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NAME CHESV - compute the solution to a complex system of linear equations A * X = B, SYNOPSIS SUBROUTINE CHESV( UPLO, N, NRHS, A, LDA, IPIV, B, LDB, WORK, LWORK, INFO ) CHARACTER UPLO INTEGER INFO, LDA, LDB, LWORK, N, NRHS INTEGER IPIV( * ) COMPLEX A( LDA, * ), B( LDB, * ), WORK( LWORK ) PURPOSE CHESV computes the solution to a complex system of linear equations A * X = B, where A is an N-by-N Hermitian matrix and X and B are N-by-NRHS matrices. The diagonal pivoting method is used to factor A as A = U * D * U**H, if UPLO = 'U', or A = L * D * L**H, if UPLO = 'L', where U (or L) is a product of permutation and unit upper (lower) triangular matrices, and D is Hermitian and block diagonal with 1-by-1 and 2-by-2 diagonal blocks. The fac- tored form of A is then used to solve the system of equa- tions A * X = B. ARGUMENTS UPLO (input) CHARACTER*1 = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored. N (input) INTEGER The number of linear equations, i.e., the order of the matrix A. N >= 0. NRHS (input) INTEGER The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0. A (input/output) COMPLEX array, dimension (LDA,N) On entry, the Hermitian matrix A. If UPLO = 'U', the leading N-by-N upper triangular part of A con- tains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading N-by-N lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper tri- angular part of A is not referenced. On exit, if INFO = 0, the block diagonal matrix D and the multipliers used to obtain the factor U or L from the factorization A = U*D*U**H or A = L*D*L**H as computed by CHETRF. LDA (input) INTEGER The leading dimension of the array A. LDA >= max(1,N). IPIV (output) INTEGER array, dimension (N) Details of the interchanges and the block structure of D, as determined by CHETRF. If IPIV(k) > 0, then rows and columns k and IPIV(k) were interchanged, and D(k,k) is a 1-by-1 diagonal block. If UPLO = 'U' and IPIV(k) = IPIV(k-1) < 0, then rows and columns k-1 and -IPIV(k) were interchanged and D(k- 1:k,k-1:k) is a 2-by-2 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 2-by-2 diagonal block. B (input/output) COMPLEX array, dimension (LDB,NRHS) On entry, the N-by-NRHS right hand side matrix B. On exit, if INFO = 0, the N-by-NRHS solution matrix X. LDB (input) INTEGER The leading dimension of the array B. LDB >= max(1,N). WORK (workspace) COMPLEX array, dimension (LWORK) On exit, if INFO = 0, WORK(1) returns the optimal LWORK. LWORK (input) INTEGER The length of WORK. LWORK >= 1, and for best per- formance LWORK >= N*NB, where NB is the optimal blocksize for CHETRF. INFO (output) INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: if INFO = i, D(i,i) is exactly zero. The fac- torization has been completed, but the block diago- nal matrix D is exactly singular, so the solution could not be computed.