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+ SUBROUTINE ZTPMV ( UPLO, TRANS, DIAG, N, AP, X, INCX )
+* .. Scalar Arguments ..
+ INTEGER INCX, N
+ CHARACTER*1 DIAG, TRANS, UPLO
+* .. Array Arguments ..
+ COMPLEX*16 AP( * ), X( * )
+* ..
+*
+* Purpose
+* =======
+*
+* ZTPMV performs one of the matrix-vector operations
+*
+* x := A*x, or x := A'*x, or x := conjg( A' )*x,
+*
+* where x is an n element vector and A is an n by n unit, or non-unit,
+* upper or lower triangular matrix, supplied in packed form.
+*
+* Parameters
+* ==========
+*
+* UPLO - CHARACTER*1.
+* On entry, UPLO specifies whether the matrix is an upper or
+* lower triangular matrix as follows:
+*
+* UPLO = 'U' or 'u' A is an upper triangular matrix.
+*
+* UPLO = 'L' or 'l' A is a lower triangular matrix.
+*
+* Unchanged on exit.
+*
+* TRANS - CHARACTER*1.
+* On entry, TRANS specifies the operation to be performed as
+* follows:
+*
+* TRANS = 'N' or 'n' x := A*x.
+*
+* TRANS = 'T' or 't' x := A'*x.
+*
+* TRANS = 'C' or 'c' x := conjg( A' )*x.
+*
+* Unchanged on exit.
+*
+* DIAG - CHARACTER*1.
+* On entry, DIAG specifies whether or not A is unit
+* triangular as follows:
+*
+* DIAG = 'U' or 'u' A is assumed to be unit triangular.
+*
+* DIAG = 'N' or 'n' A is not assumed to be unit
+* triangular.
+*
+* Unchanged on exit.
+*
+* N - INTEGER.
+* On entry, N specifies the order of the matrix A.
+* N must be at least zero.
+* Unchanged on exit.
+*
+* AP - COMPLEX*16 array of DIMENSION at least
+* ( ( n*( n + 1 ) )/2 ).
+* Before entry with UPLO = 'U' or 'u', the array AP must
+* contain the upper triangular matrix packed sequentially,
+* column by column, so that AP( 1 ) contains a( 1, 1 ),
+* AP( 2 ) and AP( 3 ) contain a( 1, 2 ) and a( 2, 2 )
+* respectively, and so on.
+* Before entry with UPLO = 'L' or 'l', the array AP must
+* contain the lower triangular matrix packed sequentially,
+* column by column, so that AP( 1 ) contains a( 1, 1 ),
+* AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3, 1 )
+* respectively, and so on.
+* Note that when DIAG = 'U' or 'u', the diagonal elements of
+* A are not referenced, but are assumed to be unity.
+* Unchanged on exit.
+*
+* X - COMPLEX*16 array of dimension at least
+* ( 1 + ( n - 1 )*abs( INCX ) ).
+* Before entry, the incremented array X must contain the n
+* element vector x. On exit, X is overwritten with the
+* tranformed vector x.
+*
+* INCX - INTEGER.
+* On entry, INCX specifies the increment for the elements of
+* X. INCX must not be zero.
+* Unchanged on exit.
+*
+*
+* Level 2 Blas routine.
+*
+* -- Written on 22-October-1986.
+* Jack Dongarra, Argonne National Lab.
+* Jeremy Du Croz, Nag Central Office.
+* Sven Hammarling, Nag Central Office.
+* Richard Hanson, Sandia National Labs.
+*
+*
+* .. Parameters ..
+ COMPLEX*16 ZERO
+ PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ) )
+* .. Local Scalars ..
+ COMPLEX*16 TEMP
+ INTEGER I, INFO, IX, J, JX, K, KK, KX
+ LOGICAL NOCONJ, NOUNIT
+* .. External Functions ..
+ LOGICAL LSAME
+ EXTERNAL LSAME
+* .. External Subroutines ..
+ EXTERNAL XERBLA
+* .. Intrinsic Functions ..
+ INTRINSIC DCONJG
+* ..
+* .. Executable Statements ..
+*
+* Test the input parameters.
+*
+ 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( 'ZTPMV ', INFO )
+ RETURN
+ END IF
+*
+* Quick return if possible.
+*
+ IF( N.EQ.0 )
+ $ RETURN
+*
+ NOCONJ = LSAME( TRANS, 'T' )
+ NOUNIT = LSAME( DIAG , 'N' )
+*
+* Set up the start point in X if the increment is not unity. This
+* will be ( N - 1 )*INCX too small for descending loops.
+*
+ IF( INCX.LE.0 )THEN
+ KX = 1 - ( N - 1 )*INCX
+ ELSE IF( INCX.NE.1 )THEN
+ KX = 1
+ END IF
+*
+* Start the operations. In this version the elements of AP are
+* accessed sequentially with one pass through AP.
+*
+ IF( LSAME( TRANS, 'N' ) )THEN
+*
+* Form x:= A*x.
+*
+ IF( LSAME( UPLO, 'U' ) )THEN
+ KK = 1
+ IF( INCX.EQ.1 )THEN
+ DO 20, J = 1, N
+ IF( X( J ).NE.ZERO )THEN
+ TEMP = X( J )
+ K = KK
+ DO 10, I = 1, J - 1
+ X( I ) = X( I ) + TEMP*AP( K )
+ K = K + 1
+ 10 CONTINUE
+ IF( NOUNIT )
+ $ X( J ) = X( J )*AP( KK + J - 1 )
+ END IF
+ KK = KK + J
+ 20 CONTINUE
+ ELSE
+ JX = KX
+ DO 40, J = 1, N
+ IF( X( JX ).NE.ZERO )THEN
+ TEMP = X( JX )
+ IX = KX
+ DO 30, K = KK, KK + J - 2
+ X( IX ) = X( IX ) + TEMP*AP( K )
+ IX = IX + INCX
+ 30 CONTINUE
+ IF( NOUNIT )
+ $ X( JX ) = X( JX )*AP( KK + J - 1 )
+ END IF
+ JX = JX + INCX
+ KK = KK + J
+ 40 CONTINUE
+ END IF
+ ELSE
+ KK = ( N*( N + 1 ) )/2
+ IF( INCX.EQ.1 )THEN
+ DO 60, J = N, 1, -1
+ IF( X( J ).NE.ZERO )THEN
+ TEMP = X( J )
+ K = KK
+ DO 50, I = N, J + 1, -1
+ X( I ) = X( I ) + TEMP*AP( K )
+ K = K - 1
+ 50 CONTINUE
+ IF( NOUNIT )
+ $ X( J ) = X( J )*AP( KK - N + J )
+ END IF
+ KK = KK - ( N - J + 1 )
+ 60 CONTINUE
+ ELSE
+ KX = KX + ( N - 1 )*INCX
+ JX = KX
+ DO 80, J = N, 1, -1
+ IF( X( JX ).NE.ZERO )THEN
+ TEMP = X( JX )
+ IX = KX
+ DO 70, K = KK, KK - ( N - ( J + 1 ) ), -1
+ X( IX ) = X( IX ) + TEMP*AP( K )
+ IX = IX - INCX
+ 70 CONTINUE
+ IF( NOUNIT )
+ $ X( JX ) = X( JX )*AP( KK - N + J )
+ END IF
+ JX = JX - INCX
+ KK = KK - ( N - J + 1 )
+ 80 CONTINUE
+ END IF
+ END IF
+ ELSE
+*
+* Form x := A'*x or x := conjg( A' )*x.
+*
+ IF( LSAME( UPLO, 'U' ) )THEN
+ KK = ( N*( N + 1 ) )/2
+ IF( INCX.EQ.1 )THEN
+ DO 110, J = N, 1, -1
+ TEMP = X( J )
+ K = KK - 1
+ IF( NOCONJ )THEN
+ IF( NOUNIT )
+ $ TEMP = TEMP*AP( KK )
+ DO 90, I = J - 1, 1, -1
+ TEMP = TEMP + AP( K )*X( I )
+ K = K - 1
+ 90 CONTINUE
+ ELSE
+ IF( NOUNIT )
+ $ TEMP = TEMP*DCONJG( AP( KK ) )
+ DO 100, I = J - 1, 1, -1
+ TEMP = TEMP + DCONJG( AP( K ) )*X( I )
+ K = K - 1
+ 100 CONTINUE
+ END IF
+ X( J ) = TEMP
+ KK = KK - J
+ 110 CONTINUE
+ ELSE
+ JX = KX + ( N - 1 )*INCX
+ DO 140, J = N, 1, -1
+ TEMP = X( JX )
+ IX = JX
+ IF( NOCONJ )THEN
+ IF( NOUNIT )
+ $ TEMP = TEMP*AP( KK )
+ DO 120, K = KK - 1, KK - J + 1, -1
+ IX = IX - INCX
+ TEMP = TEMP + AP( K )*X( IX )
+ 120 CONTINUE
+ ELSE
+ IF( NOUNIT )
+ $ TEMP = TEMP*DCONJG( AP( KK ) )
+ DO 130, K = KK - 1, KK - J + 1, -1
+ IX = IX - INCX
+ TEMP = TEMP + DCONJG( AP( K ) )*X( IX )
+ 130 CONTINUE
+ END IF
+ X( JX ) = TEMP
+ JX = JX - INCX
+ KK = KK - J
+ 140 CONTINUE
+ END IF
+ ELSE
+ KK = 1
+ IF( INCX.EQ.1 )THEN
+ DO 170, J = 1, N
+ TEMP = X( J )
+ K = KK + 1
+ IF( NOCONJ )THEN
+ IF( NOUNIT )
+ $ TEMP = TEMP*AP( KK )
+ DO 150, I = J + 1, N
+ TEMP = TEMP + AP( K )*X( I )
+ K = K + 1
+ 150 CONTINUE
+ ELSE
+ IF( NOUNIT )
+ $ TEMP = TEMP*DCONJG( AP( KK ) )
+ DO 160, I = J + 1, N
+ TEMP = TEMP + DCONJG( AP( K ) )*X( I )
+ K = K + 1
+ 160 CONTINUE
+ END IF
+ X( J ) = TEMP
+ KK = KK + ( N - J + 1 )
+ 170 CONTINUE
+ ELSE
+ JX = KX
+ DO 200, J = 1, N
+ TEMP = X( JX )
+ IX = JX
+ IF( NOCONJ )THEN
+ IF( NOUNIT )
+ $ TEMP = TEMP*AP( KK )
+ DO 180, K = KK + 1, KK + N - J
+ IX = IX + INCX
+ TEMP = TEMP + AP( K )*X( IX )
+ 180 CONTINUE
+ ELSE
+ IF( NOUNIT )
+ $ TEMP = TEMP*DCONJG( AP( KK ) )
+ DO 190, K = KK + 1, KK + N - J
+ IX = IX + INCX
+ TEMP = TEMP + DCONJG( AP( K ) )*X( IX )
+ 190 CONTINUE
+ END IF
+ X( JX ) = TEMP
+ JX = JX + INCX
+ KK = KK + ( N - J + 1 )
+ 200 CONTINUE
+ END IF
+ END IF
+ END IF
+*
+ RETURN
+*
+* End of ZTPMV .
+*
+ END