sppsv (3) - Linux Man Pages
subroutine sppsv (characterUPLO, integerN, integerNRHS, real, dimension( * )AP, real, dimension( ldb, * )B, integerLDB, integerINFO)
SPPSV computes the solution to system of linear equations A * X = B for OTHER matrices
SPPSV 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.
UPLO is CHARACTER*1 = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored.
N is INTEGER The number of linear equations, i.e., the order of the matrix A. N >= 0.
NRHS is INTEGER The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.
AP is 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 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 is REAL 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 is INTEGER The leading dimension of the array B. LDB >= max(1,N).
INFO is 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.
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
- November 2011
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 ]
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