lanhp(3)

NAME
lanhp - lan{hp,sp}: Hermitian/symmetric matrix, packed

SYNOPSIS

  Functions

real function clanhp (norm, uplo, n, ap, work)
CLANHP returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex Hermitian matrix supplied in packed form.
real function clansp (norm, uplo, n, ap, work)
CLANSP 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 matrix supplied in packed form.
double precision function dlansp (norm, uplo, n, ap, work)
DLANSP 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 matrix supplied in packed form.
real function slansp (norm, uplo, n, ap, work)
SLANSP 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 matrix supplied in packed form.
double precision function zlanhp (norm, uplo, n, ap, work)
ZLANHP returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex Hermitian matrix supplied in packed form.
double precision function zlansp (norm, uplo, n, ap, work)
ZLANSP 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 matrix supplied in packed form.

Detailed Description

Function Documentation

  real function clanhp (character norm, character uplo, integer n, complex, dimension( * ) ap, real, dimension( * ) work)

CLANHP returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex Hermitian matrix supplied in packed form.

Purpose:

    !>
    !> CLANHP  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 hermitian matrix A,  supplied in packed form.
    !>

Returns
    CLANHP

    !>
    !>    CLANHP = ( 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 CLANHP as described
    !>          above.
    !>

    UPLO

    !>          UPLO is CHARACTER*1
    !>          Specifies whether the upper or lower triangular part of the
    !>          hermitian matrix A is supplied.
    !>          = 'U':  Upper triangular part of A is supplied
    !>          = 'L':  Lower triangular part of A is supplied
    !>

    N

    !>          N is INTEGER
    !>          The order of the matrix A.  N >= 0.  When N = 0, CLANHP is
    !>          set to zero.
    !>

    AP

    !>          AP is COMPLEX array, dimension (N*(N+1)/2)
    !>          The upper or lower triangle of the hermitian matrix A, packed
    !>          columnwise in a linear array.  The j-th column of A is stored
    !>          in the array AP as follows:
    !>          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
    !>          if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
    !>          Note that the  imaginary parts of the diagonal elements need
    !>          not be set and are assumed to be zero.
    !>

    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 clansp (character norm, character uplo, integer n, complex, dimension( * ) ap, real, dimension( * ) work)

CLANSP 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 matrix supplied in packed form.

Purpose:

    !>
    !> 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.
    !>

Returns
    CLANSP

    !>
    !>    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
    NORM

    !>          NORM is CHARACTER*1
    !>          Specifies the value to be returned in CLANSP as described
    !>          above.
    !>

    UPLO

    !>          UPLO is CHARACTER*1
    !>          Specifies whether the upper or lower triangular part of the
    !>          symmetric matrix A is supplied.
    !>          = 'U':  Upper triangular part of A is supplied
    !>          = 'L':  Lower triangular part of A is supplied
    !>

    N

    !>          N is INTEGER
    !>          The order of the matrix A.  N >= 0.  When N = 0, CLANSP is
    !>          set to zero.
    !>

    AP

    !>          AP is COMPLEX array, dimension (N*(N+1)/2)
    !>          The upper or lower triangle of the symmetric matrix A, packed
    !>          columnwise in a linear array.  The j-th column of A is stored
    !>          in the array AP as follows:
    !>          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
    !>          if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
    !>

    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 dlansp (character norm, character uplo, integer n, double precision, dimension( * ) ap, double precision, dimension( * ) work)

DLANSP 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 matrix supplied in packed form.

Purpose:

    !>
    !> 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.
    !>

Returns
    DLANSP

    !>
    !>    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
    NORM

    !>          NORM is CHARACTER*1
    !>          Specifies the value to be returned in DLANSP as described
    !>          above.
    !>

    UPLO

    !>          UPLO is CHARACTER*1
    !>          Specifies whether the upper or lower triangular part of the
    !>          symmetric matrix A is supplied.
    !>          = 'U':  Upper triangular part of A is supplied
    !>          = 'L':  Lower triangular part of A is supplied
    !>

    N

    !>          N is INTEGER
    !>          The order of the matrix A.  N >= 0.  When N = 0, DLANSP is
    !>          set to zero.
    !>

    AP

    !>          AP is DOUBLE PRECISION array, dimension (N*(N+1)/2)
    !>          The upper or lower triangle of the symmetric matrix A, packed
    !>          columnwise in a linear array.  The j-th column of A is stored
    !>          in the array AP as follows:
    !>          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
    !>          if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
    !>

    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 slansp (character norm, character uplo, integer n, real, dimension( * ) ap, real, dimension( * ) work)

SLANSP 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 matrix supplied in packed form.

Purpose:

    !>
    !> 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.
    !>

Returns
    SLANSP

    !>
    !>    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
    NORM

    !>          NORM is CHARACTER*1
    !>          Specifies the value to be returned in SLANSP as described
    !>          above.
    !>

    UPLO

    !>          UPLO is CHARACTER*1
    !>          Specifies whether the upper or lower triangular part of the
    !>          symmetric matrix A is supplied.
    !>          = 'U':  Upper triangular part of A is supplied
    !>          = 'L':  Lower triangular part of A is supplied
    !>

    N

    !>          N is INTEGER
    !>          The order of the matrix A.  N >= 0.  When N = 0, SLANSP is
    !>          set to zero.
    !>

    AP

    !>          AP is REAL array, dimension (N*(N+1)/2)
    !>          The upper or lower triangle of the symmetric matrix A, packed
    !>          columnwise in a linear array.  The j-th column of A is stored
    !>          in the array AP as follows:
    !>          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
    !>          if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
    !>

    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 zlanhp (character norm, character uplo, integer n, complex*16, dimension( * ) ap, double precision, dimension( * ) work)

ZLANHP returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a complex Hermitian matrix supplied in packed form.

Purpose:

    !>
    !> ZLANHP  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 hermitian matrix A,  supplied in packed form.
    !>

Returns
    ZLANHP

    !>
    !>    ZLANHP = ( 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 ZLANHP as described
    !>          above.
    !>

    UPLO

    !>          UPLO is CHARACTER*1
    !>          Specifies whether the upper or lower triangular part of the
    !>          hermitian matrix A is supplied.
    !>          = 'U':  Upper triangular part of A is supplied
    !>          = 'L':  Lower triangular part of A is supplied
    !>

    N

    !>          N is INTEGER
    !>          The order of the matrix A.  N >= 0.  When N = 0, ZLANHP is
    !>          set to zero.
    !>

    AP

    !>          AP is COMPLEX*16 array, dimension (N*(N+1)/2)
    !>          The upper or lower triangle of the hermitian matrix A, packed
    !>          columnwise in a linear array.  The j-th column of A is stored
    !>          in the array AP as follows:
    !>          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
    !>          if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
    !>          Note that the  imaginary parts of the diagonal elements need
    !>          not be set and are assumed to be zero.
    !>

    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 zlansp (character norm, character uplo, integer n, complex*16, dimension( * ) ap, double precision, dimension( * ) work)

ZLANSP 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 matrix supplied in packed form.

Purpose:

    !>
    !> 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.
    !>

Returns
    ZLANSP

    !>
    !>    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
    NORM

    !>          NORM is CHARACTER*1
    !>          Specifies the value to be returned in ZLANSP as described
    !>          above.
    !>

    UPLO

    !>          UPLO is CHARACTER*1
    !>          Specifies whether the upper or lower triangular part of the
    !>          symmetric matrix A is supplied.
    !>          = 'U':  Upper triangular part of A is supplied
    !>          = 'L':  Lower triangular part of A is supplied
    !>

    N

    !>          N is INTEGER
    !>          The order of the matrix A.  N >= 0.  When N = 0, ZLANSP is
    !>          set to zero.
    !>

    AP

    !>          AP is COMPLEX*16 array, dimension (N*(N+1)/2)
    !>          The upper or lower triangle of the symmetric matrix A, packed
    !>          columnwise in a linear array.  The j-th column of A is stored
    !>          in the array AP as follows:
    !>          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
    !>          if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
    !>

    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.