NAME

lanhs - lanhs: Hessenberg

SYNOPSIS

Functions

real function clanhs (norm, n, a, lda, work)
CLANHS returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of an upper Hessenberg matrix. double precision function dlanhs (norm, n, a, lda, work)
DLANHS returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of an upper Hessenberg matrix. real function slanhs (norm, n, a, lda, work)
SLANHS returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of an upper Hessenberg matrix. double precision function zlanhs (norm, n, a, lda, work)
ZLANHS returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of an upper Hessenberg matrix.

Detailed Description

Function Documentation

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

CLANHS returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of an upper Hessenberg matrix.

Purpose:



 CLANHS  returns the value of the one norm,  or the Frobenius norm, or


 the  infinity norm,  or the  element of  largest absolute value  of a


 Hessenberg matrix A.

Returns

CLANHS



    CLANHS = ( 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 CLANHS as described


          above.



          N is INTEGER


          The order of the matrix A.  N >= 0.  When N = 0, CLANHS is


          set to zero.



          A is COMPLEX array, dimension (LDA,N)


          The n by n upper Hessenberg matrix A; the part of A below the


          first sub-diagonal 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'; otherwise, WORK is not


          referenced.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 108 of file clanhs.f.

double precision function dlanhs (character norm, integer n, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) work)

DLANHS returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of an upper Hessenberg matrix.

Purpose:



 DLANHS  returns the value of the one norm,  or the Frobenius norm, or


 the  infinity norm,  or the  element of  largest absolute value  of a


 Hessenberg matrix A.

Returns

DLANHS



    DLANHS = ( 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 DLANHS as described


          above.



          N is INTEGER


          The order of the matrix A.  N >= 0.  When N = 0, DLANHS is


          set to zero.



          A is DOUBLE PRECISION array, dimension (LDA,N)


          The n by n upper Hessenberg matrix A; the part of A below the


          first sub-diagonal 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'; otherwise, WORK is not


          referenced.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 107 of file dlanhs.f.

real function slanhs (character norm, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( * ) work)

SLANHS returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of an upper Hessenberg matrix.

Purpose:



 SLANHS  returns the value of the one norm,  or the Frobenius norm, or


 the  infinity norm,  or the  element of  largest absolute value  of a


 Hessenberg matrix A.

Returns

SLANHS



    SLANHS = ( 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 SLANHS as described


          above.



          N is INTEGER


          The order of the matrix A.  N >= 0.  When N = 0, SLANHS is


          set to zero.



          A is REAL array, dimension (LDA,N)


          The n by n upper Hessenberg matrix A; the part of A below the


          first sub-diagonal 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'; otherwise, WORK is not


          referenced.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 107 of file slanhs.f.

double precision function zlanhs (character norm, integer n, complex16, dimension( lda, ) a, integer lda, double precision, dimension( * ) work)

ZLANHS returns the value of the 1-norm, Frobenius norm, infinity-norm, or the largest absolute value of any element of an upper Hessenberg matrix.

Purpose:



 ZLANHS  returns the value of the one norm,  or the Frobenius norm, or


 the  infinity norm,  or the  element of  largest absolute value  of a


 Hessenberg matrix A.

Returns

ZLANHS



    ZLANHS = ( 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 ZLANHS as described


          above.



          N is INTEGER


          The order of the matrix A.  N >= 0.  When N = 0, ZLANHS is


          set to zero.



          A is COMPLEX*16 array, dimension (LDA,N)


          The n by n upper Hessenberg matrix A; the part of A below the


          first sub-diagonal 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'; otherwise, WORK is not


          referenced.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 108 of file zlanhs.f.

Author

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