.TH "lantp" 3 "Wed Feb 7 2024 11:30:40" "Version 3.12.0" "LAPACK" \" -*- nroff -*- .ad l .nh .SH NAME lantp \- lantp: triangular matrix, packed .SH SYNOPSIS .br .PP .SS "Functions" .in +1c .ti -1c .RI "real function \fBclantp\fP (norm, uplo, diag, n, ap, work)" .br .RI "\fBCLANTP\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 triangular matrix supplied in packed form\&. " .ti -1c .RI "double precision function \fBdlantp\fP (norm, uplo, diag, n, ap, work)" .br .RI "\fBDLANTP\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 triangular matrix supplied in packed form\&. " .ti -1c .RI "real function \fBslantp\fP (norm, uplo, diag, n, ap, work)" .br .RI "\fBSLANTP\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 triangular matrix supplied in packed form\&. " .ti -1c .RI "double precision function \fBzlantp\fP (norm, uplo, diag, n, ap, work)" .br .RI "\fBZLANTP\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 triangular matrix supplied in packed form\&. " .in -1c .SH "Detailed Description" .PP .SH "Function Documentation" .PP .SS "real function clantp (character norm, character uplo, character diag, integer n, complex, dimension( * ) ap, real, dimension( * ) work)" .PP \fBCLANTP\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 triangular matrix supplied in packed form\&. .PP \fBPurpose:\fP .RS 4 .PP .nf CLANTP returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a triangular matrix A, supplied in packed form\&. .fi .PP .RE .PP \fBReturns\fP .RS 4 CLANTP .PP .nf CLANTP = ( 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 CLANTP as described above\&. .fi .PP .br \fIUPLO\fP .PP .nf UPLO is CHARACTER*1 Specifies whether the matrix A is upper or lower triangular\&. = 'U': Upper triangular = 'L': Lower triangular .fi .PP .br \fIDIAG\fP .PP .nf DIAG is CHARACTER*1 Specifies whether or not the matrix A is unit triangular\&. = 'N': Non-unit triangular = 'U': Unit triangular .fi .PP .br \fIN\fP .PP .nf N is INTEGER The order of the matrix A\&. N >= 0\&. When N = 0, CLANTP is set to zero\&. .fi .PP .br \fIAP\fP .PP .nf AP is COMPLEX array, dimension (N*(N+1)/2) The upper or lower triangular matrix A, packed columnwise in a linear array\&. The j-th column of A is stored in the array AP as follows: if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n\&. Note that when DIAG = 'U', the elements of the array AP corresponding to the diagonal elements of the matrix A are not referenced, but are assumed to be one\&. .fi .PP .br \fIWORK\fP .PP .nf WORK is REAL array, dimension (MAX(1,LWORK)), where LWORK >= N when NORM = 'I'; 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 dlantp (character norm, character uplo, character diag, integer n, double precision, dimension( * ) ap, double precision, dimension( * ) work)" .PP \fBDLANTP\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 triangular matrix supplied in packed form\&. .PP \fBPurpose:\fP .RS 4 .PP .nf DLANTP returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a triangular matrix A, supplied in packed form\&. .fi .PP .RE .PP \fBReturns\fP .RS 4 DLANTP .PP .nf DLANTP = ( 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 DLANTP as described above\&. .fi .PP .br \fIUPLO\fP .PP .nf UPLO is CHARACTER*1 Specifies whether the matrix A is upper or lower triangular\&. = 'U': Upper triangular = 'L': Lower triangular .fi .PP .br \fIDIAG\fP .PP .nf DIAG is CHARACTER*1 Specifies whether or not the matrix A is unit triangular\&. = 'N': Non-unit triangular = 'U': Unit triangular .fi .PP .br \fIN\fP .PP .nf N is INTEGER The order of the matrix A\&. N >= 0\&. When N = 0, DLANTP is set to zero\&. .fi .PP .br \fIAP\fP .PP .nf AP is DOUBLE PRECISION array, dimension (N*(N+1)/2) The upper or lower triangular matrix A, packed columnwise in a linear array\&. The j-th column of A is stored in the array AP as follows: if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n\&. Note that when DIAG = 'U', the elements of the array AP corresponding to the diagonal elements of the matrix A are not referenced, but are assumed to be one\&. .fi .PP .br \fIWORK\fP .PP .nf WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)), where LWORK >= N when NORM = 'I'; 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 slantp (character norm, character uplo, character diag, integer n, real, dimension( * ) ap, real, dimension( * ) work)" .PP \fBSLANTP\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 triangular matrix supplied in packed form\&. .PP \fBPurpose:\fP .RS 4 .PP .nf SLANTP returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a triangular matrix A, supplied in packed form\&. .fi .PP .RE .PP \fBReturns\fP .RS 4 SLANTP .PP .nf SLANTP = ( 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 SLANTP as described above\&. .fi .PP .br \fIUPLO\fP .PP .nf UPLO is CHARACTER*1 Specifies whether the matrix A is upper or lower triangular\&. = 'U': Upper triangular = 'L': Lower triangular .fi .PP .br \fIDIAG\fP .PP .nf DIAG is CHARACTER*1 Specifies whether or not the matrix A is unit triangular\&. = 'N': Non-unit triangular = 'U': Unit triangular .fi .PP .br \fIN\fP .PP .nf N is INTEGER The order of the matrix A\&. N >= 0\&. When N = 0, SLANTP is set to zero\&. .fi .PP .br \fIAP\fP .PP .nf AP is REAL array, dimension (N*(N+1)/2) The upper or lower triangular matrix A, packed columnwise in a linear array\&. The j-th column of A is stored in the array AP as follows: if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n\&. Note that when DIAG = 'U', the elements of the array AP corresponding to the diagonal elements of the matrix A are not referenced, but are assumed to be one\&. .fi .PP .br \fIWORK\fP .PP .nf WORK is REAL array, dimension (MAX(1,LWORK)), where LWORK >= N when NORM = 'I'; 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 zlantp (character norm, character uplo, character diag, integer n, complex*16, dimension( * ) ap, double precision, dimension( * ) work)" .PP \fBZLANTP\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 triangular matrix supplied in packed form\&. .PP \fBPurpose:\fP .RS 4 .PP .nf ZLANTP returns the value of the one norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a triangular matrix A, supplied in packed form\&. .fi .PP .RE .PP \fBReturns\fP .RS 4 ZLANTP .PP .nf ZLANTP = ( 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 ZLANTP as described above\&. .fi .PP .br \fIUPLO\fP .PP .nf UPLO is CHARACTER*1 Specifies whether the matrix A is upper or lower triangular\&. = 'U': Upper triangular = 'L': Lower triangular .fi .PP .br \fIDIAG\fP .PP .nf DIAG is CHARACTER*1 Specifies whether or not the matrix A is unit triangular\&. = 'N': Non-unit triangular = 'U': Unit triangular .fi .PP .br \fIN\fP .PP .nf N is INTEGER The order of the matrix A\&. N >= 0\&. When N = 0, ZLANTP is set to zero\&. .fi .PP .br \fIAP\fP .PP .nf AP is COMPLEX*16 array, dimension (N*(N+1)/2) The upper or lower triangular matrix A, packed columnwise in a linear array\&. The j-th column of A is stored in the array AP as follows: if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n\&. Note that when DIAG = 'U', the elements of the array AP corresponding to the diagonal elements of the matrix A are not referenced, but are assumed to be one\&. .fi .PP .br \fIWORK\fP .PP .nf WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)), where LWORK >= N when NORM = 'I'; 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\&.