lantb

slantb

Functions

f32 slantb(
    const char*          norm,
    const char*          uplo,
    const char*          diag,
    const INT            n,
    const INT            k,
    const f32*  restrict AB,
    const INT            ldab,
          f32*  restrict work
);

f32 slantb(const char *norm, const char *uplo, const char *diag, const INT n, const INT k, const f32 *restrict AB, const INT ldab, f32 *restrict work)

SLANTB 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 triangular band matrix A, with (k + 1) 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

uplo

Specifies whether the matrix A is upper or lower triangular. = ‘U’: Upper triangular = ‘L’: Lower triangular

in

diag

Specifies whether or not the matrix A is unit triangular. = ‘N’: Non-unit triangular = ‘U’: Unit triangular

in

n

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

in

k

The number of super-diagonals of the matrix A if uplo = “U”, or the number of sub-diagonals of the matrix A if uplo = ‘L’. k >= 0.

in

AB

Double precision array, dimension (ldab, n). The upper or lower triangular band matrix A, stored in the first k+1 rows of AB. The j-th column of A is stored in the j-th column of the array AB as follows: if uplo = “U”, AB[k+i-j + j*ldab] = A(i,j) for max(0,j-k) <= i <= j; if uplo = “L”, AB[i-j + j*ldab] = A(i,j) for j <= i <= min(n-1,j+k). Note that when diag = “U”, the elements of the array AB corresponding to the diagonal elements of the matrix A are not referenced, but are assumed to be one.

in

ldab

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

out

work

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

dlantb

Functions

f64 dlantb(
    const char*          norm,
    const char*          uplo,
    const char*          diag,
    const INT            n,
    const INT            k,
    const f64*  restrict AB,
    const INT            ldab,
          f64*  restrict work
);

f64 dlantb(const char *norm, const char *uplo, const char *diag, const INT n, const INT k, const f64 *restrict AB, const INT ldab, f64 *restrict work)

DLANTB 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 triangular band matrix A, with (k + 1) 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

uplo

Specifies whether the matrix A is upper or lower triangular. = ‘U’: Upper triangular = ‘L’: Lower triangular

in

diag

Specifies whether or not the matrix A is unit triangular. = ‘N’: Non-unit triangular = ‘U’: Unit triangular

in

n

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

in

k

The number of super-diagonals of the matrix A if uplo = “U”, or the number of sub-diagonals of the matrix A if uplo = ‘L’. k >= 0.

in

AB

Double precision array, dimension (ldab, n). The upper or lower triangular band matrix A, stored in the first k+1 rows of AB. The j-th column of A is stored in the j-th column of the array AB as follows: if uplo = “U”, AB[k+i-j + j*ldab] = A(i,j) for max(0,j-k) <= i <= j; if uplo = “L”, AB[i-j + j*ldab] = A(i,j) for j <= i <= min(n-1,j+k). Note that when diag = “U”, the elements of the array AB corresponding to the diagonal elements of the matrix A are not referenced, but are assumed to be one.

in

ldab

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

out

work

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

clantb

Functions

f32 clantb(
    const char*          norm,
    const char*          uplo,
    const char*          diag,
    const INT            n,
    const INT            k,
    const c64*  restrict AB,
    const INT            ldab,
          f32*  restrict work
);

f32 clantb(const char *norm, const char *uplo, const char *diag, const INT n, const INT k, const c64 *restrict AB, const INT ldab, f32 *restrict work)

CLANTB 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 triangular band matrix A, with (k + 1) 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

uplo

Specifies whether the matrix A is upper or lower triangular. = ‘U’: Upper triangular = ‘L’: Lower triangular

in

diag

Specifies whether or not the matrix A is unit triangular. = ‘N’: Non-unit triangular = ‘U’: Unit triangular

in

n

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

in

k

The number of super-diagonals of the matrix A if uplo = “U”, or the number of sub-diagonals of the matrix A if uplo = ‘L’. k >= 0.

in

AB

Single complex array, dimension (ldab, n). The upper or lower triangular band matrix A, stored in the first k+1 rows of AB. The j-th column of A is stored in the j-th column of the array AB as follows: if uplo = “U”, AB[k+i-j + j*ldab] = A(i,j) for max(0,j-k) <= i <= j; if uplo = “L”, AB[i-j + j*ldab] = A(i,j) for j <= i <= min(n-1,j+k). Note that when diag = “U”, the elements of the array AB corresponding to the diagonal elements of the matrix A are not referenced, but are assumed to be one.

in

ldab

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

out

work

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

zlantb

Functions

f64 zlantb(
    const char*          norm,
    const char*          uplo,
    const char*          diag,
    const INT            n,
    const INT            k,
    const c128* restrict AB,
    const INT            ldab,
          f64*  restrict work
);

f64 zlantb(const char *norm, const char *uplo, const char *diag, const INT n, const INT k, const c128 *restrict AB, const INT ldab, f64 *restrict work)

ZLANTB 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 triangular band matrix A, with (k + 1) 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

uplo

Specifies whether the matrix A is upper or lower triangular. = ‘U’: Upper triangular = ‘L’: Lower triangular

in

diag

Specifies whether or not the matrix A is unit triangular. = ‘N’: Non-unit triangular = ‘U’: Unit triangular

in

n

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

in

k

The number of super-diagonals of the matrix A if uplo = “U”, or the number of sub-diagonals of the matrix A if uplo = ‘L’. k >= 0.

in

AB

Double complex array, dimension (ldab, n). The upper or lower triangular band matrix A, stored in the first k+1 rows of AB. The j-th column of A is stored in the j-th column of the array AB as follows: if uplo = “U”, AB[k+i-j + j*ldab] = A(i,j) for max(0,j-k) <= i <= j; if uplo = “L”, AB[i-j + j*ldab] = A(i,j) for j <= i <= min(n-1,j+k). Note that when diag = “U”, the elements of the array AB corresponding to the diagonal elements of the matrix A are not referenced, but are assumed to be one.

in

ldab

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

out

work

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