Visible to Intel only — GUID: GUID-E61D14A0-32F2-4CB9-8F79-927BF259E0C6
Visible to Intel only — GUID: GUID-E61D14A0-32F2-4CB9-8F79-927BF259E0C6
?sysv_aa
Computes the solution to a system of linear equations A * X = B for symmetric matrices.
call ssysv_aa(uplo, n, nrhs, A, lda, ipiv, B, ldb, work, lwork, info)
call csysv_aa(uplo, n, nrhs, A, lda, ipiv, B, ldb, work, lwork, info)
call dsysv_aa(uplo, n, nrhs, A, lda, ipiv, B, ldb, work, lwork, info)
call zsysv_aa(uplo, n, nrhs, A, lda, ipiv, B, ldb, work, lwork, info)
Description
The ?sysv routine computes the solution to a complex 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.
Aasen's algorithm is used to factor A as A = U * T * UT, if uplo = 'U', or A = L * T * LT, if uplo = 'L', where U (or L) is a product of permutation and unit upper (lower) triangular matrices, and T is symmetric tri-diagonal. The factored form of A is then used to solve the system of equations A * X= B.
Input Parameters
- uplo
-
CHARACTER*1
- = 'U': The upper triangle of A is stored.
- = 'L': The lower triangle of A is stored.
- n
-
INTEGER
The number of linear equations; that is, the order of the matrix A. n ≥ 0.
- nrhs
-
INTEGER
The number of right-hand sides; that is, the number of columns of the matrix B. nrhs ≥ 0.
- A
-
REAL for ssysv_aa
DOUBLE PRECISION for dsysv_aa
COMPLEX for csysv_aa
COMPLEX*16 for zsysv_aa
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.
- lda
-
INTEGER
The leading dimension of the array A.lda ≥ max(1, n).
- B
-
REAL for ssysv_aa
DOUBLE PRECISION for dsysv_aa
COMPLEX for csysv_aa
COMPLEX*16 for zsysv_aa
Array, dimension (ldb,nrhs). On entry, the n-by-nrhs right-hand side matrix B.
- ldb
-
INTEGER
The leading dimension of the array B. ldb ≥ max(1, n).
- lwork
-
INTEGER
The length of the array work.
If lwork = -1, a workspace query is assumed; the routine calculates only the optimal size of the work array and returns this value as the first entry of the work array, and no error message related to lwork is issued by XERBLA.
Output Parameters
- A
-
REAL for ssysv_aa
DOUBLE PRECISION for dsysv_aa
COMPLEX for csysv_aa
COMPLEX*16 for zsysv_aa
On exit, if info = 0, the tridiagonal matrix T and the multipliers used to obtain the factor U or L from the factorization A = U*T*UT or A = L*T*LT as computed by ?sytrf.
- ipiv
-
INTEGER
Array, dimension (n). On exit, it contains the details of the interchanges; that is, the row and column k of A were interchanged with the row and column ipiv(k).
- B
-
REAL for ssysv_aa
DOUBLE PRECISION for dsytrs_aa
COMPLEX for csysv_aa
COMPLEX*16 for zsysv_aa
On exit, if info = 0, the n-by-nrhs solution matrix X.
- work
-
REAL for ssysv_aa
DOUBLE PRECISION for dsytrs_aa
COMPLEX for csysv_aa
COMPLEX*16 for zsysv_aa
Array, dimension (MAX(1,lwork)). On exit, if info = 0, work(1) returns the optimal lwork.
- info
-
INTEGER
- = 0: Successful exit.
- < 0: If info = -i, the ith argument had an illegal value.
- > 0: If info = i, D(i,i) is exactly zero. The factorization has been completed, but the block diagonal matrix D is exactly singular, so the solution could not be computed.