Rank-2k Update of a Symmetric Matrix

Operation	TRANSA	Matrices A and B
	'N' or 'n'	n x k
	'T' or 't'	k x n

Calling Sequence

CALL DSYR2K	(UPLO, TRANSA, N, K, DALPHA, DA, LDA, DB, LDB, DBETA, DC, LDC)
CALL SSYR2K	(UPLO, TRANSA, N, K, SALPHA, SA, LDA, SB, LDB, SBETA, SC, LDC)
CALL ZSYR2K	(UPLO, TRANSA, N, K, ZALPHA, ZA, LDA, ZB, LDB, ZBETA, ZC, LDC)
CALL CSYR2K	(UPLO, TRANSA, N, K, CALPHA, CA, LDA, CB, LDB, CBETA, CC, LDC)
void dsyr2k	(char uplo, char trans, int n, int k, double dalpha, double *da, int lda, double *db, int ldb, double dbeta, double *dc, int ldc)
void ssyr2k	(char uplo, char trans, int n, int k, float salpha, float *sa, int lda, float *sb, int ldb, float sbeta, float *sc, int ldc)
void zsyr2k	(char uplo, char trans, int n, int k, doublecomplex *zalpha, doublecomplex *za, int lda, doublecomplex *zb, int ldb, doublecomplex *zbeta, doublecomplex *zc, int ldc)
void csyr2k	(char uplo, char trans, int n, int k, complex *calpha, complex *ca, int lda, complex *cb, int ldb, complex *cbeta, complex *cc, int ldc)

Arguments

UPLO	Indicates whether the values in a matrix reside in the upper or lower triangle of the array in which it is stored. The legal values for UPLO are listed below. Any value not listed below is illegal.
	'L' or 'l'	Only lower triangle of array will be referenced.
	'U' or 'u'	Only upper triangle of array will be referenced.
TRANSA	Indicates how to use the matrix. The legal values for TRANSA are listed below. Any value not listed below is illegal.
	'N' or 'n'	Use the matrix as it is stored.
	'T' or 't'	Use the transpose of the matrix
N, K	Indicate the size of matrix A as shown in the table above. N, K 0.
xALPHA	Scalar that scales the input value of the matrix stored in A.
xA	Two-dimensional array in which one of the input matrices is stored.
LDA	Leading dimension of the array A as specified in the dimension or type statement. LDA max (1,K).
	If TRANSA = 'N' or 'n', LDA max (1,N).
xB	Two-dimensional array in which one of the input matrices is stored.
LDB	Leading dimension of the array B as specified in the dimension or type statement. LDB max (1,K).
	If TRANSB = 'N' or 'n', LDB max (1,N).
xBETA	Scalar that scales the input value of the matrix stored in C.
xC	Two-dimensional array.
	On entry, an input matrix.
	On exit, the result matrix.
LDC	Leading dimension of the array C as specified in the dimension or type statement. LDC max (1,N).

Sample Program

PROGRAM TEST

IMPLICIT NONE

C

INTEGER K, LDA, LDB, LDC, N

PARAMETER (K = 2)

PARAMETER (N = 3)

PARAMETER (LDA = N)

PARAMETER (LDB = N)

PARAMETER (LDC = N)

C

DOUBLE PRECISION A(LDA,K), ALPHA, B(LDB,K), BETA, C(LDC,N)

INTEGER I, J

C

EXTERNAL DSYR2K

INTRINSIC DBLE

C

C Initialize the arrays A and B to store the matrices A and B

C shown below. Initialize the array C to store in symmetric

C form the symmetric matrix C shown below.

C

C 3 4 4 7 1 2 3

C A = 5 6 B = 5 8 C = 2 4 5

C 7 8 6 9 3 5 6

C

DATA A / 1.0D0, 1.0D0, 1.0D0, 2.0D0, 2.0D0, 2.0D0 /

DATA B / 1.0D0, 2.0D0, 1.0D0, 2.0D0, 1.0D0, 2.0D0 /

DATA C / 1.0D2, 1.0D2, 1.0D2, 8D8, 1.0D2, 1.0D2, 8D8, 8D8,

$ 1.0D2 /

C

ALPHA = 1.0D0

BETA = 1.0D0

PRINT 1000

DO 100, I = 1, N

PRINT 1010, (C(I,J), J = 1, I), (C(J,I), J = I + 1, N)

100 CONTINUE

PRINT 1020

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

PRINT 1030

DO 110, I = 1, N

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

110 CONTINUE

PRINT 1040

DO 120, I = 1, N

PRINT 1010, (B(I,J), J = 1, K)

120 CONTINUE

CALL DSYR2K ('LOWER TRIANGULAR C', 'NOT TRANSPOSED C', N, K,

$ ALPHA, A, LDA, B, LDB, BETA, C, LDC)

PRINT 1050

DO 130, I = 1, N

PRINT 1010, (C(I,J), J = 1, I), (C(J,I), J = I + 1, N)

130 CONTINUE

C

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

1010 FORMAT (3(2X, F6.1))

1020 FORMAT (/1X, 'C in symmetric form: (* in unused elements)')

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

1040 FORMAT (/1X, 'B:')

1050 FORMAT (/1X, 'AB'' + BA'' + C:')

C

END

Sample Output

C in full form:
100.0 100.0 100.0
100.0 100.0 100.0
100.0 100.0 100.0
C in symmetric form: (* in unused elements)
100.0 ****** ******
100.0 100.0 ******
100.0 100.0 100.0
A:
1.0 2.0
1.0 2.0
1.0 2.0
B:
1.0 2.0
2.0 1.0
1.0 2.0
AB' + BA' + C:
110.0 109.0 110.0
109.0 108.0 109.0
110.0 109.0 110.0