#include "blaswrap.h" #include "f2c.h" /* Subroutine */ int spotrf_(char *uplo, integer *n, real *a, integer *lda, integer *info) { /* -- LAPACK routine (version 3.1) -- Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. November 2006 Purpose ======= SPOTRF computes the Cholesky factorization of a real symmetric positive definite matrix A. The factorization has the form A = U**T * U, if UPLO = 'U', or A = L * L**T, if UPLO = 'L', where U is an upper triangular matrix and L is lower triangular. This is the block 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) REAL 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, if INFO = 0, the factor U or L from the Cholesky factorization A = U**T*U or A = L*L**T. LDA (input) INTEGER The leading dimension of the array A. LDA >= max(1,N). INFO (output) INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: if INFO = i, the leading minor of order i is not positive definite, and the factorization could not be completed. ===================================================================== Test the input parameters. Parameter adjustments */ /* Table of constant values */ static integer c__1 = 1; static integer c_n1 = -1; static real c_b13 = -1.f; static real c_b14 = 1.f; /* System generated locals */ integer a_dim1, a_offset, i__1, i__2, i__3, i__4; /* Local variables */ static integer j, jb, nb; extern logical lsame_(char *, char *); extern /* Subroutine */ int sgemm_(char *, char *, integer *, integer *, integer *, real *, real *, integer *, real *, integer *, real *, real *, integer *); static logical upper; extern /* Subroutine */ int strsm_(char *, char *, char *, char *, integer *, integer *, real *, real *, integer *, real *, integer *), ssyrk_(char *, char *, integer *, integer *, real *, real *, integer *, real *, real *, integer *), spotf2_(char *, integer *, real *, integer *, integer *), xerbla_(char *, integer *); extern integer ilaenv_(integer *, char *, char *, integer *, integer *, integer *, integer *, ftnlen, ftnlen); a_dim1 = *lda; a_offset = 1 + a_dim1; a -= a_offset; /* Function Body */ *info = 0; upper = lsame_(uplo, "U"); if (! upper && ! lsame_(uplo, "L")) { *info = -1; } else if (*n < 0) { *info = -2; } else if (*lda < max(1,*n)) { *info = -4; } if (*info != 0) { i__1 = -(*info); xerbla_("SPOTRF", &i__1); return 0; } /* Quick return if possible */ if (*n == 0) { return 0; } /* Determine the block size for this environment. */ nb = ilaenv_(&c__1, "SPOTRF", uplo, n, &c_n1, &c_n1, &c_n1, (ftnlen)6, ( ftnlen)1); if (nb <= 1 || nb >= *n) { /* Use unblocked code. */ spotf2_(uplo, n, &a[a_offset], lda, info); } else { /* Use blocked code. */ if (upper) { /* Compute the Cholesky factorization A = U'*U. */ i__1 = *n; i__2 = nb; for (j = 1; i__2 < 0 ? j >= i__1 : j <= i__1; j += i__2) { /* Update and factorize the current diagonal block and test for non-positive-definiteness. Computing MIN */ i__3 = nb, i__4 = *n - j + 1; jb = min(i__3,i__4); i__3 = j - 1; ssyrk_("Upper", "Transpose", &jb, &i__3, &c_b13, &a[j * a_dim1 + 1], lda, &c_b14, &a[j + j * a_dim1], lda); spotf2_("Upper", &jb, &a[j + j * a_dim1], lda, info); if (*info != 0) { goto L30; } if (j + jb <= *n) { /* Compute the current block row. */ i__3 = *n - j - jb + 1; i__4 = j - 1; sgemm_("Transpose", "No transpose", &jb, &i__3, &i__4, & c_b13, &a[j * a_dim1 + 1], lda, &a[(j + jb) * a_dim1 + 1], lda, &c_b14, &a[j + (j + jb) * a_dim1], lda); i__3 = *n - j - jb + 1; strsm_("Left", "Upper", "Transpose", "Non-unit", &jb, & i__3, &c_b14, &a[j + j * a_dim1], lda, &a[j + (j + jb) * a_dim1], lda); } /* L10: */ } } else { /* Compute the Cholesky factorization A = L*L'. */ i__2 = *n; i__1 = nb; for (j = 1; i__1 < 0 ? j >= i__2 : j <= i__2; j += i__1) { /* Update and factorize the current diagonal block and test for non-positive-definiteness. Computing MIN */ i__3 = nb, i__4 = *n - j + 1; jb = min(i__3,i__4); i__3 = j - 1; ssyrk_("Lower", "No transpose", &jb, &i__3, &c_b13, &a[j + a_dim1], lda, &c_b14, &a[j + j * a_dim1], lda); spotf2_("Lower", &jb, &a[j + j * a_dim1], lda, info); if (*info != 0) { goto L30; } if (j + jb <= *n) { /* Compute the current block column. */ i__3 = *n - j - jb + 1; i__4 = j - 1; sgemm_("No transpose", "Transpose", &i__3, &jb, &i__4, & c_b13, &a[j + jb + a_dim1], lda, &a[j + a_dim1], lda, &c_b14, &a[j + jb + j * a_dim1], lda); i__3 = *n - j - jb + 1; strsm_("Right", "Lower", "Transpose", "Non-unit", &i__3, & jb, &c_b14, &a[j + j * a_dim1], lda, &a[j + jb + j * a_dim1], lda); } /* L20: */ } } } goto L40; L30: *info = *info + j - 1; L40: return 0; /* End of SPOTRF */ } /* spotrf_ */