
NAMEzhptrf.f SYNOPSISFunctions/Subroutinessubroutine zhptrf (UPLO, N, AP, IPIV, INFO) Function/Subroutine Documentationsubroutine zhptrf (characterUPLO, integerN, complex*16, dimension( * )AP, integer, dimension( * )IPIV, integerINFO)ZHPTRF Purpose:ZHPTRF computes the factorization of a complex Hermitian packed matrix A using the BunchKaufman diagonal pivoting method: A = U*D*U**H or A = L*D*L**H where U (or L) is a product of permutation and unit upper (lower) triangular matrices, and D is Hermitian and block diagonal with 1by1 and 2by2 diagonal blocks. 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 order of the matrix A. N >= 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. On exit, the block diagonal matrix D and the multipliers used to obtain the factor U or L, stored as a packed triangular matrix overwriting A (see below for further details).IPIV IPIV is INTEGER array, dimension (N) Details of the interchanges and the block structure of D. 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.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, and division by zero will occur if it is used to solve a system of equations. Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
Further Details:
If UPLO = 'U', then A = U*D*U**H, where U = P(n)*U(n)* ... *P(k)U(k)* ..., i.e., U is a product of terms P(k)*U(k), where k decreases from n to 1 in steps of 1 or 2, and D is a block diagonal matrix with 1by1 and 2by2 diagonal blocks D(k). P(k) is a permutation matrix as defined by IPIV(k), and U(k) is a unit upper triangular matrix, such that if the diagonal block D(k) is of order s (s = 1 or 2), then ( I v 0 ) ks U(k) = ( 0 I 0 ) s ( 0 0 I ) nk ks s nk If s = 1, D(k) overwrites A(k,k), and v overwrites A(1:k1,k). If s = 2, the upper triangle of D(k) overwrites A(k1,k1), A(k1,k), and A(k,k), and v overwrites A(1:k2,k1:k). If UPLO = 'L', then A = L*D*L**H, where L = P(1)*L(1)* ... *P(k)*L(k)* ..., i.e., L is a product of terms P(k)*L(k), where k increases from 1 to n in steps of 1 or 2, and D is a block diagonal matrix with 1by1 and 2by2 diagonal blocks D(k). P(k) is a permutation matrix as defined by IPIV(k), and L(k) is a unit lower triangular matrix, such that if the diagonal block D(k) is of order s (s = 1 or 2), then ( I 0 0 ) k1 L(k) = ( 0 I 0 ) s ( 0 v I ) nks+1 k1 s nks+1 If s = 1, D(k) overwrites A(k,k), and v overwrites A(k+1:n,k). If s = 2, the lower triangle of D(k) overwrites A(k,k), A(k+1,k), and A(k+1,k+1), and v overwrites A(k+2:n,k:k+1). J. Lewis, Boeing Computer Services Company
Definition at line 160 of file zhptrf.f.
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