# lantr - Man Page

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.

## 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

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

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

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

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

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

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

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

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

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

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

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

NAG Ltd.

Definition at line 139 of file slantr.f.

### double precision function zlantr (character norm, character uplo, character diag, integer m, integer n, complex*16, 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

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

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

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