?sysv_aa
?sysv_aa
Computes the solution to a system of linear equations A * X = B for symmetric matrices.
lapack_int
LAPACKE_ssysv_aa
(
int
matrix_layout
,
char
uplo
,
lapack_int
n
,
lapack_int
nrhs
,
float
*
A
,
lapack_int
lda
,
lapack_int
*
ipiv
,
float
*
B
,
lapack_int
ldb
);
lapack_int
LAPACKE_dsysv_aa
(
int
matrix_layout
,
char
uplo
,
lapack_int
n
,
lapack_int
nrhs
,
double
*
A
,
lapack_int
lda
,
lapack_int
*
ipiv
,
double
*
B
,
lapack_int
ldb
);
lapack_int
LAPACKE_csysv_aa
(
int
matrix_layout
,
char
uplo
,
lapack_int
n
,
lapack_int
nrhs
,
lapack_complex_float
*
A
,
lapack_int
lda
,
lapack_int
*
ipiv
,
lapack_complex_float
*
B
,
lapack_int
ldb
);
lapack_int
LAPACKE_zsysv_aa
(
int
matrix_layout
,
char
uplo
,
lapack_int
n
,
lapack_int
nrhs
,
lapack_complex_double
*
A
,
lapack_int
lda
,
lapack_int
*
ipiv
,
lapack_complex_double
*
B
,
lapack_int
ldb
);
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 * U
T
, 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
- matrix_layout
- Specifies whether matrix storage layout is row major (LAPACK_ROW_MAJOR) or column major (LAPACK_COL_MAJOR).
- uplo
- ='U': The upper triangle of A is stored.
- ='L': The lower triangle of A is stored.
- n
- The number of linear equations; that is, the order of the matrix A.n≥ 0.
- nrhs
- The number of right-hand sides; that is, the number of columns of the matrix B.nrhs≥ 0.
- A
- Array of size max(1,On entry, the symmetric matrix A. Iflda*n).uplo='U', the leadingn-by-nupper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. Ifuplo='L', the leadingn-by-nlower 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
- The leading dimension of the arrayA.
- B
- Array of size max(1,On entry, theldb*nrhs) for column-major layout and max(1,ldb*n) for row-major layout.n-by-nrhsright-hand side matrix B.
- ldb
- The leading dimension of the arrayB.ldb≥ max(1,n) for column-major layout andldb≥nrhsfor row-major layout.
Output Parameters
- A
- On exit, ifinfo= 0, the tridiagonal matrix T and the multipliers used to obtain the factor U or L from the factorization A = U*T*UTor A = L*T*LTas computed by?sytrf.
- ipiv
- Array of sizeOn exit, it contains the details of the interchanges; that is, the row and columnn.kof A were interchanged with the row and column ipiv(k).
- B
- On exit, ifinfo= 0, then-by-nrhssolution matrix X.
Return Values
This function returns a value
info
.= 0: Successful exit.
< 0: If , the
info
= -i
i
th
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.