pbsv#

spbsv

Functions

void spbsv(
    const char*          uplo,
    const INT            n,
    const INT            kd,
    const INT            nrhs,
          f32*  restrict AB,
    const INT            ldab,
          f32*  restrict B,
    const INT            ldb,
          INT*           info
);

void spbsv(const char *uplo, const INT n, const INT kd, const INT nrhs, f32 *restrict AB, const INT ldab, f32 *restrict B, const INT ldb, INT *info)#

SPBSV computes the solution to a real system of linear equations A * X = B, where A is an N-by-N symmetric positive definite band matrix 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 band matrix, and L is a lower triangular band matrix.

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

kd

The number of super-diagonals (if uplo=’U’) or sub-diagonals (if uplo=’L’). kd >= 0.

in

nrhs

The number of right hand sides. nrhs >= 0.

inout

AB

On entry, the banded matrix A. On exit, the factor U or L. Array of dimension (ldab, n).

in

ldab

The leading dimension of AB. ldab >= kd+1.

inout

B

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

in

ldb

The leading dimension of 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 minor of order i is not positive definite.

dpbsv

Functions

void dpbsv(
    const char*          uplo,
    const INT            n,
    const INT            kd,
    const INT            nrhs,
          f64*  restrict AB,
    const INT            ldab,
          f64*  restrict B,
    const INT            ldb,
          INT*           info
);

void dpbsv(const char *uplo, const INT n, const INT kd, const INT nrhs, f64 *restrict AB, const INT ldab, f64 *restrict B, const INT ldb, INT *info)#

DPBSV computes the solution to a real system of linear equations A * X = B, where A is an N-by-N symmetric positive definite band matrix 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 band matrix, and L is a lower triangular band matrix.

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

kd

The number of super-diagonals (if uplo=’U’) or sub-diagonals (if uplo=’L’). kd >= 0.

in

nrhs

The number of right hand sides. nrhs >= 0.

inout

AB

On entry, the banded matrix A. On exit, the factor U or L. Array of dimension (ldab, n).

in

ldab

The leading dimension of AB. ldab >= kd+1.

inout

B

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

in

ldb

The leading dimension of 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 minor of order i is not positive definite.

cpbsv

Functions

void cpbsv(
    const char*          uplo,
    const INT            n,
    const INT            kd,
    const INT            nrhs,
          c64*  restrict AB,
    const INT            ldab,
          c64*  restrict B,
    const INT            ldb,
          INT*           info
);

void cpbsv(const char *uplo, const INT n, const INT kd, const INT nrhs, c64 *restrict AB, const INT ldab, c64 *restrict B, const INT ldb, INT *info)#

CPBSV computes the solution to a complex system of linear equations A * X = B, where A is an N-by-N Hermitian positive definite 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.

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

kd

The number of super-diagonals (if uplo=’U’) or sub-diagonals (if uplo=’L’). kd >= 0.

in

nrhs

The number of right hand sides. nrhs >= 0.

inout

AB

On entry, the banded matrix A. On exit, the factor U or L. Array of dimension (ldab, n).

in

ldab

The leading dimension of AB. ldab >= kd+1.

inout

B

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

in

ldb

The leading dimension of 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 minor of order i is not positive definite.

zpbsv

Functions

void zpbsv(
    const char*          uplo,
    const INT            n,
    const INT            kd,
    const INT            nrhs,
          c128* restrict AB,
    const INT            ldab,
          c128* restrict B,
    const INT            ldb,
          INT*           info
);

void zpbsv(const char *uplo, const INT n, const INT kd, const INT nrhs, c128 *restrict AB, const INT ldab, c128 *restrict B, const INT ldb, INT *info)#

ZPBSV computes the solution to a complex system of linear equations A * X = B, where A is an N-by-N Hermitian positive definite 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.

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

kd

The number of super-diagonals (if uplo=’U’) or sub-diagonals (if uplo=’L’). kd >= 0.

in

nrhs

The number of right hand sides. nrhs >= 0.

inout

AB

On entry, the banded matrix A. On exit, the factor U or L. Array of dimension (ldab, n).

in

ldab

The leading dimension of AB. ldab >= kd+1.

inout

B

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

in

ldb

The leading dimension of 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 minor of order i is not positive definite.

pbsv#

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