Rank-k Update of a Symmetric Matrix

Operation	TRANSA	Matrix A
	'N' or 'n'	n x k
	'T' or 't'	k x n

Calling Sequence

CALL DSYRK	(UPLO, TRANSA, N, K, DALPHA, DA, LDA, DBETA, DC, LDC)
CALL SSYRK	(UPLO, TRANSA, N, K, SALPHA, SA, LDA, SBETA, SC, LDC)
CALL ZSYRK	(UPLO, TRANSA, N, K, ZALPHA, ZA, LDA, ZBETA, ZC, LDC)
CALL CSYRK	(UPLO, TRANSA, N, K, CALPHA, CA, LDA, CBETA, CC, LDC)
void dsyrk	(char uplo, char trans, int n, int k, double dalpha, double *da, int lda, double dbeta, double *dc, int ldc)
void ssyrk	(char uplo, char trans, int n, int k, float salpha, float *sa, int lda, float sbeta, float *sc, int ldc)
void zsyrk	(char uplo, char trans, int n, int k, doublecomplex *zalpha, doublecomplex *za, int lda, doublecomplex *zbeta, doublecomplex *zc, int ldc)
void csyrk	(char uplo, char trans, int n, int k, complex *calpha, complex *ca, int lda, 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 stored in the array A. 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 in A.
	'T' or 't'	Use the transpose of the matrix stored in A
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 matrix 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).
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, LDC, N

PARAMETER (K = 2)

PARAMETER (N = 3)

PARAMETER (LDA = N)

PARAMETER (LDC = N)

C

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

INTEGER I, J

C

EXTERNAL DSYRK

INTRINSIC DBLE

C

C Initialize the array A to store the matrix A shown below.

C Initialize the array C to store in symmetric form the

C symmetric matrix C shown below.

C

C 3 4 1 2 3

C A = 5 6 C = 2 4 5

C 7 8 3 5 6

C

DATA A / 3.0D0, 5.0D0, 7.0D0, 4.0D0, 6.0D0, 8.0D0 /

DATA C / 1.0D0, 2.0D0, 3.0D0, 8D8, 4.0D0, 5.0D0, 8D8, 8D8,

$ 6.0D0 /

C

ALPHA = 1.0D0

BETA = 3.0D0

PRINT 1000

DO 100, I = 1, N

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

100 CONTINUE

PRINT 1020

DO 110, I = 1, N

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

110 CONTINUE

PRINT 1030

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

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

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

PRINT 1040

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, 'A:')

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

1020 FORMAT (/1X, 'C in full form:')

1030 FORMAT (/1X, 'C in symmetric form: (* in unused elements)')

1040 FORMAT (/1X, 'AA'' + C:')

C

END

Sample Output

A:
3.0 4.0
5.0 6.0
7.0 8.0
C in full form:
1.0 2.0 3.0
2.0 4.0 5.0
3.0 5.0 6.0
C in symmetric form: (* in unused elements)
1.0 ****** ******
2.0 4.0 ******
3.0 5.0 6.0
AA' + C:
28.0 45.0 62.0
45.0 73.0 98.0
62.0 98.0 131.0