lanhb(3)

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

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