*> \brief \b STRTI2 computes the inverse of a triangular matrix (unblocked algorithm). * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download STRTI2 + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE STRTI2( UPLO, DIAG, N, A, LDA, INFO ) * * .. Scalar Arguments .. * CHARACTER DIAG, UPLO * INTEGER INFO, LDA, N * .. * .. Array Arguments .. * REAL A( LDA, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> STRTI2 computes the inverse of a real upper or lower triangular *> matrix. *> *> This is the Level 2 BLAS version of the algorithm. *> \endverbatim * * Arguments: * ========== * *> \param[in] UPLO *> \verbatim *> UPLO is CHARACTER*1 *> Specifies whether the matrix A is upper or lower triangular. *> = 'U': Upper triangular *> = 'L': Lower triangular *> \endverbatim *> *> \param[in] DIAG *> \verbatim *> DIAG is CHARACTER*1 *> Specifies whether or not the matrix A is unit triangular. *> = 'N': Non-unit triangular *> = 'U': Unit triangular *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The order of the matrix A. N >= 0. *> \endverbatim *> *> \param[in,out] A *> \verbatim *> A is REAL array, dimension (LDA,N) *> On entry, the triangular matrix A. If UPLO = 'U', the *> leading n by n upper triangular part of the array A contains *> the upper triangular matrix, and the strictly lower *> triangular part of A is not referenced. If UPLO = 'L', the *> leading n by n lower triangular part of the array A contains *> the lower triangular matrix, and the strictly upper *> triangular part of A is not referenced. If DIAG = 'U', the *> diagonal elements of A are also not referenced and are *> assumed to be 1. *> *> On exit, the (triangular) inverse of the original matrix, in *> the same storage format. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. LDA >= max(1,N). *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -k, the k-th argument had an illegal value *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup realOTHERcomputational * * ===================================================================== SUBROUTINE STRTI2( UPLO, DIAG, N, A, LDA, INFO ) * * -- LAPACK computational routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. CHARACTER DIAG, UPLO INTEGER INFO, LDA, N * .. * .. Array Arguments .. REAL A( LDA, * ) * .. * * ===================================================================== * * .. Parameters .. REAL ONE PARAMETER ( ONE = 1.0E+0 ) * .. * .. Local Scalars .. LOGICAL NOUNIT, UPPER INTEGER J REAL AJJ * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL SSCAL, STRMV, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC MAX * .. * .. Executable Statements .. * * Test the input parameters. * INFO = 0 UPPER = LSAME( UPLO, 'U' ) NOUNIT = LSAME( DIAG, 'N' ) IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN INFO = -1 ELSE IF( .NOT.NOUNIT .AND. .NOT.LSAME( DIAG, 'U' ) ) THEN INFO = -2 ELSE IF( N.LT.0 ) THEN INFO = -3 ELSE IF( LDA.LT.MAX( 1, N ) ) THEN INFO = -5 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'STRTI2', -INFO ) RETURN END IF * IF( UPPER ) THEN * * Compute inverse of upper triangular matrix. * DO 10 J = 1, N IF( NOUNIT ) THEN A( J, J ) = ONE / A( J, J ) AJJ = -A( J, J ) ELSE AJJ = -ONE END IF * * Compute elements 1:j-1 of j-th column. * CALL STRMV( 'Upper', 'No transpose', DIAG, J-1, A, LDA, $ A( 1, J ), 1 ) CALL SSCAL( J-1, AJJ, A( 1, J ), 1 ) 10 CONTINUE ELSE * * Compute inverse of lower triangular matrix. * DO 20 J = N, 1, -1 IF( NOUNIT ) THEN A( J, J ) = ONE / A( J, J ) AJJ = -A( J, J ) ELSE AJJ = -ONE END IF IF( J.LT.N ) THEN * * Compute elements j+1:n of j-th column. * CALL STRMV( 'Lower', 'No transpose', DIAG, N-J, $ A( J+1, J+1 ), LDA, A( J+1, J ), 1 ) CALL SSCAL( N-J, AJJ, A( J+1, J ), 1 ) END IF 20 CONTINUE END IF * RETURN * * End of STRTI2 * END