NAME

lantr - lantr: triangular matrix

SYNOPSIS

Functions

real function clantr (norm, uplo, diag, m, n, a, lda, work)
CLANTR returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a trapezoidal or triangular matrix. double precision function dlantr (norm, uplo, diag, m, n, a, lda, work)
DLANTR returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a trapezoidal or triangular matrix. real function slantr (norm, uplo, diag, m, n, a, lda, work)
SLANTR returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a trapezoidal or triangular matrix. double precision function zlantr (norm, uplo, diag, m, n, a, lda, work)
ZLANTR returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a trapezoidal or triangular matrix.

Detailed Description

Function Documentation

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

CLANTR returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a trapezoidal or triangular matrix.

Purpose:



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


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


 trapezoidal or triangular matrix A.

Returns

CLANTR



    CLANTR = ( 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 CLANTR as described


          above.

UPLO



          UPLO is CHARACTER*1


          Specifies whether the matrix A is upper or lower trapezoidal.


          = 'U':  Upper trapezoidal


          = 'L':  Lower trapezoidal


          Note that A is triangular instead of trapezoidal if M = N.

DIAG



          DIAG is CHARACTER*1


          Specifies whether or not the matrix A has unit diagonal.


          = 'N':  Non-unit diagonal


          = 'U':  Unit diagonal



          M is INTEGER


          The number of rows of the matrix A.  M >= 0, and if


          UPLO = 'U', M <= N.  When M = 0, CLANTR is set to zero.



          N is INTEGER


          The number of columns of the matrix A.  N >= 0, and if


          UPLO = 'L', N <= M.  When N = 0, CLANTR is set to zero.



          A is COMPLEX array, dimension (LDA,N)


          The trapezoidal matrix A (A is triangular if M = N).


          If UPLO = 'U', the leading m by n upper trapezoidal part of


          the array A contains the upper trapezoidal matrix, and the


          strictly lower triangular part of A is not referenced.


          If UPLO = 'L', the leading m by n lower trapezoidal part of


          the array A contains the lower trapezoidal matrix, and the


          strictly upper triangular part of A is not referenced.  Note


          that when DIAG = 'U', the diagonal elements of A are not


          referenced and are assumed to be one.

LDA



          LDA is INTEGER


          The leading dimension of the array A.  LDA >= max(M,1).

WORK



          WORK is REAL array, dimension (MAX(1,LWORK)),


          where LWORK >= M 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 140 of file clantr.f.

double precision function dlantr (character norm, character uplo, character diag, integer m, integer n, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) work)

DLANTR returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a trapezoidal or triangular matrix.

Purpose:



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


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


 trapezoidal or triangular matrix A.

Returns

DLANTR



    DLANTR = ( 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 DLANTR as described


          above.

UPLO



          UPLO is CHARACTER*1


          Specifies whether the matrix A is upper or lower trapezoidal.


          = 'U':  Upper trapezoidal


          = 'L':  Lower trapezoidal


          Note that A is triangular instead of trapezoidal if M = N.

DIAG



          DIAG is CHARACTER*1


          Specifies whether or not the matrix A has unit diagonal.


          = 'N':  Non-unit diagonal


          = 'U':  Unit diagonal



          M is INTEGER


          The number of rows of the matrix A.  M >= 0, and if


          UPLO = 'U', M <= N.  When M = 0, DLANTR is set to zero.



          N is INTEGER


          The number of columns of the matrix A.  N >= 0, and if


          UPLO = 'L', N <= M.  When N = 0, DLANTR is set to zero.



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


          The trapezoidal matrix A (A is triangular if M = N).


          If UPLO = 'U', the leading m by n upper trapezoidal part of


          the array A contains the upper trapezoidal matrix, and the


          strictly lower triangular part of A is not referenced.


          If UPLO = 'L', the leading m by n lower trapezoidal part of


          the array A contains the lower trapezoidal matrix, and the


          strictly upper triangular part of A is not referenced.  Note


          that when DIAG = 'U', the diagonal elements of A are not


          referenced and are assumed to be one.

LDA



          LDA is INTEGER


          The leading dimension of the array A.  LDA >= max(M,1).

WORK



          WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)),


          where LWORK >= M 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 139 of file dlantr.f.

real function slantr (character norm, character uplo, character diag, integer m, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( * ) work)

SLANTR returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a trapezoidal or triangular matrix.

Purpose:



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


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


 trapezoidal or triangular matrix A.

Returns

SLANTR



    SLANTR = ( 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 SLANTR as described


          above.

UPLO



          UPLO is CHARACTER*1


          Specifies whether the matrix A is upper or lower trapezoidal.


          = 'U':  Upper trapezoidal


          = 'L':  Lower trapezoidal


          Note that A is triangular instead of trapezoidal if M = N.

DIAG



          DIAG is CHARACTER*1


          Specifies whether or not the matrix A has unit diagonal.


          = 'N':  Non-unit diagonal


          = 'U':  Unit diagonal



          M is INTEGER


          The number of rows of the matrix A.  M >= 0, and if


          UPLO = 'U', M <= N.  When M = 0, SLANTR is set to zero.



          N is INTEGER


          The number of columns of the matrix A.  N >= 0, and if


          UPLO = 'L', N <= M.  When N = 0, SLANTR is set to zero.



          A is REAL array, dimension (LDA,N)


          The trapezoidal matrix A (A is triangular if M = N).


          If UPLO = 'U', the leading m by n upper trapezoidal part of


          the array A contains the upper trapezoidal matrix, and the


          strictly lower triangular part of A is not referenced.


          If UPLO = 'L', the leading m by n lower trapezoidal part of


          the array A contains the lower trapezoidal matrix, and the


          strictly upper triangular part of A is not referenced.  Note


          that when DIAG = 'U', the diagonal elements of A are not


          referenced and are assumed to be one.

LDA



          LDA is INTEGER


          The leading dimension of the array A.  LDA >= max(M,1).

WORK



          WORK is REAL array, dimension (MAX(1,LWORK)),


          where LWORK >= M 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 139 of file slantr.f.

double precision function zlantr (character norm, character uplo, character diag, integer m, integer n, complex16, dimension( lda, ) a, integer lda, double precision, dimension( * ) work)

ZLANTR returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a trapezoidal or triangular matrix.

Purpose:



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


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


 trapezoidal or triangular matrix A.

Returns

ZLANTR



    ZLANTR = ( 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 ZLANTR as described


          above.

UPLO



          UPLO is CHARACTER*1


          Specifies whether the matrix A is upper or lower trapezoidal.


          = 'U':  Upper trapezoidal


          = 'L':  Lower trapezoidal


          Note that A is triangular instead of trapezoidal if M = N.

DIAG



          DIAG is CHARACTER*1


          Specifies whether or not the matrix A has unit diagonal.


          = 'N':  Non-unit diagonal


          = 'U':  Unit diagonal



          M is INTEGER


          The number of rows of the matrix A.  M >= 0, and if


          UPLO = 'U', M <= N.  When M = 0, ZLANTR is set to zero.



          N is INTEGER


          The number of columns of the matrix A.  N >= 0, and if


          UPLO = 'L', N <= M.  When N = 0, ZLANTR is set to zero.



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


          The trapezoidal matrix A (A is triangular if M = N).


          If UPLO = 'U', the leading m by n upper trapezoidal part of


          the array A contains the upper trapezoidal matrix, and the


          strictly lower triangular part of A is not referenced.


          If UPLO = 'L', the leading m by n lower trapezoidal part of


          the array A contains the lower trapezoidal matrix, and the


          strictly upper triangular part of A is not referenced.  Note


          that when DIAG = 'U', the diagonal elements of A are not


          referenced and are assumed to be one.

LDA



          LDA is INTEGER


          The leading dimension of the array A.  LDA >= max(M,1).

WORK



          WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)),


          where LWORK >= M 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 140 of file zlantr.f.

Author

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