#include "blaswrap.h" #include "f2c.h" /* Subroutine */ int dppsv_(char *uplo, integer *n, integer *nrhs, doublereal *ap, doublereal *b, integer *ldb, integer *info) { /* -- LAPACK driver routine (version 3.0) -- Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., Courant Institute, Argonne National Lab, and Rice University March 31, 1993 Purpose ======= DPPSV computes the solution to a real system of linear equations A * X = B, where A is an N-by-N symmetric positive definite matrix stored in packed format and X and B are N-by-NRHS matrices. The Cholesky decomposition is used to factor A as 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 a lower triangular matrix. The factored form of A is then used to solve the system of equations A * X = B. Arguments ========= UPLO (input) CHARACTER*1 = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored. N (input) INTEGER The number of linear equations, i.e., the order of the matrix A. N >= 0. NRHS (input) INTEGER The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0. AP (input/output) DOUBLE PRECISION 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 factor U or L from the Cholesky factorization A = U**T*U or A = L*L**T, in the same storage format as A. B (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS) On entry, the N-by-NRHS right hand side matrix B. On exit, if INFO = 0, the N-by-NRHS solution matrix X. LDB (input) INTEGER The leading dimension of the array B. LDB >= 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 of A is not positive definite, so the factorization could not be completed, and the solution has not been computed. 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 = 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 */ /* System generated locals */ integer b_dim1, b_offset, i__1; /* Local variables */ extern logical lsame_(char *, char *); extern /* Subroutine */ int xerbla_(char *, integer *), dpptrf_( char *, integer *, doublereal *, integer *), dpptrs_(char *, integer *, integer *, doublereal *, doublereal *, integer *, integer *); --ap; b_dim1 = *ldb; b_offset = 1 + b_dim1 * 1; b -= b_offset; /* Function Body */ *info = 0; if (! lsame_(uplo, "U") && ! lsame_(uplo, "L")) { *info = -1; } else if (*n < 0) { *info = -2; } else if (*nrhs < 0) { *info = -3; } else if (*ldb < max(1,*n)) { *info = -6; } if (*info != 0) { i__1 = -(*info); xerbla_("DPPSV ", &i__1); return 0; } /* Compute the Cholesky factorization A = U'*U or A = L*L'. */ dpptrf_(uplo, n, &ap[1], info); if (*info == 0) { /* Solve the system A*X = B, overwriting B with X. */ dpptrs_(uplo, n, nrhs, &ap[1], &b[b_offset], ldb, info); } return 0; /* End of DPPSV */ } /* dppsv_ */