Developer Reference for Intel® oneAPI Math Kernel Library for C
?pbsv
Computes the solution to the system of linear equations with a symmetric or Hermitian positive-definite band coefficient matrix A and multiple right-hand sides.
Syntax
lapack_intLAPACKE_spbsv ( intmatrix_layout , charuplo , lapack_intn , lapack_intkd , lapack_intnrhs , float*ab , lapack_intldab , float*b , lapack_intldb );
lapack_intLAPACKE_dpbsv ( intmatrix_layout , charuplo , lapack_intn , lapack_intkd , lapack_intnrhs , double*ab , lapack_intldab , double*b , lapack_intldb );
lapack_intLAPACKE_cpbsv ( intmatrix_layout , charuplo , lapack_intn , lapack_intkd , lapack_intnrhs , lapack_complex_float*ab , lapack_intldab , lapack_complex_float*b , lapack_intldb );
lapack_intLAPACKE_zpbsv ( intmatrix_layout , charuplo , lapack_intn , lapack_intkd , lapack_intnrhs , lapack_complex_double*ab , lapack_intldab , lapack_complex_double*b , lapack_intldb );
Include Files
mkl.h
Description
spbsv dpbsv cpbsv zpbsv pbsv
The routine solves for X the real or complex system of linear equations A*X = B , where A is an n -by- n symmetric/Hermitian positive definite band matrix, the columns of matrix B are individual right-hand sides, and the columns of X are the corresponding solutions.
The Cholesky decomposition is used to factor A as
A = U:code:`T`*U (real flavors) and A = U:code:`H`*U (complex flavors), if uplo = 'U'
or A = L*L^{T} (real flavors) and A = L*L^{H} (complex flavors), if uplo = 'L' ,
where U is an upper triangular band matrix and L is a lower triangular band matrix, with the same number of superdiagonals or subdiagonals as A . 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
Must be ‘U’ or ‘L’ .
Indicates whether the upper or lower triangular part of A is stored:
If uplo = 'U' , the upper triangle of A is stored.
If uplo = 'L' , the lower triangle of A is stored.
n
The order of matrix A ; n ≥ 0.
kd
The number of superdiagonals of the matrix A if uplo = 'U' , or the number of subdiagonals if uplo = 'L';kd ≥ 0.
nrhs
The number of right-hand sides, the number of columns in B; nrhs≥ 0 .
ab , b
Arrays: ab (size max(1, ldab * n )) , b of size max(1, ldb * nrhs ) for column major layout and max(1, ldb * n ) for row major layout . The array ab contains the upper or the lower triangular part of the matrix A (as specified by uplo ) in band storage (see Matrix Storage Schemes ).
The array b contains the matrix B whose columns are the right-hand sides for the systems of equations.
ldab
The leading dimension of the array ab ; ldab ≥ kd +1.
ldb
The leading dimension of b ; ldb≥ max(1, n)ldb ≥ max(1, n ) for column major layout and ldb ≥ nrhs for row major layout .
Output Parameters
ab
The upper or lower triangular part of A (in band storage) is overwritten by the Cholesky factor U or L , as specified by uplo , in the same storage format as A .
b
Overwritten by the solution matrix X .
Return Values
This function returns a value info .
If info = 0 , the execution is successful.
If info = -i , parameter i had an illegal value.
If info = i , the leading minor of order i (and therefore the matrix A itself) is not positive-definite, so the factorization could not be completed, and the solution has not been computed.
LAPACK 95 Interface Notes
There exist FORTRAN 77 and FORTRAN 95 interfaces for this routine. See the Intel® oneMKL Fortran Developer Reference for details.