Annotation of rpl/lapack/lapack/zhpevd.f, revision 1.1
1.1 ! bertrand 1: SUBROUTINE ZHPEVD( JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, LWORK,
! 2: $ RWORK, LRWORK, IWORK, LIWORK, INFO )
! 3: *
! 4: * -- LAPACK driver routine (version 3.2) --
! 5: * -- LAPACK is a software package provided by Univ. of Tennessee, --
! 6: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
! 7: * November 2006
! 8: *
! 9: * .. Scalar Arguments ..
! 10: CHARACTER JOBZ, UPLO
! 11: INTEGER INFO, LDZ, LIWORK, LRWORK, LWORK, N
! 12: * ..
! 13: * .. Array Arguments ..
! 14: INTEGER IWORK( * )
! 15: DOUBLE PRECISION RWORK( * ), W( * )
! 16: COMPLEX*16 AP( * ), WORK( * ), Z( LDZ, * )
! 17: * ..
! 18: *
! 19: * Purpose
! 20: * =======
! 21: *
! 22: * ZHPEVD computes all the eigenvalues and, optionally, eigenvectors of
! 23: * a complex Hermitian matrix A in packed storage. If eigenvectors are
! 24: * desired, it uses a divide and conquer algorithm.
! 25: *
! 26: * The divide and conquer algorithm makes very mild assumptions about
! 27: * floating point arithmetic. It will work on machines with a guard
! 28: * digit in add/subtract, or on those binary machines without guard
! 29: * digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
! 30: * Cray-2. It could conceivably fail on hexadecimal or decimal machines
! 31: * without guard digits, but we know of none.
! 32: *
! 33: * Arguments
! 34: * =========
! 35: *
! 36: * JOBZ (input) CHARACTER*1
! 37: * = 'N': Compute eigenvalues only;
! 38: * = 'V': Compute eigenvalues and eigenvectors.
! 39: *
! 40: * UPLO (input) CHARACTER*1
! 41: * = 'U': Upper triangle of A is stored;
! 42: * = 'L': Lower triangle of A is stored.
! 43: *
! 44: * N (input) INTEGER
! 45: * The order of the matrix A. N >= 0.
! 46: *
! 47: * AP (input/output) COMPLEX*16 array, dimension (N*(N+1)/2)
! 48: * On entry, the upper or lower triangle of the Hermitian matrix
! 49: * A, packed columnwise in a linear array. The j-th column of A
! 50: * is stored in the array AP as follows:
! 51: * if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
! 52: * if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
! 53: *
! 54: * On exit, AP is overwritten by values generated during the
! 55: * reduction to tridiagonal form. If UPLO = 'U', the diagonal
! 56: * and first superdiagonal of the tridiagonal matrix T overwrite
! 57: * the corresponding elements of A, and if UPLO = 'L', the
! 58: * diagonal and first subdiagonal of T overwrite the
! 59: * corresponding elements of A.
! 60: *
! 61: * W (output) DOUBLE PRECISION array, dimension (N)
! 62: * If INFO = 0, the eigenvalues in ascending order.
! 63: *
! 64: * Z (output) COMPLEX*16 array, dimension (LDZ, N)
! 65: * If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal
! 66: * eigenvectors of the matrix A, with the i-th column of Z
! 67: * holding the eigenvector associated with W(i).
! 68: * If JOBZ = 'N', then Z is not referenced.
! 69: *
! 70: * LDZ (input) INTEGER
! 71: * The leading dimension of the array Z. LDZ >= 1, and if
! 72: * JOBZ = 'V', LDZ >= max(1,N).
! 73: *
! 74: * WORK (workspace/output) COMPLEX*16 array, dimension (MAX(1,LWORK))
! 75: * On exit, if INFO = 0, WORK(1) returns the required LWORK.
! 76: *
! 77: * LWORK (input) INTEGER
! 78: * The dimension of array WORK.
! 79: * If N <= 1, LWORK must be at least 1.
! 80: * If JOBZ = 'N' and N > 1, LWORK must be at least N.
! 81: * If JOBZ = 'V' and N > 1, LWORK must be at least 2*N.
! 82: *
! 83: * If LWORK = -1, then a workspace query is assumed; the routine
! 84: * only calculates the required sizes of the WORK, RWORK and
! 85: * IWORK arrays, returns these values as the first entries of
! 86: * the WORK, RWORK and IWORK arrays, and no error message
! 87: * related to LWORK or LRWORK or LIWORK is issued by XERBLA.
! 88: *
! 89: * RWORK (workspace/output) DOUBLE PRECISION array,
! 90: * dimension (LRWORK)
! 91: * On exit, if INFO = 0, RWORK(1) returns the required LRWORK.
! 92: *
! 93: * LRWORK (input) INTEGER
! 94: * The dimension of array RWORK.
! 95: * If N <= 1, LRWORK must be at least 1.
! 96: * If JOBZ = 'N' and N > 1, LRWORK must be at least N.
! 97: * If JOBZ = 'V' and N > 1, LRWORK must be at least
! 98: * 1 + 5*N + 2*N**2.
! 99: *
! 100: * If LRWORK = -1, then a workspace query is assumed; the
! 101: * routine only calculates the required sizes of the WORK, RWORK
! 102: * and IWORK arrays, returns these values as the first entries
! 103: * of the WORK, RWORK and IWORK arrays, and no error message
! 104: * related to LWORK or LRWORK or LIWORK is issued by XERBLA.
! 105: *
! 106: * IWORK (workspace/output) INTEGER array, dimension (MAX(1,LIWORK))
! 107: * On exit, if INFO = 0, IWORK(1) returns the required LIWORK.
! 108: *
! 109: * LIWORK (input) INTEGER
! 110: * The dimension of array IWORK.
! 111: * If JOBZ = 'N' or N <= 1, LIWORK must be at least 1.
! 112: * If JOBZ = 'V' and N > 1, LIWORK must be at least 3 + 5*N.
! 113: *
! 114: * If LIWORK = -1, then a workspace query is assumed; the
! 115: * routine only calculates the required sizes of the WORK, RWORK
! 116: * and IWORK arrays, returns these values as the first entries
! 117: * of the WORK, RWORK and IWORK arrays, and no error message
! 118: * related to LWORK or LRWORK or LIWORK is issued by XERBLA.
! 119: *
! 120: * INFO (output) INTEGER
! 121: * = 0: successful exit
! 122: * < 0: if INFO = -i, the i-th argument had an illegal value.
! 123: * > 0: if INFO = i, the algorithm failed to converge; i
! 124: * off-diagonal elements of an intermediate tridiagonal
! 125: * form did not converge to zero.
! 126: *
! 127: * =====================================================================
! 128: *
! 129: * .. Parameters ..
! 130: DOUBLE PRECISION ZERO, ONE
! 131: PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
! 132: COMPLEX*16 CONE
! 133: PARAMETER ( CONE = ( 1.0D+0, 0.0D+0 ) )
! 134: * ..
! 135: * .. Local Scalars ..
! 136: LOGICAL LQUERY, WANTZ
! 137: INTEGER IINFO, IMAX, INDE, INDRWK, INDTAU, INDWRK,
! 138: $ ISCALE, LIWMIN, LLRWK, LLWRK, LRWMIN, LWMIN
! 139: DOUBLE PRECISION ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA,
! 140: $ SMLNUM
! 141: * ..
! 142: * .. External Functions ..
! 143: LOGICAL LSAME
! 144: DOUBLE PRECISION DLAMCH, ZLANHP
! 145: EXTERNAL LSAME, DLAMCH, ZLANHP
! 146: * ..
! 147: * .. External Subroutines ..
! 148: EXTERNAL DSCAL, DSTERF, XERBLA, ZDSCAL, ZHPTRD, ZSTEDC,
! 149: $ ZUPMTR
! 150: * ..
! 151: * .. Intrinsic Functions ..
! 152: INTRINSIC SQRT
! 153: * ..
! 154: * .. Executable Statements ..
! 155: *
! 156: * Test the input parameters.
! 157: *
! 158: WANTZ = LSAME( JOBZ, 'V' )
! 159: LQUERY = ( LWORK.EQ.-1 .OR. LRWORK.EQ.-1 .OR. LIWORK.EQ.-1 )
! 160: *
! 161: INFO = 0
! 162: IF( .NOT.( WANTZ .OR. LSAME( JOBZ, 'N' ) ) ) THEN
! 163: INFO = -1
! 164: ELSE IF( .NOT.( LSAME( UPLO, 'L' ) .OR. LSAME( UPLO, 'U' ) ) )
! 165: $ THEN
! 166: INFO = -2
! 167: ELSE IF( N.LT.0 ) THEN
! 168: INFO = -3
! 169: ELSE IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
! 170: INFO = -7
! 171: END IF
! 172: *
! 173: IF( INFO.EQ.0 ) THEN
! 174: IF( N.LE.1 ) THEN
! 175: LWMIN = 1
! 176: LIWMIN = 1
! 177: LRWMIN = 1
! 178: ELSE
! 179: IF( WANTZ ) THEN
! 180: LWMIN = 2*N
! 181: LRWMIN = 1 + 5*N + 2*N**2
! 182: LIWMIN = 3 + 5*N
! 183: ELSE
! 184: LWMIN = N
! 185: LRWMIN = N
! 186: LIWMIN = 1
! 187: END IF
! 188: END IF
! 189: WORK( 1 ) = LWMIN
! 190: RWORK( 1 ) = LRWMIN
! 191: IWORK( 1 ) = LIWMIN
! 192: *
! 193: IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY ) THEN
! 194: INFO = -9
! 195: ELSE IF( LRWORK.LT.LRWMIN .AND. .NOT.LQUERY ) THEN
! 196: INFO = -11
! 197: ELSE IF( LIWORK.LT.LIWMIN .AND. .NOT.LQUERY ) THEN
! 198: INFO = -13
! 199: END IF
! 200: END IF
! 201: *
! 202: IF( INFO.NE.0 ) THEN
! 203: CALL XERBLA( 'ZHPEVD', -INFO )
! 204: RETURN
! 205: ELSE IF( LQUERY ) THEN
! 206: RETURN
! 207: END IF
! 208: *
! 209: * Quick return if possible
! 210: *
! 211: IF( N.EQ.0 )
! 212: $ RETURN
! 213: *
! 214: IF( N.EQ.1 ) THEN
! 215: W( 1 ) = AP( 1 )
! 216: IF( WANTZ )
! 217: $ Z( 1, 1 ) = CONE
! 218: RETURN
! 219: END IF
! 220: *
! 221: * Get machine constants.
! 222: *
! 223: SAFMIN = DLAMCH( 'Safe minimum' )
! 224: EPS = DLAMCH( 'Precision' )
! 225: SMLNUM = SAFMIN / EPS
! 226: BIGNUM = ONE / SMLNUM
! 227: RMIN = SQRT( SMLNUM )
! 228: RMAX = SQRT( BIGNUM )
! 229: *
! 230: * Scale matrix to allowable range, if necessary.
! 231: *
! 232: ANRM = ZLANHP( 'M', UPLO, N, AP, RWORK )
! 233: ISCALE = 0
! 234: IF( ANRM.GT.ZERO .AND. ANRM.LT.RMIN ) THEN
! 235: ISCALE = 1
! 236: SIGMA = RMIN / ANRM
! 237: ELSE IF( ANRM.GT.RMAX ) THEN
! 238: ISCALE = 1
! 239: SIGMA = RMAX / ANRM
! 240: END IF
! 241: IF( ISCALE.EQ.1 ) THEN
! 242: CALL ZDSCAL( ( N*( N+1 ) ) / 2, SIGMA, AP, 1 )
! 243: END IF
! 244: *
! 245: * Call ZHPTRD to reduce Hermitian packed matrix to tridiagonal form.
! 246: *
! 247: INDE = 1
! 248: INDTAU = 1
! 249: INDRWK = INDE + N
! 250: INDWRK = INDTAU + N
! 251: LLWRK = LWORK - INDWRK + 1
! 252: LLRWK = LRWORK - INDRWK + 1
! 253: CALL ZHPTRD( UPLO, N, AP, W, RWORK( INDE ), WORK( INDTAU ),
! 254: $ IINFO )
! 255: *
! 256: * For eigenvalues only, call DSTERF. For eigenvectors, first call
! 257: * ZUPGTR to generate the orthogonal matrix, then call ZSTEDC.
! 258: *
! 259: IF( .NOT.WANTZ ) THEN
! 260: CALL DSTERF( N, W, RWORK( INDE ), INFO )
! 261: ELSE
! 262: CALL ZSTEDC( 'I', N, W, RWORK( INDE ), Z, LDZ, WORK( INDWRK ),
! 263: $ LLWRK, RWORK( INDRWK ), LLRWK, IWORK, LIWORK,
! 264: $ INFO )
! 265: CALL ZUPMTR( 'L', UPLO, 'N', N, N, AP, WORK( INDTAU ), Z, LDZ,
! 266: $ WORK( INDWRK ), IINFO )
! 267: END IF
! 268: *
! 269: * If matrix was scaled, then rescale eigenvalues appropriately.
! 270: *
! 271: IF( ISCALE.EQ.1 ) THEN
! 272: IF( INFO.EQ.0 ) THEN
! 273: IMAX = N
! 274: ELSE
! 275: IMAX = INFO - 1
! 276: END IF
! 277: CALL DSCAL( IMAX, ONE / SIGMA, W, 1 )
! 278: END IF
! 279: *
! 280: WORK( 1 ) = LWMIN
! 281: RWORK( 1 ) = LRWMIN
! 282: IWORK( 1 ) = LIWMIN
! 283: RETURN
! 284: *
! 285: * End of ZHPEVD
! 286: *
! 287: END
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