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

.in +1c
.ti -1c
.RI "subroutine \fBcgetri\fP (n, a, lda, ipiv, work, lwork, info)"
.br
.RI "\fBCGETRI\fP "
.ti -1c
.RI "subroutine \fBdgetri\fP (n, a, lda, ipiv, work, lwork, info)"
.br
.RI "\fBDGETRI\fP "
.ti -1c
.RI "subroutine \fBsgetri\fP (n, a, lda, ipiv, work, lwork, info)"
.br
.RI "\fBSGETRI\fP "
.ti -1c
.RI "subroutine \fBzgetri\fP (n, a, lda, ipiv, work, lwork, info)"
.br
.RI "\fBZGETRI\fP "
.in -1c
.SH "Detailed Description"
.PP 

.SH "Function Documentation"
.PP 
.SS "subroutine cgetri (integer n, complex, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, complex, dimension( * ) work, integer lwork, integer info)"

.PP
\fBCGETRI\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 CGETRI computes the inverse of a matrix using the LU factorization
 computed by CGETRF\&.

 This method inverts U and then computes inv(A) by solving the system
 inv(A)*L = inv(U) for inv(A)\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIN\fP 
.PP
.nf
          N is INTEGER
          The order of the matrix A\&.  N >= 0\&.
.fi
.PP
.br
\fIA\fP 
.PP
.nf
          A is COMPLEX array, dimension (LDA,N)
          On entry, the factors L and U from the factorization
          A = P*L*U as computed by CGETRF\&.
          On exit, if INFO = 0, the inverse of the original matrix A\&.
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
          LDA is INTEGER
          The leading dimension of the array A\&.  LDA >= max(1,N)\&.
.fi
.PP
.br
\fIIPIV\fP 
.PP
.nf
          IPIV is INTEGER array, dimension (N)
          The pivot indices from CGETRF; for 1<=i<=N, row i of the
          matrix was interchanged with row IPIV(i)\&.
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
          WORK is COMPLEX array, dimension (MAX(1,LWORK))
          On exit, if INFO=0, then WORK(1) returns the optimal LWORK\&.
.fi
.PP
.br
\fILWORK\fP 
.PP
.nf
          LWORK is INTEGER
          The dimension of the array WORK\&.  LWORK >= max(1,N)\&.
          For optimal performance LWORK >= N*NB, where NB is
          the optimal blocksize returned by ILAENV\&.

          If LWORK = -1, then a workspace query is assumed; the routine
          only calculates the optimal size of the WORK array, returns
          this value as the first entry of the WORK array, and no error
          message related to LWORK is issued by XERBLA\&.
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
          INFO is INTEGER
          = 0:  successful exit
          < 0:  if INFO = -i, the i-th argument had an illegal value
          > 0:  if INFO = i, U(i,i) is exactly zero; the matrix is
                singular and its inverse could not be computed\&.
.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 dgetri (integer n, double precision, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, double precision, dimension( * ) work, integer lwork, integer info)"

.PP
\fBDGETRI\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 DGETRI computes the inverse of a matrix using the LU factorization
 computed by DGETRF\&.

 This method inverts U and then computes inv(A) by solving the system
 inv(A)*L = inv(U) for inv(A)\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIN\fP 
.PP
.nf
          N is INTEGER
          The order of the matrix A\&.  N >= 0\&.
.fi
.PP
.br
\fIA\fP 
.PP
.nf
          A is DOUBLE PRECISION array, dimension (LDA,N)
          On entry, the factors L and U from the factorization
          A = P*L*U as computed by DGETRF\&.
          On exit, if INFO = 0, the inverse of the original matrix A\&.
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
          LDA is INTEGER
          The leading dimension of the array A\&.  LDA >= max(1,N)\&.
.fi
.PP
.br
\fIIPIV\fP 
.PP
.nf
          IPIV is INTEGER array, dimension (N)
          The pivot indices from DGETRF; for 1<=i<=N, row i of the
          matrix was interchanged with row IPIV(i)\&.
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
          WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
          On exit, if INFO=0, then WORK(1) returns the optimal LWORK\&.
.fi
.PP
.br
\fILWORK\fP 
.PP
.nf
          LWORK is INTEGER
          The dimension of the array WORK\&.  LWORK >= max(1,N)\&.
          For optimal performance LWORK >= N*NB, where NB is
          the optimal blocksize returned by ILAENV\&.

          If LWORK = -1, then a workspace query is assumed; the routine
          only calculates the optimal size of the WORK array, returns
          this value as the first entry of the WORK array, and no error
          message related to LWORK is issued by XERBLA\&.
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
          INFO is INTEGER
          = 0:  successful exit
          < 0:  if INFO = -i, the i-th argument had an illegal value
          > 0:  if INFO = i, U(i,i) is exactly zero; the matrix is
                singular and its inverse could not be computed\&.
.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 sgetri (integer n, real, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, real, dimension( * ) work, integer lwork, integer info)"

.PP
\fBSGETRI\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 SGETRI computes the inverse of a matrix using the LU factorization
 computed by SGETRF\&.

 This method inverts U and then computes inv(A) by solving the system
 inv(A)*L = inv(U) for inv(A)\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIN\fP 
.PP
.nf
          N is INTEGER
          The order of the matrix A\&.  N >= 0\&.
.fi
.PP
.br
\fIA\fP 
.PP
.nf
          A is REAL array, dimension (LDA,N)
          On entry, the factors L and U from the factorization
          A = P*L*U as computed by SGETRF\&.
          On exit, if INFO = 0, the inverse of the original matrix A\&.
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
          LDA is INTEGER
          The leading dimension of the array A\&.  LDA >= max(1,N)\&.
.fi
.PP
.br
\fIIPIV\fP 
.PP
.nf
          IPIV is INTEGER array, dimension (N)
          The pivot indices from SGETRF; for 1<=i<=N, row i of the
          matrix was interchanged with row IPIV(i)\&.
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
          WORK is REAL array, dimension (MAX(1,LWORK))
          On exit, if INFO=0, then WORK(1) returns the optimal LWORK\&.
.fi
.PP
.br
\fILWORK\fP 
.PP
.nf
          LWORK is INTEGER
          The dimension of the array WORK\&.  LWORK >= max(1,N)\&.
          For optimal performance LWORK >= N*NB, where NB is
          the optimal blocksize returned by ILAENV\&.

          If LWORK = -1, then a workspace query is assumed; the routine
          only calculates the optimal size of the WORK array, returns
          this value as the first entry of the WORK array, and no error
          message related to LWORK is issued by XERBLA\&.
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
          INFO is INTEGER
          = 0:  successful exit
          < 0:  if INFO = -i, the i-th argument had an illegal value
          > 0:  if INFO = i, U(i,i) is exactly zero; the matrix is
                singular and its inverse could not be computed\&.
.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 zgetri (integer n, complex*16, dimension( lda, * ) a, integer lda, integer, dimension( * ) ipiv, complex*16, dimension( * ) work, integer lwork, integer info)"

.PP
\fBZGETRI\fP  
.PP
\fBPurpose:\fP
.RS 4

.PP
.nf
 ZGETRI computes the inverse of a matrix using the LU factorization
 computed by ZGETRF\&.

 This method inverts U and then computes inv(A) by solving the system
 inv(A)*L = inv(U) for inv(A)\&.
.fi
.PP
 
.RE
.PP
\fBParameters\fP
.RS 4
\fIN\fP 
.PP
.nf
          N is INTEGER
          The order of the matrix A\&.  N >= 0\&.
.fi
.PP
.br
\fIA\fP 
.PP
.nf
          A is COMPLEX*16 array, dimension (LDA,N)
          On entry, the factors L and U from the factorization
          A = P*L*U as computed by ZGETRF\&.
          On exit, if INFO = 0, the inverse of the original matrix A\&.
.fi
.PP
.br
\fILDA\fP 
.PP
.nf
          LDA is INTEGER
          The leading dimension of the array A\&.  LDA >= max(1,N)\&.
.fi
.PP
.br
\fIIPIV\fP 
.PP
.nf
          IPIV is INTEGER array, dimension (N)
          The pivot indices from ZGETRF; for 1<=i<=N, row i of the
          matrix was interchanged with row IPIV(i)\&.
.fi
.PP
.br
\fIWORK\fP 
.PP
.nf
          WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
          On exit, if INFO=0, then WORK(1) returns the optimal LWORK\&.
.fi
.PP
.br
\fILWORK\fP 
.PP
.nf
          LWORK is INTEGER
          The dimension of the array WORK\&.  LWORK >= max(1,N)\&.
          For optimal performance LWORK >= N*NB, where NB is
          the optimal blocksize returned by ILAENV\&.

          If LWORK = -1, then a workspace query is assumed; the routine
          only calculates the optimal size of the WORK array, returns
          this value as the first entry of the WORK array, and no error
          message related to LWORK is issued by XERBLA\&.
.fi
.PP
.br
\fIINFO\fP 
.PP
.nf
          INFO is INTEGER
          = 0:  successful exit
          < 0:  if INFO = -i, the i-th argument had an illegal value
          > 0:  if INFO = i, U(i,i) is exactly zero; the matrix is
                singular and its inverse could not be computed\&.
.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\&.