#include "blaswrap.h" #include "f2c.h" /* Subroutine */ int chetrf_(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 ======= CHETRF computes the factorization of a complex Hermitian matrix A using the Bunch-Kaufman diagonal pivoting method. The form of the factorization is A = U*D*U**H or A = L*D*L**H where U (or L) is a product of permutation and unit upper (lower) triangular matrices, and D is Hermitian and block diagonal 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 Hermitian 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. 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 chetf2_(char *, integer *, complex *, integer *, integer *, integer *); static integer kb, nb; extern /* Subroutine */ int clahef_(char *, integer *, integer *, integer *, complex *, integer *, integer *, complex *, integer *, integer *), xerbla_(char *, integer *); extern integer ilaenv_(integer *, char *, char *, integer *, integer *, integer *, integer *, ftnlen, ftnlen); 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, "CHETRF", 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_("CHETRF", &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, "CHETRF", 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 CLAHEF; 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 */ clahef_(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 */ chetf2_(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 CLAHEF; 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; clahef_(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; chetf2_(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 CHETRF */ } /* chetrf_ */ #undef a_ref #undef a_subscr