.TH "lantr" 3 "Wed Feb 7 2024 11:30:40" "Version 3.12.0" "LAPACK" \" -*- nroff -*- .ad l .nh .SH NAME lantr \- lantr: triangular matrix .SH SYNOPSIS .br .PP .SS "Functions" .in +1c .ti -1c .RI "real function \fBclantr\fP (norm, uplo, diag, m, n, a, lda, work)" .br .RI "\fBCLANTR\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 trapezoidal or triangular matrix\&. " .ti -1c .RI "double precision function \fBdlantr\fP (norm, uplo, diag, m, n, a, lda, work)" .br .RI "\fBDLANTR\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 trapezoidal or triangular matrix\&. " .ti -1c .RI "real function \fBslantr\fP (norm, uplo, diag, m, n, a, lda, work)" .br .RI "\fBSLANTR\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 trapezoidal or triangular matrix\&. " .ti -1c .RI "double precision function \fBzlantr\fP (norm, uplo, diag, m, n, a, lda, work)" .br .RI "\fBZLANTR\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 trapezoidal or triangular matrix\&. " .in -1c .SH "Detailed Description" .PP .SH "Function Documentation" .PP .SS "real function clantr (character norm, character uplo, character diag, integer m, integer n, complex, dimension( lda, * ) a, integer lda, real, dimension( * ) work)" .PP \fBCLANTR\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 trapezoidal or triangular matrix\&. .PP \fBPurpose:\fP .RS 4 .PP .nf CLANTR 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\&. .fi .PP .RE .PP \fBReturns\fP .RS 4 CLANTR .PP .nf CLANTR = ( 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 CLANTR as described above\&. .fi .PP .br \fIUPLO\fP .PP .nf 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\&. .fi .PP .br \fIDIAG\fP .PP .nf DIAG is CHARACTER*1 Specifies whether or not the matrix A has unit diagonal\&. = 'N': Non-unit diagonal = 'U': Unit diagonal .fi .PP .br \fIM\fP .PP .nf M is INTEGER The number of rows of the matrix A\&. M >= 0, and if UPLO = 'U', M <= N\&. When M = 0, CLANTR is set to zero\&. .fi .PP .br \fIN\fP .PP .nf N is INTEGER The number of columns of the matrix A\&. N >= 0, and if UPLO = 'L', N <= M\&. When N = 0, CLANTR is set to zero\&. .fi .PP .br \fIA\fP .PP .nf A is COMPLEX 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\&. .fi .PP .br \fILDA\fP .PP .nf LDA is INTEGER The leading dimension of the array A\&. LDA >= max(M,1)\&. .fi .PP .br \fIWORK\fP .PP .nf WORK is REAL array, dimension (MAX(1,LWORK)), where LWORK >= M 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 dlantr (character norm, character uplo, character diag, integer m, integer n, double precision, dimension( lda, * ) a, integer lda, double precision, dimension( * ) work)" .PP \fBDLANTR\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 trapezoidal or triangular matrix\&. .PP \fBPurpose:\fP .RS 4 .PP .nf DLANTR 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\&. .fi .PP .RE .PP \fBReturns\fP .RS 4 DLANTR .PP .nf DLANTR = ( 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 DLANTR as described above\&. .fi .PP .br \fIUPLO\fP .PP .nf 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\&. .fi .PP .br \fIDIAG\fP .PP .nf DIAG is CHARACTER*1 Specifies whether or not the matrix A has unit diagonal\&. = 'N': Non-unit diagonal = 'U': Unit diagonal .fi .PP .br \fIM\fP .PP .nf M is INTEGER The number of rows of the matrix A\&. M >= 0, and if UPLO = 'U', M <= N\&. When M = 0, DLANTR is set to zero\&. .fi .PP .br \fIN\fP .PP .nf N is INTEGER The number of columns of the matrix A\&. N >= 0, and if UPLO = 'L', N <= M\&. When N = 0, DLANTR is set to zero\&. .fi .PP .br \fIA\fP .PP .nf A is DOUBLE PRECISION 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\&. .fi .PP .br \fILDA\fP .PP .nf LDA is INTEGER The leading dimension of the array A\&. LDA >= max(M,1)\&. .fi .PP .br \fIWORK\fP .PP .nf WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)), where LWORK >= M 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 slantr (character norm, character uplo, character diag, integer m, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( * ) work)" .PP \fBSLANTR\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 trapezoidal or triangular matrix\&. .PP \fBPurpose:\fP .RS 4 .PP .nf 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\&. .fi .PP .RE .PP \fBReturns\fP .RS 4 SLANTR .PP .nf 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\&. .fi .PP .RE .PP \fBParameters\fP .RS 4 \fINORM\fP .PP .nf NORM is CHARACTER*1 Specifies the value to be returned in SLANTR as described above\&. .fi .PP .br \fIUPLO\fP .PP .nf 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\&. .fi .PP .br \fIDIAG\fP .PP .nf DIAG is CHARACTER*1 Specifies whether or not the matrix A has unit diagonal\&. = 'N': Non-unit diagonal = 'U': Unit diagonal .fi .PP .br \fIM\fP .PP .nf 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\&. .fi .PP .br \fIN\fP .PP .nf 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\&. .fi .PP .br \fIA\fP .PP .nf 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\&. .fi .PP .br \fILDA\fP .PP .nf LDA is INTEGER The leading dimension of the array A\&. LDA >= max(M,1)\&. .fi .PP .br \fIWORK\fP .PP .nf WORK is REAL array, dimension (MAX(1,LWORK)), where LWORK >= M 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 zlantr (character norm, character uplo, character diag, integer m, integer n, complex*16, dimension( lda, * ) a, integer lda, double precision, dimension( * ) work)" .PP \fBZLANTR\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 trapezoidal or triangular matrix\&. .PP \fBPurpose:\fP .RS 4 .PP .nf ZLANTR 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\&. .fi .PP .RE .PP \fBReturns\fP .RS 4 ZLANTR .PP .nf ZLANTR = ( 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 ZLANTR as described above\&. .fi .PP .br \fIUPLO\fP .PP .nf 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\&. .fi .PP .br \fIDIAG\fP .PP .nf DIAG is CHARACTER*1 Specifies whether or not the matrix A has unit diagonal\&. = 'N': Non-unit diagonal = 'U': Unit diagonal .fi .PP .br \fIM\fP .PP .nf M is INTEGER The number of rows of the matrix A\&. M >= 0, and if UPLO = 'U', M <= N\&. When M = 0, ZLANTR is set to zero\&. .fi .PP .br \fIN\fP .PP .nf N is INTEGER The number of columns of the matrix A\&. N >= 0, and if UPLO = 'L', N <= M\&. When N = 0, ZLANTR is set to zero\&. .fi .PP .br \fIA\fP .PP .nf A is COMPLEX*16 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\&. .fi .PP .br \fILDA\fP .PP .nf LDA is INTEGER The leading dimension of the array A\&. LDA >= max(M,1)\&. .fi .PP .br \fIWORK\fP .PP .nf WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)), where LWORK >= M 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\&.