfo); } else { /* Use unblocked code to factorize columns 1:k of A */ csytf2_(uplo, &k, &a[a_offset], lda, &ipiv[1], &iinfo); kb = k; } /* Set INFO on the first occurrence of a zero pivot */ if (*info == 0 && iinfo > 0) { *info = iinfo; } /* Decrease K and return to the start of the main loop */ k -= kb; 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 KB, where KB is the number of columns factorized by CLASYF; KB is either NB or NB-1, or N-K+1 for the last block */ k = 1; L20: /* If K > N, exit from loop */ if (k > *n) { goto L40; } if (k <= *n - nb) { /* Factorize columns k:k+kb-1 of A and use blocked code to update columns k+kb:n */ i__1 = *n - k + 1; clasyf_(uplo, &i__1, &nb, &kb, &a_ref(k, k), lda, &ipiv[k], &work[ 1], n, &iinfo); } else { /* Use unblocked code to factorize columns k:n of A */ i__1 = *n - k + 1; csytf2_(uplo, &i__1, &a_ref(k, k), lda, &ipiv[k], &iinfo); kb = *n - k + 1; } /* Set INFO on the first occurrence of a zero pivot */ if (*info == 0 && iinfo > 0) { *info = iinfo + k - 1; } /* Adjust IPIV */ i__1 = k + kb - 1; for (j = k; j <= i__1; ++j) { if (ipiv[j] > 0) { ipiv[j] = ipiv[j] + k - 1; } else { ipiv[j] = ipiv[j] - k + 1; } /* L30: */ } /* Increase K and return to the start of the main loop */ k += kb; goto L20; } L40: work[1].r = (real) lwkopt, work[1].i = 0.f; return 0; /* End of CSYTRF */ } /* csytrf_ */ #undef a_ref #undef a_subscr