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/dsbmv.f b/blas/dsbmv.f
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+ SUBROUTINE DSBMV(UPLO,N,K,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
+* .. Scalar Arguments ..
+ DOUBLE PRECISION ALPHA,BETA
+ INTEGER INCX,INCY,K,LDA,N
+ CHARACTER UPLO
+* ..
+* .. Array Arguments ..
+ DOUBLE PRECISION A(LDA,*),X(*),Y(*)
+* ..
+*
+* Purpose
+* =======
+*
+* DSBMV performs the matrix-vector operation
+*
+* y := alpha*A*x + beta*y,
+*
+* where alpha and beta are scalars, x and y are n element vectors and
+* A is an n by n symmetric band matrix, with k super-diagonals.
+*
+* Arguments
+* ==========
+*
+* UPLO - CHARACTER*1.
+* On entry, UPLO specifies whether the upper or lower
+* triangular part of the band matrix A is being supplied as
+* follows:
+*
+* UPLO = 'U' or 'u' The upper triangular part of A is
+* being supplied.
+*
+* UPLO = 'L' or 'l' The lower triangular part of A is
+* being supplied.
+*
+* 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, K specifies the number of super-diagonals of the
+* matrix A. K must satisfy 0 .le. K.
+* Unchanged on exit.
+*
+* ALPHA - DOUBLE PRECISION.
+* On entry, ALPHA specifies the scalar alpha.
+* Unchanged on exit.
+*
+* A - DOUBLE PRECISION 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 symmetric matrix, 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 the upper
+* triangular part of a symmetric 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 symmetric matrix, 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 the lower
+* triangular part of a symmetric 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
+*
+* 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 - DOUBLE PRECISION array of DIMENSION at least
+* ( 1 + ( n - 1 )*abs( INCX ) ).
+* Before entry, the incremented array X must contain the
+* vector x.
+* Unchanged on exit.
+*
+* INCX - INTEGER.
+* On entry, INCX specifies the increment for the elements of
+* X. INCX must not be zero.
+* Unchanged on exit.
+*
+* BETA - DOUBLE PRECISION.
+* On entry, BETA specifies the scalar beta.
+* Unchanged on exit.
+*
+* Y - DOUBLE PRECISION array of DIMENSION at least
+* ( 1 + ( n - 1 )*abs( INCY ) ).
+* Before entry, the incremented array Y must contain the
+* vector y. On exit, Y is overwritten by the updated vector y.
+*
+* INCY - INTEGER.
+* On entry, INCY specifies the increment for the elements of
+* Y. INCY 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 ..
+ DOUBLE PRECISION ONE,ZERO
+ PARAMETER (ONE=1.0D+0,ZERO=0.0D+0)
+* ..
+* .. Local Scalars ..
+ DOUBLE PRECISION TEMP1,TEMP2
+ INTEGER I,INFO,IX,IY,J,JX,JY,KPLUS1,KX,KY,L
+* ..
+* .. External Functions ..
+ LOGICAL LSAME
+ EXTERNAL LSAME
+* ..
+* .. External Subroutines ..
+ EXTERNAL XERBLA
+* ..
+* .. Intrinsic Functions ..
+ INTRINSIC MAX,MIN
+* ..
+*
+* Test the input parameters.
+*
+ INFO = 0
+ IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN
+ INFO = 1
+ ELSE IF (N.LT.0) THEN
+ INFO = 2
+ ELSE IF (K.LT.0) THEN
+ INFO = 3
+ ELSE IF (LDA.LT. (K+1)) THEN
+ INFO = 6
+ ELSE IF (INCX.EQ.0) THEN
+ INFO = 8
+ ELSE IF (INCY.EQ.0) THEN
+ INFO = 11
+ END IF
+ IF (INFO.NE.0) THEN
+ CALL XERBLA('DSBMV ',INFO)
+ RETURN
+ END IF
+*
+* Quick return if possible.
+*
+ IF ((N.EQ.0) .OR. ((ALPHA.EQ.ZERO).AND. (BETA.EQ.ONE))) RETURN
+*
+* Set up the start points in X and Y.
+*
+ IF (INCX.GT.0) THEN
+ KX = 1
+ ELSE
+ KX = 1 - (N-1)*INCX
+ END IF
+ IF (INCY.GT.0) THEN
+ KY = 1
+ ELSE
+ KY = 1 - (N-1)*INCY
+ END IF
+*
+* Start the operations. In this version the elements of the array A
+* are accessed sequentially with one pass through A.
+*
+* First form y := beta*y.
+*
+ IF (BETA.NE.ONE) THEN
+ IF (INCY.EQ.1) THEN
+ IF (BETA.EQ.ZERO) THEN
+ DO 10 I = 1,N
+ Y(I) = ZERO
+ 10 CONTINUE
+ ELSE
+ DO 20 I = 1,N
+ Y(I) = BETA*Y(I)
+ 20 CONTINUE
+ END IF
+ ELSE
+ IY = KY
+ IF (BETA.EQ.ZERO) THEN
+ DO 30 I = 1,N
+ Y(IY) = ZERO
+ IY = IY + INCY
+ 30 CONTINUE
+ ELSE
+ DO 40 I = 1,N
+ Y(IY) = BETA*Y(IY)
+ IY = IY + INCY
+ 40 CONTINUE
+ END IF
+ END IF
+ END IF
+ IF (ALPHA.EQ.ZERO) RETURN
+ IF (LSAME(UPLO,'U')) THEN
+*
+* Form y when upper triangle of A is stored.
+*
+ KPLUS1 = K + 1
+ IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN
+ DO 60 J = 1,N
+ TEMP1 = ALPHA*X(J)
+ TEMP2 = ZERO
+ L = KPLUS1 - J
+ DO 50 I = MAX(1,J-K),J - 1
+ Y(I) = Y(I) + TEMP1*A(L+I,J)
+ TEMP2 = TEMP2 + A(L+I,J)*X(I)
+ 50 CONTINUE
+ Y(J) = Y(J) + TEMP1*A(KPLUS1,J) + ALPHA*TEMP2
+ 60 CONTINUE
+ ELSE
+ JX = KX
+ JY = KY
+ DO 80 J = 1,N
+ TEMP1 = ALPHA*X(JX)
+ TEMP2 = ZERO
+ IX = KX
+ IY = KY
+ L = KPLUS1 - J
+ DO 70 I = MAX(1,J-K),J - 1
+ Y(IY) = Y(IY) + TEMP1*A(L+I,J)
+ TEMP2 = TEMP2 + A(L+I,J)*X(IX)
+ IX = IX + INCX
+ IY = IY + INCY
+ 70 CONTINUE
+ Y(JY) = Y(JY) + TEMP1*A(KPLUS1,J) + ALPHA*TEMP2
+ JX = JX + INCX
+ JY = JY + INCY
+ IF (J.GT.K) THEN
+ KX = KX + INCX
+ KY = KY + INCY
+ END IF
+ 80 CONTINUE
+ END IF
+ ELSE
+*
+* Form y when lower triangle of A is stored.
+*
+ IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN
+ DO 100 J = 1,N
+ TEMP1 = ALPHA*X(J)
+ TEMP2 = ZERO
+ Y(J) = Y(J) + TEMP1*A(1,J)
+ L = 1 - J
+ DO 90 I = J + 1,MIN(N,J+K)
+ Y(I) = Y(I) + TEMP1*A(L+I,J)
+ TEMP2 = TEMP2 + A(L+I,J)*X(I)
+ 90 CONTINUE
+ Y(J) = Y(J) + ALPHA*TEMP2
+ 100 CONTINUE
+ ELSE
+ JX = KX
+ JY = KY
+ DO 120 J = 1,N
+ TEMP1 = ALPHA*X(JX)
+ TEMP2 = ZERO
+ Y(JY) = Y(JY) + TEMP1*A(1,J)
+ L = 1 - J
+ IX = JX
+ IY = JY
+ DO 110 I = J + 1,MIN(N,J+K)
+ IX = IX + INCX
+ IY = IY + INCY
+ Y(IY) = Y(IY) + TEMP1*A(L+I,J)
+ TEMP2 = TEMP2 + A(L+I,J)*X(IX)
+ 110 CONTINUE
+ Y(JY) = Y(JY) + ALPHA*TEMP2
+ JX = JX + INCX
+ JY = JY + INCY
+ 120 CONTINUE
+ END IF
+ END IF
+*
+ RETURN
+*
+* End of DSBMV .
+*
+ END