*DECK STPSV SUBROUTINE STPSV (UPLO, TRANS, DIAG, N, AP, X, INCX) C***BEGIN PROLOGUE STPSV C***PURPOSE Solve one of the systems of equations. C***LIBRARY SLATEC (BLAS) C***CATEGORY D1B4 C***TYPE SINGLE PRECISION (STPSV-S, DTPSV-D, CTPSV-C) C***KEYWORDS LEVEL 2 BLAS, LINEAR ALGEBRA C***AUTHOR Dongarra, J. J., (ANL) C Du Croz, J., (NAG) C Hammarling, S., (NAG) C Hanson, R. J., (SNLA) C***DESCRIPTION C C STPSV solves one of the systems of equations C C A*x = b, or A'*x = b, C C where b and x are n element vectors and A is an n by n unit, or C non-unit, upper or lower triangular matrix, supplied in packed form. C C No test for singularity or near-singularity is included in this C routine. Such tests must be performed before calling this routine. C C Parameters C ========== C C UPLO - CHARACTER*1. C On entry, UPLO specifies whether the matrix is an upper or C lower triangular matrix as follows: C C UPLO = 'U' or 'u' A is an upper triangular matrix. C C UPLO = 'L' or 'l' A is a lower triangular matrix. C C Unchanged on exit. C C TRANS - CHARACTER*1. C On entry, TRANS specifies the equations to be solved as C follows: C C TRANS = 'N' or 'n' A*x = b. C C TRANS = 'T' or 't' A'*x = b. C C TRANS = 'C' or 'c' A'*x = b. C C Unchanged on exit. C C DIAG - CHARACTER*1. C On entry, DIAG specifies whether or not A is unit C triangular as follows: C C DIAG = 'U' or 'u' A is assumed to be unit triangular. C C DIAG = 'N' or 'n' A is not assumed to be unit C triangular. C C Unchanged on exit. C C N - INTEGER. C On entry, N specifies the order of the matrix A. C N must be at least zero. C Unchanged on exit. C C AP - REAL array of DIMENSION at least C ( ( n*( n + 1))/2). C Before entry with UPLO = 'U' or 'u', the array AP must C contain the upper triangular matrix packed sequentially, C column by column, so that AP( 1 ) contains a( 1, 1 ), C AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 ) C respectively, and so on. C Before entry with UPLO = 'L' or 'l', the array AP must C contain the lower triangular matrix packed sequentially, C column by column, so that AP( 1 ) contains a( 1, 1 ), C AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 ) C respectively, and so on. C Note that when DIAG = 'U' or 'u', the diagonal elements of C A are not referenced, but are assumed to be unity. C Unchanged on exit. C C X - REAL array of dimension at least C ( 1 + ( n - 1 )*abs( INCX ) ). C Before entry, the incremented array X must contain the n C element right-hand side vector b. On exit, X is overwritten C with the solution vector x. C C INCX - INTEGER. C On entry, INCX specifies the increment for the elements of C X. INCX must not be zero. C Unchanged on exit. C C***REFERENCES Dongarra, J. J., Du Croz, J., Hammarling, S., and C Hanson, R. J. An extended set of Fortran basic linear C algebra subprograms. ACM TOMS, Vol. 14, No. 1, C pp. 1-17, March 1988. C***ROUTINES CALLED LSAME, XERBLA C***REVISION HISTORY (YYMMDD) C 861022 DATE WRITTEN C 910605 Modified to meet SLATEC prologue standards. Only comment C lines were modified. (BKS) C***END PROLOGUE STPSV C .. Scalar Arguments .. INTEGER INCX, N CHARACTER*1 DIAG, TRANS, UPLO C .. Array Arguments .. REAL AP( * ), X( * ) C .. Parameters .. REAL ZERO PARAMETER ( ZERO = 0.0E+0 ) C .. Local Scalars .. REAL TEMP INTEGER I, INFO, IX, J, JX, K, KK, KX LOGICAL NOUNIT C .. External Functions .. LOGICAL LSAME EXTERNAL LSAME C .. External Subroutines .. EXTERNAL XERBLA C***FIRST EXECUTABLE STATEMENT STPSV C C Test the input parameters. C INFO = 0 IF ( .NOT.LSAME( UPLO , 'U' ).AND. $ .NOT.LSAME( UPLO , 'L' ) )THEN INFO = 1 ELSE IF( .NOT.LSAME( TRANS, 'N' ).AND. $ .NOT.LSAME( TRANS, 'T' ).AND. $ .NOT.LSAME( TRANS, 'C' ) )THEN INFO = 2 ELSE IF( .NOT.LSAME( DIAG , 'U' ).AND. $ .NOT.LSAME( DIAG , 'N' ) )THEN INFO = 3 ELSE IF( N.LT.0 )THEN INFO = 4 ELSE IF( INCX.EQ.0 )THEN INFO = 7 END IF IF( INFO.NE.0 )THEN CALL XERBLA( 'STPSV ', INFO ) RETURN END IF C C Quick return if possible. C IF( N.EQ.0 ) $ RETURN C NOUNIT = LSAME( DIAG, 'N' ) C C Set up the start point in X if the increment is not unity. This C will be ( N - 1 )*INCX too small for descending loops. C IF( INCX.LE.0 )THEN KX = 1 - ( N - 1 )*INCX ELSE IF( INCX.NE.1 )THEN KX = 1 END IF C C Start the operations. In this version the elements of AP are C accessed sequentially with one pass through AP. C IF( LSAME( TRANS, 'N' ) )THEN C C Form x := inv( A )*x. C IF( LSAME( UPLO, 'U' ) )THEN KK = ( N*( N + 1 ) )/2 IF( INCX.EQ.1 )THEN DO 20, J = N, 1, -1 IF( X( J ).NE.ZERO )THEN IF( NOUNIT ) $ X( J ) = X( J )/AP( KK ) TEMP = X( J ) K = KK - 1 DO 10, I = J - 1, 1, -1 X( I ) = X( I ) - TEMP*AP( K ) K = K - 1 10 CONTINUE END IF KK = KK - J 20 CONTINUE ELSE JX = KX + ( N - 1 )*INCX DO 40, J = N, 1, -1 IF( X( JX ).NE.ZERO )THEN IF( NOUNIT ) $ X( JX ) = X( JX )/AP( KK ) TEMP = X( JX ) IX = JX DO 30, K = KK - 1, KK - J + 1, -1 IX = IX - INCX X( IX ) = X( IX ) - TEMP*AP( K ) 30 CONTINUE END IF JX = JX - INCX KK = KK - J 40 CONTINUE END IF ELSE KK = 1 IF( INCX.EQ.1 )THEN DO 60, J = 1, N IF( X( J ).NE.ZERO )THEN IF( NOUNIT ) $ X( J ) = X( J )/AP( KK ) TEMP = X( J ) K = KK + 1 DO 50, I = J + 1, N X( I ) = X( I ) - TEMP*AP( K ) K = K + 1 50 CONTINUE END IF KK = KK + ( N - J + 1 ) 60 CONTINUE ELSE JX = KX DO 80, J = 1, N IF( X( JX ).NE.ZERO )THEN IF( NOUNIT ) $ X( JX ) = X( JX )/AP( KK ) TEMP = X( JX ) IX = JX DO 70, K = KK + 1, KK + N - J IX = IX + INCX X( IX ) = X( IX ) - TEMP*AP( K ) 70 CONTINUE END IF JX = JX + INCX KK = KK + ( N - J + 1 ) 80 CONTINUE END IF END IF ELSE C C Form x := inv( A' )*x. C IF( LSAME( UPLO, 'U' ) )THEN KK = 1 IF( INCX.EQ.1 )THEN DO 100, J = 1, N TEMP = X( J ) K = KK DO 90, I = 1, J - 1 TEMP = TEMP - AP( K )*X( I ) K = K + 1 90 CONTINUE IF( NOUNIT ) $ TEMP = TEMP/AP( KK + J - 1 ) X( J ) = TEMP KK = KK + J 100 CONTINUE ELSE JX = KX DO 120, J = 1, N TEMP = X( JX ) IX = KX DO 110, K = KK, KK + J - 2 TEMP = TEMP - AP( K )*X( IX ) IX = IX + INCX 110 CONTINUE IF( NOUNIT ) $ TEMP = TEMP/AP( KK + J - 1 ) X( JX ) = TEMP JX = JX + INCX KK = KK + J 120 CONTINUE END IF ELSE KK = ( N*( N + 1 ) )/2 IF( INCX.EQ.1 )THEN DO 140, J = N, 1, -1 TEMP = X( J ) K = KK DO 130, I = N, J + 1, -1 TEMP = TEMP - AP( K )*X( I ) K = K - 1 130 CONTINUE IF( NOUNIT ) $ TEMP = TEMP/AP( KK - N + J ) X( J ) = TEMP KK = KK - ( N - J + 1 ) 140 CONTINUE ELSE KX = KX + ( N - 1 )*INCX JX = KX DO 160, J = N, 1, -1 TEMP = X( JX ) IX = KX DO 150, K = KK, KK - ( N - ( J + 1 ) ), -1 TEMP = TEMP - AP( K )*X( IX ) IX = IX - INCX 150 CONTINUE IF( NOUNIT ) $ TEMP = TEMP/AP( KK - N + J ) X( JX ) = TEMP JX = JX - INCX KK = KK - (N - J + 1 ) 160 CONTINUE END IF END IF END IF C RETURN C C End of STPSV . C END