lantb - Man Page

lantb: triangular matrix, banded

Synopsis

Functions

real function clantb (norm, uplo, diag, n, k, ab, ldab, work)
CLANTB 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 band matrix.
double precision function dlantb (norm, uplo, diag, n, k, ab, ldab, work)
DLANTB 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 band matrix.
real function slantb (norm, uplo, diag, n, k, ab, ldab, work)
SLANTB 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 band matrix.
double precision function zlantb (norm, uplo, diag, n, k, ab, ldab, work)
ZLANTB 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 band matrix.

Detailed Description

Function Documentation

real function clantb (character norm, character uplo, character diag, integer n, integer k, complex, dimension( ldab, * ) ab, integer ldab, real, dimension( * ) work)

CLANTB 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 band matrix.  

Purpose:

 CLANTB  returns the value of the one norm,  or the Frobenius norm, or
 the  infinity norm,  or the element of  largest absolute value  of an
 n by n triangular band matrix A,  with ( k + 1 ) diagonals.
Returns

CLANTB 

    CLANTB = ( 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 CLANTB 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

          N is INTEGER
          The order of the matrix A.  N >= 0.  When N = 0, CLANTB is
          set to zero.

K

          K is INTEGER
          The number of super-diagonals of the matrix A if UPLO = 'U',
          or the number of sub-diagonals of the matrix A if UPLO = 'L'.
          K >= 0.

AB

          AB is COMPLEX array, dimension (LDAB,N)
          The upper or lower triangular band matrix A, stored in the
          first k+1 rows of AB.  The j-th column of A is stored
          in the j-th column of the array AB as follows:
          if UPLO = 'U', AB(k+1+i-j,j) = A(i,j) for max(1,j-k)<=i<=j;
          if UPLO = 'L', AB(1+i-j,j)   = A(i,j) for j<=i<=min(n,j+k).
          Note that when DIAG = 'U', the elements of the array AB
          corresponding to the diagonal elements of the matrix A are
          not referenced, but are assumed to be one.

LDAB

          LDAB is INTEGER
          The leading dimension of the array AB.  LDAB >= K+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 139 of file clantb.f.

double precision function dlantb (character norm, character uplo, character diag, integer n, integer k, double precision, dimension( ldab, * ) ab, integer ldab, double precision, dimension( * ) work)

DLANTB 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 band matrix.  

Purpose:

 DLANTB  returns the value of the one norm,  or the Frobenius norm, or
 the  infinity norm,  or the element of  largest absolute value  of an
 n by n triangular band matrix A,  with ( k + 1 ) diagonals.
Returns

DLANTB 

    DLANTB = ( 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 DLANTB 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

          N is INTEGER
          The order of the matrix A.  N >= 0.  When N = 0, DLANTB is
          set to zero.

K

          K is INTEGER
          The number of super-diagonals of the matrix A if UPLO = 'U',
          or the number of sub-diagonals of the matrix A if UPLO = 'L'.
          K >= 0.

AB

          AB is DOUBLE PRECISION array, dimension (LDAB,N)
          The upper or lower triangular band matrix A, stored in the
          first k+1 rows of AB.  The j-th column of A is stored
          in the j-th column of the array AB as follows:
          if UPLO = 'U', AB(k+1+i-j,j) = A(i,j) for max(1,j-k)<=i<=j;
          if UPLO = 'L', AB(1+i-j,j)   = A(i,j) for j<=i<=min(n,j+k).
          Note that when DIAG = 'U', the elements of the array AB
          corresponding to the diagonal elements of the matrix A are
          not referenced, but are assumed to be one.

LDAB

          LDAB is INTEGER
          The leading dimension of the array AB.  LDAB >= K+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 138 of file dlantb.f.

real function slantb (character norm, character uplo, character diag, integer n, integer k, real, dimension( ldab, * ) ab, integer ldab, real, dimension( * ) work)

SLANTB 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 band matrix.  

Purpose:

 SLANTB  returns the value of the one norm,  or the Frobenius norm, or
 the  infinity norm,  or the element of  largest absolute value  of an
 n by n triangular band matrix A,  with ( k + 1 ) diagonals.
Returns

SLANTB 

    SLANTB = ( 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 SLANTB 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

          N is INTEGER
          The order of the matrix A.  N >= 0.  When N = 0, SLANTB is
          set to zero.

K

          K is INTEGER
          The number of super-diagonals of the matrix A if UPLO = 'U',
          or the number of sub-diagonals of the matrix A if UPLO = 'L'.
          K >= 0.

AB

          AB is REAL array, dimension (LDAB,N)
          The upper or lower triangular band matrix A, stored in the
          first k+1 rows of AB.  The j-th column of A is stored
          in the j-th column of the array AB as follows:
          if UPLO = 'U', AB(k+1+i-j,j) = A(i,j) for max(1,j-k)<=i<=j;
          if UPLO = 'L', AB(1+i-j,j)   = A(i,j) for j<=i<=min(n,j+k).
          Note that when DIAG = 'U', the elements of the array AB
          corresponding to the diagonal elements of the matrix A are
          not referenced, but are assumed to be one.

LDAB

          LDAB is INTEGER
          The leading dimension of the array AB.  LDAB >= K+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 138 of file slantb.f.

double precision function zlantb (character norm, character uplo, character diag, integer n, integer k, complex*16, dimension( ldab, * ) ab, integer ldab, double precision, dimension( * ) work)

ZLANTB 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 band matrix.  

Purpose:

 ZLANTB  returns the value of the one norm,  or the Frobenius norm, or
 the  infinity norm,  or the element of  largest absolute value  of an
 n by n triangular band matrix A,  with ( k + 1 ) diagonals.
Returns

ZLANTB 

    ZLANTB = ( 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 ZLANTB 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

          N is INTEGER
          The order of the matrix A.  N >= 0.  When N = 0, ZLANTB is
          set to zero.

K

          K is INTEGER
          The number of super-diagonals of the matrix A if UPLO = 'U',
          or the number of sub-diagonals of the matrix A if UPLO = 'L'.
          K >= 0.

AB

          AB is COMPLEX*16 array, dimension (LDAB,N)
          The upper or lower triangular band matrix A, stored in the
          first k+1 rows of AB.  The j-th column of A is stored
          in the j-th column of the array AB as follows:
          if UPLO = 'U', AB(k+1+i-j,j) = A(i,j) for max(1,j-k)<=i<=j;
          if UPLO = 'L', AB(1+i-j,j)   = A(i,j) for j<=i<=min(n,j+k).
          Note that when DIAG = 'U', the elements of the array AB
          corresponding to the diagonal elements of the matrix A are
          not referenced, but are assumed to be one.

LDAB

          LDAB is INTEGER
          The leading dimension of the array AB.  LDAB >= K+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 139 of file zlantb.f.

Author

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Tue Nov 28 2023 12:08:43 Version 3.12.0 LAPACK