SUBROUTINE STRTRI( UPLO, DIAG, N, A, LDA, INFO ) * * -- LAPACK routine (version 3.2) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * November 2006 * * .. Scalar Arguments .. CHARACTER DIAG, UPLO INTEGER INFO, LDA, N * .. * .. Array Arguments .. REAL A( LDA, * ) * .. * * Purpose * ======= * * STRTRI computes the inverse of a real upper or lower triangular * matrix A. * * This is the Level 3 BLAS version of the algorithm. * * Arguments * ========= * * UPLO (input) CHARACTER*1 * = 'U': A is upper triangular; * = 'L': A is lower triangular. * * DIAG (input) CHARACTER*1 * = 'N': A is non-unit triangular; * = 'U': A is unit triangular. * * N (input) INTEGER * The order of the matrix A. N >= 0. * * A (input/output) 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. * * LDA (input) INTEGER * The leading dimension of the array A. LDA >= max(1,N). * * INFO (output) 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. * * ===================================================================== * * .. Parameters .. REAL ONE, ZERO PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 ) * .. * .. Local Scalars .. LOGICAL NOUNIT, UPPER INTEGER J, JB, NB, NN * .. * .. External Functions .. LOGICAL LSAME INTEGER ILAENV EXTERNAL LSAME, ILAENV * .. * .. External Subroutines .. EXTERNAL STRMM, STRSM, STRTI2, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC MAX, MIN * .. * .. 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( 'STRTRI', -INFO ) RETURN END IF * * Quick return if possible * IF( N.EQ.0 ) \$ RETURN * * Check for singularity if non-unit. * IF( NOUNIT ) THEN DO 10 INFO = 1, N IF( A( INFO, INFO ).EQ.ZERO ) \$ RETURN 10 CONTINUE INFO = 0 END IF * * Determine the block size for this environment. * NB = ILAENV( 1, 'STRTRI', UPLO // DIAG, N, -1, -1, -1 ) IF( NB.LE.1 .OR. NB.GE.N ) THEN * * Use unblocked code * CALL STRTI2( UPLO, DIAG, N, A, LDA, INFO ) ELSE * * Use blocked code * IF( UPPER ) THEN * * Compute inverse of upper triangular matrix * DO 20 J = 1, N, NB JB = MIN( NB, N-J+1 ) * * Compute rows 1:j-1 of current block column * CALL STRMM( 'Left', 'Upper', 'No transpose', DIAG, J-1, \$ JB, ONE, A, LDA, A( 1, J ), LDA ) CALL STRSM( 'Right', 'Upper', 'No transpose', DIAG, J-1, \$ JB, -ONE, A( J, J ), LDA, A( 1, J ), LDA ) * * Compute inverse of current diagonal block * CALL STRTI2( 'Upper', DIAG, JB, A( J, J ), LDA, INFO ) 20 CONTINUE ELSE * * Compute inverse of lower triangular matrix * NN = ( ( N-1 ) / NB )*NB + 1 DO 30 J = NN, 1, -NB JB = MIN( NB, N-J+1 ) IF( J+JB.LE.N ) THEN * * Compute rows j+jb:n of current block column * CALL STRMM( 'Left', 'Lower', 'No transpose', DIAG, \$ N-J-JB+1, JB, ONE, A( J+JB, J+JB ), LDA, \$ A( J+JB, J ), LDA ) CALL STRSM( 'Right', 'Lower', 'No transpose', DIAG, \$ N-J-JB+1, JB, -ONE, A( J, J ), LDA, \$ A( J+JB, J ), LDA ) END IF * * Compute inverse of current diagonal block * CALL STRTI2( 'Lower', DIAG, JB, A( J, J ), LDA, INFO ) 30 CONTINUE END IF END IF * RETURN * * End of STRTRI * END