.TH "lauum" 3 "Wed Feb 7 2024 11:30:40" "Version 3.12.0" "LAPACK" \" -*- nroff -*-
.ad l
.nh
.SH NAME
lauum \- lauum: triangular multiply: U^H U
.SH SYNOPSIS
.br
.PP
.SS "Functions"

.in +1c
.ti -1c
.RI "subroutine \fBclauum\fP (uplo, n, a, lda, info)"
.br
.RI "\fBCLAUUM\fP computes the product UUH or LHL, where U and L are upper or lower triangular matrices (blocked algorithm)\&. "
.ti -1c
.RI "subroutine \fBdlauum\fP (uplo, n, a, lda, info)"
.br
.RI "\fBDLAUUM\fP computes the product UUH or LHL, where U and L are upper or lower triangular matrices (blocked algorithm)\&. "
.ti -1c
.RI "subroutine \fBslauum\fP (uplo, n, a, lda, info)"
.br
.RI "\fBSLAUUM\fP computes the product UUH or LHL, where U and L are upper or lower triangular matrices (blocked algorithm)\&. "
.ti -1c
.RI "subroutine \fBzlauum\fP (uplo, n, a, lda, info)"
.br
.RI "\fBZLAUUM\fP computes the product UUH or LHL, where U and L are upper or lower triangular matrices (blocked algorithm)\&. "
.in -1c
.SH "Detailed Description"
.PP 

.SH "Function Documentation"
.PP 
.SS "subroutine clauum (character uplo, integer n, complex, dimension( lda, * ) a, integer lda, integer info)"

.PP
\fBCLAUUM\fP computes the product UUH or LHL, where U and L are upper or lower triangular matrices (blocked algorithm)\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 CLAUUM computes the product U * U**H or L**H * L, where the triangular
 factor U or L is stored in the upper or lower triangular part of
 the array A\&.

 If UPLO = 'U' or 'u' then the upper triangle of the result is stored,
 overwriting the factor U in A\&.
 If UPLO = 'L' or 'l' then the lower triangle of the result is stored,
 overwriting the factor L in A\&.

 This is the blocked form of the algorithm, calling Level 3 BLAS\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIUPLO\fP 
.PP
.nf
          UPLO is CHARACTER*1
          Specifies whether the triangular factor stored in the array A
          is upper or lower triangular:
          = 'U':  Upper triangular
          = 'L':  Lower triangular
.fi
.PP
.br
\fIN\fP 
.PP
.nf
          N is INTEGER
          The order of the triangular factor U or L\&.  N >= 0\&.
.fi
.PP
.br
\fIA\fP 
.PP
.nf
          A is COMPLEX array, dimension (LDA,N)
          On entry, the triangular factor U or L\&.
          On exit, if UPLO = 'U', the upper triangle of A is
          overwritten with the upper triangle of the product U * U**H;
          if UPLO = 'L', the lower triangle of A is overwritten with
          the lower triangle of the product L**H * L\&.
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
          LDA is INTEGER
          The leading dimension of the array A\&.  LDA >= max(1,N)\&.
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
          INFO is INTEGER
          = 0: successful exit
          < 0: if INFO = -k, the k-th argument had an illegal value
.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 "subroutine dlauum (character uplo, integer n, double precision, dimension( lda, * ) a, integer lda, integer info)"

.PP
\fBDLAUUM\fP computes the product UUH or LHL, where U and L are upper or lower triangular matrices (blocked algorithm)\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 DLAUUM computes the product U * U**T or L**T * L, where the triangular
 factor U or L is stored in the upper or lower triangular part of
 the array A\&.

 If UPLO = 'U' or 'u' then the upper triangle of the result is stored,
 overwriting the factor U in A\&.
 If UPLO = 'L' or 'l' then the lower triangle of the result is stored,
 overwriting the factor L in A\&.

 This is the blocked form of the algorithm, calling Level 3 BLAS\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIUPLO\fP 
.PP
.nf
          UPLO is CHARACTER*1
          Specifies whether the triangular factor stored in the array A
          is upper or lower triangular:
          = 'U':  Upper triangular
          = 'L':  Lower triangular
.fi
.PP
.br
\fIN\fP 
.PP
.nf
          N is INTEGER
          The order of the triangular factor U or L\&.  N >= 0\&.
.fi
.PP
.br
\fIA\fP 
.PP
.nf
          A is DOUBLE PRECISION array, dimension (LDA,N)
          On entry, the triangular factor U or L\&.
          On exit, if UPLO = 'U', the upper triangle of A is
          overwritten with the upper triangle of the product U * U**T;
          if UPLO = 'L', the lower triangle of A is overwritten with
          the lower triangle of the product L**T * L\&.
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
          LDA is INTEGER
          The leading dimension of the array A\&.  LDA >= max(1,N)\&.
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
          INFO is INTEGER
          = 0: successful exit
          < 0: if INFO = -k, the k-th argument had an illegal value
.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 "subroutine slauum (character uplo, integer n, real, dimension( lda, * ) a, integer lda, integer info)"

.PP
\fBSLAUUM\fP computes the product UUH or LHL, where U and L are upper or lower triangular matrices (blocked algorithm)\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 SLAUUM computes the product U * U**T or L**T * L, where the triangular
 factor U or L is stored in the upper or lower triangular part of
 the array A\&.

 If UPLO = 'U' or 'u' then the upper triangle of the result is stored,
 overwriting the factor U in A\&.
 If UPLO = 'L' or 'l' then the lower triangle of the result is stored,
 overwriting the factor L in A\&.

 This is the blocked form of the algorithm, calling Level 3 BLAS\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIUPLO\fP 
.PP
.nf
          UPLO is CHARACTER*1
          Specifies whether the triangular factor stored in the array A
          is upper or lower triangular:
          = 'U':  Upper triangular
          = 'L':  Lower triangular
.fi
.PP
.br
\fIN\fP 
.PP
.nf
          N is INTEGER
          The order of the triangular factor U or L\&.  N >= 0\&.
.fi
.PP
.br
\fIA\fP 
.PP
.nf
          A is REAL array, dimension (LDA,N)
          On entry, the triangular factor U or L\&.
          On exit, if UPLO = 'U', the upper triangle of A is
          overwritten with the upper triangle of the product U * U**T;
          if UPLO = 'L', the lower triangle of A is overwritten with
          the lower triangle of the product L**T * L\&.
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
          LDA is INTEGER
          The leading dimension of the array A\&.  LDA >= max(1,N)\&.
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
          INFO is INTEGER
          = 0: successful exit
          < 0: if INFO = -k, the k-th argument had an illegal value
.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 "subroutine zlauum (character uplo, integer n, complex*16, dimension( lda, * ) a, integer lda, integer info)"

.PP
\fBZLAUUM\fP computes the product UUH or LHL, where U and L are upper or lower triangular matrices (blocked algorithm)\&.  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 ZLAUUM computes the product U * U**H or L**H * L, where the triangular
 factor U or L is stored in the upper or lower triangular part of
 the array A\&.

 If UPLO = 'U' or 'u' then the upper triangle of the result is stored,
 overwriting the factor U in A\&.
 If UPLO = 'L' or 'l' then the lower triangle of the result is stored,
 overwriting the factor L in A\&.

 This is the blocked form of the algorithm, calling Level 3 BLAS\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIUPLO\fP 
.PP
.nf
          UPLO is CHARACTER*1
          Specifies whether the triangular factor stored in the array A
          is upper or lower triangular:
          = 'U':  Upper triangular
          = 'L':  Lower triangular
.fi
.PP
.br
\fIN\fP 
.PP
.nf
          N is INTEGER
          The order of the triangular factor U or L\&.  N >= 0\&.
.fi
.PP
.br
\fIA\fP 
.PP
.nf
          A is COMPLEX*16 array, dimension (LDA,N)
          On entry, the triangular factor U or L\&.
          On exit, if UPLO = 'U', the upper triangle of A is
          overwritten with the upper triangle of the product U * U**H;
          if UPLO = 'L', the lower triangle of A is overwritten with
          the lower triangle of the product L**H * L\&.
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
          LDA is INTEGER
          The leading dimension of the array A\&.  LDA >= max(1,N)\&.
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
          INFO is INTEGER
          = 0: successful exit
          < 0: if INFO = -k, the k-th argument had an illegal value
.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 
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