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

.in +1c
.ti -1c
.RI "real function \fBclanhe\fP (norm, uplo, n, a, lda, work)"
.br
.RI "\fBCLANHE\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 complex Hermitian matrix\&. "
.ti -1c
.RI "real function \fBclansy\fP (norm, uplo, n, a, lda, work)"
.br
.RI "\fBCLANSY\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 complex symmetric matrix\&. "
.ti -1c
.RI "double precision function \fBdlansy\fP (norm, uplo, n, a, lda, work)"
.br
.RI "\fBDLANSY\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 real symmetric matrix\&. "
.ti -1c
.RI "real function \fBslansy\fP (norm, uplo, n, a, lda, work)"
.br
.RI "\fBSLANSY\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 real symmetric matrix\&. "
.ti -1c
.RI "double precision function \fBzlanhe\fP (norm, uplo, n, a, lda, work)"
.br
.RI "\fBZLANHE\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 complex Hermitian matrix\&. "
.ti -1c
.RI "double precision function \fBzlansy\fP (norm, uplo, n, a, lda, work)"
.br
.RI "\fBZLANSY\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 complex symmetric matrix\&. "
.in -1c
.SH "Detailed Description"
.PP 

.SH "Function Documentation"
.PP 
.SS "real function clanhe (character norm, character uplo, integer n, complex, dimension( lda, * ) a, integer lda, real, dimension( * ) work)"

.PP
\fBCLANHE\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 complex Hermitian matrix\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 CLANHE  returns the value of the one norm,  or the Frobenius norm, or
 the  infinity norm,  or the  element of  largest absolute value  of a
 complex hermitian matrix A\&.
.fi
.PP
.RE
.PP
\fBReturns\fP
.RS 4
CLANHE 
.PP
.nf
    CLANHE = ( 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 CLANHE as described
          above\&.
.fi
.PP
.br
\fIUPLO\fP 
.PP
.nf
          UPLO is CHARACTER*1
          Specifies whether the upper or lower triangular part of the
          hermitian matrix A is to be referenced\&.
          = 'U':  Upper triangular part of A is referenced
          = 'L':  Lower triangular part of A is referenced
.fi
.PP
.br
\fIN\fP 
.PP
.nf
          N is INTEGER
          The order of the matrix A\&.  N >= 0\&.  When N = 0, CLANHE is
          set to zero\&.
.fi
.PP
.br
\fIA\fP 
.PP
.nf
          A is COMPLEX array, dimension (LDA,N)
          The hermitian matrix A\&.  If UPLO = 'U', the leading n by n
          upper triangular part of A contains the upper triangular part
          of the matrix A, and the strictly lower triangular part of A
          is not referenced\&.  If UPLO = 'L', the leading n by n lower
          triangular part of A contains the lower triangular part of
          the matrix A, and the strictly upper triangular part of A is
          not referenced\&. Note that the imaginary parts of the diagonal
          elements need not be set and are assumed to be zero\&.
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
          LDA is INTEGER
          The leading dimension of the array A\&.  LDA >= max(N,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 clansy (character norm, character uplo, integer n, complex, dimension( lda, * ) a, integer lda, real, dimension( * ) work)"

.PP
\fBCLANSY\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 complex symmetric matrix\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 CLANSY  returns the value of the one norm,  or the Frobenius norm, or
 the  infinity norm,  or the  element of  largest absolute value  of a
 complex symmetric matrix A\&.
.fi
.PP
.RE
.PP
\fBReturns\fP
.RS 4
CLANSY 
.PP
.nf
    CLANSY = ( 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 CLANSY as described
          above\&.
.fi
.PP
.br
\fIUPLO\fP 
.PP
.nf
          UPLO is CHARACTER*1
          Specifies whether the upper or lower triangular part of the
          symmetric matrix A is to be referenced\&.
          = 'U':  Upper triangular part of A is referenced
          = 'L':  Lower triangular part of A is referenced
.fi
.PP
.br
\fIN\fP 
.PP
.nf
          N is INTEGER
          The order of the matrix A\&.  N >= 0\&.  When N = 0, CLANSY is
          set to zero\&.
.fi
.PP
.br
\fIA\fP 
.PP
.nf
          A is COMPLEX array, dimension (LDA,N)
          The symmetric matrix A\&.  If UPLO = 'U', the leading n by n
          upper triangular part of A contains the upper triangular part
          of the matrix A, and the strictly lower triangular part of A
          is not referenced\&.  If UPLO = 'L', the leading n by n lower
          triangular part of A contains the lower triangular part of
          the matrix A, and the strictly upper triangular part of A is
          not referenced\&.
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
          LDA is INTEGER
          The leading dimension of the array A\&.  LDA >= max(N,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 dlansy (character norm, character uplo, integer n, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) work)"

.PP
\fBDLANSY\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 real symmetric matrix\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 DLANSY  returns the value of the one norm,  or the Frobenius norm, or
 the  infinity norm,  or the  element of  largest absolute value  of a
 real symmetric matrix A\&.
.fi
.PP
.RE
.PP
\fBReturns\fP
.RS 4
DLANSY 
.PP
.nf
    DLANSY = ( 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 DLANSY as described
          above\&.
.fi
.PP
.br
\fIUPLO\fP 
.PP
.nf
          UPLO is CHARACTER*1
          Specifies whether the upper or lower triangular part of the
          symmetric matrix A is to be referenced\&.
          = 'U':  Upper triangular part of A is referenced
          = 'L':  Lower triangular part of A is referenced
.fi
.PP
.br
\fIN\fP 
.PP
.nf
          N is INTEGER
          The order of the matrix A\&.  N >= 0\&.  When N = 0, DLANSY is
          set to zero\&.
.fi
.PP
.br
\fIA\fP 
.PP
.nf
          A is DOUBLE PRECISION array, dimension (LDA,N)
          The symmetric matrix A\&.  If UPLO = 'U', the leading n by n
          upper triangular part of A contains the upper triangular part
          of the matrix A, and the strictly lower triangular part of A
          is not referenced\&.  If UPLO = 'L', the leading n by n lower
          triangular part of A contains the lower triangular part of
          the matrix A, and the strictly upper triangular part of A is
          not referenced\&.
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
          LDA is INTEGER
          The leading dimension of the array A\&.  LDA >= max(N,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 slansy (character norm, character uplo, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( * ) work)"

.PP
\fBSLANSY\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 real symmetric matrix\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 SLANSY  returns the value of the one norm,  or the Frobenius norm, or
 the  infinity norm,  or the  element of  largest absolute value  of a
 real symmetric matrix A\&.
.fi
.PP
.RE
.PP
\fBReturns\fP
.RS 4
SLANSY 
.PP
.nf
    SLANSY = ( 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 SLANSY as described
          above\&.
.fi
.PP
.br
\fIUPLO\fP 
.PP
.nf
          UPLO is CHARACTER*1
          Specifies whether the upper or lower triangular part of the
          symmetric matrix A is to be referenced\&.
          = 'U':  Upper triangular part of A is referenced
          = 'L':  Lower triangular part of A is referenced
.fi
.PP
.br
\fIN\fP 
.PP
.nf
          N is INTEGER
          The order of the matrix A\&.  N >= 0\&.  When N = 0, SLANSY is
          set to zero\&.
.fi
.PP
.br
\fIA\fP 
.PP
.nf
          A is REAL array, dimension (LDA,N)
          The symmetric matrix A\&.  If UPLO = 'U', the leading n by n
          upper triangular part of A contains the upper triangular part
          of the matrix A, and the strictly lower triangular part of A
          is not referenced\&.  If UPLO = 'L', the leading n by n lower
          triangular part of A contains the lower triangular part of
          the matrix A, and the strictly upper triangular part of A is
          not referenced\&.
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
          LDA is INTEGER
          The leading dimension of the array A\&.  LDA >= max(N,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 zlanhe (character norm, character uplo, integer n, complex*16, dimension( lda, * ) a, integer lda, double precision, dimension( * ) work)"

.PP
\fBZLANHE\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 complex Hermitian matrix\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 ZLANHE  returns the value of the one norm,  or the Frobenius norm, or
 the  infinity norm,  or the  element of  largest absolute value  of a
 complex hermitian matrix A\&.
.fi
.PP
.RE
.PP
\fBReturns\fP
.RS 4
ZLANHE 
.PP
.nf
    ZLANHE = ( 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 ZLANHE as described
          above\&.
.fi
.PP
.br
\fIUPLO\fP 
.PP
.nf
          UPLO is CHARACTER*1
          Specifies whether the upper or lower triangular part of the
          hermitian matrix A is to be referenced\&.
          = 'U':  Upper triangular part of A is referenced
          = 'L':  Lower triangular part of A is referenced
.fi
.PP
.br
\fIN\fP 
.PP
.nf
          N is INTEGER
          The order of the matrix A\&.  N >= 0\&.  When N = 0, ZLANHE is
          set to zero\&.
.fi
.PP
.br
\fIA\fP 
.PP
.nf
          A is COMPLEX*16 array, dimension (LDA,N)
          The hermitian matrix A\&.  If UPLO = 'U', the leading n by n
          upper triangular part of A contains the upper triangular part
          of the matrix A, and the strictly lower triangular part of A
          is not referenced\&.  If UPLO = 'L', the leading n by n lower
          triangular part of A contains the lower triangular part of
          the matrix A, and the strictly upper triangular part of A is
          not referenced\&. Note that the imaginary parts of the diagonal
          elements need not be set and are assumed to be zero\&.
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
          LDA is INTEGER
          The leading dimension of the array A\&.  LDA >= max(N,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 zlansy (character norm, character uplo, integer n, complex*16, dimension( lda, * ) a, integer lda, double precision, dimension( * ) work)"

.PP
\fBZLANSY\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 complex symmetric matrix\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 ZLANSY  returns the value of the one norm,  or the Frobenius norm, or
 the  infinity norm,  or the  element of  largest absolute value  of a
 complex symmetric matrix A\&.
.fi
.PP
.RE
.PP
\fBReturns\fP
.RS 4
ZLANSY 
.PP
.nf
    ZLANSY = ( 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 ZLANSY as described
          above\&.
.fi
.PP
.br
\fIUPLO\fP 
.PP
.nf
          UPLO is CHARACTER*1
          Specifies whether the upper or lower triangular part of the
          symmetric matrix A is to be referenced\&.
          = 'U':  Upper triangular part of A is referenced
          = 'L':  Lower triangular part of A is referenced
.fi
.PP
.br
\fIN\fP 
.PP
.nf
          N is INTEGER
          The order of the matrix A\&.  N >= 0\&.  When N = 0, ZLANSY is
          set to zero\&.
.fi
.PP
.br
\fIA\fP 
.PP
.nf
          A is COMPLEX*16 array, dimension (LDA,N)
          The symmetric matrix A\&.  If UPLO = 'U', the leading n by n
          upper triangular part of A contains the upper triangular part
          of the matrix A, and the strictly lower triangular part of A
          is not referenced\&.  If UPLO = 'L', the leading n by n lower
          triangular part of A contains the lower triangular part of
          the matrix A, and the strictly upper triangular part of A is
          not referenced\&.
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
          LDA is INTEGER
          The leading dimension of the array A\&.  LDA >= max(N,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\&.