poequ#

Functions

void spoequ(
    const INT           n,
    const f32* restrict A,
    const INT           lda,
          f32* restrict S,
          f32*          scond,
          f32*          amax,
          INT*          info
);
void spoequ(const INT n, const f32 *restrict A, const INT lda, f32 *restrict S, f32 *scond, f32 *amax, INT *info)#

SPOEQU computes row and column scalings intended to equilibrate a symmetric positive definite matrix A and reduce its condition number (with respect to the two-norm).

S contains the scale factors, S(i) = 1/sqrt(A(i,i)), chosen so that the scaled matrix B with elements B(i,j) = S(i)*A(i,j)*S(j) has ones on the diagonal. This choice of S puts the condition number of B within a factor N of the smallest possible condition number over all possible diagonal scalings.

Parameters

in
n

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

in
A

Array of dimension (lda, n). The n-by-n symmetric positive definite matrix whose scaling factors are to be computed. Only the diagonal elements of A are referenced.

in
lda

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

out
S

Array of dimension n. If info=0, S contains the scale factors for A.

out
scond

If info=0, S contains the ratio of the smallest S(i) to the largest S(i). If scond>=0.1 and amax is neither too large nor too small, it is not worth scaling by S.

out
amax

Absolute value of largest matrix element. If amax is very close to overflow or very close to underflow, the matrix should be scaled.

out
info

  • info=0: successful exit

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

  • info>0: if info=i, the i-th diagonal element is nonpositive.

Functions

void dpoequ(
    const INT           n,
    const f64* restrict A,
    const INT           lda,
          f64* restrict S,
          f64*          scond,
          f64*          amax,
          INT*          info
);
void dpoequ(const INT n, const f64 *restrict A, const INT lda, f64 *restrict S, f64 *scond, f64 *amax, INT *info)#

DPOEQU computes row and column scalings intended to equilibrate a symmetric positive definite matrix A and reduce its condition number (with respect to the two-norm).

S contains the scale factors, S(i) = 1/sqrt(A(i,i)), chosen so that the scaled matrix B with elements B(i,j) = S(i)*A(i,j)*S(j) has ones on the diagonal. This choice of S puts the condition number of B within a factor N of the smallest possible condition number over all possible diagonal scalings.

Parameters

in
n

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

in
A

Array of dimension (lda, n). The n-by-n symmetric positive definite matrix whose scaling factors are to be computed. Only the diagonal elements of A are referenced.

in
lda

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

out
S

Array of dimension n. If info=0, S contains the scale factors for A.

out
scond

If info=0, S contains the ratio of the smallest S(i) to the largest S(i). If scond>=0.1 and amax is neither too large nor too small, it is not worth scaling by S.

out
amax

Absolute value of largest matrix element. If amax is very close to overflow or very close to underflow, the matrix should be scaled.

out
info

  • info=0: successful exit

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

  • info>0: if info=i, the i-th diagonal element is nonpositive.

Functions

void cpoequ(
    const INT           n,
    const c64* restrict A,
    const INT           lda,
          f32* restrict S,
          f32*          scond,
          f32*          amax,
          INT*          info
);
void cpoequ(const INT n, const c64 *restrict A, const INT lda, f32 *restrict S, f32 *scond, f32 *amax, INT *info)#

CPOEQU computes row and column scalings intended to equilibrate a Hermitian positive definite matrix A and reduce its condition number (with respect to the two-norm).

S contains the scale factors, S(i) = 1/sqrt(A(i,i)), chosen so that the scaled matrix B with elements B(i,j) = S(i)*A(i,j)*S(j) has ones on the diagonal. This choice of S puts the condition number of B within a factor N of the smallest possible condition number over all possible diagonal scalings.

Parameters

in
n

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

in
A

Array of dimension (lda, n). The n-by-n Hermitian positive definite matrix whose scaling factors are to be computed. Only the diagonal elements of A are referenced.

in
lda

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

out
S

Array of dimension n. If info=0, S contains the scale factors for A.

out
scond

If info=0, S contains the ratio of the smallest S(i) to the largest S(i). If scond>=0.1 and amax is neither too large nor too small, it is not worth scaling by S.

out
amax

Absolute value of largest matrix element. If amax is very close to overflow or very close to underflow, the matrix should be scaled.

out
info

  • info=0: successful exit

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

  • info>0: if info=i, the i-th diagonal element is nonpositive.

Functions

void zpoequ(
    const INT            n,
    const c128* restrict A,
    const INT            lda,
          f64*  restrict S,
          f64*           scond,
          f64*           amax,
          INT*           info
);
void zpoequ(const INT n, const c128 *restrict A, const INT lda, f64 *restrict S, f64 *scond, f64 *amax, INT *info)#

ZPOEQU computes row and column scalings intended to equilibrate a Hermitian positive definite matrix A and reduce its condition number (with respect to the two-norm).

S contains the scale factors, S(i) = 1/sqrt(A(i,i)), chosen so that the scaled matrix B with elements B(i,j) = S(i)*A(i,j)*S(j) has ones on the diagonal. This choice of S puts the condition number of B within a factor N of the smallest possible condition number over all possible diagonal scalings.

Parameters

in
n

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

in
A

Array of dimension (lda, n). The n-by-n Hermitian positive definite matrix whose scaling factors are to be computed. Only the diagonal elements of A are referenced.

in
lda

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

out
S

Array of dimension n. If info=0, S contains the scale factors for A.

out
scond

If info=0, S contains the ratio of the smallest S(i) to the largest S(i). If scond>=0.1 and amax is neither too large nor too small, it is not worth scaling by S.

out
amax

Absolute value of largest matrix element. If amax is very close to overflow or very close to underflow, the matrix should be scaled.

out
info

  • info=0: successful exit

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

  • info>0: if info=i, the i-th diagonal element is nonpositive.