NAME

lantp - lantp: triangular matrix, packed

SYNOPSIS

Functions

real function clantp (norm, uplo, diag, n, ap, work)
CLANTP returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a triangular matrix supplied in packed form. double precision function dlantp (norm, uplo, diag, n, ap, work)
DLANTP returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a triangular matrix supplied in packed form. real function slantp (norm, uplo, diag, n, ap, work)
SLANTP returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a triangular matrix supplied in packed form. double precision function zlantp (norm, uplo, diag, n, ap, work)
ZLANTP returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a triangular matrix supplied in packed form.

Detailed Description

Function Documentation

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

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

Purpose:



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


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


 triangular matrix A, supplied in packed form.

Returns

CLANTP



    CLANTP = ( 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 CLANTP as described


          above.

UPLO



          UPLO is CHARACTER*1


          Specifies whether the matrix A is upper or lower triangular.


          = 'U':  Upper triangular


          = 'L':  Lower triangular

DIAG



          DIAG is CHARACTER*1


          Specifies whether or not the matrix A is unit triangular.


          = 'N':  Non-unit triangular


          = 'U':  Unit triangular



          N is INTEGER


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


          set to zero.



          AP is COMPLEX array, dimension (N*(N+1)/2)


          The upper or lower triangular 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 when DIAG = 'U', the elements of the array AP


          corresponding to the diagonal elements of the matrix A are


          not referenced, but are assumed to be one.

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 124 of file clantp.f.

double precision function dlantp (character norm, character uplo, character diag, integer n, double precision, dimension( * ) ap, double precision, dimension( * ) work)

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

Purpose:



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


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


 triangular matrix A, supplied in packed form.

Returns

DLANTP



    DLANTP = ( 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 DLANTP as described


          above.

UPLO



          UPLO is CHARACTER*1


          Specifies whether the matrix A is upper or lower triangular.


          = 'U':  Upper triangular


          = 'L':  Lower triangular

DIAG



          DIAG is CHARACTER*1


          Specifies whether or not the matrix A is unit triangular.


          = 'N':  Non-unit triangular


          = 'U':  Unit triangular



          N is INTEGER


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


          set to zero.



          AP is DOUBLE PRECISION array, dimension (N*(N+1)/2)


          The upper or lower triangular 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 when DIAG = 'U', the elements of the array AP


          corresponding to the diagonal elements of the matrix A are


          not referenced, but are assumed to be one.

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 123 of file dlantp.f.

real function slantp (character norm, character uplo, character diag, integer n, real, dimension( * ) ap, real, dimension( * ) work)

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

Purpose:



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


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


 triangular matrix A, supplied in packed form.

Returns

SLANTP



    SLANTP = ( 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 SLANTP as described


          above.

UPLO



          UPLO is CHARACTER*1


          Specifies whether the matrix A is upper or lower triangular.


          = 'U':  Upper triangular


          = 'L':  Lower triangular

DIAG



          DIAG is CHARACTER*1


          Specifies whether or not the matrix A is unit triangular.


          = 'N':  Non-unit triangular


          = 'U':  Unit triangular



          N is INTEGER


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


          set to zero.



          AP is REAL array, dimension (N*(N+1)/2)


          The upper or lower triangular 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 when DIAG = 'U', the elements of the array AP


          corresponding to the diagonal elements of the matrix A are


          not referenced, but are assumed to be one.

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 123 of file slantp.f.

double precision function zlantp (character norm, character uplo, character diag, integer n, complex16, dimension( ) ap, double precision, dimension( * ) work)

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

Purpose:



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


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


 triangular matrix A, supplied in packed form.

Returns

ZLANTP



    ZLANTP = ( 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 ZLANTP as described


          above.

UPLO



          UPLO is CHARACTER*1


          Specifies whether the matrix A is upper or lower triangular.


          = 'U':  Upper triangular


          = 'L':  Lower triangular

DIAG



          DIAG is CHARACTER*1


          Specifies whether or not the matrix A is unit triangular.


          = 'N':  Non-unit triangular


          = 'U':  Unit triangular



          N is INTEGER


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


          set to zero.



          AP is COMPLEX*16 array, dimension (N*(N+1)/2)


          The upper or lower triangular 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 when DIAG = 'U', the elements of the array AP


          corresponding to the diagonal elements of the matrix A are


          not referenced, but are assumed to be one.

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 124 of file zlantp.f.

Author

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