sysv_aa

ssysv_aa

Functions

void ssysv_aa(
    const char*          uplo,
    const INT            n,
    const INT            nrhs,
          f32*  restrict A,
    const INT            lda,
          INT*  restrict ipiv,
          f32*  restrict B,
    const INT            ldb,
          f32*  restrict work,
    const INT            lwork,
          INT*           info
);

void ssysv_aa(const char *uplo, const INT n, const INT nrhs, f32 *restrict A, const INT lda, INT *restrict ipiv, f32 *restrict B, const INT ldb, f32 *restrict work, const INT lwork, INT *info)

SSYSV_AA computes the solution to a real system of linear equations A * X = B, where A is an N-by-N symmetric matrix and X and B are N-by-NRHS matrices.

Aasen’s algorithm is used to factor A as A = U**T * T * U, if UPLO = ‘U’, or A = L * T * L**T, if UPLO = ‘L’, where U (or L) is a product of permutation and unit upper (lower) triangular matrices, and T is symmetric tridiagonal. The factored form of A is then used to solve the system of equations A * X = B.

Parameters

in

uplo

• 'U': Upper triangle of A is stored

• 'L': Lower triangle of A is stored

in

n

The number of linear equations, i.e., 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.

inout

A

Array of dimension (lda,n). On entry, the symmetric matrix A. If uplo='U', the leading n-by-n upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If uplo='L', the leading n-by-n lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced. On exit, if info=0, the tridiagonal matrix T and the multipliers used to obtain the factor U or L from the factorization A = U**T*T*U or A = L*T*L**T as computed by ssytrf_aa.

in

lda

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

out

ipiv

Array of dimension n. On exit, it contains the details of the interchanges, i.e., the row and column k of A were interchanged with the row and column ipiv[k].

inout

B

Array of dimension (ldb,nrhs). On entry, the n-by-nrhs right hand side matrix B. On exit, if info=0, the n-by-nrhs solution matrix X.

in

ldb

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

out

work

Array of dimension max(1,lwork). On exit, if info=0, work[0] returns the optimal lwork.

in

lwork

The length of work. lwork>=max(1,2*n,3*n-2), and for the best performance, lwork>=n*nb, where nb is the optimal block size for ssytrf_aa. If lwork=-1, then a workspace query is assumed; the routine only calculates the optimal size of the work array, returns this value as the first entry of the work array, and no error message related to lwork is issued.

out

info

• info=0: successful exit

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

• info>0: if info=i, D(i,i) is exactly zero. The factorization has been completed, but the block diagonal matrix D is exactly singular, so the solution could not be computed.

dsysv_aa

Functions

void dsysv_aa(
    const char*          uplo,
    const INT            n,
    const INT            nrhs,
          f64*  restrict A,
    const INT            lda,
          INT*  restrict ipiv,
          f64*  restrict B,
    const INT            ldb,
          f64*  restrict work,
    const INT            lwork,
          INT*           info
);

void dsysv_aa(const char *uplo, const INT n, const INT nrhs, f64 *restrict A, const INT lda, INT *restrict ipiv, f64 *restrict B, const INT ldb, f64 *restrict work, const INT lwork, INT *info)

DSYSV_AA computes the solution to a real system of linear equations A * X = B, where A is an N-by-N symmetric matrix and X and B are N-by-NRHS matrices.

Aasen’s algorithm is used to factor A as A = U**T * T * U, if UPLO = ‘U’, or A = L * T * L**T, if UPLO = ‘L’, where U (or L) is a product of permutation and unit upper (lower) triangular matrices, and T is symmetric tridiagonal. The factored form of A is then used to solve the system of equations A * X = B.

Parameters

in

uplo

• 'U': Upper triangle of A is stored

• 'L': Lower triangle of A is stored

in

n

The number of linear equations, i.e., 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.

inout

A

Array of dimension (lda,n). On entry, the symmetric matrix A. If uplo='U', the leading n-by-n upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If uplo='L', the leading n-by-n lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced. On exit, if info=0, the tridiagonal matrix T and the multipliers used to obtain the factor U or L from the factorization A = U**T*T*U or A = L*T*L**T as computed by dsytrf_aa.

in

lda

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

out

ipiv

Array of dimension n. On exit, it contains the details of the interchanges, i.e., the row and column k of A were interchanged with the row and column ipiv[k].

inout

B

Array of dimension (ldb,nrhs). On entry, the n-by-nrhs right hand side matrix B. On exit, if info=0, the n-by-nrhs solution matrix X.

in

ldb

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

out

work

Array of dimension max(1,lwork). On exit, if info=0, work[0] returns the optimal lwork.

in

lwork

The length of work. lwork>=max(1,2*n,3*n-2), and for the best performance, lwork>=n*nb, where nb is the optimal block size for dsytrf_aa. If lwork=-1, then a workspace query is assumed; the routine only calculates the optimal size of the work array, returns this value as the first entry of the work array, and no error message related to lwork is issued.

out

info

• info=0: successful exit

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

• info>0: if info=i, D(i,i) is exactly zero. The factorization has been completed, but the block diagonal matrix D is exactly singular, so the solution could not be computed.

csysv_aa

Functions

void csysv_aa(
    const char*          uplo,
    const INT            n,
    const INT            nrhs,
          c64*  restrict A,
    const INT            lda,
          INT*  restrict ipiv,
          c64*  restrict B,
    const INT            ldb,
          c64*  restrict work,
    const INT            lwork,
          INT*           info
);

void csysv_aa(const char *uplo, const INT n, const INT nrhs, c64 *restrict A, const INT lda, INT *restrict ipiv, c64 *restrict B, const INT ldb, c64 *restrict work, const INT lwork, INT *info)

CSYSV_AA computes the solution to a complex system of linear equations A * X = B, where A is an N-by-N symmetric matrix and X and B are N-by-NRHS matrices.

Aasen’s algorithm is used to factor A as A = U**T * T * U, if UPLO = ‘U’, or A = L * T * L**T, if UPLO = ‘L’, where U (or L) is a product of permutation and unit upper (lower) triangular matrices, and T is symmetric tridiagonal. The factored form of A is then used to solve the system of equations A * X = B.

Parameters

in

uplo

• 'U': Upper triangle of A is stored

• 'L': Lower triangle of A is stored

in

n

The number of linear equations, i.e., 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.

inout

A

Complex array of dimension (lda,n). On entry, the symmetric matrix A. If uplo='U', the leading n-by-n upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If uplo='L', the leading n-by-n lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced. On exit, if info=0, the tridiagonal matrix T and the multipliers used to obtain the factor U or L from the factorization A = U**T*T*U or A = L*T*L**T as computed by csytrf_aa.

in

lda

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

out

ipiv

Array of dimension n. On exit, it contains the details of the interchanges, i.e., the row and column k of A were interchanged with the row and column ipiv[k].

inout

B

Complex array of dimension (ldb,nrhs). On entry, the n-by-nrhs right hand side matrix B. On exit, if info=0, the n-by-nrhs solution matrix X.

in

ldb

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

out

work

Complex array of dimension max(1,lwork). On exit, if info=0, work[0] returns the optimal lwork.

in

lwork

The length of work. lwork>=max(1,2*n,3*n-2), and for the best performance, lwork>=n*nb, where nb is the optimal block size for csytrf_aa. If lwork=-1, then a workspace query is assumed; the routine only calculates the optimal size of the work array, returns this value as the first entry of the work array, and no error message related to lwork is issued.

out

info

• info=0: successful exit

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

• info>0: if info=i, D(i,i) is exactly zero. The factorization has been completed, but the block diagonal matrix D is exactly singular, so the solution could not be computed.

zsysv_aa

Functions

void zsysv_aa(
    const char*          uplo,
    const INT            n,
    const INT            nrhs,
          c128* restrict A,
    const INT            lda,
          INT*  restrict ipiv,
          c128* restrict B,
    const INT            ldb,
          c128* restrict work,
    const INT            lwork,
          INT*           info
);

void zsysv_aa(const char *uplo, const INT n, const INT nrhs, c128 *restrict A, const INT lda, INT *restrict ipiv, c128 *restrict B, const INT ldb, c128 *restrict work, const INT lwork, INT *info)

ZSYSV_AA computes the solution to a complex system of linear equations A * X = B, where A is an N-by-N symmetric matrix and X and B are N-by-NRHS matrices.

Aasen’s algorithm is used to factor A as A = U**T * T * U, if UPLO = ‘U’, or A = L * T * L**T, if UPLO = ‘L’, where U (or L) is a product of permutation and unit upper (lower) triangular matrices, and T is symmetric tridiagonal. The factored form of A is then used to solve the system of equations A * X = B.

Parameters

in

uplo

• 'U': Upper triangle of A is stored

• 'L': Lower triangle of A is stored

in

n

The number of linear equations, i.e., 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.

inout

A

Complex array of dimension (lda,n). On entry, the symmetric matrix A. If uplo='U', the leading n-by-n upper triangular part of A contains the upper triangular part of the matrix A, and the strictly lower triangular part of A is not referenced. If uplo='L', the leading n-by-n lower triangular part of A contains the lower triangular part of the matrix A, and the strictly upper triangular part of A is not referenced. On exit, if info=0, the tridiagonal matrix T and the multipliers used to obtain the factor U or L from the factorization A = U**T*T*U or A = L*T*L**T as computed by zsytrf_aa.

in

lda

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

out

ipiv

Array of dimension n. On exit, it contains the details of the interchanges, i.e., the row and column k of A were interchanged with the row and column ipiv[k].

inout

B

Complex array of dimension (ldb,nrhs). On entry, the n-by-nrhs right hand side matrix B. On exit, if info=0, the n-by-nrhs solution matrix X.

in

ldb

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

out

work

Complex array of dimension max(1,lwork). On exit, if info=0, work[0] returns the optimal lwork.

in

lwork

The length of work. lwork>=max(1,2*n,3*n-2), and for the best performance, lwork>=n*nb, where nb is the optimal block size for zsytrf_aa. If lwork=-1, then a workspace query is assumed; the routine only calculates the optimal size of the work array, returns this value as the first entry of the work array, and no error message related to lwork is issued.

out

info

• info=0: successful exit

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

• info>0: if info=i, D(i,i) is exactly zero. The factorization has been completed, but the block diagonal matrix D is exactly singular, so the solution could not be computed.