SPBTRS(3F) SPBTRS(3F)
SPBTRS  solve a system of linear equations A*X = B with a symmetric
positive definite band matrix A using the Cholesky factorization A =
U**T*U or A = L*L**T computed by SPBTRF
SUBROUTINE SPBTRS( UPLO, N, KD, NRHS, AB, LDAB, B, LDB, INFO )
CHARACTER UPLO
INTEGER INFO, KD, LDAB, LDB, N, NRHS
REAL AB( LDAB, * ), B( LDB, * )
SPBTRS solves a system of linear equations A*X = B with a symmetric
positive definite band matrix A using the Cholesky factorization A =
U**T*U or A = L*L**T computed by SPBTRF.
UPLO (input) CHARACTER*1
= 'U': Upper triangular factor stored in AB;
= 'L': Lower triangular factor stored in AB.
N (input) INTEGER
The order of the matrix A. N >= 0.
KD (input) INTEGER
The number of superdiagonals of the matrix A if UPLO = 'U', or
the number of subdiagonals if UPLO = 'L'. KD >= 0.
NRHS (input) INTEGER
The number of right hand sides, i.e., the number of columns of
the matrix B. NRHS >= 0.
AB (input) REAL array, dimension (LDAB,N)
The triangular factor U or L from the Cholesky factorization A =
U**T*U or A = L*L**T of the band matrix A, stored in the first
KD+1 rows of the array. The jth column of U or L is stored in
the jth column of the array AB as follows: if UPLO ='U',
AB(kd+1+ij,j) = U(i,j) for max(1,jkd)<=i<=j; if UPLO ='L',
AB(1+ij,j) = L(i,j) for j<=i<=min(n,j+kd).
LDAB (input) INTEGER
The leading dimension of the array AB. LDAB >= KD+1.
B (input/output) REAL array, dimension (LDB,NRHS)
On entry, the right hand side matrix B. On exit, the solution
matrix X.
Page 1
SPBTRS(3F) SPBTRS(3F)
LDB (input) INTEGER
The leading dimension of the array B. LDB >= max(1,N).
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = i, the ith argument had an illegal value
SPBTRS(3F) SPBTRS(3F)
SPBTRS  solve a system of linear equations A*X = B with a symmetric
positive definite band matrix A using the Cholesky factorization A =
U**T*U or A = L*L**T computed by SPBTRF
SUBROUTINE SPBTRS( UPLO, N, KD, NRHS, AB, LDAB, B, LDB, INFO )
CHARACTER UPLO
INTEGER INFO, KD, LDAB, LDB, N, NRHS
REAL AB( LDAB, * ), B( LDB, * )
SPBTRS solves a system of linear equations A*X = B with a symmetric
positive definite band matrix A using the Cholesky factorization A =
U**T*U or A = L*L**T computed by SPBTRF.
UPLO (input) CHARACTER*1
= 'U': Upper triangular factor stored in AB;
= 'L': Lower triangular factor stored in AB.
N (input) INTEGER
The order of the matrix A. N >= 0.
KD (input) INTEGER
The number of superdiagonals of the matrix A if UPLO = 'U', or
the number of subdiagonals if UPLO = 'L'. KD >= 0.
NRHS (input) INTEGER
The number of right hand sides, i.e., the number of columns of
the matrix B. NRHS >= 0.
AB (input) REAL array, dimension (LDAB,N)
The triangular factor U or L from the Cholesky factorization A =
U**T*U or A = L*L**T of the band matrix A, stored in the first
KD+1 rows of the array. The jth column of U or L is stored in
the jth column of the array AB as follows: if UPLO ='U',
AB(kd+1+ij,j) = U(i,j) for max(1,jkd)<=i<=j; if UPLO ='L',
AB(1+ij,j) = L(i,j) for j<=i<=min(n,j+kd).
LDAB (input) INTEGER
The leading dimension of the array AB. LDAB >= KD+1.
B (input/output) REAL array, dimension (LDB,NRHS)
On entry, the right hand side matrix B. On exit, the solution
matrix X.
Page 1
SPBTRS(3F) SPBTRS(3F)
LDB (input) INTEGER
The leading dimension of the array B. LDB >= max(1,N).
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = i, the ith argument had an illegal value
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