syconvf_rook

ssyconvf_rook

Functions

void ssyconvf_rook(
    const char*          uplo,
    const char*          way,
    const INT            n,
          f32*  restrict A,
    const INT            lda,
          f32*  restrict E,
    const INT*  restrict ipiv,
          INT*           info
);

void ssyconvf_rook(const char *uplo, const char *way, const INT n, f32 *restrict A, const INT lda, f32 *restrict E, const INT *restrict ipiv, INT *info)

If parameter WAY = ‘C’: SSYCONVF_ROOK converts the factorization output format used in SSYTRF_ROOK provided on entry in parameter A into the factorization output format used in SSYTRF_RK (or SSYTRF_BK) that is stored on exit in parameters A and E.

IPIV format for SSYTRF_ROOK and SSYTRF_RK (or SSYTRF_BK) is the same and is not converted.

If parameter WAY = ‘R’: SSYCONVF_ROOK performs the conversion in reverse direction, i.e. converts the factorization output format used in SSYTRF_RK (or SSYTRF_BK) provided on entry in parameters A and E into the factorization output format used in SSYTRF_ROOK that is stored on exit in parameter A. IPIV format for SSYTRF_ROOK and SSYTRF_RK (or SSYTRF_BK) is the same and is not converted.

1) by ssytrf_rook, if way='C'; 2) by ssytrf_rk (or ssytrf_bk), if way='R'.

The ipiv format is the same for all these routines.

On exit, is not changed.

Parameters

in

uplo

• 'U': Upper triangular

• 'L': Lower triangular

in

way

• 'C': Convert

• 'R': Revert

in

n

The order of the matrix A. n>=0.

inout

A

Array of dimension (lda,n).

                 1) If `way='C'`:

                 On entry, contains factorization details in format
                 used in `ssytrf_rook`:

                 - all elements of the symmetric block diagonal
                   matrix D on the diagonal of A and on
                   superdiagonal (or subdiagonal) of A, and
                 - If `uplo='U'`: multipliers used to obtain factor
                   U in the superdiagonal part of A. If `uplo='L'`:
                   multipliers used to obtain factor L in the
                   superdiagonal part of A.

                 On exit, contains factorization details in format
                 used in `ssytrf_rk` or `ssytrf_bk`:

                 - Only diagonal elements of the symmetric block
                   diagonal matrix D on the diagonal of A, i.e.
                   `D(k,k)=A(k,k)`; (superdiagonal (or subdiagonal)
                   elements of D are stored on exit in array `E`),
                   and
                 - If `uplo='U'`: factor U in the superdiagonal part
                   of A. If `uplo='L'`: factor L in the subdiagonal
                   part of A.

                 2) If `way='R'`:

                 On entry, contains factorization details in format
                 used in `ssytrf_rk` or `ssytrf_bk`:

                 - Only diagonal elements of the symmetric block
                   diagonal matrix D on the diagonal of A, i.e.
                   `D(k,k)=A(k,k)`; (superdiagonal (or subdiagonal)
                   elements of D are stored on exit in array `E`),
                   and
                 - If `uplo='U'`: factor U in the superdiagonal part
                   of A. If `uplo='L'`: factor L in the subdiagonal
                   part of A.

                 On exit, contains factorization details in format
                 used in `ssytrf_rook`:

                 - all elements of the symmetric block diagonal
                   matrix D on the diagonal of A and on
                   superdiagonal (or subdiagonal) of A, and
                 - If `uplo='U'`: multipliers used to obtain factor
                   U in the superdiagonal part of A. If `uplo='L'`:
                   multipliers used to obtain factor L in the
                   superdiagonal part of A.

in

lda

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

inout

E

Array of dimension n.

                 1) If `way='C'`:

                 On entry, just a workspace.

                 On exit, contains the superdiagonal (or
                 subdiagonal) elements of the symmetric block
                 diagonal matrix D with 1-by-1 or 2-by-2 diagonal
                 blocks, where if `uplo='U'`: `E[i]=D(i-1,i)`,
                 `i=1:n-1`, `E[0]` is set to 0; if `uplo='L'`:
                 `E[i]=D(i+1,i)`, `i=0:n-2`, `E[n-1]` is set to 0.

                 2) If `way='R'`:

                 On entry, contains the superdiagonal (or
                 subdiagonal) elements of the symmetric block
                 diagonal matrix D with 1-by-1 or 2-by-2 diagonal
                 blocks, where if `uplo='U'`: `E[i]=D(i-1,i)`,
                 `i=1:n-1`, `E[0]` not referenced; if `uplo='L'`:
                 `E[i]=D(i+1,i)`, `i=0:n-2`, `E[n-1]` not referenced.

                 On exit, is not changed.

in

ipiv

Array of dimension n. On entry, details of the interchanges and the block structure of D as determined:

out

info

• info=0: successful exit

• info<0: if info=-i, the i-th argument had an illegal value

dsyconvf_rook

Functions

void dsyconvf_rook(
    const char*          uplo,
    const char*          way,
    const INT            n,
          f64*  restrict A,
    const INT            lda,
          f64*  restrict E,
    const INT*  restrict ipiv,
          INT*           info
);

void dsyconvf_rook(const char *uplo, const char *way, const INT n, f64 *restrict A, const INT lda, f64 *restrict E, const INT *restrict ipiv, INT *info)

If parameter WAY = ‘C’: DSYCONVF_ROOK converts the factorization output format used in DSYTRF_ROOK provided on entry in parameter A into the factorization output format used in DSYTRF_RK (or DSYTRF_BK) that is stored on exit in parameters A and E.

IPIV format for DSYTRF_ROOK and DSYTRF_RK (or DSYTRF_BK) is the same and is not converted.

If parameter WAY = ‘R’: DSYCONVF_ROOK performs the conversion in reverse direction, i.e. converts the factorization output format used in DSYTRF_RK (or DSYTRF_BK) provided on entry in parameters A and E into the factorization output format used in DSYTRF_ROOK that is stored on exit in parameter A. IPIV format for DSYTRF_ROOK and DSYTRF_RK (or DSYTRF_BK) is the same and is not converted.

1) by dsytrf_rook, if way='C'; 2) by dsytrf_rk (or dsytrf_bk), if way='R'.

The ipiv format is the same for all these routines.

On exit, is not changed.

Parameters

in

uplo

• 'U': Upper triangular

• 'L': Lower triangular

in

way

• 'C': Convert

• 'R': Revert

in

n

The order of the matrix A. n>=0.

inout

A

Array of dimension (lda,n).

                 1) If `way='C'`:

                 On entry, contains factorization details in format
                 used in `dsytrf_rook`:

                 - all elements of the symmetric block diagonal
                   matrix D on the diagonal of A and on
                   superdiagonal (or subdiagonal) of A, and
                 - If `uplo='U'`: multipliers used to obtain factor
                   U in the superdiagonal part of A. If `uplo='L'`:
                   multipliers used to obtain factor L in the
                   superdiagonal part of A.

                 On exit, contains factorization details in format
                 used in `dsytrf_rk` or `dsytrf_bk`:

                 - Only diagonal elements of the symmetric block
                   diagonal matrix D on the diagonal of A, i.e.
                   `D(k,k)=A(k,k)`; (superdiagonal (or subdiagonal)
                   elements of D are stored on exit in array `E`),
                   and
                 - If `uplo='U'`: factor U in the superdiagonal part
                   of A. If `uplo='L'`: factor L in the subdiagonal
                   part of A.

                 2) If `way='R'`:

                 On entry, contains factorization details in format
                 used in `dsytrf_rk` or `dsytrf_bk`:

                 - Only diagonal elements of the symmetric block
                   diagonal matrix D on the diagonal of A, i.e.
                   `D(k,k)=A(k,k)`; (superdiagonal (or subdiagonal)
                   elements of D are stored on exit in array `E`),
                   and
                 - If `uplo='U'`: factor U in the superdiagonal part
                   of A. If `uplo='L'`: factor L in the subdiagonal
                   part of A.

                 On exit, contains factorization details in format
                 used in `dsytrf_rook`:

                 - all elements of the symmetric block diagonal
                   matrix D on the diagonal of A and on
                   superdiagonal (or subdiagonal) of A, and
                 - If `uplo='U'`: multipliers used to obtain factor
                   U in the superdiagonal part of A. If `uplo='L'`:
                   multipliers used to obtain factor L in the
                   superdiagonal part of A.

in

lda

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

inout

E

Array of dimension n.

                 1) If `way='C'`:

                 On entry, just a workspace.

                 On exit, contains the superdiagonal (or
                 subdiagonal) elements of the symmetric block
                 diagonal matrix D with 1-by-1 or 2-by-2 diagonal
                 blocks, where if `uplo='U'`: `E[i]=D(i-1,i)`,
                 `i=1:n-1`, `E[0]` is set to 0; if `uplo='L'`:
                 `E[i]=D(i+1,i)`, `i=0:n-2`, `E[n-1]` is set to 0.

                 2) If `way='R'`:

                 On entry, contains the superdiagonal (or
                 subdiagonal) elements of the symmetric block
                 diagonal matrix D with 1-by-1 or 2-by-2 diagonal
                 blocks, where if `uplo='U'`: `E[i]=D(i-1,i)`,
                 `i=1:n-1`, `E[0]` not referenced; if `uplo='L'`:
                 `E[i]=D(i+1,i)`, `i=0:n-2`, `E[n-1]` not referenced.

                 On exit, is not changed.

in

ipiv

Array of dimension n. On entry, details of the interchanges and the block structure of D as determined:

out

info

• info=0: successful exit

• info<0: if info=-i, the i-th argument had an illegal value

csyconvf_rook

Functions

void csyconvf_rook(
    const char*          uplo,
    const char*          way,
    const INT            n,
          c64*  restrict A,
    const INT            lda,
          c64*  restrict E,
    const INT*  restrict ipiv,
          INT*           info
);

void csyconvf_rook(const char *uplo, const char *way, const INT n, c64 *restrict A, const INT lda, c64 *restrict E, const INT *restrict ipiv, INT *info)

If parameter WAY = ‘C’: CSYCONVF_ROOK converts the factorization output format used in CSYTRF_ROOK provided on entry in parameter A into the factorization output format used in CSYTRF_RK (or ZSYTRF_BK) that is stored on exit in parameters A and E.

IPIV format for CSYTRF_ROOK and CSYTRF_RK (or ZSYTRF_BK) is the same and is not converted.

If parameter WAY = ‘R’: CSYCONVF_ROOK performs the conversion in reverse direction, i.e. converts the factorization output format used in CSYTRF_RK (or ZSYTRF_BK) provided on entry in parameters A and E into the factorization output format used in CSYTRF_ROOK that is stored on exit in parameter A. IPIV format for CSYTRF_ROOK and CSYTRF_RK (or ZSYTRF_BK) is the same and is not converted.

1) by csytrf_rook, if way='C'; 2) by csytrf_rk (or zsytrf_bk), if way='R'.

The ipiv format is the same for all these routines.

On exit, is not changed.

Parameters

in

uplo

• 'U': Upper triangular

• 'L': Lower triangular

in

way

• 'C': Convert

• 'R': Revert

in

n

The order of the matrix A. n>=0.

inout

A

Complex array of dimension (lda,n).

                 1) If `way='C'`:

                 On entry, contains factorization details in format
                 used in `csytrf_rook`:

                 - all elements of the symmetric block diagonal
                   matrix D on the diagonal of A and on
                   superdiagonal (or subdiagonal) of A, and
                 - If `uplo='U'`: multipliers used to obtain factor
                   U in the superdiagonal part of A. If `uplo='L'`:
                   multipliers used to obtain factor L in the
                   superdiagonal part of A.

                 On exit, contains factorization details in format
                 used in `csytrf_rk` or `zsytrf_bk`:

                 - Only diagonal elements of the symmetric block
                   diagonal matrix D on the diagonal of A, i.e.
                   `D(k,k)=A(k,k)`; (superdiagonal (or subdiagonal)
                   elements of D are stored on exit in array `E`),
                   and
                 - If `uplo='U'`: factor U in the superdiagonal part
                   of A. If `uplo='L'`: factor L in the subdiagonal
                   part of A.

                 2) If `way='R'`:

                 On entry, contains factorization details in format
                 used in `csytrf_rk` or `zsytrf_bk`:

                 - Only diagonal elements of the symmetric block
                   diagonal matrix D on the diagonal of A, i.e.
                   `D(k,k)=A(k,k)`; (superdiagonal (or subdiagonal)
                   elements of D are stored on exit in array `E`),
                   and
                 - If `uplo='U'`: factor U in the superdiagonal part
                   of A. If `uplo='L'`: factor L in the subdiagonal
                   part of A.

                 On exit, contains factorization details in format
                 used in `csytrf_rook`:

                 - all elements of the symmetric block diagonal
                   matrix D on the diagonal of A and on
                   superdiagonal (or subdiagonal) of A, and
                 - If `uplo='U'`: multipliers used to obtain factor
                   U in the superdiagonal part of A. If `uplo='L'`:
                   multipliers used to obtain factor L in the
                   superdiagonal part of A.

in

lda

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

inout

E

Complex array of dimension n.

                 1) If `way='C'`:

                 On entry, just a workspace.

                 On exit, contains the superdiagonal (or
                 subdiagonal) elements of the symmetric block
                 diagonal matrix D with 1-by-1 or 2-by-2 diagonal
                 blocks, where if `uplo='U'`: `E[i]=D(i-1,i)`,
                 `i=1:n-1`, `E[0]` is set to 0; if `uplo='L'`:
                 `E[i]=D(i+1,i)`, `i=0:n-2`, `E[n-1]` is set to 0.

                 2) If `way='R'`:

                 On entry, contains the superdiagonal (or
                 subdiagonal) elements of the symmetric block
                 diagonal matrix D with 1-by-1 or 2-by-2 diagonal
                 blocks, where if `uplo='U'`: `E[i]=D(i-1,i)`,
                 `i=1:n-1`, `E[0]` not referenced; if `uplo='L'`:
                 `E[i]=D(i+1,i)`, `i=0:n-2`, `E[n-1]` not referenced.

                 On exit, is not changed.

in

ipiv

Array of dimension n. On entry, details of the interchanges and the block structure of D as determined:

out

info

• info=0: successful exit

• info<0: if info=-i, the i-th argument had an illegal value

zsyconvf_rook

Functions

void zsyconvf_rook(
    const char*          uplo,
    const char*          way,
    const INT            n,
          c128* restrict A,
    const INT            lda,
          c128* restrict E,
    const INT*  restrict ipiv,
          INT*           info
);

void zsyconvf_rook(const char *uplo, const char *way, const INT n, c128 *restrict A, const INT lda, c128 *restrict E, const INT *restrict ipiv, INT *info)

If parameter WAY = ‘C’: ZSYCONVF_ROOK converts the factorization output format used in ZSYTRF_ROOK provided on entry in parameter A into the factorization output format used in ZSYTRF_RK (or ZSYTRF_BK) that is stored on exit in parameters A and E.

IPIV format for ZSYTRF_ROOK and ZSYTRF_RK (or ZSYTRF_BK) is the same and is not converted.

If parameter WAY = ‘R’: ZSYCONVF_ROOK performs the conversion in reverse direction, i.e. converts the factorization output format used in ZSYTRF_RK (or ZSYTRF_BK) provided on entry in parameters A and E into the factorization output format used in ZSYTRF_ROOK that is stored on exit in parameter A. IPIV format for ZSYTRF_ROOK and ZSYTRF_RK (or ZSYTRF_BK) is the same and is not converted.

1) by zsytrf_rook, if way='C'; 2) by zsytrf_rk (or zsytrf_bk), if way='R'.

The ipiv format is the same for all these routines.

On exit, is not changed.

Parameters

in

uplo

• 'U': Upper triangular

• 'L': Lower triangular

in

way

• 'C': Convert

• 'R': Revert

in

n

The order of the matrix A. n>=0.

inout

A

Complex array of dimension (lda,n).

                 1) If `way='C'`:

                 On entry, contains factorization details in format
                 used in `zsytrf_rook`:

                 - all elements of the symmetric block diagonal
                   matrix D on the diagonal of A and on
                   superdiagonal (or subdiagonal) of A, and
                 - If `uplo='U'`: multipliers used to obtain factor
                   U in the superdiagonal part of A. If `uplo='L'`:
                   multipliers used to obtain factor L in the
                   superdiagonal part of A.

                 On exit, contains factorization details in format
                 used in `zsytrf_rk` or `zsytrf_bk`:

                 - Only diagonal elements of the symmetric block
                   diagonal matrix D on the diagonal of A, i.e.
                   `D(k,k)=A(k,k)`; (superdiagonal (or subdiagonal)
                   elements of D are stored on exit in array `E`),
                   and
                 - If `uplo='U'`: factor U in the superdiagonal part
                   of A. If `uplo='L'`: factor L in the subdiagonal
                   part of A.

                 2) If `way='R'`:

                 On entry, contains factorization details in format
                 used in `zsytrf_rk` or `zsytrf_bk`:

                 - Only diagonal elements of the symmetric block
                   diagonal matrix D on the diagonal of A, i.e.
                   `D(k,k)=A(k,k)`; (superdiagonal (or subdiagonal)
                   elements of D are stored on exit in array `E`),
                   and
                 - If `uplo='U'`: factor U in the superdiagonal part
                   of A. If `uplo='L'`: factor L in the subdiagonal
                   part of A.

                 On exit, contains factorization details in format
                 used in `zsytrf_rook`:

                 - all elements of the symmetric block diagonal
                   matrix D on the diagonal of A and on
                   superdiagonal (or subdiagonal) of A, and
                 - If `uplo='U'`: multipliers used to obtain factor
                   U in the superdiagonal part of A. If `uplo='L'`:
                   multipliers used to obtain factor L in the
                   superdiagonal part of A.

in

lda

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

inout

E

Complex array of dimension n.

                 1) If `way='C'`:

                 On entry, just a workspace.

                 On exit, contains the superdiagonal (or
                 subdiagonal) elements of the symmetric block
                 diagonal matrix D with 1-by-1 or 2-by-2 diagonal
                 blocks, where if `uplo='U'`: `E[i]=D(i-1,i)`,
                 `i=1:n-1`, `E[0]` is set to 0; if `uplo='L'`:
                 `E[i]=D(i+1,i)`, `i=0:n-2`, `E[n-1]` is set to 0.

                 2) If `way='R'`:

                 On entry, contains the superdiagonal (or
                 subdiagonal) elements of the symmetric block
                 diagonal matrix D with 1-by-1 or 2-by-2 diagonal
                 blocks, where if `uplo='U'`: `E[i]=D(i-1,i)`,
                 `i=1:n-1`, `E[0]` not referenced; if `uplo='L'`:
                 `E[i]=D(i+1,i)`, `i=0:n-2`, `E[n-1]` not referenced.

                 On exit, is not changed.

in

ipiv

Array of dimension n. On entry, details of the interchanges and the block structure of D as determined:

out

info

• info=0: successful exit

• info<0: if info=-i, the i-th argument had an illegal value