lanhb - lan{hb,sb}: Hermitian/symmetric matrix, banded

Generated automatically by Doxygen for LAPACK from the source code. Version 3.12.0 Sun Jul 20 2025 01:40:05 lanhb(3)

realfunctionclanhb(characternorm,characteruplo,integern,integerk,complex,dimension(ldab,*)ab,integerldab,real,dimension(*)work)CLANHB returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a Hermitian band matrix. Purpose: CLANHB 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 hermitian band matrix A, with k super-diagonals. Returns CLANHB CLANHB = ( 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. ParametersNORM NORM is CHARACTER*1 Specifies the value to be returned in CLANHB as described above. UPLO UPLO is CHARACTER*1 Specifies whether the upper or lower triangular part of the band matrix A is supplied. = 'U': Upper triangular = 'L': Lower triangular N N is INTEGER The order of the matrix A. N >= 0. When N = 0, CLANHB is set to zero. K K is INTEGER The number of super-diagonals or sub-diagonals of the band matrix A. K >= 0. AB AB is COMPLEX array, dimension (LDAB,N) The upper or lower triangle of the hermitian 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+1+i-j,j) = A(i,j) for max(1,j-k)<=i<=j; if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+k). Note that the imaginary parts of the diagonal elements need not be set and are assumed to be zero. LDAB LDAB is INTEGER The leading dimension of the array AB. LDAB >= K+1. WORK WORK is REAL array, dimension (MAX(1,LWORK)), where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise, WORK is not referenced. Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. realfunctionclansb(characternorm,characteruplo,integern,integerk,complex,dimension(ldab,*)ab,integerldab,real,dimension(*)work)CLANSB returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a symmetric band matrix. Purpose: CLANSB 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 symmetric band matrix A, with k super-diagonals. Returns CLANSB CLANSB = ( 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. ParametersNORM NORM is CHARACTER*1 Specifies the value to be returned in CLANSB as described above. UPLO UPLO is CHARACTER*1 Specifies whether the upper or lower triangular part of the band matrix A is supplied. = 'U': Upper triangular part is supplied = 'L': Lower triangular part is supplied N N is INTEGER The order of the matrix A. N >= 0. When N = 0, CLANSB is set to zero. K K is INTEGER The number of super-diagonals or sub-diagonals of the band matrix A. K >= 0. AB AB is COMPLEX array, dimension (LDAB,N) The upper or lower triangle of the symmetric 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+1+i-j,j) = A(i,j) for max(1,j-k)<=i<=j; if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+k). LDAB LDAB is INTEGER The leading dimension of the array AB. LDAB >= K+1. WORK WORK is REAL array, dimension (MAX(1,LWORK)), where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise, WORK is not referenced. Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. doubleprecisionfunctiondlansb(characternorm,characteruplo,integern,integerk,doubleprecision,dimension(ldab,*)ab,integerldab,doubleprecision,dimension(*)work)DLANSB returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a symmetric band matrix. Purpose: DLANSB 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 symmetric band matrix A, with k super-diagonals. Returns DLANSB DLANSB = ( 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. ParametersNORM NORM is CHARACTER*1 Specifies the value to be returned in DLANSB as described above. UPLO UPLO is CHARACTER*1 Specifies whether the upper or lower triangular part of the band matrix A is supplied. = 'U': Upper triangular part is supplied = 'L': Lower triangular part is supplied N N is INTEGER The order of the matrix A. N >= 0. When N = 0, DLANSB is set to zero. K K is INTEGER The number of super-diagonals or sub-diagonals of the band matrix A. K >= 0. AB AB is DOUBLE PRECISION array, dimension (LDAB,N) The upper or lower triangle of the symmetric 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+1+i-j,j) = A(i,j) for max(1,j-k)<=i<=j; if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+k). LDAB LDAB is INTEGER The leading dimension of the array AB. LDAB >= K+1. WORK WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)), where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise, WORK is not referenced. Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. realfunctionslansb(characternorm,characteruplo,integern,integerk,real,dimension(ldab,*)ab,integerldab,real,dimension(*)work)SLANSB returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a symmetric band matrix. Purpose: SLANSB 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 symmetric band matrix A, with k super-diagonals. Returns SLANSB SLANSB = ( 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. ParametersNORM NORM is CHARACTER*1 Specifies the value to be returned in SLANSB as described above. UPLO UPLO is CHARACTER*1 Specifies whether the upper or lower triangular part of the band matrix A is supplied. = 'U': Upper triangular part is supplied = 'L': Lower triangular part is supplied N N is INTEGER The order of the matrix A. N >= 0. When N = 0, SLANSB is set to zero. K K is INTEGER The number of super-diagonals or sub-diagonals of the band matrix A. K >= 0. AB AB is REAL array, dimension (LDAB,N) The upper or lower triangle of the symmetric 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+1+i-j,j) = A(i,j) for max(1,j-k)<=i<=j; if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+k). LDAB LDAB is INTEGER The leading dimension of the array AB. LDAB >= K+1. WORK WORK is REAL array, dimension (MAX(1,LWORK)), where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise, WORK is not referenced. Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. doubleprecisionfunctionzlanhb(characternorm,characteruplo,integern,integerk,complex*16,dimension(ldab,*)ab,integerldab,doubleprecision,dimension(*)work)ZLANHB returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a Hermitian band matrix. Purpose: ZLANHB 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 hermitian band matrix A, with k super-diagonals. Returns ZLANHB ZLANHB = ( 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. ParametersNORM NORM is CHARACTER*1 Specifies the value to be returned in ZLANHB as described above. UPLO UPLO is CHARACTER*1 Specifies whether the upper or lower triangular part of the band matrix A is supplied. = 'U': Upper triangular = 'L': Lower triangular N N is INTEGER The order of the matrix A. N >= 0. When N = 0, ZLANHB is set to zero. K K is INTEGER The number of super-diagonals or sub-diagonals of the band matrix A. K >= 0. AB AB is COMPLEX*16 array, dimension (LDAB,N) The upper or lower triangle of the hermitian 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+1+i-j,j) = A(i,j) for max(1,j-k)<=i<=j; if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+k). Note that the imaginary parts of the diagonal elements need not be set and are assumed to be zero. LDAB LDAB is INTEGER The leading dimension of the array AB. LDAB >= K+1. WORK WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)), where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise, WORK is not referenced. Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. doubleprecisionfunctionzlansb(characternorm,characteruplo,integern,integerk,complex*16,dimension(ldab,*)ab,integerldab,doubleprecision,dimension(*)work)ZLANSB returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a symmetric band matrix. Purpose: ZLANSB 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 symmetric band matrix A, with k super-diagonals. Returns ZLANSB ZLANSB = ( 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. ParametersNORM NORM is CHARACTER*1 Specifies the value to be returned in ZLANSB as described above. UPLO UPLO is CHARACTER*1 Specifies whether the upper or lower triangular part of the band matrix A is supplied. = 'U': Upper triangular part is supplied = 'L': Lower triangular part is supplied N N is INTEGER The order of the matrix A. N >= 0. When N = 0, ZLANSB is set to zero. K K is INTEGER The number of super-diagonals or sub-diagonals of the band matrix A. K >= 0. AB AB is COMPLEX*16 array, dimension (LDAB,N) The upper or lower triangle of the symmetric 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+1+i-j,j) = A(i,j) for max(1,j-k)<=i<=j; if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+k). LDAB LDAB is INTEGER The leading dimension of the array AB. LDAB >= K+1. WORK WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)), where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise, WORK is not referenced. Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd.

lanhb - lan{hb,sb}: Hermitian/symmetric matrix, banded

Functions real function clanhb (norm, uplo, n, k, ab, ldab, work) CLANHB returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a Hermitian band matrix. real function clansb (norm, uplo, n, k, ab, ldab, work) CLANSB returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a symmetric band matrix. double precision function dlansb (norm, uplo, n, k, ab, ldab, work) DLANSB returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a symmetric band matrix. real function slansb (norm, uplo, n, k, ab, ldab, work) SLANSB returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a symmetric band matrix. double precision function zlanhb (norm, uplo, n, k, ab, ldab, work) ZLANHB returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a Hermitian band matrix. double precision function zlansb (norm, uplo, n, k, ab, ldab, work) ZLANSB returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a symmetric band matrix.