#include "blaswrap.h" #include "f2c.h" /* Subroutine */ int cpptrf_(char *uplo, integer *n, complex *ap, integer * info) { /* -- LAPACK routine (version 3.0) -- Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., Courant Institute, Argonne National Lab, and Rice University September 30, 1994 Purpose ======= CPPTRF computes the Cholesky factorization of a complex Hermitian positive definite matrix A stored in packed format. The factorization has the form A = U**H * U, if UPLO = 'U', or A = L * L**H, 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) COMPLEX array, dimension (N*(N+1)/2) On entry, the upper or lower triangle of the Hermitian 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**H*U or A = L*L**H, 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 Hermitian matrix A: a11 a12 a13 a14 a22 a23 a24 a33 a34 (aij = conjg(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, i__3; real r__1; complex q__1, q__2; /* Builtin functions */ double sqrt(doublereal); /* Local variables */ extern /* Subroutine */ int chpr_(char *, integer *, real *, complex *, integer *, complex *); static integer j; extern /* Complex */ VOID cdotc_(complex *, integer *, complex *, integer *, complex *, integer *); extern logical lsame_(char *, char *); static logical upper; extern /* Subroutine */ int ctpsv_(char *, char *, char *, integer *, complex *, complex *, integer *); static integer jc, jj; extern /* Subroutine */ int csscal_(integer *, real *, complex *, integer *), xerbla_(char *, integer *); static real ajj; --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_("CPPTRF", &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; ctpsv_("Upper", "Conjugate transpose", "Non-unit", &i__2, &ap[ 1], &ap[jc], &c__1); } /* Compute U(J,J) and test for non-positive-definiteness. */ i__2 = jj; r__1 = ap[i__2].r; i__3 = j - 1; cdotc_(&q__2, &i__3, &ap[jc], &c__1, &ap[jc], &c__1); q__1.r = r__1 - q__2.r, q__1.i = -q__2.i; ajj = q__1.r; if (ajj <= 0.f) { i__2 = jj; ap[i__2].r = ajj, ap[i__2].i = 0.f; goto L30; } i__2 = jj; r__1 = sqrt(ajj); ap[i__2].r = r__1, ap[i__2].i = 0.f; /* 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. */ i__2 = jj; ajj = ap[i__2].r; if (ajj <= 0.f) { i__2 = jj; ap[i__2].r = ajj, ap[i__2].i = 0.f; goto L30; } ajj = sqrt(ajj); i__2 = jj; ap[i__2].r = ajj, ap[i__2].i = 0.f; /* 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; csscal_(&i__2, &r__1, &ap[jj + 1], &c__1); i__2 = *n - j; chpr_("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 CPPTRF */ } /* cpptrf_ */