1ZPPSV(1) LAPACK driver routine (version 3.1) ZPPSV(1)
2
6 ZPPSV - the solution to a complex system of linear equations A * X =
7 B,
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10 SUBROUTINE ZPPSV( UPLO, N, NRHS, AP, B, LDB, INFO )
11 CHARACTER UPLO
13 INTEGER INFO, LDB, N, NRHS
15 COMPLEX*16 AP( * ), B( LDB, * )
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19 ZPPSV computes the solution to a complex system of linear equations
20 A * X = B, where A is an N-by-N Hermitian positive definite matrix
21 stored in packed format and X and B are N-by-NRHS matrices.
22 The Cholesky decomposition is used to factor A as
24 A = U**H* U, if UPLO = 'U', or
25 A = L * L**H, if UPLO = 'L',
26 where U is an upper triangular matrix and L is a lower triangular
27 matrix. The factored form of A is then used to solve the system of
28 equations A * X = B.
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32 UPLO (input) CHARACTER*1
33 = 'U': Upper triangle of A is stored;
34 = 'L': Lower triangle of A is stored.
35 N (input) INTEGER
37 The number of linear equations, i.e., the order of the matrix
38 A. N >= 0.
39 NRHS (input) INTEGER
41 The number of right hand sides, i.e., the number of columns of
42 the matrix B. NRHS >= 0.
43 AP (input/output) COMPLEX*16 array, dimension (N*(N+1)/2)
45 On entry, the upper or lower triangle of the Hermitian matrix
46 A, packed columnwise in a linear array. The j-th column of A
47 is stored in the array AP as follows: if UPLO = 'U', AP(i +
48 (j-1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i +
49 (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. See below for further
50 details.
51 On exit, if INFO = 0, the factor U or L from the Cholesky fac‐
53 torization A = U**H*U or A = L*L**H, in the same storage format
54 as A.
55 B (input/output) COMPLEX*16 array, dimension (LDB,NRHS)
57 On entry, the N-by-NRHS right hand side matrix B. On exit, if
58 INFO = 0, the N-by-NRHS solution matrix X.
59 LDB (input) INTEGER
61 The leading dimension of the array B. LDB >= max(1,N).
62 INFO (output) INTEGER
64 = 0: successful exit
65 < 0: if INFO = -i, the i-th argument had an illegal value
66 > 0: if INFO = i, the leading minor of order i of A is not
67 positive definite, so the factorization could not be completed,
68 and the solution has not been computed.
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71 The packed storage scheme is illustrated by the following example when
72 N = 4, UPLO = 'U':
73 Two-dimensional storage of the Hermitian matrix A:
75 a11 a12 a13 a14
77 a22 a23 a24
78 a33 a34 (aij = conjg(aji))
79 a44
80 Packed storage of the upper triangle of A:
82 AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]
84 LAPACK driver routine (version 3.N1o)vember 2006 ZPPSV(1)