Contents
cpbsv - compute the solution to a complex system of linear
equations A * X = B,
SUBROUTINE CPBSV(UPLO, N, NDIAG, NRHS, A, LDA, B, LDB, INFO)
CHARACTER * 1 UPLO
COMPLEX A(LDA,*), B(LDB,*)
INTEGER N, NDIAG, NRHS, LDA, LDB, INFO
SUBROUTINE CPBSV_64(UPLO, N, NDIAG, NRHS, A, LDA, B, LDB, INFO)
CHARACTER * 1 UPLO
COMPLEX A(LDA,*), B(LDB,*)
INTEGER*8 N, NDIAG, NRHS, LDA, LDB, INFO
F95 INTERFACE
SUBROUTINE PBSV(UPLO, [N], NDIAG, [NRHS], A, [LDA], B, [LDB], [INFO])
CHARACTER(LEN=1) :: UPLO
COMPLEX, DIMENSION(:,:) :: A, B
INTEGER :: N, NDIAG, NRHS, LDA, LDB, INFO
SUBROUTINE PBSV_64(UPLO, [N], NDIAG, [NRHS], A, [LDA], B, [LDB],
[INFO])
CHARACTER(LEN=1) :: UPLO
COMPLEX, DIMENSION(:,:) :: A, B
INTEGER(8) :: N, NDIAG, NRHS, LDA, LDB, INFO
C INTERFACE
#include <sunperf.h>
void cpbsv(char uplo, int n, int ndiag, int nrhs, complex
*a, int lda, complex *b, int ldb, int *info);
void cpbsv_64(char uplo, long n, long ndiag, long nrhs, com-
plex *a, long lda, complex *b, long ldb, long
*info);
cpbsv computes the solution to a complex system of linear
equations
A * X = B, where A is an N-by-N Hermitian positive defin-
ite band matrix and X and B are N-by-NRHS matrices.
The Cholesky decomposition is used to factor A as
A = U**H * U, if UPLO = 'U', or
A = L * L**H, if UPLO = 'L',
where U is an upper triangular band matrix, and L is a lower
triangular band matrix, with the same number of superdiago-
nals or subdiagonals as A. The factored form of A is then
used to solve the system of equations A * X = B.
UPLO (input)
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
N (input) The number of linear equations, i.e., the order of
the matrix A. N >= 0.
NDIAG (input)
The number of superdiagonals of the matrix A if
UPLO = 'U', or the number of subdiagonals if UPLO
= 'L'. NDIAG >= 0.
NRHS (input)
The number of right hand sides, i.e., the number
of columns of the matrix B. NRHS >= 0.
A (input/output)
On entry, the upper or lower triangle of the Her-
mitian band matrix A, stored in the first NDIAG+1
rows of the array. The j-th column of A is stored
in the j-th column of the array A as follows: if
UPLO = 'U', A(NDIAG+1+i-j,j) = A(i,j) for
max(1,j-NDIAG)<=i<=j; if UPLO = 'L', A(1+i-j,j)
= A(i,j) for j<=i<=min(N,j+NDIAG). See below for
further details.
On exit, if INFO = 0, the triangular factor U or L
from the Cholesky factorization A = U**H*U or A =
L*L**H of the band matrix A, in the same storage
format as A.
LDA (input)
The leading dimension of the array A. LDA >=
NDIAG+1.
B (input/output)
On entry, the N-by-NRHS right hand side matrix B.
On exit, if INFO = 0, the N-by-NRHS solution
matrix X.
LDB (input)
The leading dimension of the array B. LDB >=
max(1,N).
INFO (output)
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an ille-
gal value
> 0: if INFO = i, the leading minor of order i of
A is not positive definite, so the factorization
could not be completed, and the solution has not
been computed.
The band storage scheme is illustrated by the following
example, when N = 6, NDIAG = 2, and UPLO = 'U':
On entry: On exit:
* * a13 a24 a35 a46 * * u13 u24 u35
u46
* a12 a23 a34 a45 a56 * u12 u23 u34 u45
u56
a11 a22 a33 a44 a55 a66 u11 u22 u33 u44 u55
u66
Similarly, if UPLO = 'L' the format of A is as follows:
On entry: On exit:
a11 a22 a33 a44 a55 a66 l11 l22 l33 l44 l55
l66
a21 a32 a43 a54 a65 * l21 l32 l43 l54 l65
*
a31 a42 a53 a64 * * l31 l42 l53 l64 *
*
Array elements marked * are not used by the routine.