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lanhp(3) LAPACK 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

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