Provided by: liblapack-doc_3.12.0-3build1.1_all bug

NAME

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

SYNOPSIS

   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.

Detailed Description

Function Documentation

   real function clanhb (character norm, character uplo, integer n, integer k, complex,
       dimension( ldab, * ) ab, integer ldab, 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.

       Parameters
           NORM

                     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.

   real function clansb (character norm, character uplo, integer n, integer k, complex,
       dimension( ldab, * ) ab, integer ldab, 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.

       Parameters
           NORM

                     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.

   double precision function dlansb (character norm, character uplo, integer n, integer k, double
       precision, dimension( ldab, * ) ab, integer ldab, double precision, 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.

       Parameters
           NORM

                     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.

   real function slansb (character norm, character uplo, integer n, integer k, real, dimension(
       ldab, * ) ab, integer ldab, 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.

       Parameters
           NORM

                     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.

   double precision function zlanhb (character norm, character uplo, integer n, integer k,
       complex*16, dimension( ldab, * ) ab, integer ldab, double precision, 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.

       Parameters
           NORM

                     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.

   double precision function zlansb (character norm, character uplo, integer n, integer k,
       complex*16, dimension( ldab, * ) ab, integer ldab, double precision, 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.

       Parameters
           NORM

                     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.

Author

       Generated automatically by Doxygen for LAPACK from the source code.