trtrs

strtrs

Functions

void strtrs(
    const char*          uplo,
    const char*          trans,
    const char*          diag,
    const INT            n,
    const INT            nrhs,
    const f32*  restrict A,
    const INT            lda,
          f32*  restrict B,
    const INT            ldb,
          INT*           info
);

void strtrs(const char *uplo, const char *trans, const char *diag, const INT n, const INT nrhs, const f32 *restrict A, const INT lda, f32 *restrict B, const INT ldb, INT *info)

STRTRS solves a triangular system of the form.

A * X = B or A**T * X = B,

where A is a triangular matrix of order N, and B is an N-by-NRHS matrix.

This routine verifies that A is nonsingular, but callers should note that only exact singularity is detected. It is conceivable for one or more diagonal elements of A to be subnormally tiny numbers without this routine signalling an error.

If a possible loss of numerical precision due to near-singular matrices is a concern, the caller should verify that A is nonsingular within some tolerance before calling this routine.

Parameters

in

uplo

= ‘U’: A is upper triangular; = ‘L’: A is lower triangular.

in

trans

Specifies the form of the system of equations:

• ’N’: A * X = B (No transpose)

• ’T’: A**T * X = B (Transpose)

• ’C’: A**H * X = B (Conjugate transpose = Transpose)

in

diag

= ‘N’: A is non-unit triangular; = ‘U’: A is unit triangular.

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

A

Double precision array, dimension (lda, n). The triangular matrix A. If uplo = “U”, the leading N-by-N upper triangular part of the array A contains the upper triangular matrix, and the strictly lower triangular part of A is not referenced. If uplo = “L”, the leading N-by-N lower triangular part of the array A contains the lower triangular matrix, and the strictly upper triangular part of A is not referenced. If diag = “U”, the diagonal elements of A are also not referenced and are assumed to be 1.

in

lda

The leading dimension of the array A. lda >= max(1,n).

inout

B

Double precision array, dimension (ldb, nrhs). On entry, the right hand side matrix B. On exit, if info = 0, the solution matrix X.

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 i-th diagonal element of A is exactly zero, indicating that the matrix is singular and the solutions X have not been computed.

dtrtrs

Functions

void dtrtrs(
    const char*          uplo,
    const char*          trans,
    const char*          diag,
    const INT            n,
    const INT            nrhs,
    const f64*  restrict A,
    const INT            lda,
          f64*  restrict B,
    const INT            ldb,
          INT*           info
);

void dtrtrs(const char *uplo, const char *trans, const char *diag, const INT n, const INT nrhs, const f64 *restrict A, const INT lda, f64 *restrict B, const INT ldb, INT *info)

DTRTRS solves a triangular system of the form.

A * X = B or A**T * X = B,

where A is a triangular matrix of order N, and B is an N-by-NRHS matrix.

This routine verifies that A is nonsingular, but callers should note that only exact singularity is detected. It is conceivable for one or more diagonal elements of A to be subnormally tiny numbers without this routine signalling an error.

If a possible loss of numerical precision due to near-singular matrices is a concern, the caller should verify that A is nonsingular within some tolerance before calling this routine.

Parameters

in

uplo

= ‘U’: A is upper triangular; = ‘L’: A is lower triangular.

in

trans

Specifies the form of the system of equations:

• ’N’: A * X = B (No transpose)

• ’T’: A**T * X = B (Transpose)

• ’C’: A**H * X = B (Conjugate transpose = Transpose)

in

diag

= ‘N’: A is non-unit triangular; = ‘U’: A is unit triangular.

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

A

Double precision array, dimension (lda, n). The triangular matrix A. If uplo = “U”, the leading N-by-N upper triangular part of the array A contains the upper triangular matrix, and the strictly lower triangular part of A is not referenced. If uplo = “L”, the leading N-by-N lower triangular part of the array A contains the lower triangular matrix, and the strictly upper triangular part of A is not referenced. If diag = “U”, the diagonal elements of A are also not referenced and are assumed to be 1.

in

lda

The leading dimension of the array A. lda >= max(1,n).

inout

B

Double precision array, dimension (ldb, nrhs). On entry, the right hand side matrix B. On exit, if info = 0, the solution matrix X.

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 i-th diagonal element of A is exactly zero, indicating that the matrix is singular and the solutions X have not been computed.

ctrtrs

Functions

void ctrtrs(
    const char*          uplo,
    const char*          trans,
    const char*          diag,
    const INT            n,
    const INT            nrhs,
    const c64*  restrict A,
    const INT            lda,
          c64*  restrict B,
    const INT            ldb,
          INT*           info
);

void ctrtrs(const char *uplo, const char *trans, const char *diag, const INT n, const INT nrhs, const c64 *restrict A, const INT lda, c64 *restrict B, const INT ldb, INT *info)

CTRTRS solves a triangular system of the form.

A * X = B, A**T * X = B, or A**H * X = B,

where A is a triangular matrix of order N, and B is an N-by-NRHS matrix.

This routine verifies that A is nonsingular, but callers should note that only exact singularity is detected. It is conceivable for one or more diagonal elements of A to be subnormally tiny numbers without this routine signalling an error.

If a possible loss of numerical precision due to near-singular matrices is a concern, the caller should verify that A is nonsingular within some tolerance before calling this routine.

Parameters

in

uplo

= ‘U’: A is upper triangular; = ‘L’: A is lower triangular.

in

trans

Specifies the form of the system of equations:

• ’N’: A * X = B (No transpose)

• ’T’: A**T * X = B (Transpose)

• ’C’: A**H * X = B (Conjugate transpose)

in

diag

= ‘N’: A is non-unit triangular; = ‘U’: A is unit triangular.

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

A

Single complex array, dimension (lda, n). The triangular matrix A. If uplo = “U”, the leading N-by-N upper triangular part of the array A contains the upper triangular matrix, and the strictly lower triangular part of A is not referenced. If uplo = “L”, the leading N-by-N lower triangular part of the array A contains the lower triangular matrix, and the strictly upper triangular part of A is not referenced. If diag = “U”, the diagonal elements of A are also not referenced and are assumed to be 1.

in

lda

The leading dimension of the array A. lda >= max(1,n).

inout

B

Single complex array, dimension (ldb, nrhs). On entry, the right hand side matrix B. On exit, if info = 0, the solution matrix X.

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 i-th diagonal element of A is exactly zero, indicating that the matrix is singular and the solutions X have not been computed.

ztrtrs

Functions

void ztrtrs(
    const char*          uplo,
    const char*          trans,
    const char*          diag,
    const INT            n,
    const INT            nrhs,
    const c128* restrict A,
    const INT            lda,
          c128* restrict B,
    const INT            ldb,
          INT*           info
);

void ztrtrs(const char *uplo, const char *trans, const char *diag, const INT n, const INT nrhs, const c128 *restrict A, const INT lda, c128 *restrict B, const INT ldb, INT *info)

ZTRTRS solves a triangular system of the form.

A * X = B, A**T * X = B, or A**H * X = B,

where A is a triangular matrix of order N, and B is an N-by-NRHS matrix.

This routine verifies that A is nonsingular, but callers should note that only exact singularity is detected. It is conceivable for one or more diagonal elements of A to be subnormally tiny numbers without this routine signalling an error.

If a possible loss of numerical precision due to near-singular matrices is a concern, the caller should verify that A is nonsingular within some tolerance before calling this routine.

Parameters

in

uplo

= ‘U’: A is upper triangular; = ‘L’: A is lower triangular.

in

trans

Specifies the form of the system of equations:

• ’N’: A * X = B (No transpose)

• ’T’: A**T * X = B (Transpose)

• ’C’: A**H * X = B (Conjugate transpose)

in

diag

= ‘N’: A is non-unit triangular; = ‘U’: A is unit triangular.

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

A

Double complex array, dimension (lda, n). The triangular matrix A. If uplo = “U”, the leading N-by-N upper triangular part of the array A contains the upper triangular matrix, and the strictly lower triangular part of A is not referenced. If uplo = “L”, the leading N-by-N lower triangular part of the array A contains the lower triangular matrix, and the strictly upper triangular part of A is not referenced. If diag = “U”, the diagonal elements of A are also not referenced and are assumed to be 1.

in

lda

The leading dimension of the array A. lda >= max(1,n).

inout

B

Double complex array, dimension (ldb, nrhs). On entry, the right hand side matrix B. On exit, if info = 0, the solution matrix X.

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 i-th diagonal element of A is exactly zero, indicating that the matrix is singular and the solutions X have not been computed.