pptrs#

Functions

void spptrs(
    const char*          uplo,
    const INT            n,
    const INT            nrhs,
    const f32*  restrict AP,
          f32*  restrict B,
    const INT            ldb,
          INT*           info
);
void spptrs(const char *uplo, const INT n, const INT nrhs, const f32 *restrict AP, f32 *restrict B, const INT ldb, INT *info)#

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

in
uplo

  • 'U': Upper triangle of A is stored

  • 'L': Lower triangle of A is stored

in
n

The order of the matrix A. n>=0.

in
nrhs

The number of right hand sides, i.e., the number of columns of the matrix B. nrhs>=0.

in
AP

Array of 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*(j+1)/2] = U(i,j) for 0<=i<=j; if uplo='L', AP[i + j*(2*n-j-1)/2] = L(i,j) for j<=i<=n-1.

inout
B

Array of dimension (ldb, nrhs). On entry, the right hand side matrix B. On exit, the solution matrix X.

in
ldb

The leading dimension of the array B. ldb>=max(1,n).

out
info

  • info=0: successful exit

  • info<0: if info=-i, the i-th argument had an illegal value

Functions

void dpptrs(
    const char*          uplo,
    const INT            n,
    const INT            nrhs,
    const f64*  restrict AP,
          f64*  restrict B,
    const INT            ldb,
          INT*           info
);
void dpptrs(const char *uplo, const INT n, const INT nrhs, const f64 *restrict AP, f64 *restrict B, const INT ldb, INT *info)#

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

in
uplo

  • 'U': Upper triangle of A is stored

  • 'L': Lower triangle of A is stored

in
n

The order of the matrix A. n>=0.

in
nrhs

The number of right hand sides, i.e., the number of columns of the matrix B. nrhs>=0.

in
AP

Array of 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*(j+1)/2] = U(i,j) for 0<=i<=j; if uplo='L', AP[i + j*(2*n-j-1)/2] = L(i,j) for j<=i<=n-1.

inout
B

Array of dimension (ldb, nrhs). On entry, the right hand side matrix B. On exit, the solution matrix X.

in
ldb

The leading dimension of the array B. ldb>=max(1,n).

out
info

  • info=0: successful exit

  • info<0: if info=-i, the i-th argument had an illegal value

Functions

void cpptrs(
    const char*          uplo,
    const INT            n,
    const INT            nrhs,
    const c64*  restrict AP,
          c64*  restrict B,
    const INT            ldb,
          INT*           info
);
void cpptrs(const char *uplo, const INT n, const INT nrhs, const c64 *restrict AP, c64 *restrict B, const INT ldb, INT *info)#

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

in
uplo

  • 'U': Upper triangle of A is stored

  • 'L': Lower triangle of A is stored

in
n

The order of the matrix A. n>=0.

in
nrhs

The number of right hand sides, i.e., the number of columns of the matrix B. nrhs>=0.

in
AP

Array of 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*(j+1)/2] = U(i,j) for 0<=i<=j; if uplo='L', AP[i + j*(2*n-j-1)/2] = L(i,j) for j<=i<=n-1.

inout
B

Array of dimension (ldb, nrhs). On entry, the right hand side matrix B. On exit, the solution matrix X.

in
ldb

The leading dimension of the array B. ldb>=max(1,n).

out
info

  • info=0: successful exit

  • info<0: if info=-i, the i-th argument had an illegal value

Functions

void zpptrs(
    const char*          uplo,
    const INT            n,
    const INT            nrhs,
    const c128* restrict AP,
          c128* restrict B,
    const INT            ldb,
          INT*           info
);
void zpptrs(const char *uplo, const INT n, const INT nrhs, const c128 *restrict AP, c128 *restrict B, const INT ldb, INT *info)#

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

in
uplo

  • 'U': Upper triangle of A is stored

  • 'L': Lower triangle of A is stored

in
n

The order of the matrix A. n>=0.

in
nrhs

The number of right hand sides, i.e., the number of columns of the matrix B. nrhs>=0.

in
AP

Array of 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*(j+1)/2] = U(i,j) for 0<=i<=j; if uplo='L', AP[i + j*(2*n-j-1)/2] = L(i,j) for j<=i<=n-1.

inout
B

Array of dimension (ldb, nrhs). On entry, the right hand side matrix B. On exit, the solution matrix X.

in
ldb

The leading dimension of the array B. ldb>=max(1,n).

out
info

  • info=0: successful exit

  • info<0: if info=-i, the i-th argument had an illegal value