Squashed 'third_party/eigen/' content from commit 61d72f6
Change-Id: Iccc90fa0b55ab44037f018046d2fcffd90d9d025
git-subtree-dir: third_party/eigen
git-subtree-split: 61d72f6383cfa842868c53e30e087b0258177257
diff --git a/blas/ctbmv.f b/blas/ctbmv.f
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+ SUBROUTINE CTBMV(UPLO,TRANS,DIAG,N,K,A,LDA,X,INCX)
+* .. Scalar Arguments ..
+ INTEGER INCX,K,LDA,N
+ CHARACTER DIAG,TRANS,UPLO
+* ..
+* .. Array Arguments ..
+ COMPLEX A(LDA,*),X(*)
+* ..
+*
+* Purpose
+* =======
+*
+* CTBMV 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 band matrix, with ( k + 1 ) diagonals.
+*
+* Arguments
+* ==========
+*
+* 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.
+*
+* K - INTEGER.
+* On entry with UPLO = 'U' or 'u', K specifies the number of
+* super-diagonals of the matrix A.
+* On entry with UPLO = 'L' or 'l', K specifies the number of
+* sub-diagonals of the matrix A.
+* K must satisfy 0 .le. K.
+* Unchanged on exit.
+*
+* A - COMPLEX array of DIMENSION ( LDA, n ).
+* Before entry with UPLO = 'U' or 'u', the leading ( k + 1 )
+* by n part of the array A must contain the upper triangular
+* band part of the matrix of coefficients, supplied column by
+* column, with the leading diagonal of the matrix in row
+* ( k + 1 ) of the array, the first super-diagonal starting at
+* position 2 in row k, and so on. The top left k by k triangle
+* of the array A is not referenced.
+* The following program segment will transfer an upper
+* triangular band matrix from conventional full matrix storage
+* to band storage:
+*
+* DO 20, J = 1, N
+* M = K + 1 - J
+* DO 10, I = MAX( 1, J - K ), J
+* A( M + I, J ) = matrix( I, J )
+* 10 CONTINUE
+* 20 CONTINUE
+*
+* Before entry with UPLO = 'L' or 'l', the leading ( k + 1 )
+* by n part of the array A must contain the lower triangular
+* band part of the matrix of coefficients, supplied column by
+* column, with the leading diagonal of the matrix in row 1 of
+* the array, the first sub-diagonal starting at position 1 in
+* row 2, and so on. The bottom right k by k triangle of the
+* array A is not referenced.
+* The following program segment will transfer a lower
+* triangular band matrix from conventional full matrix storage
+* to band storage:
+*
+* DO 20, J = 1, N
+* M = 1 - J
+* DO 10, I = J, MIN( N, J + K )
+* A( M + I, J ) = matrix( I, J )
+* 10 CONTINUE
+* 20 CONTINUE
+*
+* Note that when DIAG = 'U' or 'u' the elements of the array A
+* corresponding to the diagonal elements of the matrix are not
+* referenced, but are assumed to be unity.
+* Unchanged on exit.
+*
+* LDA - INTEGER.
+* On entry, LDA specifies the first dimension of A as declared
+* in the calling (sub) program. LDA must be at least
+* ( k + 1 ).
+* Unchanged on exit.
+*
+* X - COMPLEX 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.
+*
+* Further Details
+* ===============
+*
+* 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 ZERO
+ PARAMETER (ZERO= (0.0E+0,0.0E+0))
+* ..
+* .. Local Scalars ..
+ COMPLEX TEMP
+ INTEGER I,INFO,IX,J,JX,KPLUS1,KX,L
+ LOGICAL NOCONJ,NOUNIT
+* ..
+* .. External Functions ..
+ LOGICAL LSAME
+ EXTERNAL LSAME
+* ..
+* .. External Subroutines ..
+ EXTERNAL XERBLA
+* ..
+* .. Intrinsic Functions ..
+ INTRINSIC CONJG,MAX,MIN
+* ..
+*
+* 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 (K.LT.0) THEN
+ INFO = 5
+ ELSE IF (LDA.LT. (K+1)) THEN
+ INFO = 7
+ ELSE IF (INCX.EQ.0) THEN
+ INFO = 9
+ END IF
+ IF (INFO.NE.0) THEN
+ CALL XERBLA('CTBMV ',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 A are
+* accessed sequentially with one pass through A.
+*
+ IF (LSAME(TRANS,'N')) THEN
+*
+* Form x := A*x.
+*
+ IF (LSAME(UPLO,'U')) THEN
+ KPLUS1 = K + 1
+ IF (INCX.EQ.1) THEN
+ DO 20 J = 1,N
+ IF (X(J).NE.ZERO) THEN
+ TEMP = X(J)
+ L = KPLUS1 - J
+ DO 10 I = MAX(1,J-K),J - 1
+ X(I) = X(I) + TEMP*A(L+I,J)
+ 10 CONTINUE
+ IF (NOUNIT) X(J) = X(J)*A(KPLUS1,J)
+ END IF
+ 20 CONTINUE
+ ELSE
+ JX = KX
+ DO 40 J = 1,N
+ IF (X(JX).NE.ZERO) THEN
+ TEMP = X(JX)
+ IX = KX
+ L = KPLUS1 - J
+ DO 30 I = MAX(1,J-K),J - 1
+ X(IX) = X(IX) + TEMP*A(L+I,J)
+ IX = IX + INCX
+ 30 CONTINUE
+ IF (NOUNIT) X(JX) = X(JX)*A(KPLUS1,J)
+ END IF
+ JX = JX + INCX
+ IF (J.GT.K) KX = KX + INCX
+ 40 CONTINUE
+ END IF
+ ELSE
+ IF (INCX.EQ.1) THEN
+ DO 60 J = N,1,-1
+ IF (X(J).NE.ZERO) THEN
+ TEMP = X(J)
+ L = 1 - J
+ DO 50 I = MIN(N,J+K),J + 1,-1
+ X(I) = X(I) + TEMP*A(L+I,J)
+ 50 CONTINUE
+ IF (NOUNIT) X(J) = X(J)*A(1,J)
+ END IF
+ 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
+ L = 1 - J
+ DO 70 I = MIN(N,J+K),J + 1,-1
+ X(IX) = X(IX) + TEMP*A(L+I,J)
+ IX = IX - INCX
+ 70 CONTINUE
+ IF (NOUNIT) X(JX) = X(JX)*A(1,J)
+ END IF
+ JX = JX - INCX
+ IF ((N-J).GE.K) KX = KX - INCX
+ 80 CONTINUE
+ END IF
+ END IF
+ ELSE
+*
+* Form x := A'*x or x := conjg( A' )*x.
+*
+ IF (LSAME(UPLO,'U')) THEN
+ KPLUS1 = K + 1
+ IF (INCX.EQ.1) THEN
+ DO 110 J = N,1,-1
+ TEMP = X(J)
+ L = KPLUS1 - J
+ IF (NOCONJ) THEN
+ IF (NOUNIT) TEMP = TEMP*A(KPLUS1,J)
+ DO 90 I = J - 1,MAX(1,J-K),-1
+ TEMP = TEMP + A(L+I,J)*X(I)
+ 90 CONTINUE
+ ELSE
+ IF (NOUNIT) TEMP = TEMP*CONJG(A(KPLUS1,J))
+ DO 100 I = J - 1,MAX(1,J-K),-1
+ TEMP = TEMP + CONJG(A(L+I,J))*X(I)
+ 100 CONTINUE
+ END IF
+ X(J) = TEMP
+ 110 CONTINUE
+ ELSE
+ KX = KX + (N-1)*INCX
+ JX = KX
+ DO 140 J = N,1,-1
+ TEMP = X(JX)
+ KX = KX - INCX
+ IX = KX
+ L = KPLUS1 - J
+ IF (NOCONJ) THEN
+ IF (NOUNIT) TEMP = TEMP*A(KPLUS1,J)
+ DO 120 I = J - 1,MAX(1,J-K),-1
+ TEMP = TEMP + A(L+I,J)*X(IX)
+ IX = IX - INCX
+ 120 CONTINUE
+ ELSE
+ IF (NOUNIT) TEMP = TEMP*CONJG(A(KPLUS1,J))
+ DO 130 I = J - 1,MAX(1,J-K),-1
+ TEMP = TEMP + CONJG(A(L+I,J))*X(IX)
+ IX = IX - INCX
+ 130 CONTINUE
+ END IF
+ X(JX) = TEMP
+ JX = JX - INCX
+ 140 CONTINUE
+ END IF
+ ELSE
+ IF (INCX.EQ.1) THEN
+ DO 170 J = 1,N
+ TEMP = X(J)
+ L = 1 - J
+ IF (NOCONJ) THEN
+ IF (NOUNIT) TEMP = TEMP*A(1,J)
+ DO 150 I = J + 1,MIN(N,J+K)
+ TEMP = TEMP + A(L+I,J)*X(I)
+ 150 CONTINUE
+ ELSE
+ IF (NOUNIT) TEMP = TEMP*CONJG(A(1,J))
+ DO 160 I = J + 1,MIN(N,J+K)
+ TEMP = TEMP + CONJG(A(L+I,J))*X(I)
+ 160 CONTINUE
+ END IF
+ X(J) = TEMP
+ 170 CONTINUE
+ ELSE
+ JX = KX
+ DO 200 J = 1,N
+ TEMP = X(JX)
+ KX = KX + INCX
+ IX = KX
+ L = 1 - J
+ IF (NOCONJ) THEN
+ IF (NOUNIT) TEMP = TEMP*A(1,J)
+ DO 180 I = J + 1,MIN(N,J+K)
+ TEMP = TEMP + A(L+I,J)*X(IX)
+ IX = IX + INCX
+ 180 CONTINUE
+ ELSE
+ IF (NOUNIT) TEMP = TEMP*CONJG(A(1,J))
+ DO 190 I = J + 1,MIN(N,J+K)
+ TEMP = TEMP + CONJG(A(L+I,J))*X(IX)
+ IX = IX + INCX
+ 190 CONTINUE
+ END IF
+ X(JX) = TEMP
+ JX = JX + INCX
+ 200 CONTINUE
+ END IF
+ END IF
+ END IF
+*
+ RETURN
+*
+* End of CTBMV .
+*
+ END