pbtrf#

spbtrf

Functions

void spbtrf(
    const char*          uplo,
    const INT            n,
    const INT            kd,
          f32*  restrict AB,
    const INT            ldab,
          INT*           info
);

void spbtrf(const char *uplo, const INT n, const INT kd, f32 *restrict AB, const INT ldab, INT *info)#

SPBTRF computes the Cholesky factorization of a real symmetric positive definite band matrix A.

The factorization has the form 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 lower triangular.

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.

inout

AB

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

in

ldab

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

out

info

= 0: successful exit
< 0: if info = -i, the i-th argument had an illegal value
> 0: if info = k, the leading minor of order k is not positive definite.

dpbtrf

Functions

void dpbtrf(
    const char*          uplo,
    const INT            n,
    const INT            kd,
          f64*  restrict AB,
    const INT            ldab,
          INT*           info
);

void dpbtrf(const char *uplo, const INT n, const INT kd, f64 *restrict AB, const INT ldab, INT *info)#

DPBTRF computes the Cholesky factorization of a real symmetric positive definite band matrix A.

The factorization has the form 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 lower triangular.

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.

inout

AB

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

in

ldab

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

out

info

= 0: successful exit
< 0: if info = -i, the i-th argument had an illegal value
> 0: if info = k, the leading minor of order k is not positive definite.

cpbtrf

Functions

void cpbtrf(
    const char*          uplo,
    const INT            n,
    const INT            kd,
          c64*  restrict AB,
    const INT            ldab,
          INT*           info
);

void cpbtrf(const char *uplo, const INT n, const INT kd, c64 *restrict AB, const INT ldab, INT *info)#

CPBTRF computes the Cholesky factorization of a complex Hermitian positive definite band matrix A.

The factorization has the form 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 lower triangular.

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.

inout

AB

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

in

ldab

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

out

info

= 0: successful exit
< 0: if info = -i, the i-th argument had an illegal value
> 0: if info = k, the leading minor of order k is not positive definite.

zpbtrf

Functions

void zpbtrf(
    const char*          uplo,
    const INT            n,
    const INT            kd,
          c128* restrict AB,
    const INT            ldab,
          INT*           info
);

void zpbtrf(const char *uplo, const INT n, const INT kd, c128 *restrict AB, const INT ldab, INT *info)#

ZPBTRF computes the Cholesky factorization of a complex Hermitian positive definite band matrix A.

The factorization has the form 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 lower triangular.

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.

inout

AB

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

in

ldab

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

out

info

= 0: successful exit
< 0: if info = -i, the i-th argument had an illegal value
> 0: if info = k, the leading minor of order k is not positive definite.

pbtrf#

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