lansp#

slansp

Functions

f32 slansp(
    const char*          norm,
    const char*          uplo,
    const INT            n,
    const f32*  restrict AP,
          f32*  restrict work
);

f32 slansp(const char *norm, const char *uplo, const INT n, const f32 *restrict AP, f32 *restrict work)#

SLANSP returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric matrix A, supplied in packed form.

SLANSP = ( max(abs(A(i,j))), NORM = ‘M’ or ‘m’ ( ( norm1(A), NORM = ‘1’, ‘O’ or ‘o’ ( ( normI(A), NORM = ‘I’ or ‘i’ ( ( normF(A), NORM = ‘F’, ‘f’, ‘E’ or ‘e’

where norm1 denotes the one norm of a matrix (maximum column sum), normI denotes the infinity norm of a matrix (maximum row sum) and normF denotes the Frobenius norm of a matrix (square root of sum of squares). Note that max(abs(A(i,j))) is not a consistent matrix norm.

Parameters

in

norm

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

in

uplo

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

in

n

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

in

AP

The upper or lower triangle of the symmetric matrix A, packed columnwise in a linear array. Array of dimension (n*(n+1)/2).

out

work

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

dlansp

Functions

f64 dlansp(
    const char*          norm,
    const char*          uplo,
    const INT            n,
    const f64*  restrict AP,
          f64*  restrict work
);

f64 dlansp(const char *norm, const char *uplo, const INT n, const f64 *restrict AP, f64 *restrict work)#

DLANSP returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric matrix A, supplied in packed form.

DLANSP = ( max(abs(A(i,j))), NORM = ‘M’ or ‘m’ ( ( norm1(A), NORM = ‘1’, ‘O’ or ‘o’ ( ( normI(A), NORM = ‘I’ or ‘i’ ( ( normF(A), NORM = ‘F’, ‘f’, ‘E’ or ‘e’

where norm1 denotes the one norm of a matrix (maximum column sum), normI denotes the infinity norm of a matrix (maximum row sum) and normF denotes the Frobenius norm of a matrix (square root of sum of squares). Note that max(abs(A(i,j))) is not a consistent matrix norm.

Parameters

in

norm

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

in

uplo

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

in

n

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

in

AP

The upper or lower triangle of the symmetric matrix A, packed columnwise in a linear array. Array of dimension (n*(n+1)/2).

out

work

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

clansp

Functions

f32 clansp(
    const char*          norm,
    const char*          uplo,
    const INT            n,
    const c64*  restrict AP,
          f32*  restrict work
);

f32 clansp(const char *norm, const char *uplo, const INT n, const c64 *restrict AP, f32 *restrict work)#

CLANSP returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex symmetric matrix A, supplied in packed form.

CLANSP = ( max(abs(A(i,j))), NORM = ‘M’ or ‘m’ ( ( norm1(A), NORM = ‘1’, ‘O’ or ‘o’ ( ( normI(A), NORM = ‘I’ or ‘i’ ( ( normF(A), NORM = ‘F’, ‘f’, ‘E’ or ‘e’

where norm1 denotes the one norm of a matrix (maximum column sum), normI denotes the infinity norm of a matrix (maximum row sum) and normF denotes the Frobenius norm of a matrix (square root of sum of squares). Note that max(abs(A(i,j))) is not a consistent matrix norm.

Parameters

in

norm

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

in

uplo

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

in

n

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

in

AP

The upper or lower triangle of the symmetric matrix A, packed columnwise in a linear array. Array of dimension (n*(n+1)/2).

out

work

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

zlansp

Functions

f64 zlansp(
    const char*          norm,
    const char*          uplo,
    const INT            n,
    const c128* restrict AP,
          f64*  restrict work
);

f64 zlansp(const char *norm, const char *uplo, const INT n, const c128 *restrict AP, f64 *restrict work)#

ZLANSP returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex symmetric matrix A, supplied in packed form.

ZLANSP = ( max(abs(A(i,j))), NORM = ‘M’ or ‘m’ ( ( norm1(A), NORM = ‘1’, ‘O’ or ‘o’ ( ( normI(A), NORM = ‘I’ or ‘i’ ( ( normF(A), NORM = ‘F’, ‘f’, ‘E’ or ‘e’

where norm1 denotes the one norm of a matrix (maximum column sum), normI denotes the infinity norm of a matrix (maximum row sum) and normF denotes the Frobenius norm of a matrix (square root of sum of squares). Note that max(abs(A(i,j))) is not a consistent matrix norm.

Parameters

in

norm

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

in

uplo

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

in

n

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

in

AP

The upper or lower triangle of the symmetric matrix A, packed columnwise in a linear array. Array of dimension (n*(n+1)/2).

out

work

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

lansp#

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