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Functions/Subroutines | |
| subroutine | ssysv_rk (uplo, n, nrhs, a, lda, e, ipiv, b, ldb, work, lwork, info) |
| SSYSV_RK computes the solution to system of linear equations A * X = B for SY matrices | |
| subroutine ssysv_rk | ( | character | uplo, |
| integer | n, | ||
| integer | nrhs, | ||
| real, dimension( lda, * ) | a, | ||
| integer | lda, | ||
| real, dimension( * ) | e, | ||
| integer, dimension( * ) | ipiv, | ||
| real, dimension( ldb, * ) | b, | ||
| integer | ldb, | ||
| real, dimension( * ) | work, | ||
| integer | lwork, | ||
| integer | info ) |
SSYSV_RK computes the solution to system of linear equations A * X = B for SY matrices
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!> SSYSV_RK computes the solution to a real system of linear !> equations A * X = B, where A is an N-by-N symmetric matrix !> and X and B are N-by-NRHS matrices. !> !> The bounded Bunch-Kaufman (rook) diagonal pivoting method is used !> to factor A as !> A = P*U*D*(U**T)*(P**T), if UPLO = 'U', or !> A = P*L*D*(L**T)*(P**T), if UPLO = 'L', !> where U (or L) is unit upper (or lower) triangular matrix, !> U**T (or L**T) is the transpose of U (or L), P is a permutation !> matrix, P**T is the transpose of P, and D is symmetric and block !> diagonal with 1-by-1 and 2-by-2 diagonal blocks. !> !> SSYTRF_RK is called to compute the factorization of a real !> symmetric matrix. The factored form of A is then used to solve !> the system of equations A * X = B by calling BLAS3 routine SSYTRS_3. !>
| [in] | UPLO | !> UPLO is CHARACTER*1 !> Specifies whether the upper or lower triangular part of the !> symmetric matrix A is stored: !> = 'U': Upper triangle of A is stored; !> = 'L': Lower triangle of A is stored. !> |
| [in] | N | !> N is INTEGER !> The number of linear equations, i.e., the order of the !> matrix A. N >= 0. !> |
| [in] | NRHS | !> NRHS is INTEGER !> The number of right hand sides, i.e., the number of columns !> of the matrix B. NRHS >= 0. !> |
| [in,out] | A | !> A is REAL array, dimension (LDA,N) !> On entry, the symmetric matrix A. !> If UPLO = 'U': the leading N-by-N upper triangular part !> of A contains 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 triangular part of A is not !> referenced. !> !> On exit, if INFO = 0, diagonal of the block diagonal !> matrix D and factors U or L as computed by SSYTRF_RK: !> a) ONLY diagonal elements of the symmetric block diagonal !> matrix D on the diagonal of A, i.e. D(k,k) = A(k,k); !> (superdiagonal (or subdiagonal) elements of D !> are stored on exit in array E), and !> b) If UPLO = 'U': factor U in the superdiagonal part of A. !> If UPLO = 'L': factor L in the subdiagonal part of A. !> !> For more info see the description of DSYTRF_RK routine. !> |
| [in] | LDA | !> LDA is INTEGER !> The leading dimension of the array A. LDA >= max(1,N). !> |
| [out] | E | !> E is REAL array, dimension (N) !> On exit, contains the output computed by the factorization !> routine DSYTRF_RK, i.e. the superdiagonal (or subdiagonal) !> elements of the symmetric block diagonal matrix D !> with 1-by-1 or 2-by-2 diagonal blocks, where !> If UPLO = 'U': E(i) = D(i-1,i), i=2:N, E(1) is set to 0; !> If UPLO = 'L': E(i) = D(i+1,i), i=1:N-1, E(N) is set to 0. !> !> NOTE: For 1-by-1 diagonal block D(k), where !> 1 <= k <= N, the element E(k) is set to 0 in both !> UPLO = 'U' or UPLO = 'L' cases. !> !> For more info see the description of DSYTRF_RK routine. !> |
| [out] | IPIV | !> IPIV is INTEGER array, dimension (N) !> Details of the interchanges and the block structure of D, !> as determined by SSYTRF_RK. !> !> For more info see the description of DSYTRF_RK routine. !> |
| [in,out] | B | !> B is REAL 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. !> |
| [in] | LDB | !> LDB is INTEGER !> The leading dimension of the array B. LDB >= max(1,N). !> |
| [out] | WORK | !> WORK is REAL array, dimension ( MAX(1,LWORK) ). !> Work array used in the factorization stage. !> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. !> |
| [in] | LWORK | !> LWORK is INTEGER !> The length of WORK. LWORK >= 1. For best performance !> of factorization stage LWORK >= max(1,N*NB), where NB is !> the optimal blocksize for DSYTRF_RK. !> !> If LWORK = -1, then a workspace query is assumed; !> the routine only calculates the optimal size of the WORK !> array for factorization stage, returns this value as !> the first entry of the WORK array, and no error message !> related to LWORK is issued by XERBLA. !> |
| [out] | INFO | !> INFO is INTEGER !> = 0: successful exit !> !> < 0: If INFO = -k, the k-th argument had an illegal value !> !> > 0: If INFO = k, the matrix A is singular, because: !> If UPLO = 'U': column k in the upper !> triangular part of A contains all zeros. !> If UPLO = 'L': column k in the lower !> triangular part of A contains all zeros. !> !> Therefore D(k,k) is exactly zero, and superdiagonal !> elements of column k of U (or subdiagonal elements of !> column k of L ) are all zeros. The factorization has !> been completed, but the block diagonal matrix D is !> exactly singular, and division by zero will occur if !> it is used to solve a system of equations. !> !> NOTE: INFO only stores the first occurrence of !> a singularity, any subsequent occurrence of singularity !> is not stored in INFO even though the factorization !> always completes. !> |
!> !> December 2016, Igor Kozachenko, !> Computer Science Division, !> University of California, Berkeley !> !> September 2007, Sven Hammarling, Nicholas J. Higham, Craig Lucas, !> School of Mathematics, !> University of Manchester !> !>
Definition at line 226 of file ssysv_rk.f.
1.15.0