1ZPPSV(1) LAPACK driver routine (version 3.2) ZPPSV(1)
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6 ZPPSV - computes the solution to a complex system of linear equations
7 A * X = 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
23 A = U**H* U, if UPLO = 'U', or
24 A = L * L**H, if UPLO = 'L',
25 where U is an upper triangular matrix and L is a lower triangular
26 matrix. The factored form of A is then used to solve the system of
27 equations A * X = B.
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30 UPLO (input) CHARACTER*1
31 = 'U': Upper triangle of A is stored;
32 = 'L': Lower triangle of A is stored.
33 N (input) INTEGER
35 The number of linear equations, i.e., the order of the matrix
36 A. N >= 0.
37 NRHS (input) INTEGER
39 The number of right hand sides, i.e., the number of columns of
40 the matrix B. NRHS >= 0.
41 AP (input/output) COMPLEX*16 array, dimension (N*(N+1)/2)
43 On entry, the upper or lower triangle of the Hermitian matrix
44 A, packed columnwise in a linear array. The j-th column of A
45 is stored in the array AP as follows: if UPLO = 'U', AP(i +
46 (j-1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i +
47 (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n. See below for further
48 details. On exit, if INFO = 0, the factor U or L from the
49 Cholesky factorization A = U**H*U or A = L*L**H, in the same
50 storage format as A.
51 B (input/output) COMPLEX*16 array, dimension (LDB,NRHS)
53 On entry, the N-by-NRHS right hand side matrix B. On exit, if
54 INFO = 0, the N-by-NRHS solution matrix X.
55 LDB (input) INTEGER
57 The leading dimension of the array B. LDB >= max(1,N).
58 INFO (output) INTEGER
60 = 0: successful exit
61 < 0: if INFO = -i, the i-th argument had an illegal value
62 > 0: if INFO = i, the leading minor of order i of A is not
63 positive definite, so the factorization could not be completed,
64 and the solution has not been computed.
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67 The packed storage scheme is illustrated by the following example when
68 N = 4, UPLO = 'U':
69 Two-dimensional storage of the Hermitian matrix A:
70 a11 a12 a13 a14
71 a22 a23 a24
72 a33 a34 (aij = conjg(aji))
73 a44
74 Packed storage of the upper triangle of A:
75 AP = [ a11, a12, a22, a13, a23, a33, a14, a24, a34, a44 ]
76 LAPACK driver routine (version 3.N2o)vember 2008 ZPPSV(1)