sysv

ssysv

Functions

void ssysv(
    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(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 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.

The diagonal pivoting method is used to factor A as A = U * D * U**T, if UPLO = ‘U’, or A = L * D * L**T, if UPLO = ‘L’, where U (or L) is a product of permutation and unit upper (lower) triangular matrices, and D is symmetric and block diagonal with 1-by-1 and 2-by-2 diagonal blocks. 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

Double precision array, 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, the block diagonal matrix D and the multipliers used to obtain the factor U or L from the factorization A = U*D*U**T or A = L*D*L**T as computed by SSYTRF.

in

lda

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

out

ipiv

Integer array, dimension (n). Details of the interchanges and the block structure of D, as determined by SSYTRF.

inout

B

Double precision array, 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

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

in

lwork

The length of work. lwork >= 1, and for best performance lwork >= optimal NB * N. 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 by XERBLA.

out

info

• = 0: successful exit

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

• > 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

Functions

void dsysv(
    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(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 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.

The diagonal pivoting method is used to factor A as A = U * D * U**T, if UPLO = ‘U’, or A = L * D * L**T, if UPLO = ‘L’, where U (or L) is a product of permutation and unit upper (lower) triangular matrices, and D is symmetric and block diagonal with 1-by-1 and 2-by-2 diagonal blocks. 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

Double precision array, 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, the block diagonal matrix D and the multipliers used to obtain the factor U or L from the factorization A = U*D*U**T or A = L*D*L**T as computed by DSYTRF.

in

lda

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

out

ipiv

Integer array, dimension (n). Details of the interchanges and the block structure of D, as determined by DSYTRF.

inout

B

Double precision array, 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

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

in

lwork

The length of work. lwork >= 1, and for best performance lwork >= optimal NB * N. 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 by XERBLA.

out

info

• = 0: successful exit

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

• > 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

Functions

void csysv(
    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(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 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.

The diagonal pivoting method is used to factor A as A = U * D * U**T, if UPLO = ‘U’, or A = L * D * L**T, if UPLO = ‘L’, where U (or L) is a product of permutation and unit upper (lower) triangular matrices, and D is symmetric and block diagonal with 1-by-1 and 2-by-2 diagonal blocks. 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

Single complex array, 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, the block diagonal matrix D and the multipliers used to obtain the factor U or L from the factorization A = U*D*U**T or A = L*D*L**T as computed by CSYTRF.

in

lda

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

out

ipiv

Integer array, dimension (n). Details of the interchanges and the block structure of D, as determined by CSYTRF.

inout

B

Single complex array, 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

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

in

lwork

The length of work. lwork >= 1, and for best performance lwork >= optimal NB * N. 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 by XERBLA.

out

info

• = 0: successful exit

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

• > 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

Functions

void zsysv(
    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(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 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.

The diagonal pivoting method is used to factor A as A = U * D * U**T, if UPLO = ‘U’, or A = L * D * L**T, if UPLO = ‘L’, where U (or L) is a product of permutation and unit upper (lower) triangular matrices, and D is symmetric and block diagonal with 1-by-1 and 2-by-2 diagonal blocks. 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

Double complex array, 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, the block diagonal matrix D and the multipliers used to obtain the factor U or L from the factorization A = U*D*U**T or A = L*D*L**T as computed by ZSYTRF.

in

lda

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

out

ipiv

Integer array, dimension (n). Details of the interchanges and the block structure of D, as determined by ZSYTRF.

inout

B

Double complex array, 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

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

in

lwork

The length of work. lwork >= 1, and for best performance lwork >= optimal NB * N. 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 by XERBLA.

out

info

• = 0: successful exit

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

• > 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.