ppsv#

sppsv

Functions

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

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

SPPSV computes the solution to a real system of linear equations A * X = B, where A is an N-by-N symmetric positive definite matrix stored in packed format and X and B are N-by-NRHS matrices.

The Cholesky decomposition is used to factor A as A = U**T * U, if UPLO = ‘U’, or A = L * L**T, if UPLO = ‘L’, where U is an upper triangular matrix and L is a lower triangular matrix. The factored form of A is then used to solve the system of equations A * X = B.

Parameters

in

uplo

= ‘U’: Upper triangle of A is stored; = ‘L’: Lower triangle of A is stored.

in

n

The number of linear equations, i.e., 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.

inout

AP

On entry, the upper or lower triangle of the symmetric matrix A, packed columnwise in a linear array. On exit, if info = 0, the factor U or L from the Cholesky factorization A = U**T*U or A = L*L**T. Array of dimension (n*(n+1)/2).

inout

B

On entry, the N-by-NRHS right hand side matrix B. On exit, if info = 0, the N-by-NRHS solution matrix X. Array of dimension (ldb, nrhs).

in

ldb

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

out

info

= 0: successful exit
< 0: if info = -i, the i-th argument had an illegal value
> 0: if info = i, the leading principal minor of order i of A is not positive, so the factorization could not be completed, and the solution has not been computed.

dppsv

Functions

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

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

DPPSV computes the solution to a real system of linear equations A * X = B, where A is an N-by-N symmetric positive definite matrix stored in packed format and X and B are N-by-NRHS matrices.

The Cholesky decomposition is used to factor A as A = U**T * U, if UPLO = ‘U’, or A = L * L**T, if UPLO = ‘L’, where U is an upper triangular matrix and L is a lower triangular matrix. The factored form of A is then used to solve the system of equations A * X = B.

Parameters

in

uplo

= ‘U’: Upper triangle of A is stored; = ‘L’: Lower triangle of A is stored.

in

n

The number of linear equations, i.e., 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.

inout

AP

On entry, the upper or lower triangle of the symmetric matrix A, packed columnwise in a linear array. On exit, if info = 0, the factor U or L from the Cholesky factorization A = U**T*U or A = L*L**T. Array of dimension (n*(n+1)/2).

inout

B

On entry, the N-by-NRHS right hand side matrix B. On exit, if info = 0, the N-by-NRHS solution matrix X. Array of dimension (ldb, nrhs).

in

ldb

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

out

info

= 0: successful exit
< 0: if info = -i, the i-th argument had an illegal value
> 0: if info = i, the leading principal minor of order i of A is not positive, so the factorization could not be completed, and the solution has not been computed.

cppsv

Functions

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

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

CPPSV computes the solution to a complex system of linear equations A * X = B, where A is an N-by-N Hermitian positive definite matrix stored in packed format 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 matrix and L is a lower triangular matrix. The factored form of A is then used to solve the system of equations A * X = B.

Parameters

in

uplo

= ‘U’: Upper triangle of A is stored; = ‘L’: Lower triangle of A is stored.

in

n

The number of linear equations, i.e., 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.

inout

AP

On entry, the upper or lower triangle of the Hermitian matrix A, packed columnwise in a linear array. On exit, if info = 0, the factor U or L from the Cholesky factorization A = U**H*U or A = L*L**H. Array of dimension (n*(n+1)/2).

inout

B

On entry, the N-by-NRHS right hand side matrix B. On exit, if info = 0, the N-by-NRHS solution matrix X. Array of dimension (ldb, nrhs).

in

ldb

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

out

info

= 0: successful exit
< 0: if info = -i, the i-th argument had an illegal value
> 0: if info = i, the leading principal minor of order i of A is not positive, so the factorization could not be completed, and the solution has not been computed.

zppsv

Functions

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

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

ZPPSV computes the solution to a complex system of linear equations A * X = B, where A is an N-by-N Hermitian positive definite matrix stored in packed format 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 matrix and L is a lower triangular matrix. The factored form of A is then used to solve the system of equations A * X = B.

Parameters

in

uplo

= ‘U’: Upper triangle of A is stored; = ‘L’: Lower triangle of A is stored.

in

n

The number of linear equations, i.e., 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.

inout

AP

On entry, the upper or lower triangle of the Hermitian matrix A, packed columnwise in a linear array. On exit, if info = 0, the factor U or L from the Cholesky factorization A = U**H*U or A = L*L**H. Array of dimension (n*(n+1)/2).

inout

B

On entry, the N-by-NRHS right hand side matrix B. On exit, if info = 0, the N-by-NRHS solution matrix X. Array of dimension (ldb, nrhs).

in

ldb

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

out

info

= 0: successful exit
< 0: if info = -i, the i-th argument had an illegal value
> 0: if info = i, the leading principal minor of order i of A is not positive, so the factorization could not be completed, and the solution has not been computed.

ppsv#

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