Annotation of rpl/lapack/blas/zhemm.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE ZHEMM(SIDE,UPLO,M,N,ALPHA,A,LDA,B,LDB,BETA,C,LDC)
! 2: * .. Scalar Arguments ..
! 3: DOUBLE COMPLEX ALPHA,BETA
! 4: INTEGER LDA,LDB,LDC,M,N
! 5: CHARACTER SIDE,UPLO
! 6: * ..
! 7: * .. Array Arguments ..
! 8: DOUBLE COMPLEX A(LDA,*),B(LDB,*),C(LDC,*)
! 9: * ..
! 10: *
! 11: * Purpose
! 12: * =======
! 13: *
! 14: * ZHEMM performs one of the matrix-matrix operations
! 15: *
! 16: * C := alpha*A*B + beta*C,
! 17: *
! 18: * or
! 19: *
! 20: * C := alpha*B*A + beta*C,
! 21: *
! 22: * where alpha and beta are scalars, A is an hermitian matrix and B and
! 23: * C are m by n matrices.
! 24: *
! 25: * Arguments
! 26: * ==========
! 27: *
! 28: * SIDE - CHARACTER*1.
! 29: * On entry, SIDE specifies whether the hermitian matrix A
! 30: * appears on the left or right in the operation as follows:
! 31: *
! 32: * SIDE = 'L' or 'l' C := alpha*A*B + beta*C,
! 33: *
! 34: * SIDE = 'R' or 'r' C := alpha*B*A + beta*C,
! 35: *
! 36: * Unchanged on exit.
! 37: *
! 38: * UPLO - CHARACTER*1.
! 39: * On entry, UPLO specifies whether the upper or lower
! 40: * triangular part of the hermitian matrix A is to be
! 41: * referenced as follows:
! 42: *
! 43: * UPLO = 'U' or 'u' Only the upper triangular part of the
! 44: * hermitian matrix is to be referenced.
! 45: *
! 46: * UPLO = 'L' or 'l' Only the lower triangular part of the
! 47: * hermitian matrix is to be referenced.
! 48: *
! 49: * Unchanged on exit.
! 50: *
! 51: * M - INTEGER.
! 52: * On entry, M specifies the number of rows of the matrix C.
! 53: * M must be at least zero.
! 54: * Unchanged on exit.
! 55: *
! 56: * N - INTEGER.
! 57: * On entry, N specifies the number of columns of the matrix C.
! 58: * N must be at least zero.
! 59: * Unchanged on exit.
! 60: *
! 61: * ALPHA - COMPLEX*16 .
! 62: * On entry, ALPHA specifies the scalar alpha.
! 63: * Unchanged on exit.
! 64: *
! 65: * A - COMPLEX*16 array of DIMENSION ( LDA, ka ), where ka is
! 66: * m when SIDE = 'L' or 'l' and is n otherwise.
! 67: * Before entry with SIDE = 'L' or 'l', the m by m part of
! 68: * the array A must contain the hermitian matrix, such that
! 69: * when UPLO = 'U' or 'u', the leading m by m upper triangular
! 70: * part of the array A must contain the upper triangular part
! 71: * of the hermitian matrix and the strictly lower triangular
! 72: * part of A is not referenced, and when UPLO = 'L' or 'l',
! 73: * the leading m by m lower triangular part of the array A
! 74: * must contain the lower triangular part of the hermitian
! 75: * matrix and the strictly upper triangular part of A is not
! 76: * referenced.
! 77: * Before entry with SIDE = 'R' or 'r', the n by n part of
! 78: * the array A must contain the hermitian matrix, such that
! 79: * when UPLO = 'U' or 'u', the leading n by n upper triangular
! 80: * part of the array A must contain the upper triangular part
! 81: * of the hermitian matrix and the strictly lower triangular
! 82: * part of A is not referenced, and when UPLO = 'L' or 'l',
! 83: * the leading n by n lower triangular part of the array A
! 84: * must contain the lower triangular part of the hermitian
! 85: * matrix and the strictly upper triangular part of A is not
! 86: * referenced.
! 87: * Note that the imaginary parts of the diagonal elements need
! 88: * not be set, they are assumed to be zero.
! 89: * Unchanged on exit.
! 90: *
! 91: * LDA - INTEGER.
! 92: * On entry, LDA specifies the first dimension of A as declared
! 93: * in the calling (sub) program. When SIDE = 'L' or 'l' then
! 94: * LDA must be at least max( 1, m ), otherwise LDA must be at
! 95: * least max( 1, n ).
! 96: * Unchanged on exit.
! 97: *
! 98: * B - COMPLEX*16 array of DIMENSION ( LDB, n ).
! 99: * Before entry, the leading m by n part of the array B must
! 100: * contain the matrix B.
! 101: * Unchanged on exit.
! 102: *
! 103: * LDB - INTEGER.
! 104: * On entry, LDB specifies the first dimension of B as declared
! 105: * in the calling (sub) program. LDB must be at least
! 106: * max( 1, m ).
! 107: * Unchanged on exit.
! 108: *
! 109: * BETA - COMPLEX*16 .
! 110: * On entry, BETA specifies the scalar beta. When BETA is
! 111: * supplied as zero then C need not be set on input.
! 112: * Unchanged on exit.
! 113: *
! 114: * C - COMPLEX*16 array of DIMENSION ( LDC, n ).
! 115: * Before entry, the leading m by n part of the array C must
! 116: * contain the matrix C, except when beta is zero, in which
! 117: * case C need not be set on entry.
! 118: * On exit, the array C is overwritten by the m by n updated
! 119: * matrix.
! 120: *
! 121: * LDC - INTEGER.
! 122: * On entry, LDC specifies the first dimension of C as declared
! 123: * in the calling (sub) program. LDC must be at least
! 124: * max( 1, m ).
! 125: * Unchanged on exit.
! 126: *
! 127: * Further Details
! 128: * ===============
! 129: *
! 130: * Level 3 Blas routine.
! 131: *
! 132: * -- Written on 8-February-1989.
! 133: * Jack Dongarra, Argonne National Laboratory.
! 134: * Iain Duff, AERE Harwell.
! 135: * Jeremy Du Croz, Numerical Algorithms Group Ltd.
! 136: * Sven Hammarling, Numerical Algorithms Group Ltd.
! 137: *
! 138: * =====================================================================
! 139: *
! 140: * .. External Functions ..
! 141: LOGICAL LSAME
! 142: EXTERNAL LSAME
! 143: * ..
! 144: * .. External Subroutines ..
! 145: EXTERNAL XERBLA
! 146: * ..
! 147: * .. Intrinsic Functions ..
! 148: INTRINSIC DBLE,DCONJG,MAX
! 149: * ..
! 150: * .. Local Scalars ..
! 151: DOUBLE COMPLEX TEMP1,TEMP2
! 152: INTEGER I,INFO,J,K,NROWA
! 153: LOGICAL UPPER
! 154: * ..
! 155: * .. Parameters ..
! 156: DOUBLE COMPLEX ONE
! 157: PARAMETER (ONE= (1.0D+0,0.0D+0))
! 158: DOUBLE COMPLEX ZERO
! 159: PARAMETER (ZERO= (0.0D+0,0.0D+0))
! 160: * ..
! 161: *
! 162: * Set NROWA as the number of rows of A.
! 163: *
! 164: IF (LSAME(SIDE,'L')) THEN
! 165: NROWA = M
! 166: ELSE
! 167: NROWA = N
! 168: END IF
! 169: UPPER = LSAME(UPLO,'U')
! 170: *
! 171: * Test the input parameters.
! 172: *
! 173: INFO = 0
! 174: IF ((.NOT.LSAME(SIDE,'L')) .AND. (.NOT.LSAME(SIDE,'R'))) THEN
! 175: INFO = 1
! 176: ELSE IF ((.NOT.UPPER) .AND. (.NOT.LSAME(UPLO,'L'))) THEN
! 177: INFO = 2
! 178: ELSE IF (M.LT.0) THEN
! 179: INFO = 3
! 180: ELSE IF (N.LT.0) THEN
! 181: INFO = 4
! 182: ELSE IF (LDA.LT.MAX(1,NROWA)) THEN
! 183: INFO = 7
! 184: ELSE IF (LDB.LT.MAX(1,M)) THEN
! 185: INFO = 9
! 186: ELSE IF (LDC.LT.MAX(1,M)) THEN
! 187: INFO = 12
! 188: END IF
! 189: IF (INFO.NE.0) THEN
! 190: CALL XERBLA('ZHEMM ',INFO)
! 191: RETURN
! 192: END IF
! 193: *
! 194: * Quick return if possible.
! 195: *
! 196: IF ((M.EQ.0) .OR. (N.EQ.0) .OR.
! 197: + ((ALPHA.EQ.ZERO).AND. (BETA.EQ.ONE))) RETURN
! 198: *
! 199: * And when alpha.eq.zero.
! 200: *
! 201: IF (ALPHA.EQ.ZERO) THEN
! 202: IF (BETA.EQ.ZERO) THEN
! 203: DO 20 J = 1,N
! 204: DO 10 I = 1,M
! 205: C(I,J) = ZERO
! 206: 10 CONTINUE
! 207: 20 CONTINUE
! 208: ELSE
! 209: DO 40 J = 1,N
! 210: DO 30 I = 1,M
! 211: C(I,J) = BETA*C(I,J)
! 212: 30 CONTINUE
! 213: 40 CONTINUE
! 214: END IF
! 215: RETURN
! 216: END IF
! 217: *
! 218: * Start the operations.
! 219: *
! 220: IF (LSAME(SIDE,'L')) THEN
! 221: *
! 222: * Form C := alpha*A*B + beta*C.
! 223: *
! 224: IF (UPPER) THEN
! 225: DO 70 J = 1,N
! 226: DO 60 I = 1,M
! 227: TEMP1 = ALPHA*B(I,J)
! 228: TEMP2 = ZERO
! 229: DO 50 K = 1,I - 1
! 230: C(K,J) = C(K,J) + TEMP1*A(K,I)
! 231: TEMP2 = TEMP2 + B(K,J)*DCONJG(A(K,I))
! 232: 50 CONTINUE
! 233: IF (BETA.EQ.ZERO) THEN
! 234: C(I,J) = TEMP1*DBLE(A(I,I)) + ALPHA*TEMP2
! 235: ELSE
! 236: C(I,J) = BETA*C(I,J) + TEMP1*DBLE(A(I,I)) +
! 237: + ALPHA*TEMP2
! 238: END IF
! 239: 60 CONTINUE
! 240: 70 CONTINUE
! 241: ELSE
! 242: DO 100 J = 1,N
! 243: DO 90 I = M,1,-1
! 244: TEMP1 = ALPHA*B(I,J)
! 245: TEMP2 = ZERO
! 246: DO 80 K = I + 1,M
! 247: C(K,J) = C(K,J) + TEMP1*A(K,I)
! 248: TEMP2 = TEMP2 + B(K,J)*DCONJG(A(K,I))
! 249: 80 CONTINUE
! 250: IF (BETA.EQ.ZERO) THEN
! 251: C(I,J) = TEMP1*DBLE(A(I,I)) + ALPHA*TEMP2
! 252: ELSE
! 253: C(I,J) = BETA*C(I,J) + TEMP1*DBLE(A(I,I)) +
! 254: + ALPHA*TEMP2
! 255: END IF
! 256: 90 CONTINUE
! 257: 100 CONTINUE
! 258: END IF
! 259: ELSE
! 260: *
! 261: * Form C := alpha*B*A + beta*C.
! 262: *
! 263: DO 170 J = 1,N
! 264: TEMP1 = ALPHA*DBLE(A(J,J))
! 265: IF (BETA.EQ.ZERO) THEN
! 266: DO 110 I = 1,M
! 267: C(I,J) = TEMP1*B(I,J)
! 268: 110 CONTINUE
! 269: ELSE
! 270: DO 120 I = 1,M
! 271: C(I,J) = BETA*C(I,J) + TEMP1*B(I,J)
! 272: 120 CONTINUE
! 273: END IF
! 274: DO 140 K = 1,J - 1
! 275: IF (UPPER) THEN
! 276: TEMP1 = ALPHA*A(K,J)
! 277: ELSE
! 278: TEMP1 = ALPHA*DCONJG(A(J,K))
! 279: END IF
! 280: DO 130 I = 1,M
! 281: C(I,J) = C(I,J) + TEMP1*B(I,K)
! 282: 130 CONTINUE
! 283: 140 CONTINUE
! 284: DO 160 K = J + 1,N
! 285: IF (UPPER) THEN
! 286: TEMP1 = ALPHA*DCONJG(A(J,K))
! 287: ELSE
! 288: TEMP1 = ALPHA*A(K,J)
! 289: END IF
! 290: DO 150 I = 1,M
! 291: C(I,J) = C(I,J) + TEMP1*B(I,K)
! 292: 150 CONTINUE
! 293: 160 CONTINUE
! 294: 170 CONTINUE
! 295: END IF
! 296: *
! 297: RETURN
! 298: *
! 299: * End of ZHEMM .
! 300: *
! 301: END
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