1DSYSV(1) LAPACK driver routine (version 3.1) DSYSV(1)
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6 DSYSV - the solution to a real system of linear equations A * X = B,
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9 SUBROUTINE DSYSV( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK, LWORK,
10 INFO )
11 CHARACTER UPLO
13 INTEGER INFO, LDA, LDB, LWORK, N, NRHS
15 INTEGER IPIV( * )
17 DOUBLE PRECISION A( LDA, * ), B( LDB, * ), WORK( * )
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21 DSYSV computes the solution to a real system of linear equations
22 A * X = B, where A is an N-by-N symmetric matrix and X and B are N-
23 by-NRHS matrices.
24 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.
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35 UPLO (input) CHARACTER*1
36 = 'U': Upper triangle of A is stored;
37 = 'L': Lower triangle of A is stored.
38 N (input) INTEGER
40 The number of linear equations, i.e., the order of the matrix
41 A. N >= 0.
42 NRHS (input) INTEGER
44 The number of right hand sides, i.e., the number of columns of
45 the matrix B. NRHS >= 0.
46 A (input/output) DOUBLE PRECISION array, dimension (LDA,N)
48 On entry, the symmetric matrix A. If UPLO = 'U', the leading
49 N-by-N upper triangular part of A contains the upper triangular
50 part of the matrix A, and the strictly lower triangular part of
51 A is not referenced. If UPLO = 'L', the leading N-by-N lower
52 triangular part of A contains the lower triangular part of the
53 matrix A, and the strictly upper triangular part of A is not
54 referenced.
55 On exit, if INFO = 0, the block diagonal matrix D and the mul‐
57 tipliers used to obtain the factor U or L from the factoriza‐
58 tion A = U*D*U**T or A = L*D*L**T as computed by DSYTRF.
59 LDA (input) INTEGER
61 The leading dimension of the array A. LDA >= max(1,N).
62 IPIV (output) INTEGER array, dimension (N)
64 Details of the interchanges and the block structure of D, as
65 determined by DSYTRF. If IPIV(k) > 0, then rows and columns k
66 and IPIV(k) were interchanged, and D(k,k) is a 1-by-1 diagonal
67 block. If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0, then rows
68 and columns k-1 and -IPIV(k) were interchanged and
69 D(k-1:k,k-1:k) is a 2-by-2 diagonal block. If UPLO = 'L' and
70 IPIV(k) = IPIV(k+1) < 0, then rows and columns k+1 and -IPIV(k)
71 were interchanged and D(k:k+1,k:k+1) is a 2-by-2 diagonal
72 block.
73 B (input/output) DOUBLE PRECISION array, dimension (LDB,NRHS)
75 On entry, the N-by-NRHS right hand side matrix B. On exit, if
76 INFO = 0, the N-by-NRHS solution matrix X.
77 LDB (input) INTEGER
79 The leading dimension of the array B. LDB >= max(1,N).
80 WORK (workspace/output) DOUBLE PRECISION array, dimension
82 (MAX(1,LWORK))
83 On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
84 LWORK (input) INTEGER
86 The length of WORK. LWORK >= 1, and for best performance LWORK
87 >= max(1,N*NB), where NB is the optimal blocksize for DSYTRF.
88 If LWORK = -1, then a workspace query is assumed; the routine
90 only calculates the optimal size of the WORK array, returns
91 this value as the first entry of the WORK array, and no error
92 message related to LWORK is issued by XERBLA.
93 INFO (output) INTEGER
95 = 0: successful exit
96 < 0: if INFO = -i, the i-th argument had an illegal value
97 > 0: if INFO = i, D(i,i) is exactly zero. The factorization
98 has been completed, but the block diagonal matrix D is exactly
99 singular, so the solution could not be computed.
100 LAPACK driver routine (version 3.N1o)vember 2006 DSYSV(1)