Provided by: liblapack-doc_3.12.0-3build1.1_all 
NAME
pptrs - pptrs: triangular solve using factor
SYNOPSIS
Functions
subroutine cpptrs (uplo, n, nrhs, ap, b, ldb, info)
CPPTRS
subroutine dpptrs (uplo, n, nrhs, ap, b, ldb, info)
DPPTRS
subroutine spptrs (uplo, n, nrhs, ap, b, ldb, info)
SPPTRS
subroutine zpptrs (uplo, n, nrhs, ap, b, ldb, info)
ZPPTRS
Detailed Description
Function Documentation
subroutine cpptrs (character uplo, integer n, integer nrhs, complex, dimension( * ) ap, complex, dimension(
ldb, * ) b, integer ldb, integer info)
CPPTRS
Purpose:
CPPTRS solves a system of linear equations A*X = B with a Hermitian
positive definite matrix A in packed storage using the Cholesky
factorization A = U**H*U or A = L*L**H computed by CPPTRF.
Parameters
UPLO
UPLO is CHARACTER*1
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
N
N is INTEGER
The order of the matrix A. N >= 0.
NRHS
NRHS is INTEGER
The number of right hand sides, i.e., the number of columns
of the matrix B. NRHS >= 0.
AP
AP is COMPLEX array, dimension (N*(N+1)/2)
The triangular factor U or L from the Cholesky factorization
A = U**H*U or A = L*L**H, packed columnwise in a linear
array. The j-th column of U or L is stored in the array AP
as follows:
if UPLO = 'U', AP(i + (j-1)*j/2) = U(i,j) for 1<=i<=j;
if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = L(i,j) for j<=i<=n.
B
B is COMPLEX array, dimension (LDB,NRHS)
On entry, the right hand side matrix B.
On exit, the solution matrix X.
LDB
LDB is INTEGER
The leading dimension of the array B. LDB >= max(1,N).
INFO
INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
subroutine dpptrs (character uplo, integer n, integer nrhs, double precision, dimension( * ) ap, double
precision, dimension( ldb, * ) b, integer ldb, integer info)
DPPTRS
Purpose:
DPPTRS solves a system of linear equations A*X = B with a symmetric
positive definite matrix A in packed storage using the Cholesky
factorization A = U**T*U or A = L*L**T computed by DPPTRF.
Parameters
UPLO
UPLO is CHARACTER*1
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
N
N is INTEGER
The order of the matrix A. N >= 0.
NRHS
NRHS is INTEGER
The number of right hand sides, i.e., the number of columns
of the matrix B. NRHS >= 0.
AP
AP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
The triangular factor U or L from the Cholesky factorization
A = U**T*U or A = L*L**T, packed columnwise in a linear
array. The j-th column of U or L is stored in the array AP
as follows:
if UPLO = 'U', AP(i + (j-1)*j/2) = U(i,j) for 1<=i<=j;
if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = L(i,j) for j<=i<=n.
B
B is DOUBLE PRECISION array, dimension (LDB,NRHS)
On entry, the right hand side matrix B.
On exit, the solution matrix X.
LDB
LDB is INTEGER
The leading dimension of the array B. LDB >= max(1,N).
INFO
INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
subroutine spptrs (character uplo, integer n, integer nrhs, real, dimension( * ) ap, real, dimension( ldb, *
) b, integer ldb, integer info)
SPPTRS
Purpose:
SPPTRS solves a system of linear equations A*X = B with a symmetric
positive definite matrix A in packed storage using the Cholesky
factorization A = U**T*U or A = L*L**T computed by SPPTRF.
Parameters
UPLO
UPLO is CHARACTER*1
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
N
N is INTEGER
The order of the matrix A. N >= 0.
NRHS
NRHS is INTEGER
The number of right hand sides, i.e., the number of columns
of the matrix B. NRHS >= 0.
AP
AP is REAL array, dimension (N*(N+1)/2)
The triangular factor U or L from the Cholesky factorization
A = U**T*U or A = L*L**T, packed columnwise in a linear
array. The j-th column of U or L is stored in the array AP
as follows:
if UPLO = 'U', AP(i + (j-1)*j/2) = U(i,j) for 1<=i<=j;
if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = L(i,j) for j<=i<=n.
B
B is REAL array, dimension (LDB,NRHS)
On entry, the right hand side matrix B.
On exit, the solution matrix X.
LDB
LDB is INTEGER
The leading dimension of the array B. LDB >= max(1,N).
INFO
INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
subroutine zpptrs (character uplo, integer n, integer nrhs, complex*16, dimension( * ) ap, complex*16,
dimension( ldb, * ) b, integer ldb, integer info)
ZPPTRS
Purpose:
ZPPTRS solves a system of linear equations A*X = B with a Hermitian
positive definite matrix A in packed storage using the Cholesky
factorization A = U**H * U or A = L * L**H computed by ZPPTRF.
Parameters
UPLO
UPLO is CHARACTER*1
= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.
N
N is INTEGER
The order of the matrix A. N >= 0.
NRHS
NRHS is INTEGER
The number of right hand sides, i.e., the number of columns
of the matrix B. NRHS >= 0.
AP
AP is COMPLEX*16 array, dimension (N*(N+1)/2)
The triangular factor U or L from the Cholesky factorization
A = U**H * U or A = L * L**H, packed columnwise in a linear
array. The j-th column of U or L is stored in the array AP
as follows:
if UPLO = 'U', AP(i + (j-1)*j/2) = U(i,j) for 1<=i<=j;
if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = L(i,j) for j<=i<=n.
B
B is COMPLEX*16 array, dimension (LDB,NRHS)
On entry, the right hand side matrix B.
On exit, the solution matrix X.
LDB
LDB is INTEGER
The leading dimension of the array B. LDB >= max(1,N).
INFO
INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Author
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Version 3.12.0 Fri Aug 9 2024 02:33:22 pptrs(3)