
NAMEzhpsv.f SYNOPSISFunctions/Subroutinessubroutine zhpsv (UPLO, N, NRHS, AP, IPIV, B, LDB, INFO) Function/Subroutine Documentationsubroutine zhpsv (characterUPLO, integerN, integerNRHS, complex*16, dimension( * )AP, integer, dimension( * )IPIV, complex*16, dimension( ldb, * )B, integerLDB, integerINFO)ZHPSV computes the solution to system of linear equations A * X = B for OTHER matrices Purpose:ZHPSV computes the solution to a complex system of linear equations A * X = B, where A is an NbyN Hermitian matrix stored in packed format and X and B are NbyNRHS matrices. The diagonal pivoting method is used to factor A as A = U * D * U**H, if UPLO = 'U', or A = L * D * L**H, if UPLO = 'L', where U (or L) is a product of permutation and unit upper (lower) triangular matrices, D is Hermitian and block diagonal with 1by1 and 2by2 diagonal blocks. The factored form of A is then used to solve the system of equations A * X = B. UPLO
Author:
UPLO is CHARACTER*1 = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored.N N is INTEGER The number of linear equations, i.e., the order of the matrix A. N >= 0.NRHS NRHS is INTEGER The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.AP AP is COMPLEX*16 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 jth column of A is stored in the array AP as follows: if UPLO = 'U', AP(i + (j1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j1)*(2nj)/2) = A(i,j) for j<=i<=n. See below for further details. On exit, the block diagonal matrix D and the multipliers used to obtain the factor U or L from the factorization A = U*D*U**H or A = L*D*L**H as computed by ZHPTRF, stored as a packed triangular matrix in the same storage format as A.IPIV IPIV is INTEGER array, dimension (N) Details of the interchanges and the block structure of D, as determined by ZHPTRF. If IPIV(k) > 0, then rows and columns k and IPIV(k) were interchanged, and D(k,k) is a 1by1 diagonal block. If UPLO = 'U' and IPIV(k) = IPIV(k1) < 0, then rows and columns k1 and IPIV(k) were interchanged and D(k1:k,k1:k) is a 2by2 diagonal block. If UPLO = 'L' and IPIV(k) = IPIV(k+1) < 0, then rows and columns k+1 and IPIV(k) were interchanged and D(k:k+1,k:k+1) is a 2by2 diagonal block.B B is COMPLEX*16 array, dimension (LDB,NRHS) On entry, the NbyNRHS right hand side matrix B. On exit, if INFO = 0, the NbyNRHS solution matrix X.LDB LDB is INTEGER The leading dimension of the array B. LDB >= max(1,N).INFO INFO is INTEGER = 0: successful exit < 0: if INFO = i, the ith argument had an illegal value > 0: if INFO = i, D(i,i) is exactly zero. The factorization has been completed, but the block diagonal matrix D is exactly singular, so the solution could not be computed. Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
Further Details:
The packed storage scheme is illustrated by the following example when N = 4, UPLO = 'U': Twodimensional 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 ] AuthorGenerated automatically by Doxygen for LAPACK from the source code.
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