#include "blaswrap.h" #include "f2c.h" /* Subroutine */ int spptrf_(char *uplo, integer *n, real *ap, integer *info) { /* -- LAPACK routine (version 3.1) -- Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. November 2006 Purpose ======= SPPTRF computes the Cholesky factorization of a real symmetric positive definite matrix A stored in packed format. 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. 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. AP (input/output) REAL array, dimension (N*(N+1)/2) On entry, the upper or lower triangle of the symmetric matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array AP as follows: if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. See below for further details. On exit, if INFO = 0, the triangular factor U or L from the Cholesky factorization A = U**T*U or A = L*L**T, in the same storage format as A. 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. Further Details ======= ======= The packed storage scheme is illustrated by the following example when N = 4, UPLO = 'U': Two-dimensional storage of the symmetric matrix A: a11 a12 a13 a14 a22 a23 a24 a33 a34 (aij = aji) a44 Packed storage of the upper triangle of A: AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ] ===================================================================== Test the input parameters. Parameter adjustments */ /* Table of constant values */ static integer c__1 = 1; static real c_b16 = -1.f; /* System generated locals */ integer i__1, i__2; real r__1; /* Builtin functions */ double sqrt(doublereal); /* Local variables */ static integer j, jc, jj; static real ajj; extern doublereal sdot_(integer *, real *, integer *, real *, integer *); extern /* Subroutine */ int sspr_(char *, integer *, real *, real *, integer *, real *); extern logical lsame_(char *, char *); extern /* Subroutine */ int sscal_(integer *, real *, real *, integer *); static logical upper; extern /* Subroutine */ int stpsv_(char *, char *, char *, integer *, real *, real *, integer *), xerbla_(char * , integer *); --ap; /* Function Body */ *info = 0; upper = lsame_(uplo, "U"); if (! upper && ! lsame_(uplo, "L")) { *info = -1; } else if (*n < 0) { *info = -2; } if (*info != 0) { i__1 = -(*info); xerbla_("SPPTRF", &i__1); return 0; } /* Quick return if possible */ if (*n == 0) { return 0; } if (upper) { /* Compute the Cholesky factorization A = U'*U. */ jj = 0; i__1 = *n; for (j = 1; j <= i__1; ++j) { jc = jj + 1; jj += j; /* Compute elements 1:J-1 of column J. */ if (j > 1) { i__2 = j - 1; stpsv_("Upper", "Transpose", "Non-unit", &i__2, &ap[1], &ap[ jc], &c__1); } /* Compute U(J,J) and test for non-positive-definiteness. */ i__2 = j - 1; ajj = ap[jj] - sdot_(&i__2, &ap[jc], &c__1, &ap[jc], &c__1); if (ajj <= 0.f) { ap[jj] = ajj; goto L30; } ap[jj] = sqrt(ajj); /* L10: */ } } else { /* Compute the Cholesky factorization A = L*L'. */ jj = 1; i__1 = *n; for (j = 1; j <= i__1; ++j) { /* Compute L(J,J) and test for non-positive-definiteness. */ ajj = ap[jj]; if (ajj <= 0.f) { ap[jj] = ajj; goto L30; } ajj = sqrt(ajj); ap[jj] = ajj; /* Compute elements J+1:N of column J and update the trailing submatrix. */ if (j < *n) { i__2 = *n - j; r__1 = 1.f / ajj; sscal_(&i__2, &r__1, &ap[jj + 1], &c__1); i__2 = *n - j; sspr_("Lower", &i__2, &c_b16, &ap[jj + 1], &c__1, &ap[jj + *n - j + 1]); jj = jj + *n - j + 1; } /* L20: */ } } goto L40; L30: *info = j; L40: return 0; /* End of SPPTRF */ } /* spptrf_ */