SUBROUTINE ZTPTRI( UPLO, DIAG, N, AP, INFO ) * * -- LAPACK routine (version 3.1) -- * Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. * November 2006 * * .. Scalar Arguments .. CHARACTER DIAG, UPLO INTEGER INFO, N * .. * .. Array Arguments .. COMPLEX*16 AP( * ) * .. * * Purpose * ======= * * ZTPTRI computes the inverse of a complex upper or lower triangular * matrix A stored in packed format. * * 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. * * AP (input/output) COMPLEX*16 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. * * 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. * * Further Details * =============== * * 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 * * ===================================================================== * * .. Parameters .. COMPLEX*16 ONE, ZERO PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ), \$ ZERO = ( 0.0D+0, 0.0D+0 ) ) * .. * .. Local Scalars .. LOGICAL NOUNIT, UPPER INTEGER J, JC, JCLAST, JJ COMPLEX*16 AJJ * .. * .. External Functions .. LOGICAL LSAME EXTERNAL LSAME * .. * .. External Subroutines .. EXTERNAL XERBLA, ZSCAL, ZTPMV * .. * .. 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( 'ZTPTRI', -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 ZTPMV( 'Upper', 'No transpose', DIAG, J-1, AP, \$ AP( JC ), 1 ) CALL ZSCAL( 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 ZTPMV( 'Lower', 'No transpose', DIAG, N-J, \$ AP( JCLAST ), AP( JC+1 ), 1 ) CALL ZSCAL( N-J, AJJ, AP( JC+1 ), 1 ) END IF JCLAST = JC JC = JC - N + J - 2 40 CONTINUE END IF * RETURN * * End of ZTPTRI * END