pttrs#

spttrs

Functions

void spttrs(
    const INT           n,
    const INT           nrhs,
    const f32* restrict D,
    const f32* restrict E,
          f32* restrict B,
    const INT           ldb,
          INT*          info
);

void spttrs(const INT n, const INT nrhs, const f32 *restrict D, const f32 *restrict E, f32 *restrict B, const INT ldb, INT *info)#

SPTTRS solves a tridiagonal system of the form A * X = B using the L*D*L**T factorization of A computed by SPTTRF.

D is a diagonal matrix specified in the vector D, L is a unit bidiagonal matrix whose subdiagonal is specified in the vector E, and X and B are N by NRHS matrices.

Parameters

in

n

The order of the tridiagonal 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

D

Double precision array, dimension (n). The n diagonal elements of the diagonal matrix D from the L*D*L**T factorization of A.

in

E

Double precision array, dimension (n-1). The (n-1) subdiagonal elements of the unit bidiagonal factor L from the L*D*L**T factorization of A. E can also be regarded as the superdiagonal of the unit bidiagonal factor U from the factorization A = U**T*D*U.

inout

B

Double precision array, dimension (ldb, nrhs). On entry, the right hand side vectors B for the system of linear equations. On exit, the solution vectors, X.

in

ldb

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

out

info

= 0: successful exit
< 0: if info = -k, the k-th argument had an illegal value

dpttrs

Functions

void dpttrs(
    const INT           n,
    const INT           nrhs,
    const f64* restrict D,
    const f64* restrict E,
          f64* restrict B,
    const INT           ldb,
          INT*          info
);

void dpttrs(const INT n, const INT nrhs, const f64 *restrict D, const f64 *restrict E, f64 *restrict B, const INT ldb, INT *info)#

DPTTRS solves a tridiagonal system of the form A * X = B using the L*D*L**T factorization of A computed by DPTTRF.

D is a diagonal matrix specified in the vector D, L is a unit bidiagonal matrix whose subdiagonal is specified in the vector E, and X and B are N by NRHS matrices.

Parameters

in

n

The order of the tridiagonal 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

D

Double precision array, dimension (n). The n diagonal elements of the diagonal matrix D from the L*D*L**T factorization of A.

in

E

Double precision array, dimension (n-1). The (n-1) subdiagonal elements of the unit bidiagonal factor L from the L*D*L**T factorization of A. E can also be regarded as the superdiagonal of the unit bidiagonal factor U from the factorization A = U**T*D*U.

inout

B

Double precision array, dimension (ldb, nrhs). On entry, the right hand side vectors B for the system of linear equations. On exit, the solution vectors, X.

in

ldb

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

out

info

= 0: successful exit
< 0: if info = -k, the k-th argument had an illegal value

cpttrs

Functions

void cpttrs(
    const char*          uplo,
    const INT            n,
    const INT            nrhs,
    const f32*  restrict D,
    const c64*  restrict E,
          c64*  restrict B,
    const INT            ldb,
          INT*           info
);

void cpttrs(const char *uplo, const INT n, const INT nrhs, const f32 *restrict D, const c64 *restrict E, c64 *restrict B, const INT ldb, INT *info)#

CPTTRS solves a tridiagonal system of the form A * X = B using the factorization A = U**H D U or A = L*D*L**H computed by CPTTRF.

D is a diagonal matrix specified in the vector D, U (or L) is a unit bidiagonal matrix whose superdiagonal (subdiagonal) is specified in the vector E, and X and B are N by NRHS matrices.

Parameters

in

uplo

Specifies the form of the factorization and whether the vector E is the superdiagonal of the upper bidiagonal factor U or the subdiagonal of the lower bidiagonal factor L. = ‘U’: A = U**H *D*U, E is the superdiagonal of U = ‘L’: A = L*D*L**H, E is the subdiagonal of L

in

n

The order of the tridiagonal 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

D

Single precision array, dimension (n). The n diagonal elements of the diagonal matrix D from the factorization A = U**H *D*U or A = L*D*L**H.

in

E

Complex*16 array, dimension (n-1). If UPLO = ‘U’, the (n-1) superdiagonal elements of the unit bidiagonal factor U from the factorization A = U**H*D*U. If UPLO = ‘L’, the (n-1) subdiagonal elements of the unit bidiagonal factor L from the factorization A = L*D*L**H.

inout

B

Complex*16 array, dimension (ldb, nrhs). On entry, the right hand side vectors B for the system of linear equations. On exit, the solution vectors, X.

in

ldb

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

out

info

= 0: successful exit
< 0: if info = -k, the k-th argument had an illegal value

zpttrs

Functions

void zpttrs(
    const char*          uplo,
    const INT            n,
    const INT            nrhs,
    const f64*  restrict D,
    const c128* restrict E,
          c128* restrict B,
    const INT            ldb,
          INT*           info
);

void zpttrs(const char *uplo, const INT n, const INT nrhs, const f64 *restrict D, const c128 *restrict E, c128 *restrict B, const INT ldb, INT *info)#

ZPTTRS solves a tridiagonal system of the form A * X = B using the factorization A = U**H D U or A = L*D*L**H computed by ZPTTRF.

D is a diagonal matrix specified in the vector D, U (or L) is a unit bidiagonal matrix whose superdiagonal (subdiagonal) is specified in the vector E, and X and B are N by NRHS matrices.

Parameters

in

uplo

Specifies the form of the factorization and whether the vector E is the superdiagonal of the upper bidiagonal factor U or the subdiagonal of the lower bidiagonal factor L. = ‘U’: A = U**H *D*U, E is the superdiagonal of U = ‘L’: A = L*D*L**H, E is the subdiagonal of L

in

n

The order of the tridiagonal 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

D

Double precision array, dimension (n). The n diagonal elements of the diagonal matrix D from the factorization A = U**H *D*U or A = L*D*L**H.

in

E

Complex*16 array, dimension (n-1). If UPLO = ‘U’, the (n-1) superdiagonal elements of the unit bidiagonal factor U from the factorization A = U**H*D*U. If UPLO = ‘L’, the (n-1) subdiagonal elements of the unit bidiagonal factor L from the factorization A = L*D*L**H.

inout

B

Complex*16 array, dimension (ldb, nrhs). On entry, the right hand side vectors B for the system of linear equations. On exit, the solution vectors, X.

in

ldb

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

out

info

= 0: successful exit
< 0: if info = -k, the k-th argument had an illegal value

pttrs#

This Page