poequ#
Functions
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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
innThe order of the matrix A. n >= 0.
inAThe n-by-n symmetric positive definite matrix whose scaling factors are to be computed. Only the diagonal elements of A are referenced. Array of dimension (lda, n).
inldaThe leading dimension of the array A. lda >= max(1, n).
outSIf info = 0, S contains the scale factors for A. Array of dimension (n).
outscondIf 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.
outamaxAbsolute value of largest matrix element. If amax is very close to overflow or very close to underflow, the matrix should be scaled.
outinfo= 0: successful exit
< 0: if info = -i, the i-th argument had an illegal value
> 0: if info = i, the i-th diagonal element is nonpositive.
void spoequ(
const INT n,
const f32* restrict A,
const INT lda,
f32* restrict S,
f32* scond,
f32* amax,
INT* info
);
Functions
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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
innThe order of the matrix A. n >= 0.
inAThe n-by-n symmetric positive definite matrix whose scaling factors are to be computed. Only the diagonal elements of A are referenced. Array of dimension (lda, n).
inldaThe leading dimension of the array A. lda >= max(1, n).
outSIf info = 0, S contains the scale factors for A. Array of dimension (n).
outscondIf 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.
outamaxAbsolute value of largest matrix element. If amax is very close to overflow or very close to underflow, the matrix should be scaled.
outinfo= 0: successful exit
< 0: if info = -i, the i-th argument had an illegal value
> 0: if info = i, the i-th diagonal element is nonpositive.
void dpoequ(
const INT n,
const f64* restrict A,
const INT lda,
f64* restrict S,
f64* scond,
f64* amax,
INT* info
);
Functions
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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
innThe order of the matrix A. n >= 0.
inAThe n-by-n Hermitian positive definite matrix whose scaling factors are to be computed. Only the diagonal elements of A are referenced. Array of dimension (lda, n).
inldaThe leading dimension of the array A. lda >= max(1, n).
outSIf info = 0, S contains the scale factors for A. Array of dimension (n).
outscondIf 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.
outamaxAbsolute value of largest matrix element. If amax is very close to overflow or very close to underflow, the matrix should be scaled.
outinfo= 0: successful exit
< 0: if info = -i, the i-th argument had an illegal value
> 0: if info = i, the i-th diagonal element is nonpositive.
void cpoequ(
const INT n,
const c64* restrict A,
const INT lda,
f32* restrict S,
f32* scond,
f32* amax,
INT* info
);
Functions
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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
innThe order of the matrix A. n >= 0.
inAThe n-by-n Hermitian positive definite matrix whose scaling factors are to be computed. Only the diagonal elements of A are referenced. Array of dimension (lda, n).
inldaThe leading dimension of the array A. lda >= max(1, n).
outSIf info = 0, S contains the scale factors for A. Array of dimension (n).
outscondIf 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.
outamaxAbsolute value of largest matrix element. If amax is very close to overflow or very close to underflow, the matrix should be scaled.
outinfo= 0: successful exit
< 0: if info = -i, the i-th argument had an illegal value
> 0: if info = i, the i-th diagonal element is nonpositive.
void zpoequ(
const INT n,
const c128* restrict A,
const INT lda,
f64* restrict S,
f64* scond,
f64* amax,
INT* info
);