.TH "lanhb" 3 "Wed Feb 7 2024 11:30:40" "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
lanhb \- lan{hb,sb}: Hermitian/symmetric matrix, banded
.SH SYNOPSIS
.br
.PP
.SS "Functions"

.in +1c
.ti -1c
.RI "real function \fBclanhb\fP (norm, uplo, n, k, ab, ldab, work)"
.br
.RI "\fBCLANHB\fP returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a Hermitian band matrix\&. "
.ti -1c
.RI "real function \fBclansb\fP (norm, uplo, n, k, ab, ldab, work)"
.br
.RI "\fBCLANSB\fP returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a symmetric band matrix\&. "
.ti -1c
.RI "double precision function \fBdlansb\fP (norm, uplo, n, k, ab, ldab, work)"
.br
.RI "\fBDLANSB\fP returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a symmetric band matrix\&. "
.ti -1c
.RI "real function \fBslansb\fP (norm, uplo, n, k, ab, ldab, work)"
.br
.RI "\fBSLANSB\fP returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a symmetric band matrix\&. "
.ti -1c
.RI "double precision function \fBzlanhb\fP (norm, uplo, n, k, ab, ldab, work)"
.br
.RI "\fBZLANHB\fP returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a Hermitian band matrix\&. "
.ti -1c
.RI "double precision function \fBzlansb\fP (norm, uplo, n, k, ab, ldab, work)"
.br
.RI "\fBZLANSB\fP returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a symmetric band matrix\&. "
.in -1c
.SH "Detailed Description"
.PP 

.SH "Function Documentation"
.PP 
.SS "real function clanhb (character norm, character uplo, integer n, integer k, complex, dimension( ldab, * ) ab, integer ldab, real, dimension( * ) work)"

.PP
\fBCLANHB\fP returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a Hermitian band matrix\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 CLANHB  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 hermitian band matrix A,  with k super-diagonals\&.
.fi
.PP
.RE
.PP
\fBReturns\fP
.RS 4
CLANHB 
.PP
.nf
    CLANHB = ( 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\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fINORM\fP 
.PP
.nf
          NORM is CHARACTER*1
          Specifies the value to be returned in CLANHB as described
          above\&.
.fi
.PP
.br
\fIUPLO\fP 
.PP
.nf
          UPLO is CHARACTER*1
          Specifies whether the upper or lower triangular part of the
          band matrix A is supplied\&.
          = 'U':  Upper triangular
          = 'L':  Lower triangular
.fi
.PP
.br
\fIN\fP 
.PP
.nf
          N is INTEGER
          The order of the matrix A\&.  N >= 0\&.  When N = 0, CLANHB is
          set to zero\&.
.fi
.PP
.br
\fIK\fP 
.PP
.nf
          K is INTEGER
          The number of super-diagonals or sub-diagonals of the
          band matrix A\&.  K >= 0\&.
.fi
.PP
.br
\fIAB\fP 
.PP
.nf
          AB is COMPLEX array, dimension (LDAB,N)
          The upper or lower triangle of the hermitian 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 the imaginary parts of the diagonal elements need
          not be set and are assumed to be zero\&.
.fi
.PP
.br
\fILDAB\fP 
.PP
.nf
          LDAB is INTEGER
          The leading dimension of the array AB\&.  LDAB >= K+1\&.
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
          WORK is REAL array, dimension (MAX(1,LWORK)),
          where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,
          WORK is not referenced\&.
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 
.PP
Univ\&. of California Berkeley 
.PP
Univ\&. of Colorado Denver 
.PP
NAG Ltd\&. 
.RE
.PP

.SS "real function clansb (character norm, character uplo, integer n, integer k, complex, dimension( ldab, * ) ab, integer ldab, real, dimension( * ) work)"

.PP
\fBCLANSB\fP returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a symmetric band matrix\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 CLANSB  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 symmetric band matrix A,  with k super-diagonals\&.
.fi
.PP
.RE
.PP
\fBReturns\fP
.RS 4
CLANSB 
.PP
.nf
    CLANSB = ( 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\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fINORM\fP 
.PP
.nf
          NORM is CHARACTER*1
          Specifies the value to be returned in CLANSB as described
          above\&.
.fi
.PP
.br
\fIUPLO\fP 
.PP
.nf
          UPLO is CHARACTER*1
          Specifies whether the upper or lower triangular part of the
          band matrix A is supplied\&.
          = 'U':  Upper triangular part is supplied
          = 'L':  Lower triangular part is supplied
.fi
.PP
.br
\fIN\fP 
.PP
.nf
          N is INTEGER
          The order of the matrix A\&.  N >= 0\&.  When N = 0, CLANSB is
          set to zero\&.
.fi
.PP
.br
\fIK\fP 
.PP
.nf
          K is INTEGER
          The number of super-diagonals or sub-diagonals of the
          band matrix A\&.  K >= 0\&.
.fi
.PP
.br
\fIAB\fP 
.PP
.nf
          AB is COMPLEX array, dimension (LDAB,N)
          The upper or lower triangle of the symmetric 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)\&.
.fi
.PP
.br
\fILDAB\fP 
.PP
.nf
          LDAB is INTEGER
          The leading dimension of the array AB\&.  LDAB >= K+1\&.
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
          WORK is REAL array, dimension (MAX(1,LWORK)),
          where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,
          WORK is not referenced\&.
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 
.PP
Univ\&. of California Berkeley 
.PP
Univ\&. of Colorado Denver 
.PP
NAG Ltd\&. 
.RE
.PP

.SS "double precision function dlansb (character norm, character uplo, integer n, integer k, double precision, dimension( ldab, * ) ab, integer ldab, double precision, dimension( * ) work)"

.PP
\fBDLANSB\fP returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a symmetric band matrix\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 DLANSB  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 symmetric band matrix A,  with k super-diagonals\&.
.fi
.PP
.RE
.PP
\fBReturns\fP
.RS 4
DLANSB 
.PP
.nf
    DLANSB = ( 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\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fINORM\fP 
.PP
.nf
          NORM is CHARACTER*1
          Specifies the value to be returned in DLANSB as described
          above\&.
.fi
.PP
.br
\fIUPLO\fP 
.PP
.nf
          UPLO is CHARACTER*1
          Specifies whether the upper or lower triangular part of the
          band matrix A is supplied\&.
          = 'U':  Upper triangular part is supplied
          = 'L':  Lower triangular part is supplied
.fi
.PP
.br
\fIN\fP 
.PP
.nf
          N is INTEGER
          The order of the matrix A\&.  N >= 0\&.  When N = 0, DLANSB is
          set to zero\&.
.fi
.PP
.br
\fIK\fP 
.PP
.nf
          K is INTEGER
          The number of super-diagonals or sub-diagonals of the
          band matrix A\&.  K >= 0\&.
.fi
.PP
.br
\fIAB\fP 
.PP
.nf
          AB is DOUBLE PRECISION array, dimension (LDAB,N)
          The upper or lower triangle of the symmetric 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)\&.
.fi
.PP
.br
\fILDAB\fP 
.PP
.nf
          LDAB is INTEGER
          The leading dimension of the array AB\&.  LDAB >= K+1\&.
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
          WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
          where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,
          WORK is not referenced\&.
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 
.PP
Univ\&. of California Berkeley 
.PP
Univ\&. of Colorado Denver 
.PP
NAG Ltd\&. 
.RE
.PP

.SS "real function slansb (character norm, character uplo, integer n, integer k, real, dimension( ldab, * ) ab, integer ldab, real, dimension( * ) work)"

.PP
\fBSLANSB\fP returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a symmetric band matrix\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 SLANSB  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 symmetric band matrix A,  with k super-diagonals\&.
.fi
.PP
.RE
.PP
\fBReturns\fP
.RS 4
SLANSB 
.PP
.nf
    SLANSB = ( 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\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fINORM\fP 
.PP
.nf
          NORM is CHARACTER*1
          Specifies the value to be returned in SLANSB as described
          above\&.
.fi
.PP
.br
\fIUPLO\fP 
.PP
.nf
          UPLO is CHARACTER*1
          Specifies whether the upper or lower triangular part of the
          band matrix A is supplied\&.
          = 'U':  Upper triangular part is supplied
          = 'L':  Lower triangular part is supplied
.fi
.PP
.br
\fIN\fP 
.PP
.nf
          N is INTEGER
          The order of the matrix A\&.  N >= 0\&.  When N = 0, SLANSB is
          set to zero\&.
.fi
.PP
.br
\fIK\fP 
.PP
.nf
          K is INTEGER
          The number of super-diagonals or sub-diagonals of the
          band matrix A\&.  K >= 0\&.
.fi
.PP
.br
\fIAB\fP 
.PP
.nf
          AB is REAL array, dimension (LDAB,N)
          The upper or lower triangle of the symmetric 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)\&.
.fi
.PP
.br
\fILDAB\fP 
.PP
.nf
          LDAB is INTEGER
          The leading dimension of the array AB\&.  LDAB >= K+1\&.
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
          WORK is REAL array, dimension (MAX(1,LWORK)),
          where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,
          WORK is not referenced\&.
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 
.PP
Univ\&. of California Berkeley 
.PP
Univ\&. of Colorado Denver 
.PP
NAG Ltd\&. 
.RE
.PP

.SS "double precision function zlanhb (character norm, character uplo, integer n, integer k, complex*16, dimension( ldab, * ) ab, integer ldab, double precision, dimension( * ) work)"

.PP
\fBZLANHB\fP returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a Hermitian band matrix\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 ZLANHB  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 hermitian band matrix A,  with k super-diagonals\&.
.fi
.PP
.RE
.PP
\fBReturns\fP
.RS 4
ZLANHB 
.PP
.nf
    ZLANHB = ( 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\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fINORM\fP 
.PP
.nf
          NORM is CHARACTER*1
          Specifies the value to be returned in ZLANHB as described
          above\&.
.fi
.PP
.br
\fIUPLO\fP 
.PP
.nf
          UPLO is CHARACTER*1
          Specifies whether the upper or lower triangular part of the
          band matrix A is supplied\&.
          = 'U':  Upper triangular
          = 'L':  Lower triangular
.fi
.PP
.br
\fIN\fP 
.PP
.nf
          N is INTEGER
          The order of the matrix A\&.  N >= 0\&.  When N = 0, ZLANHB is
          set to zero\&.
.fi
.PP
.br
\fIK\fP 
.PP
.nf
          K is INTEGER
          The number of super-diagonals or sub-diagonals of the
          band matrix A\&.  K >= 0\&.
.fi
.PP
.br
\fIAB\fP 
.PP
.nf
          AB is COMPLEX*16 array, dimension (LDAB,N)
          The upper or lower triangle of the hermitian 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 the imaginary parts of the diagonal elements need
          not be set and are assumed to be zero\&.
.fi
.PP
.br
\fILDAB\fP 
.PP
.nf
          LDAB is INTEGER
          The leading dimension of the array AB\&.  LDAB >= K+1\&.
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
          WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
          where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,
          WORK is not referenced\&.
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 
.PP
Univ\&. of California Berkeley 
.PP
Univ\&. of Colorado Denver 
.PP
NAG Ltd\&. 
.RE
.PP

.SS "double precision function zlansb (character norm, character uplo, integer n, integer k, complex*16, dimension( ldab, * ) ab, integer ldab, double precision, dimension( * ) work)"

.PP
\fBZLANSB\fP returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a symmetric band matrix\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 ZLANSB  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 symmetric band matrix A,  with k super-diagonals\&.
.fi
.PP
.RE
.PP
\fBReturns\fP
.RS 4
ZLANSB 
.PP
.nf
    ZLANSB = ( 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\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fINORM\fP 
.PP
.nf
          NORM is CHARACTER*1
          Specifies the value to be returned in ZLANSB as described
          above\&.
.fi
.PP
.br
\fIUPLO\fP 
.PP
.nf
          UPLO is CHARACTER*1
          Specifies whether the upper or lower triangular part of the
          band matrix A is supplied\&.
          = 'U':  Upper triangular part is supplied
          = 'L':  Lower triangular part is supplied
.fi
.PP
.br
\fIN\fP 
.PP
.nf
          N is INTEGER
          The order of the matrix A\&.  N >= 0\&.  When N = 0, ZLANSB is
          set to zero\&.
.fi
.PP
.br
\fIK\fP 
.PP
.nf
          K is INTEGER
          The number of super-diagonals or sub-diagonals of the
          band matrix A\&.  K >= 0\&.
.fi
.PP
.br
\fIAB\fP 
.PP
.nf
          AB is COMPLEX*16 array, dimension (LDAB,N)
          The upper or lower triangle of the symmetric 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)\&.
.fi
.PP
.br
\fILDAB\fP 
.PP
.nf
          LDAB is INTEGER
          The leading dimension of the array AB\&.  LDAB >= K+1\&.
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
          WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)),
          where LWORK >= N when NORM = 'I' or '1' or 'O'; otherwise,
          WORK is not referenced\&.
.fi
.PP
 
.RE
.PP
\fBAuthor\fP
.RS 4
Univ\&. of Tennessee 
.PP
Univ\&. of California Berkeley 
.PP
Univ\&. of Colorado Denver 
.PP
NAG Ltd\&. 
.RE
.PP

.SH "Author"
.PP 
Generated automatically by Doxygen for LAPACK from the source code\&.