Rank-1 Update to a Hermitian Matrix

Calling Sequence

CALL ZHER	(UPLO, N, DALPHA, ZX, INCX, ZA, LDA)
CALL CHER	(UPLO, N, SALPHA, CX, INCX, CA, LDA)
void zher	(char uplo, int n, double dalpha, doublecomplex *zx, int incx, doublecomplex *za, int lda)
void cher	(char uplo, int n, float salpha, complex *cx, int incx, complex *ca, int lda)

---

Note - The type of the scalar xALPHA is real.

---

Arguments

UPLO	Indicates whether the values in a matrix reside in the upper or lower triangle of the array in which the matrix is stored. The legal values for UPLO are listed below. Any value not listed below is illegal.
	'L' or 'l'	Only the lower triangle of the array will be referenced.
	'U' or 'u'	Only the upper triangle of the array will be referenced.
N	Size of a matrix with N rows and N columns. N 0.
xALPHA	Scalar that scales the input value of the matrix A.
xX	X and INCX describe a vector of length N. X contains an input vector.
INCX	Scalar that contains the storage spacing between successive elements of the vector. INCX 0. If INCX = 1, then elements of the vector are contiguous in memory. INCX may take on values besides 1 to allow the programmer to extract from a matrix a vector that is not stored in contiguous memory locations.
	If X is a one-dimensional array and INCX = -1 then the array will be accessed in reverse order.
	If X is a two-dimensional array and INCX = LDA then the vector will be a row of the array.
	If X is a two-dimensional array and INCX = LDA+1 then the vector will be a diagonal of the array.
xA	Two-dimensional array.
	On entry, the input matrix.
	On exit, the result matrix.
LDA	Leading dimension of the array A as specified in a dimension or type statement. LDA max(1,N).

Sample Program

PROGRAM TEST

IMPLICIT NONE

C

REAL RZERO

COMPLEX ONE

INTEGER LDA, N

PARAMETER (N = 3)

PARAMETER (LDA = N)

PARAMETER (ONE = (1.0E0,0.0E0))

PARAMETER (RZERO = 0.0E0)

C

COMPLEX A(LDA,N), ONE, X(N)

INTEGER I, J

C

EXTERNAL CHER

INTRINSIC CONJG, REAL

C

C Initialize the array A to store in Hermitian form the matrix

C A shown below. Initialize the array X to store the vector X

C shown below.

C

C 1+0i 2+2i 3+3i 1-1i

C A = 2-2i 2+0i 3+3i x = 2-2i

C 3-3i 3-3i 3+0i 3-3i

C

DATA A / (1.0,8E8), (8E8,8E8), (8E8,8E8),

$ (2.0,2.0), (2.0,8E8), (8E8,8E8),

$ (3.0,3.0), (3.0,3.0), (3.0,8E8) /

DATA X / (1.0,-1.0), (2.0,-2.0), (3.0,-3.0) /

C

PRINT 1000

DO 100, I = 1, N

PRINT 1010, (A(J,I), J = 1, I - 1), REAL(A(I,I)), RZERO,

$ (CONJG(A(I,J)), J = I + 1, N)

100 CONTINUE

PRINT 1020

DO 110, I = 1, N

PRINT 1010, (A(I,J), J = 1, N)

110 CONTINUE

PRINT 1030

DO 120, I = 1, N

PRINT 1040, X(I)

120 CONTINUE

CALL CHER ('UPPER TRIANGULAR A', N, ONE, X, 1, A, LDA)

PRINT 1050

DO 130, I = 1, N

PRINT 1010, (A(J,I), J = 1, I - 1), REAL(A(I,I)), RZERO,

$ (CONJG(A(I,J)), J = I + 1, N)

130 CONTINUE

PRINT 1060

DO 140, I = 1, N

PRINT 1010, (A(I,J), J = 1, N)

140 CONTINUE

C

1000 FORMAT (1X, 'A in full form:')

1010 FORMAT (1X, 3(2X, '(', F5.1, ',', F5.1, ')'))

1020 FORMAT (/1X, 'A in Hermitian form: ',

$ '(* in unused elements)')

1030 FORMAT (/1X, 'x:')

1040 FORMAT (3X, '(', F5.1, ',', F5.1, ')')

1050 FORMAT (/1X, 'A + xx'' in full form:')

1060 FORMAT (/1X, 'A + xx'' in Hermitian form: ',

$ '(* in unused elements)')

C

END

Sample Output

A in full form:
( 1.0, 0.0) ( 2.0, -2.0) ( 3.0, -3.0)
( 2.0, 2.0) ( 2.0, 0.0) ( 3.0, -3.0)
( 3.0, 3.0) ( 3.0, 3.0) ( 3.0, 0.0)
A in Hermitian form: (* in unused elements)
( 1.0,*****) ( 2.0, 2.0) ( 3.0, 3.0)
(*****,*****) ( 2.0,*****) ( 3.0, 3.0)
(*****,*****) (*****,*****) ( 3.0,*****)
x:
( 1.0, -1.0)
( 2.0, -2.0)
( 3.0, -3.0)
A + xx' in full form:
( 3.0, 0.0) ( 6.0, -2.0) ( 9.0, -3.0)
( 6.0, 2.0) ( 10.0, 0.0) ( 15.0, -3.0)
( 9.0, 3.0) ( 15.0, 3.0) ( 21.0, 0.0)
A + xx' in Hermitian form: (* in unused elements)
( 3.0, 0.0) ( 6.0, 2.0) ( 9.0, 3.0)
(*****,*****) ( 10.0, 0.0) ( 15.0, 3.0)
(*****,*****) (*****,*****) ( 21.0, 0.0)