pbequ#

Functions

void spbequ(
    const char*          uplo,
    const INT            n,
    const INT            kd,
    const f32*  restrict AB,
    const INT            ldab,
          f32*  restrict S,
          f32*           scond,
          f32*           amax,
          INT*           info
);
void spbequ(const char *uplo, const INT n, const INT kd, const f32 *restrict AB, const INT ldab, f32 *restrict S, f32 *scond, f32 *amax, INT *info)#

SPBEQU computes row and column scalings intended to equilibrate a symmetric positive definite band 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.

Parameters

in
uplo

= ‘U’: Upper triangular of A is stored = ‘L’: Lower triangular of A is stored

in
n

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

in
kd

The number of super-diagonals (if uplo=’U’) or sub-diagonals (if uplo=’L’). kd >= 0.

in
AB

The banded matrix A. Array of dimension (ldab, n).

in
ldab

The leading dimension of AB. ldab >= kd+1.

out
S

The scale factors for A. Array of dimension (n).

out
scond

Ratio of smallest to largest S(i).

out
amax

Absolute value of largest matrix element.

out
info

  • = 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.

Functions

void dpbequ(
    const char*          uplo,
    const INT            n,
    const INT            kd,
    const f64*  restrict AB,
    const INT            ldab,
          f64*  restrict S,
          f64*           scond,
          f64*           amax,
          INT*           info
);
void dpbequ(const char *uplo, const INT n, const INT kd, const f64 *restrict AB, const INT ldab, f64 *restrict S, f64 *scond, f64 *amax, INT *info)#

DPBEQU computes row and column scalings intended to equilibrate a symmetric positive definite band 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.

Parameters

in
uplo

= ‘U’: Upper triangular of A is stored = ‘L’: Lower triangular of A is stored

in
n

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

in
kd

The number of super-diagonals (if uplo=’U’) or sub-diagonals (if uplo=’L’). kd >= 0.

in
AB

The banded matrix A. Array of dimension (ldab, n).

in
ldab

The leading dimension of AB. ldab >= kd+1.

out
S

The scale factors for A. Array of dimension (n).

out
scond

Ratio of smallest to largest S(i).

out
amax

Absolute value of largest matrix element.

out
info

  • = 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.

Functions

void cpbequ(
    const char*          uplo,
    const INT            n,
    const INT            kd,
    const c64*  restrict AB,
    const INT            ldab,
          f32*  restrict S,
          f32*           scond,
          f32*           amax,
          INT*           info
);
void cpbequ(const char *uplo, const INT n, const INT kd, const c64 *restrict AB, const INT ldab, f32 *restrict S, f32 *scond, f32 *amax, INT *info)#

CPBEQU computes row and column scalings intended to equilibrate a Hermitian positive definite band 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.

Parameters

in
uplo

= ‘U’: Upper triangular of A is stored = ‘L’: Lower triangular of A is stored

in
n

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

in
kd

The number of super-diagonals (if uplo=’U’) or sub-diagonals (if uplo=’L’). kd >= 0.

in
AB

The banded matrix A. Array of dimension (ldab, n).

in
ldab

The leading dimension of AB. ldab >= kd+1.

out
S

The scale factors for A. Array of dimension (n).

out
scond

Ratio of smallest to largest S(i).

out
amax

Absolute value of largest matrix element.

out
info

  • = 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.

Functions

void zpbequ(
    const char*          uplo,
    const INT            n,
    const INT            kd,
    const c128* restrict AB,
    const INT            ldab,
          f64*  restrict S,
          f64*           scond,
          f64*           amax,
          INT*           info
);
void zpbequ(const char *uplo, const INT n, const INT kd, const c128 *restrict AB, const INT ldab, f64 *restrict S, f64 *scond, f64 *amax, INT *info)#

ZPBEQU computes row and column scalings intended to equilibrate a Hermitian positive definite band 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.

Parameters

in
uplo

= ‘U’: Upper triangular of A is stored = ‘L’: Lower triangular of A is stored

in
n

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

in
kd

The number of super-diagonals (if uplo=’U’) or sub-diagonals (if uplo=’L’). kd >= 0.

in
AB

The banded matrix A. Array of dimension (ldab, n).

in
ldab

The leading dimension of AB. ldab >= kd+1.

out
S

The scale factors for A. Array of dimension (n).

out
scond

Ratio of smallest to largest S(i).

out
amax

Absolute value of largest matrix element.

out
info

  • = 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.

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