1ZSYSV(1) LAPACK driver routine (version 3.2) ZSYSV(1)
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6 ZSYSV - computes the solution to a complex system of linear equations
7 A * X = B,
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10 SUBROUTINE ZSYSV( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK, LWORK,
11 INFO )
12 CHARACTER UPLO
14 INTEGER INFO, LDA, LDB, LWORK, N, NRHS
16 INTEGER IPIV( * )
18 COMPLEX*16 A( LDA, * ), B( LDB, * ), WORK( * )
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22 ZSYSV computes the solution to a complex system of linear equations
23 A * X = B, where A is an N-by-N symmetric matrix and X and B are N-
24 by-NRHS matrices.
25 The diagonal pivoting method is used to factor A as
26 A = U * D * U**T, if UPLO = 'U', or
27 A = L * D * L**T, if UPLO = 'L',
28 where U (or L) is a product of permutation and unit upper (lower) tri‐
29 angular matrices, and D is symmetric and block diagonal with 1-by-1 and
30 2-by-2 diagonal blocks. The factored form of A is then used to solve
31 the system of equations A * X = B.
32
34 UPLO (input) CHARACTER*1
35 = 'U': Upper triangle of A is stored;
36 = 'L': Lower triangle of A is stored.
37 N (input) INTEGER
39 The number of linear equations, i.e., the order of the matrix
40 A. N >= 0.
41 NRHS (input) INTEGER
43 The number of right hand sides, i.e., the number of columns of
44 the matrix B. NRHS >= 0.
45 A (input/output) COMPLEX*16 array, dimension (LDA,N)
47 On entry, the symmetric matrix A. If UPLO = 'U', the leading
48 N-by-N upper triangular part of A contains the upper triangular
49 part of the matrix A, and the strictly lower triangular part of
50 A is not referenced. If UPLO = 'L', the leading N-by-N lower
51 triangular part of A contains the lower triangular part of the
52 matrix A, and the strictly upper triangular part of A is not
53 referenced. On exit, if INFO = 0, the block diagonal matrix D
54 and the multipliers used to obtain the factor U or L from the
55 factorization A = U*D*U**T or A = L*D*L**T as computed by
56 ZSYTRF.
57 LDA (input) INTEGER
59 The leading dimension of the array A. LDA >= max(1,N).
60 IPIV (output) INTEGER array, dimension (N)
62 Details of the interchanges and the block structure of D, as
63 determined by ZSYTRF. If IPIV(k) > 0, then rows and columns k
64 and IPIV(k) were interchanged, and D(k,k) is a 1-by-1 diagonal
65 block. If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0, then rows
66 and columns k-1 and -IPIV(k) were interchanged and
67 D(k-1:k,k-1:k) is a 2-by-2 diagonal block. If UPLO = 'L' and
68 IPIV(k) = IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k)
69 were interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal
70 block.
71 B (input/output) COMPLEX*16 array, dimension (LDB,NRHS)
73 On entry, the N-by-NRHS right hand side matrix B. On exit, if
74 INFO = 0, the N-by-NRHS solution matrix X.
75 LDB (input) INTEGER
77 The leading dimension of the array B. LDB >= max(1,N).
78 WORK (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK))
80 On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
81 LWORK (input) INTEGER
83 The length of WORK. LWORK >= 1, and for best performance LWORK
84 >= max(1,N*NB), where NB is the optimal blocksize for ZSYTRF.
85 If LWORK = -1, then a workspace query is assumed; the routine
86 only calculates the optimal size of the WORK array, returns
87 this value as the first entry of the WORK array, and no error
88 message related to LWORK is issued by XERBLA.
89 INFO (output) INTEGER
91 = 0: successful exit
92 < 0: if INFO = -i, the i-th argument had an illegal value
93 > 0: if INFO = i, D(i,i) is exactly zero. The factorization
94 has been completed, but the block diagonal matrix D is exactly
95 singular, so the solution could not be computed.
96 LAPACK driver routine (version 3.N2o)vember 2008 ZSYSV(1)