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---
:name: zpbtrs
:md5sum: 6cb711d6aca361e6d95f0a88051dda8c
:category: :subroutine
:arguments:
- uplo:
:type: char
:intent: input
- n:
:type: integer
:intent: input
- kd:
:type: integer
:intent: input
- nrhs:
:type: integer
:intent: input
- ab:
:type: doublecomplex
:intent: input
:dims:
- ldab
- n
- ldab:
:type: integer
:intent: input
- b:
:type: doublecomplex
:intent: input/output
:dims:
- ldb
- nrhs
- ldb:
:type: integer
:intent: input
- info:
:type: integer
:intent: output
:substitutions: {}
:fortran_help: " SUBROUTINE ZPBTRS( UPLO, N, KD, NRHS, AB, LDAB, B, LDB, INFO )\n\n\
* Purpose\n\
* =======\n\
*\n\
* ZPBTRS solves a system of linear equations A*X = B with a Hermitian\n\
* positive definite band matrix A using the Cholesky factorization\n\
* A = U**H*U or A = L*L**H computed by ZPBTRF.\n\
*\n\n\
* Arguments\n\
* =========\n\
*\n\
* UPLO (input) CHARACTER*1\n\
* = 'U': Upper triangular factor stored in AB;\n\
* = 'L': Lower triangular factor stored in AB.\n\
*\n\
* N (input) INTEGER\n\
* The order of the matrix A. N >= 0.\n\
*\n\
* KD (input) INTEGER\n\
* The number of superdiagonals of the matrix A if UPLO = 'U',\n\
* or the number of subdiagonals if UPLO = 'L'. KD >= 0.\n\
*\n\
* NRHS (input) INTEGER\n\
* The number of right hand sides, i.e., the number of columns\n\
* of the matrix B. NRHS >= 0.\n\
*\n\
* AB (input) COMPLEX*16 array, dimension (LDAB,N)\n\
* The triangular factor U or L from the Cholesky factorization\n\
* A = U**H*U or A = L*L**H of the band matrix A, stored in the\n\
* first KD+1 rows of the array. The j-th column of U or L is\n\
* stored in the j-th column of the array AB as follows:\n\
* if UPLO ='U', AB(kd+1+i-j,j) = U(i,j) for max(1,j-kd)<=i<=j;\n\
* if UPLO ='L', AB(1+i-j,j) = L(i,j) for j<=i<=min(n,j+kd).\n\
*\n\
* LDAB (input) INTEGER\n\
* The leading dimension of the array AB. LDAB >= KD+1.\n\
*\n\
* B (input/output) COMPLEX*16 array, dimension (LDB,NRHS)\n\
* On entry, the right hand side matrix B.\n\
* On exit, the solution matrix X.\n\
*\n\
* LDB (input) INTEGER\n\
* The leading dimension of the array B. LDB >= max(1,N).\n\
*\n\
* INFO (output) INTEGER\n\
* = 0: successful exit\n\
* < 0: if INFO = -i, the i-th argument had an illegal value\n\
*\n\n\
* =====================================================================\n\
*\n\
* .. Local Scalars ..\n LOGICAL UPPER\n INTEGER J\n\
* ..\n\
* .. External Functions ..\n LOGICAL LSAME\n EXTERNAL LSAME\n\
* ..\n\
* .. External Subroutines ..\n EXTERNAL XERBLA, ZTBSV\n\
* ..\n\
* .. Intrinsic Functions ..\n INTRINSIC MAX\n\
* ..\n"
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