mirror of
https://gitlab.com/libeigen/eigen.git
synced 2024-12-27 07:29:52 +08:00
203 lines
5.8 KiB
Fortran
203 lines
5.8 KiB
Fortran
SUBROUTINE SSPR(UPLO,N,ALPHA,X,INCX,AP)
|
|
* .. Scalar Arguments ..
|
|
REAL ALPHA
|
|
INTEGER INCX,N
|
|
CHARACTER UPLO
|
|
* ..
|
|
* .. Array Arguments ..
|
|
REAL AP(*),X(*)
|
|
* ..
|
|
*
|
|
* Purpose
|
|
* =======
|
|
*
|
|
* SSPR performs the symmetric rank 1 operation
|
|
*
|
|
* A := alpha*x*x' + A,
|
|
*
|
|
* where alpha is a real scalar, x is an n element vector and A is an
|
|
* n by n symmetric matrix, supplied in packed form.
|
|
*
|
|
* Arguments
|
|
* ==========
|
|
*
|
|
* UPLO - CHARACTER*1.
|
|
* On entry, UPLO specifies whether the upper or lower
|
|
* triangular part of the matrix A is supplied in the packed
|
|
* array AP as follows:
|
|
*
|
|
* UPLO = 'U' or 'u' The upper triangular part of A is
|
|
* supplied in AP.
|
|
*
|
|
* UPLO = 'L' or 'l' The lower triangular part of A is
|
|
* supplied in AP.
|
|
*
|
|
* Unchanged on exit.
|
|
*
|
|
* N - INTEGER.
|
|
* On entry, N specifies the order of the matrix A.
|
|
* N must be at least zero.
|
|
* Unchanged on exit.
|
|
*
|
|
* ALPHA - REAL .
|
|
* On entry, ALPHA specifies the scalar alpha.
|
|
* Unchanged on exit.
|
|
*
|
|
* X - REAL array of dimension at least
|
|
* ( 1 + ( n - 1 )*abs( INCX ) ).
|
|
* Before entry, the incremented array X must contain the n
|
|
* element 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.
|
|
*
|
|
* AP - REAL array of DIMENSION at least
|
|
* ( ( n*( n + 1 ) )/2 ).
|
|
* Before entry with UPLO = 'U' or 'u', the array AP must
|
|
* contain the upper triangular part of the symmetric 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. On exit, the array
|
|
* AP is overwritten by the upper triangular part of the
|
|
* updated matrix.
|
|
* Before entry with UPLO = 'L' or 'l', the array AP must
|
|
* contain the lower triangular part of the symmetric 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. On exit, the array
|
|
* AP is overwritten by the lower triangular part of the
|
|
* updated matrix.
|
|
*
|
|
* 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 ..
|
|
REAL ZERO
|
|
PARAMETER (ZERO=0.0E+0)
|
|
* ..
|
|
* .. Local Scalars ..
|
|
REAL TEMP
|
|
INTEGER I,INFO,IX,J,JX,K,KK,KX
|
|
* ..
|
|
* .. External Functions ..
|
|
LOGICAL LSAME
|
|
EXTERNAL LSAME
|
|
* ..
|
|
* .. External Subroutines ..
|
|
EXTERNAL XERBLA
|
|
* ..
|
|
*
|
|
* 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 (INCX.EQ.0) THEN
|
|
INFO = 5
|
|
END IF
|
|
IF (INFO.NE.0) THEN
|
|
CALL XERBLA('SSPR ',INFO)
|
|
RETURN
|
|
END IF
|
|
*
|
|
* Quick return if possible.
|
|
*
|
|
IF ((N.EQ.0) .OR. (ALPHA.EQ.ZERO)) RETURN
|
|
*
|
|
* Set the start point in X if the increment is not unity.
|
|
*
|
|
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 the array AP
|
|
* are accessed sequentially with one pass through AP.
|
|
*
|
|
KK = 1
|
|
IF (LSAME(UPLO,'U')) THEN
|
|
*
|
|
* Form A when upper triangle is stored in AP.
|
|
*
|
|
IF (INCX.EQ.1) THEN
|
|
DO 20 J = 1,N
|
|
IF (X(J).NE.ZERO) THEN
|
|
TEMP = ALPHA*X(J)
|
|
K = KK
|
|
DO 10 I = 1,J
|
|
AP(K) = AP(K) + X(I)*TEMP
|
|
K = K + 1
|
|
10 CONTINUE
|
|
END IF
|
|
KK = KK + J
|
|
20 CONTINUE
|
|
ELSE
|
|
JX = KX
|
|
DO 40 J = 1,N
|
|
IF (X(JX).NE.ZERO) THEN
|
|
TEMP = ALPHA*X(JX)
|
|
IX = KX
|
|
DO 30 K = KK,KK + J - 1
|
|
AP(K) = AP(K) + X(IX)*TEMP
|
|
IX = IX + INCX
|
|
30 CONTINUE
|
|
END IF
|
|
JX = JX + INCX
|
|
KK = KK + J
|
|
40 CONTINUE
|
|
END IF
|
|
ELSE
|
|
*
|
|
* Form A when lower triangle is stored in AP.
|
|
*
|
|
IF (INCX.EQ.1) THEN
|
|
DO 60 J = 1,N
|
|
IF (X(J).NE.ZERO) THEN
|
|
TEMP = ALPHA*X(J)
|
|
K = KK
|
|
DO 50 I = J,N
|
|
AP(K) = AP(K) + X(I)*TEMP
|
|
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
|
|
TEMP = ALPHA*X(JX)
|
|
IX = JX
|
|
DO 70 K = KK,KK + N - J
|
|
AP(K) = AP(K) + X(IX)*TEMP
|
|
IX = IX + INCX
|
|
70 CONTINUE
|
|
END IF
|
|
JX = JX + INCX
|
|
KK = KK + N - J + 1
|
|
80 CONTINUE
|
|
END IF
|
|
END IF
|
|
*
|
|
RETURN
|
|
*
|
|
* End of SSPR .
|
|
*
|
|
END
|