langb#

Functions

f32 slangb(
    const char*          norm,
    const INT            n,
    const INT            kl,
    const INT            ku,
    const f32*  restrict AB,
    const INT            ldab,
          f32*  restrict work
);
f32 slangb(const char *norm, const INT n, const INT kl, const INT ku, const f32 *restrict AB, const INT ldab, f32 *restrict work)#

SLANGB returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n band matrix A, with kl sub-diagonals and ku super-diagonals.

Parameters

in
norm

Specifies the value to be returned: = ‘M’ or ‘m’: max(abs(A(i,j))) = “1”, ‘O’ or ‘o’: norm1(A) (max column sum) = ‘I’ or ‘i’: normI(A) (max row sum) = “F”, “f”, ‘E’ or ‘e’: normF(A) (Frobenius norm)

in
n

The order of the matrix A. n >= 0. When n = 0, slangb returns zero.

in
kl

The number of sub-diagonals of the matrix A. kl >= 0.

in
ku

The number of super-diagonals of the matrix A. ku >= 0.

in
AB

Double precision array, dimension (ldab, n). The band matrix A, stored in rows 0 to kl+ku (0-based). The j-th column of A is stored in the j-th column of the array AB as follows: AB[ku+i-j + j*ldab] = A(i,j) for max(0,j-ku) <= i <= min(n-1,j+kl).

in
ldab

The leading dimension of the array AB. ldab >= kl+ku+1.

out
work

Double precision array, dimension (max(1, lwork)). where lwork >= n when norm = ‘I’; otherwise, work is not referenced.

Functions

f64 dlangb(
    const char*          norm,
    const INT            n,
    const INT            kl,
    const INT            ku,
    const f64*  restrict AB,
    const INT            ldab,
          f64*  restrict work
);
f64 dlangb(const char *norm, const INT n, const INT kl, const INT ku, const f64 *restrict AB, const INT ldab, f64 *restrict work)#

DLANGB returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n band matrix A, with kl sub-diagonals and ku super-diagonals.

Parameters

in
norm

Specifies the value to be returned: = ‘M’ or ‘m’: max(abs(A(i,j))) = “1”, ‘O’ or ‘o’: norm1(A) (max column sum) = ‘I’ or ‘i’: normI(A) (max row sum) = “F”, “f”, ‘E’ or ‘e’: normF(A) (Frobenius norm)

in
n

The order of the matrix A. n >= 0. When n = 0, dlangb returns zero.

in
kl

The number of sub-diagonals of the matrix A. kl >= 0.

in
ku

The number of super-diagonals of the matrix A. ku >= 0.

in
AB

Double precision array, dimension (ldab, n). The band matrix A, stored in rows 0 to kl+ku (0-based). The j-th column of A is stored in the j-th column of the array AB as follows: AB[ku+i-j + j*ldab] = A(i,j) for max(0,j-ku) <= i <= min(n-1,j+kl).

in
ldab

The leading dimension of the array AB. ldab >= kl+ku+1.

out
work

Double precision array, dimension (max(1, lwork)). where lwork >= n when norm = ‘I’; otherwise, work is not referenced.

Functions

f32 clangb(
    const char*          norm,
    const INT            n,
    const INT            kl,
    const INT            ku,
    const c64*  restrict AB,
    const INT            ldab,
          f32*  restrict work
);
f32 clangb(const char *norm, const INT n, const INT kl, const INT ku, const c64 *restrict AB, const INT ldab, f32 *restrict work)#

CLANGB returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n band matrix A, with kl sub-diagonals and ku super-diagonals.

Parameters

in
norm

Specifies the value to be returned: = ‘M’ or ‘m’: max(abs(A(i,j))) = “1”, ‘O’ or ‘o’: norm1(A) (max column sum) = ‘I’ or ‘i’: normI(A) (max row sum) = “F”, “f”, ‘E’ or ‘e’: normF(A) (Frobenius norm)

in
n

The order of the matrix A. n >= 0. When n = 0, clangb returns zero.

in
kl

The number of sub-diagonals of the matrix A. kl >= 0.

in
ku

The number of super-diagonals of the matrix A. ku >= 0.

in
AB

Single complex array, dimension (ldab, n). The band matrix A, stored in rows 0 to kl+ku (0-based). The j-th column of A is stored in the j-th column of the array AB as follows: AB[ku+i-j + j*ldab] = A(i,j) for max(0,j-ku) <= i <= min(n-1,j+kl).

in
ldab

The leading dimension of the array AB. ldab >= kl+ku+1.

out
work

Single precision array, dimension (max(1, lwork)). where lwork >= n when norm = ‘I’; otherwise, work is not referenced.

Functions

f64 zlangb(
    const char*          norm,
    const INT            n,
    const INT            kl,
    const INT            ku,
    const c128* restrict AB,
    const INT            ldab,
          f64*  restrict work
);
f64 zlangb(const char *norm, const INT n, const INT kl, const INT ku, const c128 *restrict AB, const INT ldab, f64 *restrict work)#

ZLANGB returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of an n by n band matrix A, with kl sub-diagonals and ku super-diagonals.

Parameters

in
norm

Specifies the value to be returned: = ‘M’ or ‘m’: max(abs(A(i,j))) = “1”, ‘O’ or ‘o’: norm1(A) (max column sum) = ‘I’ or ‘i’: normI(A) (max row sum) = “F”, “f”, ‘E’ or ‘e’: normF(A) (Frobenius norm)

in
n

The order of the matrix A. n >= 0. When n = 0, zlangb returns zero.

in
kl

The number of sub-diagonals of the matrix A. kl >= 0.

in
ku

The number of super-diagonals of the matrix A. ku >= 0.

in
AB

Double complex array, dimension (ldab, n). The band matrix A, stored in rows 0 to kl+ku (0-based). The j-th column of A is stored in the j-th column of the array AB as follows: AB[ku+i-j + j*ldab] = A(i,j) for max(0,j-ku) <= i <= min(n-1,j+kl).

in
ldab

The leading dimension of the array AB. ldab >= kl+ku+1.

out
work

Double precision array, dimension (max(1, lwork)). where lwork >= n when norm = ‘I’; otherwise, work is not referenced.

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