*> \brief \b STPTRI * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download STPTRI + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE STPTRI( UPLO, DIAG, N, AP, INFO ) * * .. Scalar Arguments .. * CHARACTER DIAG, UPLO * INTEGER INFO, N * .. * .. Array Arguments .. * REAL AP( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> STPTRI computes the inverse of a real upper or lower triangular *> matrix A stored in packed format. *> \endverbatim * * Arguments: * ========== * *> \param[in] UPLO *> \verbatim *> UPLO is CHARACTER*1 *> = 'U': A is upper triangular; *> = 'L': A is lower triangular. *> \endverbatim *> *> \param[in] DIAG *> \verbatim *> DIAG is CHARACTER*1 *> = 'N': A is non-unit triangular; *> = 'U': A is unit triangular. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The order of the matrix A. N >= 0. *> \endverbatim *> *> \param[in,out] AP *> \verbatim *> AP is REAL array, dimension (N*(N+1)/2) *> On entry, the upper or lower triangular matrix A, stored *> 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)*((2*n-j)/2) = A(i,j) for j<=i<=n. *> See below for further details. *> On exit, the (triangular) inverse of the original matrix, in *> the same packed storage format. *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value *> > 0: if INFO = i, A(i,i) is exactly zero. The triangular *> matrix is singular and its inverse can not be computed. *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup realOTHERcomputational * *> \par Further Details: * ===================== *> *> \verbatim *> *> A triangular matrix A can be transferred to packed storage using one *> of the following program segments: *> *> UPLO = 'U': UPLO = 'L': *> *> JC = 1 JC = 1 *> DO 2 J = 1, N DO 2 J = 1, N *> DO 1 I = 1, J DO 1 I = J, N *> AP(JC+I-1) = A(I,J) AP(JC+I-J) = A(I,J) *> 1 CONTINUE 1 CONTINUE *> JC = JC + J JC = JC + N - J + 1 *> 2 CONTINUE 2 CONTINUE *> \endverbatim *> * ===================================================================== SUBROUTINE STPTRI( UPLO, DIAG, N, AP, 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, N * .. * .. Array Arguments .. REAL AP( * ) * .. * * ===================================================================== * * .. Parameters .. REAL ONE, ZERO PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 ) * .. * .. Local Scalars .. LOGICAL NOUNIT, UPPER INTEGER J, JC, JCLAST, JJ REAL AJJ * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL SSCAL, STPMV, XERBLA * .. * .. 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 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'STPTRI', -INFO ) RETURN END IF * * Check for singularity if non-unit. * IF( NOUNIT ) THEN IF( UPPER ) THEN JJ = 0 DO 10 INFO = 1, N JJ = JJ + INFO IF( AP( JJ ).EQ.ZERO ) \$ RETURN 10 CONTINUE ELSE JJ = 1 DO 20 INFO = 1, N IF( AP( JJ ).EQ.ZERO ) \$ RETURN JJ = JJ + N - INFO + 1 20 CONTINUE END IF INFO = 0 END IF * IF( UPPER ) THEN * * Compute inverse of upper triangular matrix. * JC = 1 DO 30 J = 1, N IF( NOUNIT ) THEN AP( JC+J-1 ) = ONE / AP( JC+J-1 ) AJJ = -AP( JC+J-1 ) ELSE AJJ = -ONE END IF * * Compute elements 1:j-1 of j-th column. * CALL STPMV( 'Upper', 'No transpose', DIAG, J-1, AP, \$ AP( JC ), 1 ) CALL SSCAL( J-1, AJJ, AP( JC ), 1 ) JC = JC + J 30 CONTINUE * ELSE * * Compute inverse of lower triangular matrix. * JC = N*( N+1 ) / 2 DO 40 J = N, 1, -1 IF( NOUNIT ) THEN AP( JC ) = ONE / AP( JC ) AJJ = -AP( JC ) ELSE AJJ = -ONE END IF IF( J.LT.N ) THEN * * Compute elements j+1:n of j-th column. * CALL STPMV( 'Lower', 'No transpose', DIAG, N-J, \$ AP( JCLAST ), AP( JC+1 ), 1 ) CALL SSCAL( N-J, AJJ, AP( JC+1 ), 1 ) END IF JCLAST = JC JC = JC - N + J - 2 40 CONTINUE END IF * RETURN * * End of STPTRI * END