lanhe(3)

NAME
lanhe - lan{he,sy}: Hermitian/symmetric matrix

SYNOPSIS

  Functions

real function clanhe (norm, uplo, n, a, lda, work)
CLANHE 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.
real function clansy (norm, uplo, n, a, lda, work)
CLANSY 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 symmetric matrix.
double precision function dlansy (norm, uplo, n, a, lda, work)
DLANSY returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric matrix.
real function slansy (norm, uplo, n, a, lda, work)
SLANSY returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric matrix.
double precision function zlanhe (norm, uplo, n, a, lda, work)
ZLANHE 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.
double precision function zlansy (norm, uplo, n, a, lda, work)
ZLANSY 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 symmetric matrix.

Detailed Description

Function Documentation

  real function clanhe (character norm, character uplo, integer n, complex, dimension( lda, * ) a, integer lda, real, dimension( * ) work)

CLANHE 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.

Purpose:

    !>
    !> CLANHE  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.
    !>

Returns
    CLANHE

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

    UPLO

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

    N

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

    A

    !>          A is COMPLEX array, dimension (LDA,N)
    !>          The hermitian matrix A.  If UPLO = 'U', the leading n by n
    !>          upper triangular part of A contains the upper triangular part
    !>          of the matrix A, and the strictly lower triangular part of A
    !>          is not referenced.  If UPLO = 'L', the leading n by n lower
    !>          triangular part of A contains the lower triangular part of
    !>          the matrix A, and the strictly upper triangular part of A is
    !>          not referenced. Note that the imaginary parts of the diagonal
    !>          elements need not be set and are assumed to be zero.
    !>

    LDA

    !>          LDA is INTEGER
    !>          The leading dimension of the array A.  LDA >= max(N,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 clansy (character norm, character uplo, integer n, complex, dimension( lda, * ) a, integer lda, real, dimension( * ) work)

CLANSY 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 symmetric matrix.

Purpose:

    !>
    !> CLANSY  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.
    !>

Returns
    CLANSY

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

    UPLO

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

    N

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

    A

    !>          A is COMPLEX array, dimension (LDA,N)
    !>          The symmetric matrix A.  If UPLO = 'U', the leading n by n
    !>          upper triangular part of A contains the upper triangular part
    !>          of the matrix A, and the strictly lower triangular part of A
    !>          is not referenced.  If UPLO = 'L', the leading n by n lower
    !>          triangular part of A contains the lower triangular part of
    !>          the matrix A, and the strictly upper triangular part of A is
    !>          not referenced.
    !>

    LDA

    !>          LDA is INTEGER
    !>          The leading dimension of the array A.  LDA >= max(N,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 dlansy (character norm, character uplo, integer n, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) work)

DLANSY returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric matrix.

Purpose:

    !>
    !> DLANSY  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.
    !>

Returns
    DLANSY

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

    UPLO

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

    N

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

    A

    !>          A is DOUBLE PRECISION array, dimension (LDA,N)
    !>          The symmetric matrix A.  If UPLO = 'U', the leading n by n
    !>          upper triangular part of A contains the upper triangular part
    !>          of the matrix A, and the strictly lower triangular part of A
    !>          is not referenced.  If UPLO = 'L', the leading n by n lower
    !>          triangular part of A contains the lower triangular part of
    !>          the matrix A, and the strictly upper triangular part of A is
    !>          not referenced.
    !>

    LDA

    !>          LDA is INTEGER
    !>          The leading dimension of the array A.  LDA >= max(N,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 slansy (character norm, character uplo, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( * ) work)

SLANSY returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a real symmetric matrix.

Purpose:

    !>
    !> SLANSY  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.
    !>

Returns
    SLANSY

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

    UPLO

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

    N

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

    A

    !>          A is REAL array, dimension (LDA,N)
    !>          The symmetric matrix A.  If UPLO = 'U', the leading n by n
    !>          upper triangular part of A contains the upper triangular part
    !>          of the matrix A, and the strictly lower triangular part of A
    !>          is not referenced.  If UPLO = 'L', the leading n by n lower
    !>          triangular part of A contains the lower triangular part of
    !>          the matrix A, and the strictly upper triangular part of A is
    !>          not referenced.
    !>

    LDA

    !>          LDA is INTEGER
    !>          The leading dimension of the array A.  LDA >= max(N,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 zlanhe (character norm, character uplo, integer n, complex*16, dimension( lda, * ) a, integer lda, double precision, dimension( * ) work)

ZLANHE 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.

Purpose:

    !>
    !> ZLANHE  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.
    !>

Returns
    ZLANHE

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

    UPLO

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

    N

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

    A

    !>          A is COMPLEX*16 array, dimension (LDA,N)
    !>          The hermitian matrix A.  If UPLO = 'U', the leading n by n
    !>          upper triangular part of A contains the upper triangular part
    !>          of the matrix A, and the strictly lower triangular part of A
    !>          is not referenced.  If UPLO = 'L', the leading n by n lower
    !>          triangular part of A contains the lower triangular part of
    !>          the matrix A, and the strictly upper triangular part of A is
    !>          not referenced. Note that the imaginary parts of the diagonal
    !>          elements need not be set and are assumed to be zero.
    !>

    LDA

    !>          LDA is INTEGER
    !>          The leading dimension of the array A.  LDA >= max(N,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 zlansy (character norm, character uplo, integer n, complex*16, dimension( lda, * ) a, integer lda, double precision, dimension( * ) work)

ZLANSY 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 symmetric matrix.

Purpose:

    !>
    !> ZLANSY  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.
    !>

Returns
    ZLANSY

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

    UPLO

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

    N

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

    A

    !>          A is COMPLEX*16 array, dimension (LDA,N)
    !>          The symmetric matrix A.  If UPLO = 'U', the leading n by n
    !>          upper triangular part of A contains the upper triangular part
    !>          of the matrix A, and the strictly lower triangular part of A
    !>          is not referenced.  If UPLO = 'L', the leading n by n lower
    !>          triangular part of A contains the lower triangular part of
    !>          the matrix A, and the strictly upper triangular part of A is
    !>          not referenced.
    !>

    LDA

    !>          LDA is INTEGER
    !>          The leading dimension of the array A.  LDA >= max(N,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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