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.

Definition at line 123 of file clanhe.f.

  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.

Definition at line 122 of file clansy.f.

  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.

Definition at line 121 of file dlansy.f.

  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.

Definition at line 121 of file slansy.f.

  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.

Definition at line 123 of file zlanhe.f.

  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.

Definition at line 122 of file zlansy.f.

Author

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