Developer Reference for Intel® oneAPI Math Kernel Library for C
p?pbsv
Solves a symmetric/Hermitian positive definite banded system of linear equations.
Syntax
voidpspbsv ( char*uplo , MKL_INT*n , MKL_INT*bw , MKL_INT*nrhs , float*a , MKL_INT*ja , MKL_INT*desca , float*b , MKL_INT*ib , MKL_INT*descb , float*work , MKL_INT*lwork , MKL_INT*info );
voidpdpbsv ( char*uplo , MKL_INT*n , MKL_INT*bw , MKL_INT*nrhs , double*a , MKL_INT*ja , MKL_INT*desca , double*b , MKL_INT*ib , MKL_INT*descb , double*work , MKL_INT*lwork , MKL_INT*info );
voidpcpbsv ( char*uplo , MKL_INT*n , MKL_INT*bw , MKL_INT*nrhs , MKL_Complex8*a , MKL_INT*ja , MKL_INT*desca , MKL_Complex8*b , MKL_INT*ib , MKL_INT*descb , MKL_Complex8*work , MKL_INT*lwork , MKL_INT*info );
voidpzpbsv ( char*uplo , MKL_INT*n , MKL_INT*bw , MKL_INT*nrhs , MKL_Complex16*a , MKL_INT*ja , MKL_INT*desca , MKL_Complex16*b , MKL_INT*ib , MKL_INT*descb , MKL_Complex16*work , MKL_INT*lwork , MKL_INT*info );
Include Files
mkl_scalapack.h
Description
pspbsv pdpbsv pcpbsv pzpbsv The p?pbsv routine function solves a system of linear equations
A(1:n, ja:ja+n-1)*X = B(ib:ib+n-1, 1:nrhs) ,
where A(1:n, ja:ja+n-1) is an n -by- n real/complex banded symmetric positive definite distributed matrix with bandwidth bw .
Cholesky factorization is used to factor a reordering of the matrix into L*L' .
Product and Performance Information Performance varies by use, configuration and other factors. Learn more at www.Intel.com/PerformanceIndex . Notice revision #20201201
Input Parameters
uplo
(global) Must be ‘U’ or ‘L’ .
Indicates whether the upper or lower triangular of A is stored. If uplo = 'U' , the upper triangular A is stored If uplo = 'L' , the lower triangular of A is stored.
n
(global) The order of the distributed matrix A(n≥ 0) .
bw
(global) The number of subdiagonals in L or U . 0 ≤ bw ≤ n-1 .
nrhs
(global) The number of right-hand sides; the number of columns in B(nrhs≥ 0) .
a
(local).
DOUBLE PRECISON for pdpbsv COMPLEX for pcpbsv DOUBLE COMPLEX for pzpbsv . Pointer into the local memory to an array with leading size lld_a ≥ (bw+1) (stored in desca ). On entry, this array contains the local pieces of the distributed matrix sub(A) to be factored.
ja
(global) The index in the global matrix A indicating the start of the matrix to be operated on (which may be either all of A or a submatrix of A ).
desca
(global and local) array of size dlen_ . The array descriptor for the distributed matrix A .
- b
-
(local) REAL for pspbsv DOUBLE PRECISON for pdpbsv COMPLEX for pcpbsv DOUBLE COMPLEX for pzpbsv . Pointer into the local memory to an array of local lead size lld_b ≥ nb . On entry, this array contains the local pieces of the right hand sides B(ib:ib+n-1, 1:nrhs) .
ib
(global) The row index in the global matrix B indicating the first row of the matrix to be operated on (which may be either all of b or a submatrix of B ).
descb
(global and local) array of size dlen .
If 1D type (dtype_b =502) , dlen ≥ 7 ; If 2D type (dtype_b =1) , dlen ≥ 9 . The array descriptor for the distributed matrix B . Contains information of mapping of B to memory.
- work
-
(local). REAL for pspbsv DOUBLE PRECISON for pdpbsv COMPLEX for pcpbsv DOUBLE COMPLEX for pzpbsv .
Temporary workspace. This space may be overwritten in between calls to functions . work must be the size given in lwork .
lwork
(local or global) Size of user-input workspace work . If lwork is too small, the minimal acceptable size will be returned in work(1)[0] and an error code is returned. lwork ≥ (nb+2*bw)*bw +max((bw*nrhs), bw*bw)
Output Parameters
- a
-
On exit, this array contains information containing details of the factorization. Note that permutations are performed on the matrix, so that the factors returned are different from those returned by LAPACK.
- b
-
On exit, contains the local piece of the solutions distributed matrix X .
- work
-
On exit, work(1)[0] contains the minimal lwork .
info
(global) If info =0, the execution is successful.
< 0 : If the i -th argument is an array and the j -entry had an illegal value, then info = -(i*100+j) , if the i -th argument is a scalar and had an illegal value, then info = -i . > 0 : If info = k ≤ NPROCS , the submatrix stored on processor info and factored locally was not positive definite, and the factorization was not completed. If info = k > NPROCS , the submatrix stored on processor info-NPROCS representing interactions with other processors was not positive definite, and the factorization was not completed.