LAPACK  3.4.2
LAPACK: Linear Algebra PACKage
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slantr.f File Reference

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Functions/Subroutines

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.

Function/Subroutine Documentation

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.

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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:
[in]NORM
          NORM is CHARACTER*1
          Specifies the value to be returned in SLANTR as described
          above.
[in]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.
[in]DIAG
          DIAG is CHARACTER*1
          Specifies whether or not the matrix A has unit diagonal.
          = 'N':  Non-unit diagonal
          = 'U':  Unit diagonal
[in]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.
[in]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.
[in]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.
[in]LDA
          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(M,1).
[out]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.
Date:
September 2012

Definition at line 141 of file slantr.f.

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