Developer Reference for Intel® oneAPI Math Kernel Library for C
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?sytrs
Solves a system of linear equations with a UDUT- or LDLT-factored symmetric coefficient matrix.
lapack_int LAPACKE_ssytrs (int matrix_layout , char uplo , lapack_int n , lapack_int nrhs , const float * a , lapack_int lda , const lapack_int * ipiv , float * b , lapack_int ldb );
lapack_int LAPACKE_dsytrs (int matrix_layout , char uplo , lapack_int n , lapack_int nrhs , const double * a , lapack_int lda , const lapack_int * ipiv , double * b , lapack_int ldb );
lapack_int LAPACKE_csytrs (int matrix_layout , char uplo , lapack_int n , lapack_int nrhs , const lapack_complex_float * a , lapack_int lda , const lapack_int * ipiv , lapack_complex_float * b , lapack_int ldb );
lapack_int LAPACKE_zsytrs (int matrix_layout , char uplo , lapack_int n , lapack_int nrhs , const lapack_complex_double * a , lapack_int lda , const lapack_int * ipiv , lapack_complex_double * b , lapack_int ldb );
- mkl.h
The routine solves for X the system of linear equations A*X = B with a symmetric matrix A, given the Bunch-Kaufman factorization of A:
if uplo='U', |
A = U*D*UT |
if uplo='L', |
A = L*D*LT, |
where U and L are upper and lower triangular matrices with unit diagonal and D is a symmetric block-diagonal matrix. The system is solved with multiple right-hand sides stored in the columns of the matrix B. You must supply to this routine the factor U (or L) and the array ipiv returned by the factorization routine ?sytrf.
matrix_layout |
Specifies whether matrix storage layout is row major (LAPACK_ROW_MAJOR) or column major (LAPACK_COL_MAJOR). |
uplo |
Must be 'U' or 'L'. Indicates how the input matrix A has been factored: If uplo = 'U', the array a stores the upper triangular factor U of the factorization A = U*D*UT. If uplo = 'L', the array a stores the lower triangular factor L of the factorization A = L*D*LT. |
n |
The order of matrix A; n≥ 0. |
nrhs |
The number of right-hand sides; nrhs≥ 0. |
ipiv |
Array, size at least max(1, n). The ipiv array, as returned by ?sytrf. |
a |
The array aof size max(1, lda*n) contains the factor U or L (see uplo). . |
b |
The array b contains the matrix B whose columns are the right-hand sides for the system of equations. The size of b is at least max(1, ldb*nrhs) for column major layout and max(1, ldb*n) for row major layout. |
lda |
The leading dimension of a; lda≥ max(1, n). |
ldb |
The leading dimension of b; ldb≥ max(1, n) for column major layout and ldb≥nrhs for row major layout. |
b |
Overwritten by the solution matrix X. |
This function returns a value info.
If info=0, the execution is successful.
If info = -i, parameter i had an illegal value.
For each right-hand side b, the computed solution is the exact solution of a perturbed system of equations (A + E)x = b, where
|E| ≤ c(n)ε P|U||D||UT|PT or |E| ≤ c(n)ε P|L||D||UT|PT
c(n) is a modest linear function of n, and ε is the machine precision.
If x0 is the true solution, the computed solution x satisfies this error bound:
where cond(A,x)= || |A-1||A| |x| ||∞ / ||x||∞≤ ||A-1||∞ ||A||∞ = κ∞(A).
Note that cond(A,x) can be much smaller than κ∞(A).
The total number of floating-point operations for one right-hand side vector is approximately 2n2 for real flavors or 8n2 for complex flavors.
To estimate the condition number κ∞(A), call ?sycon.
To refine the solution and estimate the error, call ?syrfs.